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Digital Signal Processing for
Complete Idiots
by David Smith

All Rights Reserved. No part of this publication may be reproduced
in any form or by any means, including scanning, photocopying, or
otherwise without prior written permission of the copyright holder.
Copyright © 2017

Other books in the Series:
Arduino for Complete Idiots
Control Systems for Complete Idiots
Circuit Analysis for Complete Idiots
Basic Electronics for Complete Idiots
Electromagnetic Theory for Complete Idiots
Digital Electronics for Complete Idiots

Table of Contents
PREFACE
1. SIGNALS
2. SYSTEMS
3. FOURIER ANALYSIS
4. CONVOLUTION
5. SAMPLING
6. DISCRETE FOURIER ANALYSIS
7. FAST FOURIER TRANSFORM
8. FREQUENCY RESPONSE
9. Z-TRANSFORM
10. FILTERS
APPENDIX
REFERENCES
CONTACT

PREFACE
Digital Signal Processing (DSP) is a subject of central importance in
engineering and the applied sciences. Signals are information-bearing
functions, and DSP deals with the analysis and processing of signals (by
dedicated systems) to extract or modify information. Signal processing is
necessary because signals normally contain information that is not readily
usable or understandable, or which might be disturbed by unwanted sources
such as noise. Although many signals are nonelectrical, it is common to
convert them into electrical signals for processing. Most natural signals
(such as acoustic and biomedical signals) are continuous functions of time,
with these signals being referred to as analog signals. Prior to the
development of DSP, Analog Signal Processing (ASP) and analog systems
were the only tools to deal with analog signals. Although analog systems
are still widely used, Digital Signal Processing (DSP) and digital systems
are attracting more attention, due in large part to the significant advantages
of digital systems over their analog counterparts. These advantages include
superiority in performance, speed, reliability, efficiency of storage, size and
cost. In addition, DSP can solve problems that cannot be solved using ASP,
like the spectral analysis of multi-component signals, adaptive filtering, and
operations at very low frequencies. Following the recent developments in
engineering which occurred in the 1980s and 1990s, DSP became one of the
world’s fastest growing industries. Since that time DSP has not only
impacted on traditional areas of electrical engineering, but has had far
reaching effects on other domains that deal with information such as
economics, meteorology, seismology, bioengineering, oceanology,
communications, astronomy, radar engineering, control engineering and
various other applications.
DSP is a very math intensive subject and one would require a deep
understanding in mathematics to understand various aspects of DSP. I
believe to explain science with mathematics takes skill, but to explain
science without mathematics takes even more skills. Although there are

many books which cover DSP, most of them or all of them would require a
ton of mathematics to understand even the most fundamental concepts. For
a first timer in DSP, getting their heads around advanced math topics like
Fourier transform etc. is a very hard task. Most students tend to lose interest
in DSP, because of this sole reason. Students don't stick around long enough
to discover how beautiful a subject DSP is.
In this book, I've explained or rather tried to explain the various
fundamental concepts of DSP in an intuitive manner with minimum math.
Also, I've tried to connect the various topics with real life situations
wherever possible. This way even first timers can learn the basics of DSP
with minimum effort. Hopefully the students will enjoy this different
approach to DSP. The various concepts of the subject are arranged logically
and explained in a simple reader-friendly language with MATLAB
examples.
This books is not meant to be a replacement for those standard DSP
textbooks, rather this book should be viewed as an introductory text for
beginners to come in grips with advanced level topics covered in those
books. This book will hopefully serve as inspiration to learn DSP in greater
depths.
Readers are welcome to give constructive suggestions for the improvement
of the book and please do leave a review.

1. SIGNALS
1.1 SIGNALS
Signals are Mathematical representation of functions of one or more
independent variable. A signal describes how one parameter varies with
another. For example, the variation of temperature of your room with
respect to time is a signal. Voltage changing over time in an electrical
circuit is also a signal. In this book, the independent quantity we are dealing
with is time.
There are two basic types of signals, Continuous time signals and Discrete
time signals. Continuous time signals are those signals that are defined for
every instant of time. Discrete time signals are those signals, whose values
are defined only for certain instants of time. For example, if you take the
temperature reading of your room after every hour and plot it, what you get
is a discrete time signal. The temperature values are only defined at the
hour marks and not for the entire duration of time. The value of temperature
at other instants (say at half or quarter hour marks) are simply not defined.

For Continuous time signals the independent variable is represented as t
(time) and for Discrete time signals the independent variable is represented
as n (instants of time). The dependent variable is represented as x(t) and
x[n] respectively.
1.2 BASIC CONTINUOUS TIME SIGNALS
In this section we introduce several important continuous time signals. The
proper understanding of these signals and their behavior will go a long way

in making DSP an easier subject.
1.2.1 Sinusoids
Sine waves and Cosines waves are collectively known as sinusoids or
sinusoidal signals.
Mathematically they are represented as:
where A is the Amplitude (maximum height of the signal) , ω is the angular
frequency and ɸ is the phase.
Sine waves and Cosines waves are basically the same, except that they start
at different times (ie they are 90 degrees of phase). Time period of the
signal, T = 2л /ω
Sine and cosine waves of same frequency can be represented as a single
entity using complex representation. By using Euler's relation,

This representation makes calculations a lot easier (although it may not
seem so at first glance) and is used extensively throughout this book.
1.2.2 Unit Step Signal
Unit Step Signal is mathematically defined as:
The step signal can be imagined as a switch being turned on at t = 0, after it
is turned on, the output is of constant magnitude.

The Unit step signal is discontinuous at t = 0, but for the sake of simplicity
take u(0) =1 (A Continuous signal may not be a continuous function
mathematically)
The Unit step signal is of immense importance in control engineering. It is
used to study the steady state performance of systems. Any step signal is
basically the scaled version of the Unit step signal
1.2.3 Unit Impulse Signal
Another very important basic signal is the Unit impulse signal.
It is mathematically defined as:

But, if the value of the Unit Impulse function is ∞ at t = 0, then why the
name Unit Impulse function?? The name comes from the fact that the Unit
impulse function has a unit area at t = 0.
Consider a rectangle of width ɛ and height 1/ɛ as shown in the figure. The
area of the rectangle is unity. Now make ɛ infinitesimally small, keeping
the area unity. It is very clear from this, that the Unit impulse function has
infinite magnitude at t = 0.
The height of the arrow is used to depict the scaled impulse, which
represents its area.

Think of the Impulse signal like a short pulse, like the output when a switch
is turned on and off as fast as you can. The unit Impulse function is also
known as the delta function or the delta-dirac function.
The Unit step and the Unit impulse signal are related to each other as:
This relation is self-explanatory,
for t < 0, u(t) = 0, therefore slope = 0
for t > 0, u(t) = 1, therefore slope = 1
at t = 0, u(t) changes from 0 to 1, therefore the slope = ∞

The relationship can be rewritten in another form as,
i.e. a Unit step signal can be formed by putting together infinite number of
Unit impulse signals.
1.2.4 Exponential Signal
An exponential signal is that signal which rises or decays exponentially (by
the power of e)
It is mathematically defined as:
where e is the Euler's number, C and a are constants.
The characteristics of the signal depends upon the nature of C and a. As
mentioned earlier, an exponential function with complex constant a is
basically a sinusoid.

There are other basic signals too, like the ramp signals, triangular signal etc.
But in DSP we are mostly dealing with Impulse signals and Step signals.
1.3 BASIC DISCRETE TIME SIGNALS
All the basic signals, discussed in the last section can have a discrete nature
too. Let's quickly discuss them.
1.3.1 Discrete Sinusoids

Mathematically it defined as:
All the properties of Discrete Sinusoids are the same as their continuous
counterparts.
1.3.2 Discrete Unit step signal
Discrete time Unit step signal is defined as:

The discrete step signal has unit value at n = 0.
1.3.3 Discrete Unit Impulse signal
Discrete time Unit impulse signal is defined as:
Unlike in the case of Continuous Unit impulse signal, the Discrete impulse
signal has a fixed magnitude at n = 0.

