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CONTENTS
Chapter I. Introduction and examples 1
Examples 1
Isomorphism 5
Exercises 8
Chapter II. Fourier analysis on groups 12
Introduction 12
Dual groups, Fourier transforms 13
Pontryagin duality 15
Examples 16
Exercises 16
Chapter III. Measure theoretic entropy 19
Partitions and algebras 19
Entropy of partitions 20
Conditional entropy 21
Entropy of a measure–preserving transformation 22
Exercises 23
Chapter IV. Properties of metric entropy 25
Powers of transformations 25
Zero entropy 25
Calculating h(T): theory 26
Calculating h(T): examples 28
Exercises 29
Chapter V. Entropy as an invariant 30
Non–isomorphic maps with the same entropy 30
Kolmogorov and Bernoulli automorphisms 31
The Pinsker algebra 34
Exercises 35
Chapter VI. Topological entropy I: definitions 37
Bowen’s definition 37
Definition using open covers 39
When the two definitions coincide 40
Exercises 42
Chapter VII. Topological entropy II: homogeneous mea-
sures 43
A topological Kolmogorov–Sinai type theorem 43
Examples 45
Typeset by AMS-TEX
1

2 CONTENTS
Homogeneous measures 46
The variational principle 50
Linear maps and covering spaces 50
Exercises 52
Chapter VIII. Topological entropy III: Yuzvinskii’s for-
mula 55
The adele ring 55
Automorphisms of solenoids 56
Generalizing Theorem 7.12 57
Yuzvinskii’s formula 59
The general case 59
Examples 60
Exercises 61
Chapter IX. Topological entropy IV: Periodic points 62
Periodic points for automorphisms 62
Examples 62
Expansive automorphisms of connected groups 63
Distribution of periodic points 65
Exercises 67
Chapter X. Further reading 69
Higher–dimensional actions 69
Disconnected groups 69
Appendix A. Weil’s proof of Theorem 8.1 71
Adeles 71
The embedding of the rationals 72
Characters and quasifactors 73
Appendix B. Lawton’s proof of Theorem 9.6 75
References 83

CHAPTER I
INTRODUCTION AND EXAMPLES
Ergodic theory is the study of (semi–)group actions on spaces. The basic moti-
vational example is that of a physical system evolving in time according to a fixed
set of laws.
Examples
Example 1.1. Let X denote the set of possible states of a physical system that
evolves in time. The way in which a point x ∈ X evolves in time is given by a
mapping
(x, t) → Tt(x),
where Tt(x) is the state that x moves to after t seconds. Notice that each Tt is a
function X → X. In particular, T0 is the identity map on X. Assuming that each
state x determines its future and its past completely, we can find the state that x
reaches after t + s seconds in two ways: firstly, it is by definition Tt+s(x). On the
other hand, the state x at time 0 has a unique future; after t seconds have elapsed
it is at Tt(x), and after a further s seconds it is at Ts(Tt(x)). It follows that
(1.1) Ts ◦ Tt = Ts+t
for all s, t 0. Under our assumption (that the entire past and future of a state x
is determined by x), each Tt must be a bijection on X. By (1.1), the assignment
t → Tt is a homomorphism R → Bij(X), where Bij(X) is the group of bijections of
X. That is, T is an action of the group R by bijections of the set X.
If the physical system given by the action of T on X is sampled at times 0,1,2,3,
. . . (and for our mathematical convenience, at times –1,–2, . . . as well), the trans-
formation observed on X between each time is given by a single map, namely T1.
In this case we obtain an action of Z on X by bijections, via the homomorphism
n → (T1)n
= Tn.
Example (1.1) was completely general. A more genuine physical system is given
by the following example.
Example 1.2. Consider a system of n particles in R3
, moving according to some
mechanical law. The state of the system is completely determined (in the sense that
we can – in principle – determine the complete future and past behaviour from this
data) by the positions q1, . . . , qn and momenta p1, . . . , pn of the particles. Thus
the allowed states form a subset X ⊂ R6n
. Let the laws that govern the system be
Typeset by AMS-TEX
1

2 CHAPTER 1. INTRODUCTION AND EXAMPLES
given by a Hamiltonian H : X → R, so
q̇i =
∂H
∂pi
ṗi = −
∂H
∂qi
.
(1.2)
The function H is constant along orbits of the R action given by time evolution
(equivalently, is constant along the solutions of the differential equations (1.2)).
Choose a suitable value for H, say e: we then obtain an R–action T on the set
H−1
(e), which (under some reasonable assumptions) is a submanifold of R6n
. A
fundamental observation (due to Liouville) is that Lebesgue measure on R6n
re-
stricts to give a measure on each H−1
(e) that is preserved by the R action. The
ergodic hypothesis was that the orbits of the action spread through the space so
uniformly that for any continuous function f : H−1
(e) → R, the space average of f,

H−1(e)
f would coincide with the time average, lims→∞
1
s
s
0
f(Tt(x))ds for almost
any x.
We are therefore led to the following kind of models for studying dynamical
systems: actions of a group G on a space X, preserving some natural structure that
could range from almost nothing (cardinality of sets, group actions by bijections) to
very specific structures (for example, group actions by automorphisms of compact
groups, or actions by diffeomorphisms of a smooth manifold). The most important
examples are the following.
[1] X is a probability space with σ–algebra B and measure µ. The action
T is by invertible measure–preserving transformations of (X, B, µ). This
is classical ergodic theory.
[2] X is a compact topological space, and T is an action by homeomor-
phisms of X. This is topological dynamics.
[3] X is a differentiable compact manifold, and T acts by diffeomor-
phisms of X. This is smooth ergodic theory or differentiable dynamical
systems.
[4] Algebraic dynamical systems. For instance, X is a compact abelian
group, which is a probability space with respect to Haar measure µ on the
Borel σ–algebra B, and T is a G–action by measurable automorphisms
of X. Notice that such an example sits in [1] and in [2]: a measurable
automorphism is automatically continuous, so T is automatically an
action by homeomorphisms of the compact topological space X.
More generally, the four families of examples are not unrelated: the following
theorem is the first step towards using measure–theoretic ideas to understand home-
omorphisms and diffeomorphisms.