1.3.4 Discrete Exponential signal
Discrete time Exponential signal is defined as: x[n] = C ean

1.4 BASIC SIGNAL OPERATIONS
There are 2 variable parameters in a signal: Amplitude and Time. By
varying these parameters, we can define some basic signal operations.
1.4.1 Amplitude Scaling

Amplitude scaling is nothing but multiplying the amplitude by a scalar
quantity. The factor by which the original signal is multiplied can be of any
value. If the scalar quantity is greater than one, then the resultant signal is
amplified and the process can be called as Amplification. If the scalar
quantity is less than one, then the resultant signal is attenuated and the
process is called as Attenuation.
Amplitude scaling can expressed as: y(t) = a x(t),where a is the scaling
factor.
In amplitude scaling, the signal is scaled at every instant for which the
signal is defined.
1.4.2 Addition
Addition of two or more signals is nothing but addition of their
corresponding amplitude at the same instant of time.
Multiplication operation can be expressed as: y(t) = x1(t) + x2(t)
As seen from the figure above,
-10 < t < -3 amplitude of z(t) = x1(t) + x2(t) = 0 + 2 = 2
-3 < t < 3 amplitude of z(t) = x1(t) + x2(t) = 1 + 2 = 3

3 < t < 10 amplitude of z(t) = x1(t) + x2(t) = 0 + 2 = 2
1.4.3 Multiplication
Multiplication of two signals is nothing but multiplication of their
corresponding amplitudes at the same instant of time.
Multiplication operation can be expressed as: y(t) = x1(t) x x2(t)
As seen from the figure above,
-10 < t < -3 amplitude of z (t) = x1(t) × x2(t) = 0 ×2 = 0
-3 < t < 3 amplitude of z (t) = x1(t) × x2(t) = 1 ×2 = 2
3 < t < 10 amplitude of z (t) = x1(t) × x2(t) = 0 × 2 = 0
1.4.4 Time shifting
Time shifting simply means to shift the starting instant of a signal to an
earlier or a later instant. Basically, by time shifting operation, we can fast-
forward or delay a signal.
Time shifting is mathematically expressed as: y(t) = x(t-t0)
Consider an example, say y(t) = x(t - 2). This means that the signal will
only start 2 seconds later or the signal is delayed by 2 seconds. Consider
another example, y(t) = x(t + 1). This means that the signal will start 1
second earlier or the signal is fast forward by 1 second.

1.4.5 Time scaling
Time scaling of signals involves the modification of a periodicity of the
signal, keeping its amplitude constant. In simple words, Time scaling means
either expanding or compressing a signal without changing its amplitude.
Have you ever played a song at twice the speed on your music player. Have
you wondered how it's possible?? It is possible to do so because of Time
scaling, time compressing to be exact. Have you noted that song isn't
distorted in way by doing so?? The words ,the instruments are all there and
loudness haven't increased or decreased either. That's because we aren't
doing anything to the amplitude.
It's mathematically expressed as: y(t) = x(at), where a is a constant.
When a > 1, the signal is compressed and when a < 1,the signal is
expanded. By that logic when y(t) = x(2t),the signal is compressed to half.
Seems a little odd, right?? Consider plotting a graph, and you take 10
divisions = 10 units and plot a figure(anything). Next you plot the same
graph with 10 divisions = 20 units.
What difference do you see?? The plot got compressed by half. This is
exactly what happens to a signal.
Do note, that it is not possible to time scale an impulse function.

Although we have explained the signal operations using continuous time
signals, they function in exactly in the same manner for Discrete time
signals.
1.5 MATLAB
1.5.1 Basic signals:
t= -2:1:2;
y=[zeros(1,2), ones(1,1), zeros(1,2)];
subplot(2,2,1);
stem(t,y);
ylabel('d(n)');
xlabel('unit impulse');
n=5;
t=0:1:n-1;
y1=ones(1,n);
subplot(2,2,2);
stem(t,y1);
ylabel('Amplitude');
xlabel('unit step');

n=4;
t=0:1:n-1;
subplot(2,2,3);
stem(t,t);
xlabel('unit ramp');
n=5;
t=0:1:n-1;
a=2;
y2=exp(a*t);
subplot(2,2,4);
stem(t,y2);
xlabel('Exponential');

1.5.2 Sine and Cosine Signal:
n =5;
t = -n:1:n;
subplot(1,2,1);
y = sin(t);
stem(t,y)
xlabel('n');
t = -5:1:5;
subplot(1,2,2);
y = cos(t);
stem(t,y)
xlabel('n');

2. SYSTEMS
2.1 SYSTEMS
A system is any process or combination of processes that takes signals as
input and produces signals as the output. For example, an amplifier that
takes in a signal and produces an amplified output, is a system.
Systems that take continuous time signal inputs and produces continuous
time signal outputs are called Continuous Time systems.
x(t) → y(t)
Similarly Discrete time systems are those that takes Discrete time signal
inputs and produces Discrete time signal outputs.
x[n] → y[n]
2.2 INTERCONNECTIONS OF SYSTEMS
Engineers often connect many smaller systems called sub-systems together
to form a new system. One big advantage of doing things this way is, it's
easier to model smaller systems than to model large ones. The obvious
question is how can we describe the overall input- output behavior of the
overall system in terms of sub system behavior.
Let's look at some common types of connections:
2.2.1 Series or Cascade Connection
Series (or cascade) connection is the simplest type of system
interconnection. Basically it's nothing more than connecting many systems
one after the other.

.y(t) = H2 ( H1 x(t) )
Example: A radio receiver followed by an amplifier
2.2.2 Parallel Connection
The parallel connection is another type of system interconnection. In a
Parallel connection, the same input is fed to two or more systems and the
corresponding outputs are summed at the end.
y(t) = H2 (x(t)) + H1 (x(t))
Example: Phone line connecting parallel phone microphones
2.2.3 Feedback Connection:
In the previous two interconnections, the system is completely unaware of
its output is. In the feedback interconnection, the system has knowledge of
the output

y(t) = H1 (x(t)) + H2(y(t)), for positive Feedback and y(t) = H1 (x(t)) -
H2(y(t)), for negative Feedback
2.3 PROPERTIES OF SYSTEMS
In this section we introduce a no. of basic properties of continuous and
discrete time systems.
2.3.1 Memory of the System
A system is said to be memoryless if its output for every instant depends
only on the input at the same instant i.e. memoryless systems can't
remember what happened in the past and also not predict the future (So that
rules out astrologers). For example, consider the voltage - current
relationship in a resistor.
i(t) = v(t)/R
The current at, say t = 2 depends only on the voltage at t = 2. the voltage at
t =1 or 0 or any other doesn't have any effect on the current at t = 2.
In systems with memory, past or future inputs have a role in deciding the
present output.
Example: y(t) = x(t-1)
In this system, the output of the system at t=2, y(2) depends on input at
time t=1, x(2-1) = x(1). So this system has a memory.
2.3.2 Causality
A system is said to be causal if the output at any instant depends only on the
values of the input at the present instant or past instant. In other words, a
causal system does not anticipate the future values of the input.
Example: y(t) = x(t+1)
In this system, the output of the system at t=2, y(2) depends on the input at
t=3, x(2+1) = x(3). So this system is a non causal system.
All real time physical systems are causal, because time only moves forward.
Effect occurs after cause.(Imagine a non-causal system where your today's
income depends on the job you do a year later.)

2.3.3 Time Invariance
A system is said to be time invariant, if the system behavior doesn't vary
with time. So the system behaves exactly the same way at 6 pm or 12 pm or
any other time. In other words a shift in the input signal causes a shift in the
output in time invariant systems.
Example: if y(t) = x(t) and y(t-1) = x(t-1), then system is a time invariant
system, since the input delayed by 1 second produces a output delayed by 1
second.
2.3.4 Stability
Stability is an important system property. A stable system is one in which
small inputs does not lead to drastic response. In other words, a finite input
should produce a finite output ,that doesn't grow out of control. To define
stability of a system, in DSP we use the term ‘BIBO’. It stands for Bounded
Input Bounded Output.
Example: Consider the system, y(t) = t x(t)
Say for x(t) = 2, y(t) =2t
The value of the output is not bounded. Thus this is an Unbounded system.
Unstable Systems lead to erratic responses and makes it difficult to control.
2.3.5 Linearity
Linearity is perhaps the most important system property. A Linear system is
one that obeys the Superposition property. Superposition property is a

basically a combination of 2 system properties:
1. Additivity property: The response of a system when 2 or more signals
are applied together is equal to the sum of responses when the signals are
applied individually.
if x1(t) → y1(t) and x2(t) → y2(t),
Then the system is additive if, x1(t) + x2(t) → y1(t) + y2(t)
2. Homogeneity or Scaling property: The response of a system to a scaled
input is the scaled version of the response to the unscaled input.
if x(t) → y(t), then the system obeys homogeneity, if a x(t) → a y(t)
,where a is constant.
Combining both these properties we get the superposition property.
a x1(t) + b x2(t) → a y1(t) + b y2(t)
An interesting observation to be made from this property is that, For linear
systems zero input yields zero output. (assume a = 0, then output is zero)

Although we have written these definitions using continuous time signals,
the same definition holds in discrete time.
2.4 LTI SYSTEMS
Real World systems are seldom Linear and Time Invariant in nature. But
more often than not, we model Real world systems as Linear Time Invariant
systems or LTI systems. There is a good reason to do so. It is easier to
analyze and study LTI systems. The math gets a lot easier and allows us to
use more mathematical tools for analysis or in Richard Feynman's words
"Linear systems are important because we can solve them". The advantages
of making this approximation is far greater than any disadvantages that
arises from the assumption. Even highly non Linear systems are treated as
LTI for analysis and the non linearity adjustments are made later.
Any system that we refer from this point on in this book will be an LTI
system. Several Properties of the LTI system, including the all important
Convolution property is discussed as we go along.

3. FOURIER ANALYSIS
3.1 HISTORY
The name is Fourier, Joseph Fourier. In 1807, Joseph Fourier (pronounced
Fouye) came up with a crazy idea that gave a whole new meaning to signal
processing. The idea was so crazy that, even other famous mathematicians
of the time, like Lagrange opposed it. Fourier analysis is the back bone of
the DSP and there's no getting around it. Fourier analysis is math intensive,
but we will deal with the subject in an intuitive manner with minimum
math.

3.2 FOURIER SERIES
Fourier series is a basic mathematical tool for representing periodic signals.
Using Fourier series it is possible to express periodic signals in terms of
carefully chosen sinusoids. So every periodic signal in this world can be
expressed used some combination of sinusoids. Isn't this cool??

The above figure perfectly explains the Fourier series. Notice how a series
of sinusoids (sine and cosine waves) combine to form the resultant signal,
which looks nothing like a sinusoid.(Note that the different components
have different amplitudes and different frequencies)
Let's make things more interesting. Remember the superposition property of
LTI systems from the previous chapter, this is where it comes in handy.
The superposition property states that the response of a linear system to a
sum of signals is the sum of the responses to each individual input signal.
So instead of using a single signal as the input to a system, why not input
component sinusoids to the system and add up their responses. Wouldn't
both be the same??
So the only thing we really need to know is the response of the system to
sinusoids. From this we can predict the response to other periodic signals.
This would make our lives a lot easier.
Now let's look at some math. The General expression for Fourier series is:

here a0,a1,a2...,b1,b2,b3....are the Fourier coefficients. They tell us how
much a sine or cosine wave of a particular frequency is contributing to the
resultant signal.
The value of a0 tells us how much a cosine of zero frequency (cos 0 =1, so
basically DC) is present in the final wave. a0 is also called the DC value or
the Average value or the DC offset. Since all the other terms in the
expansion are pure sinusoids, their individually average to zero, so the
average value solely depends on a0.
Since sin 0 = 0, there can't be any contribution from zero frequency sine
wave, so b0 is always 0.
The value of a1 tells us how much a cosine of fundamental frequency is
present in the final wave.
Similarly, contribution from each sinusoid in the main signal can be found
out separately. This information is very useful, it can be used to manipulate
signals in a lot of ways.
Fourier series can be expressed in a more compact form using complex
notation. Using the complex notation, we can represent the contributions
from both sine and cosine waves of the same frequency by a single
coefficient.

This is called the synthesis equation. Here the Fourier coefficients are
complex. This notation has its own advantages, it is possible to calculate all
Fourier coefficients using a single expression. Electrical engineers use j
instead of i, since i is frequently used to denote electric current.
The values of cn can be obtained using the expression:
This expression is called the analysis equation and the plot of |cn| vs n is
called the frequency spectrum of the signal.
Notice the lines corresponding to each frequency component in the above
picture. This is exactly the Frequency spectrum. It tells us how much each

frequency component contributes to the original signal. This information is
invaluable to us.
Let's look at a practical example: In earth quake prone areas, houses are
built to resist shock waves. But the earthquake is not a single frequency
signal, it has many frequency components and it's not possible to design
houses that are resistant to the entire wave. To overcome this difficulty,
seismologists and structural engineers, do Fourier analysis on earthquake
wave and use the frequency spectrum obtained, to figure out the dominant
components in the wave. This way it is possible to design houses that are
resistant to these particular frequency components in the wave.
3.4 GIBBS PHENOMENON
The main reason behind Lagrange's objection to the Fourier series was that,
he believed it is not possible to represent discontinuous functions (like
square wave) in terms of sinusoids.
Guess what, there was some merit behind Lagrange's argument. In some
way he was spot on, it is actually impossible to perfectly represent
discontinuous signals using sinusoids.
Notice how there is an overshoot at the corners of the square wave in the
figure above. When a function takes a sudden jump, the Fourier estimation
ends up overshooting that jump. This is known as Gibbs phenomenon. That
overshoot will never go to zero no matter how many terms are added
3.5 FOURIER TRANSFORM

We have now seen how the Fourier series is used to represent a periodic
function by a discrete sum of complex exponentials. But how often are
natural signals periodic?? Now that's a problem. Too bad we can't apply
Fourier series to non periodic signals.
Why don't we assume an Aperiodic signal to be a periodic signal with
infinite time period. Why don't we assume that the same pattern exists after
infinite time. This is where we introduce the Fourier transform.
The Fourier transform is used to represent a general, non periodic function
by a continuous superposition or integral of complex exponentials. The
Fourier transform can be viewed as the limit of the Fourier series of a
function when the period approaches to infinity, so the limits of integration
change from one period to (−∞,∞).
The expression for the Fourier Transform is given by:
X(ω) is a continuous function of ω. The Fourier series coefficients are
basically the sampled values of X(ω) or in other words, X(ω) forms the
envelope for the Fourier series coefficients.

To go back from Frequency domain to the time domain, we need to use the
Inverse Fourier transform:
3.6 PROPERTIES OF FOURIER TRANSFORM
3.6.1 Linearity
if x1(t) ↔ X1(ω) and x2(t) ↔ X2(ω), then
αx1(t) + βx2(t) ↔ αX1(ω) + βX2(ω)
3.6.2 Time shifting
If we were to time shift a signal, it's magnitude spectrum won't change, only
it's phase spectrum changes.

i.e. if x(t) ↔ X(ω) , then
x(t- t0) ↔ X(ω) e-jnωt0
Do note that the magnitude of e-jnωt0
= 1, so this term can only bring a
phase shift.
3.6.3 Differentiation
if x(t) ↔ X(ω), then
x'(t) ↔ jωX(ω)
3.6.4 Scaling Property
x(at) ↔ X(ω/a)/ |a|
3.6.5 Parseval's Theorem
Parseval's theorem states that the total power in the frequency domain must
equal the total power of the same signal in the time domain i.e.
The real takeaway from this Theorem is that, no information is lost by
converting a signal from time to frequency domain or vice-versa.
3.6.6 Duality
then F{X(ω)} ↔ x(-t)
For example, the Fourier transform of a square wave is a sinc function and
the Fourier transform of a sinc function is a square wave.
3.7 MATLAB

3.7.1 Fourier series of a square wave with N
harmonics
t = linspace(-2,2,10000);
f = 0*t;
N=7;
for k=-N:1:N
if(k==0) % skip the zeroth term
continue;
end;
C_k = ((1)/(pi*1i*k))*(1-exp(-pi*1i*k)); % computes the k-th
Fourier coefficient
f_k = C_k*exp(2*pi*1i*k*t); % k-th term of the series
f = f + f_k; % adds the k-th term to f
end
plot(t, f, 'LineWidth', 2);
grid on;
xlabel('t');
ylabel('f(t)');
title(strcat('Fourier synthesis of the square wave function with n=',
int2str(N), ' harmonics.' ));

Try the same plot with a higher value for N (say 1000) and observe the
Gibbs phenomenon in action.

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seek to achieve by public enactments. If, on points like those
instanced, their convictions are so strong and their determination so
great, that they will time after time submit to extreme privations in
the effort to carry them; it is a reasonable expectation that these
convictions, pushed with this determination, would soon be
expressed in law, if those who held them had predominant power.
With working men, questions concerning the regulation of labour are
of the highest interest. Candidates for Parliament would be more
likely to obtain their suffrages by pandering to their prejudices on
such questions, than in any other way. Should it be said that no evil
need be feared unless the artizan-class numerically preponderated in
the con
stit
uen
cies; it may be rejoined that not unfrequently, where
two chief political parties are nearly balanced, some other party,
though much smaller, determines the election. When we bear in
mind that the trades-unions throughout the kingdom number
600,000 members, and command a fund of £300,000—when we
remember that these trades-unions are in the habit of aiding each
other, and have even been incorporated into one national association
—when we also remember that {367} their organization is very
complete, and their power over their members mercilessly exercised;
it seems likely that at a general election their combined action would
decide the result in many towns: even though the artizans in each
case formed but a moderate portion of the constituency. How
influential small but combined bodies are, the Irish Members of our
House of Commons prove to us; and still more clearly the Irish
emigrants in America. Certainly these trade-combinations are not
less perfectly organized; nor are the motives of their members less
strong. Judge then how efficient their political action would be.
It is true that in county-con
stit
uen
cies and rural towns, the artizan
class have no power; and that in the antagonism of agriculturists
there would be a restraint on their projects. But, on the other hand,
the artizans would, on these questions, have the sympathy of many
not belonging to their own body. Numerous small shopkeepers and