EXAMPLES 3
Theorem 1.3. If X is a compact topological space, and f : X → X is a home-
omorphism, then there is a probability m defined on the Borel sets of X which is
f–invariant.
This theorem may be saying very little (if X is a compact group, and f is an
automorphism, then one possible candidate for m is the point mass at the identity),
quite a lot (if X is the circle S1
, and f is the rotation f(z) = ze2πiθ
, θ ∈ Q, what
are the possible measures m?) or a great deal (if X is the circle S1
, and f is the
rotation f(z) = ze2πiθ
, θ /
∈ Q, what are the possible measures m?). Theorem 1.3
is proved in the exercises.
A measurable space is a set X with a collection of subsets B of X such that
(1) X ∈ B,
(2) if B ∈ B then XB ∈ B,
(3) Bn ∈ B implies that
∞
n=1 Bn ∈ B.
Such a collection B is called a σ–algebra of subsets; the elements of B are the
measurable sets.
A finite measure on the measure space (X, B) is a map m : B → R0 with
m(∅) = 0 and m(
∞
n=1 Bn) =
∞
n=1 m(Bn) if {Bn} is a pairwise disjoint collection
of measurable sets. If, in addition, m(x) = 1, then (X, B, m) is a probability space.
If X is a topological space, then the Borel σ–algebra is the smallest σ–algebra
defined on X that contains all the open sets, and a measure m on X is a Borel
measure if it is defined on the Borel σ–algebra.
Example 1.4. The following are examples of probability spaces.
(1) Let X = [0, 1], with m Lebesgue measure on the interval, and B the σ–
algebra of Lebesgue measurable sets.
(2) [coin–tossing space] Let Xi = {0, 1, . . . , n − 1} for each i ∈ Z; and let
mi = (p0, . . . , pn−1) be a fixed probability vector (i.e. pj ≥ 0 and

pj = 1).
The discrete topology on Xi makes X =
∞
−∞ Xi into a compact topological
space. Subsets Aj ⊂ Xj for j = n, . . . , m define a cylinder set in X:
C =
n−1

−∞
Xi ×
m

j=n
Aj ×
∞

m+1
Xi,
and the collection of all such cylinders forms a basis of open sets for the
topology on X. Define a Borel measure m on X by setting m(C) =
m
j=n mj(Aj) and extending to all Borel sets. As an illustration, let n = 2,
and choose the measure mi = (1
2 , 1
2 ). If we identify heads with the symbol
0 and tails with the symbol 1, then (X, m) is a probability space represent-
ing a fair coin–toss repeated infinitely often. Cylinder sets correspond to
specifying the outcome of finitely many of the independent coin–tosses, and
the measure of the cylinder set is the probability of that event.
(3) [compact groups] Let X be an abelian group that is also a compact
Hausdorff space, and assume that the map (x, y) → x − y is a continuous
map from X × X in the product topology to X. Then X carries a unique
translation invariant Borel probability µ (that is, a measure µ with
µ(A + x) = µ(A)
for any Borel set A and x ∈ X). The measure µ is called Haar measure.

Let (X1, B1, m1) and (X2, B2, m2) be two measure spaces. A transformation T :
X1 → X2 is measurable if T−1
(B2) ⊂ B1, measure–preserving if it is measurable
and m1(T−1
(A)) = m2(A) for any A ∈ B2, and is an invertible measure–preserving
transformation if it is measure–preserving, bijective, and T−1
is also measure–
preserving.
Example 1.5. Let X be a compact abelian group with Haar measure µ and
Borel σ–algebra B, and let T be an endomorphism of X. Then T is a measure–
preserving transformation of (X, B, µ) (equivalently, T preserves the Haar mea-
sure). This may be seen as follows: define a new measure m on X by setting
m(A) = µ(T−1
(A)). Then m(Tx + A) = µ(T−1
(Tx + A)) = µ(x + T−1
(A)) =
µ(T−1
(A)) = m(A), so that m is a probability invariant under translation by any-
thing in the image of T; since T is onto we deduce from the uniqueness of Haar
measure that m = µ.
Three illustrations of Example 1.5. (1) Consider the additive circle T and the
endomorphism T(x) = 3x (mod 1). The pre–image under T of an interval comprises
exactly three copies of the interval, each one third the size of the original. (2)
Consider the coin–tossing space of Example 1.4(2), where we specialize to have Xi =
{0, 1} viewed as a group of two elements. Let mi be the (1
2 , 1
2 ) measure (i.e. Haar
measure on the finite group Xi. Define the shift transformation by T(x)k = xk+1.
Then T is an automorphism of the compact group X, and preserves Haar measure.
(3) Let X be the d–dimensional torus (S1
)k
, and let T be an automorphism of X.
The map T is given by a matrix [T] ∈ GL(d, Z) as usual (for instance, if d = 2
then an automorphism of (S1
)2
is a map of the form (z, w) → (za
wb
, zc
wd
) with

a b
c d

∈ GL(2, Z)).
Example 1.6. Let X be a compact abelian group with Haar measure µ and
Borel σ–algebra B, and let T be a rotation of X, T(x) = x + g for some fixed
g ∈ X. Then T is a measure–preserving transformation of (X, B, µ) by definition
of Haar measure.
Example 1.7. Let X be the coin–tossing space described in Example 1.4. Define
a map T : X → X by the left shift: T(x)k = xk+1, where x = (xk)k∈Z ∈ X.
Then T is an invertible measure–preserving transformation of X with the measure
m given in Example 1.4. The transformation T is called a Bernoulli shift, or a
Bernoulli (p0, . . . , pn−1)–shift. Bernoulli shifts are abstract versions of independent
identically distributed processes.
Isomorphism
The next step is to decide when two measure–preserving group actions are mea-
surably indistinguishable. To motivate the definition, consider the following exam-
ple of an action of N.
Let X1 = [0, 1], and let T1(x) = 2x (mod 1). Let X2 =
∞
i=0{0, 1}, with the
(1
2 , 1
2 )–measure – the one–sided coin tossing space. Let T2(x)k = xk+1, the left shift
map; this is a 2–to–1 measure–preserving transformation on X2. Let θ : X2 → X1
be the map given by
θ(x) = x0
2 + x1
4 + x2
8 + x3
16 + . . . ,
so that θ(T2(x)) = T1(θ(x)). Notice that θ is an invertible measure–preserving
transformation once we delete from X2 all sequences of 0’s and 1’s that have finitely