others who are in point of means about on their level, would go with
them in their efforts to regulate the relations of capital and labour.
Among the middle classes, too, there are not a few kindly-disposed
men who are so ignorant of political economy as to think the
artizans justified in their aims. Even among the landed class they
might find supporters. We have but to recollect the antipathy shown
by landowners in Parliament to the manufacturing interest, during
the ten-hours’ agitation, to see that it is quite possible for country
squires to join the working men in imposing restrictions unfavourable
to employers. True, the angry feeling which then prompted them has
in some measure died away. It is to be hoped, too, that they have
gained wisdom. But still, remembering the past, we must take this
contingency into account.
Here, then, is one of the dangers to which an extension of the
franchise opens the door. While the fear that the rights of property
may be directly interfered with, is absurd, it is a very rational fear
that the rights of property may be indirectly interfered with—that, by
cramping laws, {368} the capitalist may be prevented from using his
money as he finds best, and the workman from selling his labour as
he pleases. We are not prepared to say what widening of the
representation would bring about such results. We profess neither to
estimate what amount of artizan-power a £6 or a £5 borough-
franchise would give; nor to determine whether the opposing powers
would suffice to keep it in check. Our purpose here is simply to
indicate this establishment of injurious industrial regulations, as one
of the dangers to be kept in view.
Turn we now to another danger, distinct from the foregoing
though near akin to it. Next after the evils of that over-legislation
which restricts the exchange of capital and labour, come the evils of
that over-legislation which provides for the community, by State-
agency, benefits which capital and labour should be left
spontaneously to provide. And it naturally, though unfortunately,

happens, that those who lean to the one kind of over-legislation,
lean also to the other kind. Men leading laborious lives, relieved by
little in the shape of enjoyment, give willing ears to the doctrine that
the State should provide them with various positive advantages and
gratifications. The much-enduring poor cannot be expected to deal
very critically with those who promise them gratis pleasures. As a
drowning man catches at a straw, so will one whose existence is
burdensome catch at anything, no matter how unsubstantial, which
holds out the slightest hope of a little happiness. We must not,
therefore, blame the working-classes for being ready converts to
socialistic schemes, or to a belief in “the sovereign power of political
machinery.”
Not that the working-classes alone fall into these delusions.
Unfortunately they are countenanced, and have been in part misled,
by those above them. In Parliament and out of Parliament, well-
meaning men among the upper and middle ranks, have been active
apostles of these false {369} doctrines. There has ever been, and
continues to be, much law-making based on the assumption, that it
is the duty of the State, not simply to insure each citizen fair play in
the battle of life, but to help him in fighting the battle of life: having
previously taken money from his, or some one else’s, pocket to pay
the cost of doing this. And we cannot glance over the papers without
seeing how active are the agitations carried on out of doors in
furtherance of this policy; and how they threaten to become daily
more active. The doings of the Chadwick-school furnish one set of
illustrations. From those of the Shaftesbury-school other illustrations
may be gathered. And in the transactions of the body, absurdly self-
entitled “The National Association for the Promotion of Social
Science,” we find still more numerous developments of this
mischievous error.
When we say that the working-classes, and more especially the
artizan-classes, have strong leanings towards these Utopianisms
which they have unhappily been encouraged to entertain by many

who should have known better, we do not speak at random. We are
not drawing an a priori inference as to the doctrines likely to find
favour with men in their position. Nor are we guided merely by
evidence to be gathered from newspapers. We have a basis of
definite fact in the proceedings of reformed municipal governments.
These bodies have from year to year extended their functions; and
so heavy has in some cases become the consequent local taxation,
as to have caused a reaction against the political party which was
responsible. Town-councils almost exclusively Whig, have of late
been made comparatively Conservative, by the efforts of those richer
classes who suffer most from municipal extravagance. With whom,
then, has this extravagance been popular? With the poorer members
of the con
stit
uen
cies. Candidates for town-councillorships have
found no better means of obtaining the suffrages of the mass, than
the advocacy of this or the other local undertaking. To {370} build
baths and wash-houses at the expense of the town, has proved a
popular proposal. The support of public gardens out of funds raised
by local rates, has been applauded by the majority. So, too, with the
establishment of free libraries, which has, of course, met with
encouragement from working-men, and from those who wish to find
favour with them. Should some one, taking a hint from the cheap
concerts now common in our manufacturing towns, propose to
supply music at the public cost, we doubt not he would be hailed as
a friend of the people. And similarly with countless socialistic
schemes, of which, when once commenced, there is no end.
Such being the demonstrated tendencies of municipal
governments, with their extended bases of representation, is it not a
fair inference that a Central Government having a base of
representation much wider than the present, would manifest like
tendencies? We shall see the more reason for fearing this, when we
remember that those who approve of multiplied State-agencies,
would generally ally themselves with those who seek for the
legislative regulation of labour. The doctrines are near akin; and they

are, to a considerable extent, held by the same persons. If united
the two bodies would have a formidable power; and, appealed to, as
they would often be, by candidates expressing agreement on both
these points, they might, even though a minority, get unduly
represented in the legislature. Such, at least, seems to us a further
danger. Led by philanthropists having sympathies stronger than their
intellects, the working-classes are very likely to employ their
influence in increasing over-legislation: not only by agitating for
industrial regulations, but in various other ways. What extension of
franchise would make this danger a serious one, we do not pretend
to say. Here, as before, we would simply indicate a probable source
of mischief.
And now what are the safeguards? Not such as we {371} believe
will be adopted. To meet evils like those which threaten to follow the
impending political change, the common plan is to devise special
checks—minor limitations and qualifications. Not to dry up the evil at
its source but to dam it out, is, in analogous cases, the usual aim.
We have no faith in such methods. The only efficient safeguard lies
in a change of convictions and motives. And, to work a change of
this kind, there is no certain way but that of letting men directly feel
the penalties which mistaken legislation brings on them. “How is this
to be done?” the reader will doubtless ask. Simply by letting causes
and effects stand in their natural relations. Simply by taking away
those vicious arrangements which now mostly prevent men from
seeing the reactions that follow legislative actions.
At present the extension of public ad
min
i
stra
tions is popular,
mainly because there has not been established in the minds of the
people, any distinct connexion between the benefits to be gained
and the expenses to be paid. Of the conveniences or gratifications
secured to them by some new body of officials with a fund at its
disposal, they have immediate experience; but of the way in which
the costs fall on the nation, and ultimately on themselves, they have

no immediate experience. Our fiscal arrangements dissociate the
ideas of increased public expenditure and increased burdens on all
who labour; and thus encourage the superstition that law can give
gratis benefits. This is clearly the chief cause of that municipal
extravagance to which we have above adverted. The working men of
our towns possess public power, while most of them do not directly
bear public burdens. On small houses the taxes for borough-
purposes are usually paid by the landlords; and of late years, for the
sake of convenience and economy, there has grown up a system of
compounding with landlords of small houses even for the poor-rates
chargeable to their tenants. Under this {372} arrangement, at first
voluntary but now compulsory, a certain discount off the total rates
due from a number of houses is allowed to the owner, in
consideration of his paying the rates, and thus saving the authorities
trouble and loss in collection. And he is supposed to raise his rents
by the full amount of the rates charged. Thus, most municipal
electors, not paying local taxes in a separate form, are not
constantly reminded of the connexion between public expenditure
and personal costs; and hence it happens that any outlay made for
local purposes, no matter how extravagant and unreasonable, which
brings to them some kind of advantage, is regarded as pure gain. If
the corporation resolves, quite unnecessarily, to rebuild a town-hall,
the resolution is of course approved by the majority. “It is good for
trade and it costs us nothing,” is the argument which passes vaguely
through their minds. If some one proposes to buy an adjoining
estate and turn it into a public park, the working classes naturally
give their support to the proposal; for ornamental grounds cannot
but be an advantage, and though the rates may be increased that
will be no affair of theirs. Thus necessarily arises a tendency to
multiply public agencies and increase public outlay. It becomes an
established policy with popularity-hunters to advocate new works to
be executed by the town. Those who disapprove this course are in
fear that their seats may be jeopardized at the next election, should

they make a vigorous opposition. And thus do these local ad
min
i
stra
‐
tions inevitably lean towards abnormal developments.
No one can, we think, doubt that were the rates levied directly on
all electors, a check would be given to this municipal communism. If
each small occupier found that every new work undertaken by the
authorities cost him so many pence extra in the pound, he would
begin to consider with himself whether the advantage gained was
equivalent to the price paid; and would often reach a {373} negative
conclusion. It would become a question with him whether, instead of
letting the local government provide him with certain remote
advantages in return for certain moneys, he might not himself
purchase with such moneys immediate advantages of greater worth;
and, generally, he would decide that he could do this. Without
saying to what extent such a restraint would act, we may safely say
that it would be beneficial. Every one must admit that each
inhabitant of a town ought constantly to be reminded of the relation
between the work performed for him by the corporation and the sum
he pays for it. No one can deny that the habitual experience of this
relation would tend to keep the action of local governments within
proper bounds.
Similarly with the Central Government. Here the effects wrought
by public agencies are still more dissociated from the costs they
entail on each citizen. The bulk of the taxes being raised in so
unobtrusive a way, and affecting the masses in modes so difficult to
trace, it is scarcely possible for the masses to realize the fact that
the sums paid by Government for supporting schools, for facilitating
emigration, for inspecting mines, factories, railways, ships, etc., have
been in great part taken from their own pockets. The more
intelligent of them understand this as an abstract truth; but it is not
a truth present to their minds in such a definite shape as to
influence their actions. Quite otherwise, however, would it be if
taxation were direct; and the expense of every new State-agency
were felt by each citizen as an additional demand made on him by

the tax-gatherer. Then would there be a clear, constantly-recurring
experience of the truth, that for everything which the State gives
with one hand it takes away something with the other; and then
would it be less easy to propagate absurd delusions about the
powers and duties of Governments. No one can question this
conclusion who calls to mind the reason currently given for
maintaining {374} indirect taxation; namely, that the required revenue
could not otherwise be raised. Statesmen see that if instead of
taking from the citizen here a little and there a little, in ways that he
does not know or constantly forgets, the whole amount were
demanded in a lump sum, it would scarcely be possible to get it
paid. Grumbling and resistance would rise probably to disaffection.
Coercion would in hosts of cases be needed to obtain this large total
tax; which, indeed, even with this aid, could not be obtained from
the majority of the people, whose improvident habits prevent the
accumulation of considerable sums. And so the revenue would fall
immensely short of that expenditure which is supposed necessary.
This being assented to, it must perforce be admitted that under a
system of direct taxation, further extension of public ad
min
i
stra
tions,
entailing further costs, would meet with general opposition. Instead
of multiplying the functions of the State, the tendency would
obviously be to reduce their number.
Here, then, is one of the safeguards. The incidence of taxation
must be made more direct in proportion as the franchise is
extended. Our changes ought not to be in the direction of the Com
‐
pound-House
hold
ers-Act of 1851, which makes it no longer needful
for a Parliamentary elector to have paid poor-rates before giving a
vote; but they ought to be in the opposite direction. The exercise of
power over the national revenue, should be indissolubly associated
with the conscious payment of contributions to that revenue. Direct
taxation instead of being limited, as many wish, must be extended
to lower and wider classes, as fast as these classes are endowed
with political power.

Probably this proposal will be regarded with small favour by
statesmen. It is not in the nature of things for men to approve a
system which tends to restrict their powers. We know, too, that any
great extension of direct taxation will be held at present impossible;
and we are not prepared {375} to assert the contrary. This, however,
is no reason against reducing the indirect taxation and augmenting
the direct taxation as far as circumstances allow. And if when the
last had been increased and the first decreased to the greatest
extent now practicable, it were made an established principle that
any additional revenue must be raised by direct taxes, there would
be an efficient check to one of the evils likely to follow from further
political enfranchisement.
The other evil which we have pointed out as rationally to be
feared, cannot be thus met, however. Though an ever-recurring
experience of the relation between State-action and its cost, would
hinder the growth of those State-agencies which undertake to supply
citizens with positive conveniences and gratifications; it would be no
restraint on that negative and inexpensive over-legislation which
trespasses on individual freedom—it would not prevent mischievous
meddling with the relations between labour and capital. Against this
danger the only safeguards appear to be, the spread of sounder
views among the working classes, and the moral advance which
such sounder views imply.
“That is to say, the people must be educated,” responds the
reader. Yes, education is the thing wanted; but not the education for
which most men agitate. Ordinary school-training is not a
preparation for the right exercise of political power. Conclusive proof
of this is given by the fact that the artizans, from whose mistaken
ideas the most danger is to be feared, are the best informed of the
working classes. Far from promising to be a safeguard, the spread of
such education as is commonly given appears more likely to increase
the danger. Raising the working classes in general to the artizan-

level of culture, threatens to augment, rather than to diminish, their
power of working political evil. The current faith in Reading, Writing,
and Arithmetic, as fitting men for citizenship, seems to us quite {376}
unwarranted; as are, indeed, most other anticipations of the benefits
to be derived from learning lessons. There is no connexion between
the ability to parse a sentence, and a clear understanding of the
causes which determine the rate of wages. The multiplication-table
affords no aid in seeing through the fallacy that the destruction of
property is good for trade. Long practice may have produced
extremely good penmanship without having given the least power to
understand the paradox that machinery eventually increases the
number of persons employed in the trades into which it is
introduced. Nor is it proved that smatterings of mensuration,
astronomy, or geography, fit men for estimating the characters and
motives of Parliamentary candidates. Indeed we have only thus to
bring together the antecedents and the anticipated consequents, to
see how untenable is the belief in a relation between them. When
we wish a girl to become a good musician, we seat her before the
piano: we do not put drawing implements into her hands, and
expect music to come along with skill in the use of pencils and
colour-brushes. Sending a boy to pore over law-books would be
thought an extremely irrational way of preparing him for civil
engineering. And if in these and all other cases, we do not expect
fitness for any function except through instruction and exercise in
that function; why do we expect fitness for citizenship to be
produced by a discipline which has no relation to the duties of the
citizen? Probably it will be replied that by making the working man a
good reader, we give him access to sources of information from
which he may learn how to use his electoral power; and that other
studies sharpen his faculties and make him a better judge of political
questions. This is true; and the eventual tendency is unquestionably
good. But what if for a long time to come he reads only to obtain
confirmation of his errors? What if there exists a literature appealing

to his prejudices, and supplying him with fallacious arguments for
the mistaken beliefs which he naturally takes {377} up? What if he
rejects all teaching that aims to disabuse him of cherished
delusions? Must we not say that the culture which thus merely helps
the workman to establish himself in error, rather unfits than fits him
for citizenship? And do not the trades’-unions furnish evidence of
this?
How little that which people commonly call education prepares
them for the use of political power, may be judged from the
incompetency of those who have received the highest education the
country affords. Glance back at the blunders of our legislation, and
then remember that the men who committed them had mostly taken
University-degrees; and you must admit that the profoundest
ignorance of Social Science may accompany intimate acquaintance
with all which our cultivated classes regard as valuable knowledge.
Do but take a young member of Parliament, fresh from Oxford or
Cambridge, and ask him what he thinks Law should do, and why? or
what it should not do, and why? and it will become manifest that
neither his familiarity with Aristotle nor his readings in Thucydides,
have prepared him to answer the very first question a legislator
ought to solve. A single illustration will suffice to show how different
an education from that usually given, is required by legislators, and
consequently by those who elect them: we mean the illustration
which the Free-trade agitation supplies. By kings, peers, and
members of Parliament, mostly brought up at universities, trade had
been hampered by protections, prohibitions, and bounties. For
centuries had been maintained these legislative appliances which a
very moderate insight shows to be detrimental. Yet, of all the highly-
educated throughout the nation during these centuries, scarcely a
man saw how mischievous such appliances were. Not from one who
devoted himself to the most approved studies, came the work which
set politicians right on these points; but from one who left college
without a degree, and prosecuted inquiries which the established

education ignored. Adam {378} Smith examined for himself the
industrial phenomena of societies; contemplated the productive and
distributive activities going on around him; traced out their
complicated mutual dependences; and thus reached general
principles for political guidance. In recent days, those who have
most clearly understood the truths he enunciated, and by
persevering exposition have converted the nation to their views,
have not been graduates of universities. While, contrariwise, those
who have passed through the prescribed curriculum, have
commonly been the most bitter and obstinate opponents of the
changes dictated by politico-economical science. In this all-important
direction, right legislation was urged by men deficient in the so-
called best education, and was resisted by the great majority of men
who had received this so-called best education!
The truth for which we contend, and which is so strangely
overlooked, is, indeed, almost a truism. Does not our whole theory
of training imply that the right preparation for political power is
political cultivation? Must not that teaching which can alone guide
the citizen in the fulfilment of his public actions, be a teaching that
acquaints him with the effects of his public actions?
The second chief safeguard to which we must trust is, then, the
spread, not of that mere technical and miscellaneous knowledge
which men are so eagerly propagating, but of political knowledge;
or, to speak more accurately—knowledge of Social Science. Above
all, the essential thing is the establishment of a true theory of
government—a true conception of what legislation is for, and what
are its proper limits. This question which our political discussions
habitually ignore, is a question of greater moment than any other.
Inquiries which statesmen deride as speculative and unpractical, will
one day be found infinitely more practical than those which they
wade through Blue Books to master, and nightly spend many hours
in debating. The considerations that every morning fill a dozen