ISOMORPHISM 5
many 0’s or ﬁnitely many 1’s, and delete from X1 the image under θ of all such
sequences. We are therefore led to the following notion of measurable isomorphism:
two (semi–)group actions are isomorphic if, after deleting some null set in range and
domain, there is an invertible measure–preserving transformation that intertwines
the actions.
Definition 1.8. Let G be a countable group, and let T(i)
on (Xi, Bi, mi) for
i = 1, 2 be two actions of G by invertible measure–preserving transfromations. The
actions T(1)
and T(2)
are isomorphic if there are null sets N1 ∈ B1, N2 ∈ B2,
and an invertible measure–preserving transformation θ : X1N1 → X2N2 with
T
(1)
g θ(x) = θ(T
(2)
g (x)) for all x ∈ X1N1 and every g ∈ G.
The basic internal problem in ergodic theory is then the following.
Problem 1.9. Given two G–actions, how can we decide whether or not they
are isomorphic?
Problem 1.9 is intractable except in special cases (see Chapter 5). Ergodicity
and mixing provide some crude invariants for isomorphism.
Definition 1.10. A G–action T on (X, B, m) is ergodic if any set A ∈ B with
T−1
g (A) = A for all g ∈ G has m(A) = 0 or 1. Equivalently, T is ergodic if
f(Tgx) = f(x) almost everywhere for each g ∈ G, for a function f ∈ L2
(m), implies
that f is almost everywhere constant.
Theorem 1.11. An automorphism T of the n–dimensional torus (S1
)n
is er-
godic (with respect to Haar measure m) if and only if the associated matrix [T] has
no unit root eigenvalues.
Proof. The family of functions ft(k1,...,kn)(z1, . . . , zn) = zk1
1 · · · zkn
n , ki ∈ Z,
form an orthonormal basis for L2
(m). The automorphism T sends one element of
this set into another according to the rule fk(Tz) = ft[T ]k(z).
If [T] has a pth
root of unity eigenvalue (p minimal), then there is an integer
vector w ∈ Zn
{0} with
(t
[T]p
− In)w = 0.
Then the function
f = fw + fw ◦ T + · · · + fw ◦ Tp−1
is T–invariant and non–constant (since it is a sum of distinct elements of the or-
thonormal basis). It follows that T is not ergodic.
Conversely, if T is not ergodic, choose a non–constant function f ∈ L2
(m) which
is T–invariant. Enumerate the orthonormal basis {fk}k∈Zn as χ0, χ1 . . . where χ0
is the constant function 1. Let
∞
i=0 aiχi be the Fourier series of f; by Plancherel,
(1.3)
∞

i=0
|ai|2
∞.
Since f is not constant, as = 0 for some s = 0. The T–invariance of f implies that
the coeﬃcients of χs ◦ T, χs ◦ T2
, . . . are all as. By (1.3), we must therefore have
χs ◦ Tp
= χs ◦ Tq
for some p q ≥ 0. Since T is injective, we have therefore that
χs ◦ Tp−q
= χs, so there exists k such that k =t
[T]p−q
k, so [T] has a unit root
eigenvalue.

Since ergodicity is clearly preserved by measurable isomorphism, this gives exam-
ples of non–isomorphic transformations. The automorphisms of the 2–torus defined
by the matrices

0 1
−1 −1

and

2 1
−1 −1

cannot be isomorphic.
Definition 1.12. A G–action T on (X, B, m) is k–fold mixing if for any sets
B0, . . . , Bk ∈ B,
(1.4) lim
gi−gj →∞
m(T−g0 B0 ∩ T−g1 B1 ∩ · · · ∩ T−gk
Bk) = m(B0) · · · m(Bk),
where gi −gj → ∞ means that for each pair i = j the difference gi −gj leaves finite
sets in G.
In formulating k–fold mixing we may assume that g0 = 0.
The condition with 2 sets is also known as strong mixing or simply mixing; we
should also point out that many people prefer to call the above property (k + 1)–
mixing. If a G action is k–fold mixing for every k, then it is mixing of all orders.
Example 1.13. Let T be an ergodic automorphism of a compact group X.
Then T is mixing of all orders.
We shall not prove this here; it follows at once from a much stronger property
that an ergodic automorphism of a compact group must satisfy: it must behave
measurably like the shift on a coin–tossing space (see Example 1.4) for some choice
of n and (p0, . . . , pn−1).
The behaviour of several commuting compact group automorphisms is quite
different, as shown by the following fundamental example due to Ledrappier [18].
Example 1.14. [mixing ⇒ higher mixing] Let X = {x ∈ {0, 1}Z2
| x(n,m) +
x(n+1,m) + x(n,m+1) = 0 mod 2 ∀n, m ∈ Z}; this is a compact totally disconnected
group, with Haar measure µ say. Define a Z2
action on X by automorphisms as
follows: T(1,0) is the horizontal shift T(1,0)(x)(n,m) = x(n+1,m) and T(0,1) is the
vertical shift T(0,1)(x)(n,m) = x(n,m+1).
We claim that T is mixing: it is sufficient to check that for any finite sets F1
and F2 in Z2
, and any allowed maps f1 : F1 → {0, 1} and f1 : F1 → {0, 1} (allowed
meaning that each fi is a restriction of an element of X, so fi(n, m)+fi(n+1, m)+
fi(n, m + 1) = 0 mod 2 for all (n, m) with (n, m), (n + 1, m), (n, m + 1) ∈ Fi), there
is an M with the property that |(n, m)| ≥ M implies that there is an x ∈ X
with the property that x restricted to F1 is f1 and T(n,m)(x) restricted to F2
is f2. What this means is that the cylinder sets defined by specifying what we
see on F1 and F2 become independent if they are moved sufficiently far apart.
This is clear: from each Fi construct F̃i, a triangle containing Fi of the shape
(a, b) + {(c, d) | c ≥ 0, d ≥ 0, c + d ≤ K}. Then if the shapes are moved far enough
apart to ensure that the triangles do not touch, we can consistently fill in the two
shapes.
To see that T is not 2–fold mixing, it is sufficient to exhibit three sets that fail
to mix. Let B = B0 = B1 = B2 = {x | x(0,0) = 0}. Then µ(B) = 1
2 . Now notice
that for any n, x(0,0) + x(2n,0) + x(0,2n) = 0 mod 2, so
B ∩ T(2n,0)B ∩ T(0,2n)B = B ∩ T(2n,0)B,
and therefore µ(B ∩ T(2n,0)B ∩ T(0,2n)B) = 1
4 for all n, showing that T is not 2–fold
mixing.