columns {379} of The Times, are mere frivolities when compared with
the fundamental consideration—What is the proper sphere of
government? Before discussing the way in which law should regulate
some particular thing, would it not be wise to put the previous
question—Whether law ought or ought not to meddle with that
thing? and before answering this, to put the more general questions
—What law should do? and what it should leave undone? Surely, if
there are any limits at all to legislation, the settlement of these limits
must have effects far more profound than any particular Act of
Parliament can have; and must be by so much the more
momentous. Surely, if there is danger that the people may misuse
political power, it is of supreme importance that they should be
taught for what purpose political power ought alone to be used.
Did the upper classes understand their position they would, we
think, see that the diffusion of sound views on this matter more
nearly concerns their own welfare and that of the nation at large,
than any other thing whatever. Popular influence will inevitably go on
increasing. Should the masses gain a predominant power while their
ideas of social arrangements and legislative action remain as crude
as at present, there will certainly result disastrous meddlings with
the relations of capital and labour, as well as a disastrous extension
of State-ad
min
i
stra
tions. Immense damage will be inflicted: primarily
on employers; secondarily on the employed; and eventually on the
nation as a whole. If these evils can be prevented at all, they can be
prevented only by establishing in the public mind a profound
conviction that there are certain definite limits to the functions of the
State; and that these limits ought on no account to be transgressed.
Having learned what these limits are, the upper classes ought to use
all means of making them clear to the people.
In No. XXIV. of this Review, for October, 1857, we {380}
endeavoured to show that while rep
re
sen
ta
tive government is, by its
intrinsic nature, better than any other for administering justice or

insuring equitable relations among citizens, it is, by its intrinsic
nature, worse than any other for all the various additional functions
which governments commonly undertake. To the question—What is
rep
re
sen
ta
tive government good for? our reply was—“It is good,
especially good, good above all others, for doing the thing which a
government should do. It is bad, especially bad, bad above all
others, for doing the things which a government should not do.”
To this truth we may here add a correlative one. As fast as a
government, by becoming rep
re
sen
ta
tive, grows better fitted for
maintaining the rights of citizens, it grows not only unfitted for other
purposes, but dangerous for other purposes. In gaining adaptation
for the essential function of a government, it loses such adaptation
as it had for other functions; not only because its complexity is a
hindrance to administrative action, but also because in discharging
other functions it must be mischievously influenced by class bias. So
long as it is confined to the duty of preventing the aggressions of
individuals on one another, and protecting the nation at large against
external enemies, the wider its basis the better; for all men are
similarly interested in the security of life, property, and freedom to
exercise the faculties. But let it undertake to bring home positive
benefits to citizens, or to interfere with any of the special relations
between class and class, and there necessarily enters an incentive to
injustice. For in no such cases can the immediate interests of all
classes be alike. Therefore do we say that as fast as representation
is extended, the sphere of government must be contracted.
POSTSCRIPT.—Since the foregoing pages were written, Lord John
Russell has introduced his Reform Bill; and in {381} application of the
general principles we contend for, a few words may fitly be added
respecting it.
Of the extended county-franchise most will approve, save those
whose illegitimate influence is diminished by it. Adding to the rural
con
stit
uen
cies a class less directly dependent on large landowners,

can scarcely fail to be beneficial. Even should it not at first
perceptibly affect the choice of rep
re
sen
ta
tives, it will still be a good
stimulus to political education and to consequent future benefits. Of
the re-distribution of seats little is to be said, further than that,
however far short it may fall of an equitable arrangement, it is
perhaps as much as can at present be obtained.
Whether the right limit for the borough-franchise has been chosen
is, on the other hand, a question that admits of much discussion.
Some hesitation will probably be felt by all who duly weigh the
evidence on both sides. Believing, as we do, that the guidance of
abstract equity, however much it may need qualification, must never
be ignored, we should be glad were it at once practicable more
nearly to follow it; since it is certain that only as fast as the injustice
of political exclusion is brought to an end, will the many political
injustices which grow out of it disappear. Nevertheless, we are
convinced that the forms which freedom requires will not of
themselves produce the reality of freedom, in the absence of an
appropriate national character; any more than the most perfect
mechanism will do its work in the absence of a motive power. There
seems reason to think that the degree of liberty a people is capable
of in any given age, is a fixed quantity; and that any artificial
extension of it in one direction brings about an equivalent limitation
in some other direction. French republics show scarcely any more
respect for individual rights than the despotisms they supplant; and
French electors use their freedom to put themselves again in slavery.
In America the feeble restraints imposed by the {382} State are
supplemented by the strong restraints of a public opinion which, in
many respects, holds the citizens in greater bondage than here. And
if there needs a demonstration that rep
re
sen
ta
tive equality is an
insufficient safeguard for freedom, we have it in the trades’-unions
already referred to; which, purely democratic as are their
organizations, yet exercise over their members a tyranny almost
Neapolitan in its rigour and unscrupulousness. The greatest

attainable amount of individual liberty being the true end; and the
diffusion of political power being regarded mainly as a means to this
end; the real question when considering further extensions of the
franchise, is—whether the average freedom of action of citizens will
be increased?—whether men will be severally freer than before to
pursue the objects of life in their own way? Or, in the present case,
the question is—whether the good which £7, £6, or £5 householders
would do in helping to abolish existing injustices, will be partly or
wholly neutralized by the evil they may do in establishing other
injustices? The desideratum is as large an increase in the electorate
as can be made without enabling the people to carry out their
delusive schemes of over-legislation. Whether the increase proposed
is greater or less than this, is the essential point. Let us briefly
consider the evidence on each side.
As shown by Lord J. Russell’s figures, the new borough-electors
will consist mainly of artizans; and these, as we have seen, are in
great part banded together by a common wish to regulate the
relations of capital and labour. As a class, they are not as Lord J.
Russell describes them, “fitted to exercise the franchise freely and
independently.” On the contrary, there are no men in the community
so shackled. They are the slaves of the authorities they have
themselves set up. The dependence of farmers on landlords, or of
operatives on employers, is much less servile; for they can carry
their capital or labour elsewhere. But {383} the penalty for
disobedience to trades-union dictates, pursues the rebel throughout
the kingdom. Hence the great mass of the new borough-electors
must be expected to act simultaneously, on the word of command
being issued from a central council of united trades. Even while we
write we meet with fresh reason for anticipating this result. An
address from the Conference of the Building Trades to the working
classes throughout the kingdom, has just been published; thanking
them for their support; advising the maintenance of the
organization; anticipating future success in their aims; and intimating

the propriety of recommencing the nine-hours’ agitation. We must,
then, be prepared to see these industrial questions made leading
questions; for artizans have a much keener interest in them than in
any others. And we may feel certain that many elections will turn
upon them.
How many? There are some thirty boroughs in which the newly-
enfranchised will form an actual majority—will, if they act together,
be able to outvote the existing electors; even supposing the parties
into which they are now divided were to unite. In half-a-dozen other
boroughs the newly-enfranchised will form a virtual majority—will
preponderate unless the present liberal and conservative voters co-
operate with great unanimity, which they will be unlikely to do. And
the number proposed to be added to the constituency, is one-half or
more in nearly fifty other boroughs: that is, in nearly fifty other
boroughs, the new party will be able to arbitrate between the two
existing parties; and will give its support to whichever of these
promises most aid to artizan-schemes. It maybe said that in this
estimate we assume the whole of the new borough-electors to
belong to the artizan-class, which they do not. This is true. But, on
the other hand, it must be remembered that among the £10
householders there is a very considerable sprinkling of this class,
while the freemen chiefly consist of it; and hence the whole artizan
body in each constituency will probably {384} be not smaller than we
have assumed. If so, it follows that should the trades-union
organization be brought to bear on borough-elections, as it is pretty
certain to be, it may prevail in some eighty or ninety places, and
sway the votes of rep
re
sen
ta
tives in from 100 to 150 seats—
supposing, that is, that it can obtain as many eligible candidates.
Meanwhile, the county-con
stit
uen
cies in their proposed state, as
much as in their existing state, not being under trades-union
influence, may be expected to stand in antagonism to the artizan-
con
stit
uen
cies; as may also the small boroughs. It is just possible,
indeed, that irritated by the ever-growing power of a rich mercantile