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ME NH VT MA RI CT NY NJ PA DE MD VA WV NC
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1812 . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . .
1813 2 2 . . . . . . 2 1 . . 2 . . . . . . . . . . . .
1814 . . 1 . . . . . . 4 5 . . 1 . . . . . . 1 . . . .
1815 4 1 . . . . . . 1 1 1 . . 1 . . . . . . . . . .
1816 4 2 . . . . . . 2 . . 2 . . . . . . . . . . . . . .
1817 8 1 1 . . 1 2 3 5 1 . . . . . . . . . . . .
1818 5 1 . . . . 1 3 5 3 . . . . . . . . . . . . . .
1819 5 1 . . 1 . . 1 5 . . 1 . . 1 . . 2 . . . .
1820 3 1 . . 2 1 1 4 2 . . 1 2 . . . . . . . .
1821 5 5 . . . . . . 1 6 3 1 . . . . . . . . . . . .
1822 9 4 2 . . 1 3 3 4 1 . . 2 . . 1 2 . .
1823 3 3 . . . . 3 8 8 4 . . 1 4 . . 2 . . . .
1824 2 3 3 2 2 5 6 5 4 2 . . . . . . . . . .
1825 6 5 2 1 1 5 7 3 1 1 2 . . 1 . . . .
1826 1 4 1 . . 4 3 3 7 2 1 1 . . . . 1 . .
1827 4 1 1 . . 2 7 5 2 . . 1 1 1 1 1 . .
1828 4 2 3 2 . . 4 8 5 3 1 . . 1 1 1 . .
1829 6 4 3 . . 3 4 3 2 1 . . 3 . . . . 1 . .
1830 3 5 1 . . 1 3 6 5 3 1 1 1 . . 1 . .
1831 4 4 1 1 1 4 6 3 . . . . 1 . . . . . . . .
1832 5 2 3 1 1 2 5 4 2 3 . . . . 2 1 . .
1833 1 3 . . 3 4 4 4 6 3 2 2 . . 1 2 . .
1834 4 4 4 2 1 3 3 5 1 2 1 . . 1 . . . .
1835 3 . . 1 . . 2 5 3 7 3 1 . . . . . . . . . .
1836 3 5 2 1 1 7 3 5 1 1 . . . . . . 1 . .
1837 6 6 2 . . . . 6 4 3 3 2 . . 1 1 . . . .
1838 3 6 3 . . 2 7 6 6 2 1 1 . . 1 . . . .
1839 2 2 3 . . . . 3 6 1 2 . . 1 1 1 1 . .
1840 4 4 . . 1 1 6 5 5 1 . . . . . . . . . . . .
1841 4 5 1 . . 2 8 4 7 3 1 . . 1 . . 1 . .

1842 6 5 3 1 . . 4 4 4 2 3 . . 1 . . . . . .
1843 3 . . 3 1 2 6 . . 3 4 3 2 . . 3 . . . .
1844 2 1 4 1 2 5 3 3 3 3 2 1 2 . . . .
1845 2 2 3 2 2 7 5 3 2 1 2 . . 1 1 . .
1846 1 5 4 2 4 4 4 5 2 2 1 . . . . . . 2
1847 3 . . 1 . . 1 7 3 3 3 2 1 . . 1 . . . .
1848 3 3 2 2 . . 10 3 3 2 4 2 1 1 . . . .
1849 1 3 3 3 . . 8 1 3 3 3 2 1 1 1 2
1850 4 4 2 2 3 2 5 3 3 2 . . . . . . . . . .
1851 . . 1 1 1 2 5 3 3 2 3 . . 1 . . . . . .
1852 1 . . 2 1 2 7 5 7 5 1 2 . . 3 . . . .
1853 2 5 4 . . 1 6 4 2 3 1 3 . . 1 1 1
1854 3 3 4 3 2 6 1 6 2 4 3 2 1 . . 1
1855 2 1 . . 1 1 7 1 . . 3 7 1 . . 1 1 1
1856 1 1 1 1 2 4 3 4 3 . . 2 1 2 1 1
1857 2 3 2 3 2 5 7 4 1 1 2 . . 1 . . 1
1858 2 5 2 1 1 9 1 4 6 1 . . . . . . 1 . .
1859 1 2 2 2 2 4 3 4 3 2 . . . . . . . . . .
1860 2 . . 3 2 1 4 2 2 2 7 2 1 . . . . . .
1861 . . . . 1 . . . . 8 1 . . 6 3 3 . . 3 . . . .
1862 . . . . . . . . . . 7 7 . . 4 4 5 . . . . . . . .
1863 4 8 4 5 2 4 2 7 2 1 1 2 . . 1 2
Total. 159 139 88 51 67 243 196 178 109 81 67 17 38 20 11
SC GA AL MS LA OH KY TN IN IL MO AR MI FL TX
Year IA WI CA MN OR NM UT WA NE KS DT CO NV DC [X] Unk Total
1802 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1803 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 9
1804 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 9
1805 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 9
1806 . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . 9
1807 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 17
1808 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 42
1809 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 10
1810 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1811 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0
1812 . . . . . . . . . . . . . . . . . . . . . . . . . . 2 . . . . 10
1813 . . . . . . . . . . . . . . . . . . . . . . . . . . 12 . . 1 88
1814 . . . . . . . . . . . . . . . . . . . . . . . . . . 6 . . . . 146

1815 . . . . . . . . . . . . . . . . . . . . . . . . . . 12 . . . . 61
1816 . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 . . 34
1817 . . . . . . . . . . . . . . . . . . . . . . . . . . 2 . . . . 55
1818 . . 1 . . . . . . . . . . . . . . . . . . . . . . 5 . . . . 116
1819 . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . . . . 86
1820 . . . . . . . . . . . . . . . . . . . . . . . . . . 4 . . . . 67
1821 . . . . . . . . . . . . . . . . . . . . . . . . . . 2 . . . . 77
1822 . . . . . . . . . . . . . . . . . . . . . . . . . . 2 . . . . 106
1823 . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 1 106
1824 . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . 79
1825 . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . . . . 103
1826 . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . . . . 91
1827 . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . 97
1828 . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . . . . 107
1829 . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . . . . 109
1830 . . . . . . . . . . . . . . . . . . . . . . . . . . 5 . . . . 99
1831 . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . . . . 92
1832 . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3 . . 101
1833 . . . . . . . . . . . . . . . . . . . . . . . . . . 5 . . . . 106
1834 . . . . . . . . . . . . . . . . . . . . . . . . . . 2 . . . . 63
1835 . . . . . . . . . . . . . . . . . . . . . . . . . . 4 . . 1 74
1836 . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . . . . 97
1837 . . 1 . . . . . . . . . . . . . . . . . . . . . . 4 7 . . 117
1838 . . . . . . . . . . . . . . . . . . . . . . . . . . 3 26 . . 111
1839 1 . . . . . . . . . . . . . . . . . . . . . . . . 1 13 . . 76
1840 . . . . . . . . . . . . . . . . . . . . . . . . . . 1 5 . . 84
1841 . . . . . . . . . . . . . . . . . . . . . . . . . . 3 17 . . 114
1842 . . . . . . . . . . . . . . . . . . . . . . . . . . 2 18 . . 109
1843 1 1 . . . . . . . . . . . . . . . . . . . . . . . . 12 . . 60
1844 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 . . 75
1845 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 . . 81
1846 . . . . . . . . . . . . . . . . . . . . . . . . . . 1 10 . . 103
1847 2 . . . . . . . . . . . . . . . . . . . . . . . . 1 9 . . 74
1848 . . 1 . . . . . . . . . . . . . . . . . . . . . . . . 10 . . 81
1849 1 2 . . . . . . . . . . . . . . . . . . . . . . . . 10 . . 89
1850 . . 2 1 1 . . . . . . . . . . . . . . . . . . . . 10 . . 90
1851 . . . . . . . . . . . . . . . . . . . . . . . . . . 1 11 . . 71
1852 1 . . 1 . . . . . . 1 . . . . . . . . . . . . 1 16 . . 90
1853 2 . . . . . . . . 1 . . . . . . . . . . . . . . . . 10 . . 83
1854 . . 3 1 1 1 . . 1 . . . . . . . . . . . . . . 10 . . 103

1855 . . 1 2 . . . . 1 . . 1 . . 1 . . . . . . . . 10 . . 80
1856 1 2 . . . . 1 . . . . . . . . . . . . . . . . 1 10 . . 73
1857 1 . . 1 . . . . 1 . . . . . . . . . . . . . . . . 10 . . 82
1858 1 . . 1 1 . . . . . . . . 1 . . . . . . . . . . 10 . . 75
1859 . . . . . . 1 . . . . . . 1 . . 1 . . . . . . . . 10 . . 60
1860 . . . . . . . . . . . . 1 . . . . . . . . . . . . . . 10 . . 72
1861 1 3 . . 1 . . . . . . . . . . . . 1 . . . . 1 26 . . 108
1862 2 . . 2 1 . . 1 . . . . 1 1 . . 1 . . 1 13 . . 81
1863 . . . . 1 . . 1 1 . . . . . . . . . . . . 1 . . 10 . . 97
Total. 14 17 10 6 3 5 3 2 2 3 1 1 1 113 330 26 4,626
IA WI CA MN OR NM UT WA NE KS DT CO NV DC [X] Un Total
Note.—Owing to the destruction of the records by fire in 1838, the States
in which some of the Cadets resided previous to that event is given; though
it is believed they were appointed “At Large.” The President of the United
States having determined late in August, 1863, to fill all the existing
vacancies from the seceded States there were in the Fourth Class,
numbering 97, on the 19th of October, 48 thus appointed. 10 Cadets
similarly appointed had not, on that date, been examined for admission into
the Military Academy.
THE FOLLOWING STATEMENT EXHIBITS THE ACTUAL NUMBER OF CADETS WHO HAVE GRADUATED
AT THE MILITARY ACADEMY, FROM ITS ORIGIN TO THE PRESENT DATE, WITH THE STATES AND
TERRITORIES WHENCE APPOINTED.
In this table, Utah, Washington, Nebraska
and New Mexico are Territories.
Year = Year of Graduation
[X] At Large.
Un Unknown.
Ag Aggregate.
Year ME NH VT MA RI CT NY NJ PA DE MD VA WV NC
1802 . . . . . . 1 . . . . . . . . . . . . 1 . . . . . .
1803 . . . . . . 1 . . . . 1 . . . . . . . . 1 . . . .
1804 . . . . 1 1 . . . . . . . . . . . . . . . . . . . .
1805 . . . . . . . . . . 1 1 . . . . . . . . . . 1 . .
1806 . . . . 5 1 . . . . 2 1 1 . . . . . . . . 1
1807 . . . . 4 . . . . . . 1 . . . . . . . . . . . . . .
1808 . . 2 6 3 . . 1 1 . . . . 1 . . . . . . . .
1809 . . . . 2 1 . . . . 3 . . . . . . 1 . . . . . .