class, continually treading closer on their heels, the landowners,
carrying with them their dependents, might join the employed in
their dictation to employers; just as, in past times, the nobles joined
the commonalty against the kings, or the kings joined the
commonalty against the nobles. But leaving out this remote
contingency, we may fairly expect the rural con
stit
uen
cies to oppose
the large urban ones on these industrial questions. Thus, then, the
point to be decided is, whether the benefits that will result from this
extended suffrage—benefits which we doubt not will be great—may
not be secured while the ac
com
pa
ny
ing evil tendencies are kept in
check. It may be that these new artizan-electors will be powerful for
good, while their power to work evil will be in a great degree
neutralized. But this we should like to see well discussed.
On one question, however, we feel no hesitation; namely, the
question of a rate
pay
ing-qual
i
fi
ca
tion. From Lord John Russell’s
answer to Mr. Bright, and more recently from his answer to Mr. Steel,
we gather that on this point there is to be no alteration—that £6
householders will stand on the same footing that £10 householders
do at present. Now by the Com
pound-House
hold
ers-Act of 1851, to
which we have already referred, it is provided that tenants of £10
houses whose rates are paid by their {385} landlords, shall, after
having once tendered payment of rates to the authorities, be
thereafter considered as ratepayers, and have votes accordingly.
That is to say, the rate
pay
ing-qual
i
fi
ca
tion is made nominal; and that
in practice it has become so, is proved by the fact that under this
Act, 4000 electors were suddenly added to the constituency of
Manchester.
The continuance and extension of this arrangement we conceive
to be wholly vicious. Already we have shown that the incidence of
taxation ought to be made more direct as fast as popular power is
increased, and that, as diminishing the elector’s personal experience
of the costs of public ad
min
i
stra
tion, this abolition of a rate
pay
ing-
qual
i
fi
ca
tion is a retrograde step. But this is by no means the sole

ground for disapproval. The rate
pay
ing-qual
i
fi
ca
tion is a valuable
test—a test which tends to separate the more worthy of the working
classes from the less worthy. Nay more, it tends to select for
enfranchisement, those who have the moral and intellectual qualities
especially required for judicious political conduct. For what general
mental characteristic does judicious political conduct presuppose?
The power of realizing remote consequences. People who are misled
by demagogues, are those who are impressed with the proximate
results set forth to them but are not impressed by the distant
results, even when these are explained—regard them as vague,
shadowy, theoretical, and are not to be deterred by them from
clutching at a promised boon. Conversely, the wise citizen is the one
who conceives the distant evils so clearly that they are practically
present to him, and thus outweigh the immediate temptation. Now
these are just the respective char
ac
ter
is
tics of the two classes of
tenants whom a rate
pay
ing-qual
i
fi
ca
tion separates:—the one having
their rates paid by their landlords and so losing their votes; the other
paying their own rates that they may get votes:—the one unable to
resist present temptations, unable to save money, {386} and
therefore so inconvenienced by the payment of rates as to be
disfranchised rather than pay them; the other resisting present
temptations and saving money, with the view, among other ends, of
paying rates and becoming electors. Trace these respective traits to
their sources, and it becomes manifest that, on the average, the
pecuniarily improvident must be also the politically improvident; and
that the politically provident must be far more numerous among
those who are pecuniarily provident. Hence, it is folly to throw aside
a regulation under which these spontaneously separate themselves
—severally disfranchise themselves and enfranchise themselves.

{387}
“THE COLLECTIVE WISDOM.”
[First published in The Reader for April 15, 1865.]
A test of senatorial capacity is a desideratum. We rarely learn how
near the mark or how wide of the mark the calculations of
statesmen are: the slowness and complexity of social changes,
hindering, as they do, the definite comparisons of results with
anticipations. Occasionally, however, parliamentary decisions admit
of being definitely valued. One which was arrived at a few weeks
ago furnished a measure of legislative judgment too significant to be
passed by.
On the edge of the Cotswolds, just above the valley of the Severn,
occur certain springs, which, as they happen to be at the end of the
longest of the hundred streams which join to form the Thames, have
been called by a poetical fiction “the sources of the Thames.”
Names, even when poetical fictions, suggest conclusions; and
conclusions drawn from words instead of facts are equally apt to
influence conduct. Thus it happened that when, recently, there was
formed a company for supplying Cheltenham and some other places
from these springs, great opposition arose. The Times published a
paragraph headed “Threatened Absorption of the Thames,” stating
that the application of {388} this company to Parliament had “caused
some little consternation in the city of Oxford, and will, doubtless,
throughout the valley of the Thames;” and that “such a measure, if
carried out, will diminish the water of that noble river a million of

gallons per day.” A million is an alarming word—suggests something
necessarily vast. Translating words into thoughts, however, would
have calmed the fears of the Times paragraphist. Considering that a
million gallons would be contained by a room fifty-six feet cube, the
nobility of the Thames would not be much endangered by the
deduction. The simple fact is, that the current of the Thames, above
the point at which the tides influence it, discharges in twenty-four
hours eight hundred times this amount!
When the bill of this proposed water-company was brought before
the House of Commons for second reading, it became manifest that
the imaginations of our rulers were affected by such expressions as
the “sources of the Thames,” and “a million gallons daily,” in much
the same way as the imaginations of the ignorant. Though the
quantity of water proposed to be taken bears, to the quantity which
runs over Teddington weir, about the same ratio that a yard bears to
half a mile, it was thought by many members that its loss would be
a serious evil. No method of measurement would be accurate
enough to detect the difference between the Thames as it now is,
and the Thames minus the Cerney springs; and yet it was gravely
stated in the House that, were the Thames diminished in the
proposed way, “the proportion of sewage to pure water would be
seriously increased.” Taking a minute out of twelve hours, would be
taking as large a proportion as the Cheltenham people wish to take
from the Thames. Nevertheless, it was contended that to let
Cheltenham have this quantity would be “to rob the towns along the
banks of the Thames of their rights,” Though, of the Thames flowing
by each of these towns, some 999 parts out of 1,000 pass by
unused, it was held {389} that a great injustice would be committed
were one or two of these 999 parts appropriated by the inhabitants
of a town who can now obtain daily but four gallons of foul water
per head!
But the apparent inability thus shown to think of causes and
effects in something like their true quantitative relations, was still

more conspicuously shown. It was stated by several members that
the Thames Navigation Commissioners would have opposed the bill
if the commission had not been bankrupt; and this hypothetical
opposition appeared to have weight. If we may trust the reports, the
House of Commons listened with gravity to the assertion of one of
its members, that, if the Cerney springs were diverted, “shoals and
flats would be created.” Not a laugh nor a cry of “Oh! oh,” appears
to have been produced by the prophecy, that the volume and
scouring power of the Thames would be seriously affected by taking
away from it twelve gallons per second! The whole quantity which
these springs supply would be delivered by a current moving
through a pipe one foot in diameter at the rate of less than two
miles per hour. Yet, when it was said that the navigability of the
Thames would be injuriously affected by this deduction, there were
no shouts of derision. On the contrary, the House rejected the
Cheltenham Water Bill by a majority of one hundred and eighteen to
eighty-eight. It is true that the data were not presented in the above
shape. But the remarkable fact is that, even in the absence of a
specific comparison, it should not have been at once seen that the
water of springs which drain but a few square miles at most, can be
but an inappreciable part of the water which runs out of the Thames
basin, extending over several thousand square miles. In itself, this is
a matter of small moment. It interests us here simply as an example
of legislative judgment. The decision is one of those small holes
through which a wide prospect may be seen, and a disheartening
prospect it is. In a very simple case there {390} is here displayed a
scarcely credible inability to see how much effect will follow so much
cause; and yet the business of the assembly exhibiting this inability
is that of dealing with causes and effects of an extremely involved
kind. All the processes going on in society arise from the
concurrences and conflicts of human actions, which are determined
in their nature and amounts by the human constitution as it now is—
are as much results of natural causation as any other results, and

equally imply definite quantitative relations between causes and
effects. Every legislative act presupposes a diagnosis and a
prognosis; both of them involving estimations of social forces and
the work done by them. Before it can be remedied, an evil must be
traced to its source in the motives and ideas of men as they are,
living under the social conditions which exist—a problem requiring
that the actions tending toward the result shall be identified, and
that there shall be something like a true idea of the quantities of
their effects as well as the qualities. A further estimation has then to
be made of the kinds and degrees of influence that will be exerted
by the additional factors which the proposed law will set in motion:
what will be the resultants produced by the new forces coöperating
with preëxisting forces—a problem still more complicated than the
other.
We are quite prepared to hear the unhesitating reply, that men
incapable of forming an approximately true judgment on a matter of
simple physical causation may yet be very good law-makers. So
obvious will this be thought by most, that a tacit implication to the
contrary will seem to them absurd; and that it will seem to them
absurd is one of the many indications of the profound ignorance that
prevails. It is true that mere empirical generalizations which men
draw from their dealings with their fellows suffice to give them some
ideas of the proximate effects which new enactments will work; and,
seeing these, they think they see as far as needful. Discipline in
physical {391} science, however, would help to show them the futility
of calculating consequences based on such simple data. And if there
needs proof that calculations of consequences so based are futile,
we have it in the enormous labour annually entailed on the
Legislature in trying to undo the mischiefs it has previously done.
Should any say that it is useless to dwell on this incompetency,
seeing that the House of Commons contains the select of the nation,
than whose judgments no better are to be had, we reply that there
may be drawn two inferences which have important practical

bearings. In the first place, we are shown how completely the
boasted intellectual discipline of our upper classes fails to give them
the power of following out in thought, with any correctness, the
sequences of even simple phenomena, much less those of complex
phenomena. And, in the second place, we may draw the corollary,
that if the sequences of those complex phenomena which societies
display, difficult beyond all others to trace out, are so unlikely to be
understood by them, they may advantageously be restricted in their
interferences with such sequences.
In one direction, especially, shall we see reason to resist the
extension of legislative action. There has of late been urged the
proposal that the class contemptuously described as dividing its
energies between business and bethels shall have its education
regulated by the class which might, with equal justice, be described
as dividing its energies between club-rooms and game preserves.
This scheme does not seem to us a hopeful one. Considering that
during the last half century our society has been remoulded by ideas
that have come from the proposed pupil, and have had to overcome
the dogged resistance of the proposed teacher, the propriety of the
arrangement is not obvious. And if the propriety of the arrangement
is not obvious on the face of it, still less obvious does it become
when the competency of {392} the proposed teacher comes to be
measured. British intelligence, as distilled through the universities
and re-distilled into the House of Commons, is a product admitting
of such great improvement in quality, that we should be sorry to see
the present method of manufacture extended and permanently
established.