1811 1 1 3 1 . . 2 5 1 2 . . 1 1 . . . .
1812 1 . . 3 2 . . 3 4 1 1 . . . . 1 . . 1
1813 . . . . . . . . . . . . 1 . . . . . . . . . . . . . .
1814 . . 1 2 5 . . 1 9 . . 3 . . . . 1 1 . .
1815 . . . . 1 5 . . . . 14 . . 1 . . 4 2 . . 2
1817 1 . . 1 . . 1 . . 4 . . 1 . . . . 8 . . . .
1818 . . . . 1 2 . . 1 3 1 2 2 5 3 1 . .
1819 . . 1 3 4 . . 1 6 2 . . 1 3 2 1 1
1820 . . . . . . 1 . . . . 11 1 . . . . 5 3 3 1
1821 . . 1 . . 4 . . 1 6 . . 2 . . 2 1 . . 3
1822 . . 2 3 2 1 5 6 2 6 . . . . 5 1 1
1823 . . 1 3 4 1 3 5 2 3 2 . . . . 3 1
1824 1 3 . . 5 . . . . 6 . . 4 . . 3 2 . . 2
1825 . . 1 1 2 . . 1 9 3 5 . . 3 3 2 2
1826 1 2 2 1 1 . . 2 1 7 1 2 8 3 2
1827 . . . . 3 4 . . . . 6 . . 4 . . 2 4 3 2
1828 3 1 2 4 . . 5 2 1 1 . . 1 1 . . 1
1829 2 1 1 5 . . 3 7 3 4 . . 2 2 2 3
1830 2 . . 1 1 2 . . 6 1 4 1 4 2 2 1
1831 1 1 . . . . 1 . . 8 2 4 1 3 2 2 1
1832 3 3 1 2 1 1 6 1 5 . . 2 4 1 1
1833 . . 2 1 7 . . 2 5 1 5 1 1 5 1 2
1834 . . 1 2 1 . . 1 7 . . 6 . . 1 5 . . 1
1835 4 1 1 4 . . . . 11 2 4 1 2 4 3 2
1836 2 3 1 1 3 1 10 3 6 1 2 5 2 2
1837 1 1 1 6 . . 2 4 3 5 2 4 6 2 . .
1838 . . . . 2 . . . . 1 7 . . 4 . . 1 3 1 2
1839 2 1 1 2 . . 1 6 . . 5 . . 1 1 1 1
1840 3 1 . . 2 . . . . 8 1 3 . . . . 4 3 . .
1841 1 1 1 5 . . 2 6 . . 7 1 4 7 1 3
1842 1 1 1 2 2 . . 7 1 5 . . 2 7 1 3
1843 2 1 2 . . . . 1 7 2 4 . . . . 3 . . . .
1844 . . 1 . . 1 1 1 2 . . 3 1 2 1 1 . .
1845 3 . . 1 2 . . 1 8 . . 1 . . . . 2 1 . .
1846 2 1 2 4 1 1 10 1 8 . . 3 5 2 1
1847 . . . . . . . . . . . . 5 . . 3 . . . . 2 1 2
1848 1 1 . . . . . . . . 5 3 5 . . . . 1 1 3
1849 . . 1 1 2 . . 2 5 . . 3 . . . . 5 . . . .
1850 3 1 1 3 1 . . 7 . . 6 . . 3 2 2 1
1851 1 . . 1 3 . . 1 6 . . 5 . . . . 2 3 . .

1852 . . . . . . . . 1 1 7 2 4 . . 2 . . 2 . .
1853 1 1 . . 2 . . 1 5 1 3 . . 1 5 . . 2
1854 2 1 2 1 1 . . 4 1 5 . . . . 4 2 3
1855 . . 1 1 4 . . . . 7 . . 8 1 . . . . 2 . .
1856 1 . . . . . . . . . . 8 1 3 . . . . 2 1 . .
1857 2 2 . . 2 . . 2 3 1 1 . . . . 3 . . 2
1858 1 . . . . 4 . . 1 1 1 1 . . 2 . . 2 1
1859 . . . . 1 . . . . . . 4 . . 4 . . 1 1 . . . .
1860 1 . . 1 3 1 . . 7 1 3 1 1 . . 2 2
1861 3 3 1 3 1 2 15 2 10 . . 1 1 . . . .
1862 1 . . . . 3 . . 1 3 . . 2 . . . . . . . . . .
1863 . . . . 1 2 . . 1 4 1 5 . . 1 . . . . . .
Total 54 47 75 131 20 55 329 51 197 18 79 142 63 59
Year SC GA AL MS LA OH IN IL KY TN AR MO MI WI
1802 . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1803 . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1804 . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1805 . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1806 . . . . . . . . . . . . . . . . . . . . 4 . . . . . .
1807 . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1808 . . . . . . . . . . . . . . . . . . . . 1 . . . . . .
1809 . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1811 . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1812 . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1813 . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1814 . . . . . . . . . . 1 . . 1 . . . . . . . . . . 5
1815 3 . . . . . . 4 . . . . . . . . . . . . . . . . 4
1817 . . . . . . . . . . 1 . . 1 . . . . . . . . . . 1
1818 . . . . . . . . . . . . . . 1 . . . . . . . . . . 1
1819 . . . . . . 1 . . . . 1 1 . . . . . . . . . . 1
1820 . . . . . . . . 1 . . . . . . 2 . . . . . . . . 2
1821 1 . . . . . . 1 1 . . . . 1 . . . . . . . . . .
1822 . . 1 . . . . 2 . . . . 1 1 . . . . . . . . 1
1823 . . . . 1 . . . . . . . . 2 1 . . . . 1 . . 2
1824 . . . . 1 1 . . . . . . 2 1 . . . . . . . . . .
1825 2 . . . . . . . . . . . . 2 1 . . . . . . . . . .
1826 1 . . . . 1 . . 1 . . 1 1 . . 1 . . . . 1
1827 . . 1 . . . . 3 . . . . 4 . . . . . . 1 . . 1
1828 . . 1 1 1 2 2 1 . . 2 . . 1 . . . . . .

1829 3 . . . . . . 4 1 . . 2 . . . . . . . . . . 1
1830 1 . . . . 1 1 1 1 4 2 . . 1 . . . . 3
1831 1 . . . . . . 3 . . . . 2 1 . . . . . . . . . .
1832 . . 1 1 . . 3 . . 1 3 3 . . . . 1 . . 1
1833 1 2 . . . . . . 1 . . 1 2 . . 1 . . . . 2
1834 1 . . . . . . 1 1 . . 4 1 . . 1 . . . . 1
1835 3 1 . . . . 4 . . . . 4 1 . . . . . . . . 3
1836 . . . . . . . . . . 1 . . 2 1 . . . . . . . . 1
1837 2 1 . . . . . . 2 1 1 1 . . 1 1 . . 3
1838 2 2 2 2 3 . . 1 3 2 . . 1 1 . . 1
1839 . . . . . . . . 3 1 . . 3 1 . . . . . . . . 1
1840 . . . . . . 1 6 . . . . . . 3 . . . . . . . . 2
1841 . . . . . . . . 2 3 2 1 1 1 . . 1 . . . .
1842 1 2 1 1 4 1 1 3 1 . . . . . . . . 2
1843 . . . . . . . . 3 2 . . 2 1 . . 1 1 . . . .
1844 . . . . . . . . 2 . . . . 4 1 1 . . . . . . 2
1845 2 . . . . 1 4 2 . . 3 1 . . . . . . . . . .
1846 4 . . . . . . . . . . 1 1 3 . . . . . . . . 1
1847 . . . . . . . . 8 4 2 . . . . . . 1 1 . . . .
1848 . . 2 . . . . 1 1 2 . . 2 1 . . 1 1 . .
1849 2 . . 2 . . 4 2 . . 2 2 . . 1 . . . . . .
1850 2 . . . . 2 . . . . 1 2 2 . . . . . . . . . .
1851 . . 1 . . 1 2 2 1 2 3 . . . . . . . . 1
1852 . . 2 1 . . 6 2 1 2 1 . . 1 2 . . . .
1853 3 1 . . . . 8 3 2 1 2 . . 2 . . . . . .
1854 2 2 2 1 1 1 . . . . 1 . . . . . . 3 . .
1855 1 . . . . 1 2 1 2 . . . . . . . . . . . . . .
1856 . . 1 1 . . 7 3 . . 4 2 . . 1 2 . . 1
1857 4 2 . . . . 2 1 1 3 1 . . 2 . . . . . .
1858 2 1 1 . . 2 1 . . 1 1 . . . . . . . . . .
1859 . . 1 . . . . 2 . . 1 . . 1 . . . . 1 1 . .
1860 . . 1 . . . . 3 1 6 . . . . 1 . . . . . . . .
1861 . . . . . . . . 5 1 1 4 1 1 2 3 2 1
1862 . . . . . . . . 6 1 . . 1 1 . . 1 . . . . . .
1863 . . . . . . . . 3 2 . . 2 . . . . . . . . . . 2
Total. 44 26 14 15 118 48 56 5 24 17 7 50 6 139
Year DC FL [X] IA TX UT MN WA OR NM CA NE Ag
1802 . . . . . . . . . . . . . . . . . . . . . . . . 2
1803 . . . . . . . . . . . . . . . . . . . . . . . . 3

1804 . . . . . . . . . . . . . . . . . . . . . . . . 2
1805 . . . . . . . . . . . . . . . . . . . . . . . . 3
1806 . . . . . . . . . . . . . . . . . . . . . . . . 15
1807 . . . . . . . . . . . . . . . . . . . . . . . . 5
1808 . . . . . . . . . . . . . . . . . . . . . . . . 15
1809 . . . . . . . . . . . . . . . . . . . . . . . . 7
1811 . . . . . . . . . . . . . . . . . . . . . . . . 19
1812 . . . . . . . . . . . . . . . . . . . . . . . . 18
1813 . . . . . . . . . . . . . . . . . . . . . . . . 1
1814 . . . . . . . . . . . . . . . . . . . . . . . . 30
1815 . . . . . . . . . . . . . . . . . . . . . . . . 40
1817 . . . . . . . . . . . . . . . . . . . . . . . . 19
1818 . . . . . . . . . . . . . . . . . . . . . . . . 23
1819 . . . . . . . . . . . . . . . . . . . . . . . . 29
1820 . . . . . . . . . . . . . . . . . . . . . . . . 30
1821 . . . . . . . . . . . . . . . . . . . . . . . . 24
1822 . . . . . . . . . . . . . . . . . . . . . . . . 40
1823 . . . . . . . . . . . . . . . . . . . . . . . . 35
1824 . . . . . . . . . . . . . . . . . . . . . . . . 31
1825 . . . . . . . . . . . . . . . . . . . . . . . . 37
1826 1 . . . . . . . . . . . . . . . . . . . . . . 41
1827 . . . . . . . . . . . . . . . . . . . . . . . . 38
1828 . . . . . . . . . . . . . . . . . . . . . . . . 33
1829 . . . . . . . . . . . . . . . . . . . . . . . . 46
1830 . . . . . . . . . . . . . . . . . . . . . . . . 42
1831 . . . . . . . . . . . . . . . . . . . . . . . . 33
1832 . . . . . . . . . . . . . . . . . . . . . . . . 45
1833 . . . . . . . . . . . . . . . . . . . . . . . . 43
1834 1 . . . . . . . . . . . . . . . . . . . . . . 36
1835 . . 1 . . . . . . . . . . . . . . . . . . . . 56
1836 . . 2 . . . . . . . . . . . . . . . . . . . . 49
1837 . . . . . . . . . . . . . . . . . . . . . . . . 50
1838 . . 4 . . . . . . . . . . . . . . . . . . . . 45
1839 . . . . . . . . . . . . . . . . . . . . . . . . 31
1840 1 4 . . . . . . . . . . . . . . . . . . . . 42
1841 . . 2 . . . . . . . . . . . . . . . . . . . . 52
1842 . . 6 . . . . . . . . . . . . . . . . . . . . 56
1843 . . 6 1 . . . . . . . . . . . . . . . . . . 39
1844 . . 1 . . . . . . . . . . . . . . . . . . . . 25
1845 1 8 . . . . . . . . . . . . . . . . . . . . 41