{393}
POLITICAL FETICHISM.
[First published in The Reader for June 10, 1865.]
A Hindoo, who, before beginning his day’s work, salaams to a bit
of plastic clay, out of which, in a few moments, he has extemporized
a god in his own image, is an object of amazement to the European.
We read with surprise bordering on scepticism of worship done by
machinery, and of prayers which owe their supposed efficacy to the
motion given by the wind to the papers they are written on. When
told how certain of the Orientals, if displeased with their wooden
deities, take them down and beat them, men laugh and wonder.
Why should men wonder? Kindred superstitions are exhibited by
their fellows every day—superstitions that are, indeed, not so gross,
but are intrinsically of the same nature. There is an idolatry which,
instead of carving the object of its worship out of dead matter, takes
humanity for its raw material, and expects, by moulding a mass of
this humanity into a particular form, to give it powers or properties
quite different from those it had before it was moulded. In the one
case as in the other, the raw material is, as much as may be,
disguised. There are decorative appliances by which the savage
helps himself to think that he has something more than wood before
him; and the {394} citizen gives to the political agencies he has
helped to create, such imposing externals and distinctive names
expressive of power, as serve to strengthen his belief in the benefits
prayed for. Some faint reflection of that “divinity” which “doth hedge

a king” spreads down through every state department to the lowest
ranks; so that, in the eyes of the people, even the policeman puts on
along with his uniform a certain indefinable power. Nay, the mere
dead symbols of authority excite reverence in spite of better
knowledge. A legal form of words seems to have something
especially binding in it; and there is a preternatural efficiency about
a government stamp.
The parallelism is still more conspicuous between the persistency
of faith in the two cases, notwithstanding perpetual
disappointments. It is difficult to perceive how graven images, that
have been thrashed for not responding to their worshipper’s desires,
should still be reverenced and petitioned; but the difficulty of
conceiving this is diminished when we remember how, in their turns,
all the idols in our political pantheon undergo castigations for failing
to do what was expected of them, and are nevertheless daily looked
up to in the trustful hope that future prayers will be answered. The
stupidity, the slowness, the perversity, the dishonesty of officialism,
in one or other of its embodiments, are demonstrated afresh in
almost every newspaper that issues. Probably half the leading
articles written have for texts some absurd official blunder, some
exasperating official delay, some astounding official corruption, some
gross official injustice, some incredible official extravagance. And yet
these whippings, in which balked expectation continually vents itself,
are immediately followed by renewed faith: the benefits that have
not come are still hoped for, and prayers for others are put up. Along
with proof that the old State-machines are in themselves inert, and
owe such powers as they seem to have to the public opinion which
sets their parts in motion, there are continually proposed {395} new
State-machines of the same type as the old. This inexhaustible
credulity is counted on by men of the widest political experience.
Lord Palmerston, who probably knows his public better than any
other man, lately said, in reply to a charge made in the House—“I
am quite convinced that no person belonging to the government, in

whatever department he may be, high or low, would be guilty of any
breach of faith in regard to any matter confided to him.” To assert as
much in the face of facts continually disclosed, implies that Lord
Palmerston knows well that men’s faith in officialism survives all
adverse evidence.
In which case are the hopes from State-agency realized? One
might have thought that the vital interests at stake would have kept
the all-essential apparatus for administering justice up to its work;
but they do not. On the one hand, here is a man wrongly convicted,
and afterward proved to be innocent, who is “pardoned” for an
offence he did not commit; and has this as consolation for his
unmerited suffering. On the other hand, here is a man whose grave
delinquencies a Lord Chancellor overlooks, on partial restitution
being made—nay, more, countenances the granting of a pension to
him. Proved guilt is rewarded, while proved innocence is left without
compensation for pains borne and fortunes blasted! This marvellous
antithesis, if not often fully paralleled in the doings of officialism as
administrator of justice, is, in endless cases, paralleled in part. The
fact that imprisonment is the sentence on a boy for stealing a
pennyworth of fruit, while thousands of pounds may be transferred
from a public into a private purse without any positive punishment
being adjudged, is an anomaly kept in countenance by numerous
other judicial acts. Theoretically, the State is a protector of the rights
of subjects; practically, the State continually plays the part of
aggressor. Though it is a recognized principle of equity that he who
makes a false charge shall pay the costs of the {396} defence, yet,
until quite recently, the Crown has persisted in refusing to pay the
costs of citizens against whom it has brought false charges. Nay,
worse, deliberate attempts used to be made to establish charges by
corrupt means. Within the memory of those now living, the Crown,
in excise-prosecutions, bribed juries. When the verdict was for the
Crown, the custom was to give double fees; and the practice was
not put an end to until the counsel for a defendant announced in

open court that the jury should have double fees if their verdict was
for his client!
Not alone in the superior parts of our judicial apparatus is this ill-
working of officialism so thrust on men’s notice as to have become
proverbial; not alone in the life-long delays and ruinous expenses
which have made Chancery a word of dread; not alone in the
extravagances of bankruptcy courts, which lead creditors carefully to
shun them; not alone in that uncertainty which makes men submit
to gross injustice rather than risk the still grosser injustice which the
law will, as likely as not, inflict on them; but down through the lower
divisions of the judicial apparatus are all kinds of failures and
absurdities daily displayed. If may be fairly urged in mitigation of the
sarcasms current respecting the police, that among so many men
cases of misconduct and inefficiency must be frequent; but we might
have expected the orders under which they act to be just and well
considered. Very little inquiry shows that they are not. There is a
story current that, in the accounts of an Irish official, a small charge
for a telegram which an emergency had called for, was objected to
at the head office in London, and, after a long correspondence,
finally allowed, but with the understanding that in future no such
item would be passed, unless the department in London had
authorized it! We cannot vouch for this story, but we can vouch for
one which gives credibility to it. A friend who had been robbed by
his cook went to the police-office, detailed the case, gave good
reasons for inferring the direction of her {397} flight, and requested
the police to telegraph, that she might be intercepted. He was told,
however, that they could not do this without authority; and this
authority was not to be had without a long delay. The result was
that the thief, who had gone to the place supposed, escaped, and
has not since been heard of. Take another function assumed by the
police—the regulation of traffic. Daily, all through London, ten
thousand fast-going vehicles, with hard-pressed men of business in
them, are stopped by a sprinkle of slow-going carts and wagons.

Greater speed in these comparatively few carts and wagons, or
limitation of them to early and late hours, would immensely diminish
the evil. But, instead of dealing with these really great hinderances
to traffic, the police deal with that which is practically no hindrance.
Men with advertisement-boards were lately forbidden to walk about,
on the groundless plea that they are in the way; and incapables,
prevented thus from getting a shilling a day, were driven into the
ranks of paupers and thieves. Worse cases may be observed. For
years past there has been a feud between the police and the
orange-girls, who are chased hither and thither because they are
said to be obstructions to foot-passengers. Meanwhile, in some of
the chief thoroughfares, may constantly be seen men standing with
toys, which they delude children and their parents into buying by
pretending that the toys make certain sounds which they themselves
make; and when the police, quietly watching this obtainment of
money under false pretences, are asked why they do not interfere,
they reply that they have no orders. Admirable contrast! Trade
dishonestly, and you may collect a small crowd on the pavement
without complaint being made that you interrupt the traffic. Trade
honestly, and you shall be driven from the pavement-edge as an
impediment—shall be driven to dishonesty!
One might have thought that the notorious inefficiency of
officialism as a protector against injustice would have {398} made
men sceptical of its efficiency in other things. If here, where citizens
have such intense interests in getting a function well discharged,
they have failed through all these centuries in getting it well
discharged—if this agency, which is in theory the guardian of each
citizen, is in so many cases his enemy, that going to law is
suggestive of impoverishment and possible ruin; it might have been
supposed that officialism would scarcely be expected to work well
where the interests at stake are less intense. But so strong is
political fetichism, that neither these experiences, nor the parallel
experiences which every state-department affords, diminish men’s

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