1846 . . 8 . . . . . . . . . . . . . . . . . . . . 59
1847 . . 8 1 . . . . . . . . . . . . . . . . . . 38
1848 . . 7 . . . . . . . . . . . . . . . . . . . . 38
1849 1 8 . . . . . . . . . . . . . . . . . . . . 43
1850 . . 5 . . . . . . . . . . . . . . . . . . . . 44
1851 . . 6 1 . . . . . . . . . . . . . . . . . . 42
1852 . . 6 . . . . . . . . . . . . . . . . . . . . 43
1853 1 5 1 1 . . . . . . . . . . . . . . . . 52
1854 . . 6 . . 1 . . . . . . . . . . . . . . . . 46
1855 . . 3 . . . . . . . . . . . . . . . . . . . . 34
1856 . . 10 . . . . . . . . . . . . . . . . . . . . 48
1857 . . 3 1 1 . . . . . . . . . . . . . . . . 39
1858 . . 3 . . . . 1 . . . . . . . . . . . . . . 27
1859 . . 3 . . . . . . 1 . . . . . . . . . . . . 22
1860 . . 5 . . . . . . . . 1 . . . . . . . . . . 41
1861 . . 14 1 . . . . . . . . 1 1 . . . . . . 80
1862 . . 5 . . . . . . 1 . . . . . . 1 1 . . 28
1863 . . . . . . . . . . . . 1 . . . . . . . . . . 25
Total. 30 83 6 3 1 2 2 1 1 1 1 . . 2020
TABLE D.
EXHIBITING THE WHOLE NUMBER OF CADETS ADMITTED TO THE MILITARY ACADEMY FROM EACH
STATE AND TERRITORY, AND THE WHOLE NUMBER GRADUATED.
N Number
E60 No. entitl’d ’60
% Per cent. [printed as shown]
STATE AND TERRITORY.
Admitted. Graduated.
Fail’d to
Graduate.
Remain.
E60
From Total From Total % N % No. %
Alabama 1817 88 1822 26 .295 61 .693 1 .012 7
Arkansas 1827 17 1841 5 .294 . . .705 . . . . 2
California 1850 10 1862 1 .100 6 .600 3 .300 3
Connecticut 1802 102 1805 55 .539 43 .422 4 .039 4
Delaware 1806 41 1808 18 .439 22 .539 1 .022 1
Florida 1822 20 1826 6 .300 14 .700 . . . . 1
Georgia 1813 139 1815 44 .329 95 .670 . . . . 3
Illinois 1815 81 1819 30 .379 42 .519 9 .111 13
Indiana 1812 109 1814 48 .440 52 .477 9 .083 11

Iowa 1839 14 1843 6 .428 6 .428 2 .144 6
Kansas 1855 3 . . . . . . 2 .667 1 .333 1
Kentucky 1813 196 1819 83 .423 105 .531 8 .046 9
Louisiana 1817 67 1819 15 .223 51 .761 1 .016 4
Maine 1808 102 1811 54 .529 43 .422 5 .049 5
Maryland 1802 179 1802 79 .441 95 .537 5 .022 5
Massachusetts 1802 232 1802 131 .324 91 .392 10 .043 10
Michigan 1814 38 1823 17 .447 18 .474 3 .079 6
Minnesota 1850 6 1859 2 .333 2 .333 2 .333 2
Mississippi 1819 51 1823 14 .274 37 .725 . . . . 5
Missouri 1802 67 1806 24 .358 37 .552 6 .090 9
New Hampshire 1817 78 1808 47 .602 28 .359 3 .039 3
New Jersey 1803 101 1806 51 .504 45 .446 5 .050 5
New York 1802 650 1803 329 .506 289 .444 32 .050 31
North Carolina 1803 190 1805 63 .331 127 .668 . . . . 8
Ohio 1813 243 1815 118 .485 105 .432 20 .083 19
Oregon 1854 3 1861 1 .333 1 .333 1 .333 1
Pennsylvania 1804 424 1806 197 .464 203 .479 24 .057 24
Rhode Island 1814 42 1817 20 .476 20 .476 2 .048 2
South Carolina 1809 159 1806 59 .371 100 .628 . . . . 6
Tennessee 1815 178 1820 56 .314 122 .686 . . . . 10
Texas 1840 11 1853 3 .272 8 .727 . . . . 2
Vermont 1803 104 1804 75 .721 26 .250 3 .029 3
Virginia 1803 379 1803 142 .374 237 .615 4 .011 13
West Virginia 1863 1 . . . . . . . . . . 1 1.000 1
Wisconsin 1837 17 1848 7 .411 7 .412 3 .177 6
Dist. of Columbia 1806 113 1811 50 .443 62 .549 1 .008 1
New Mexico 1852 5 1861 1 .200 3 .600 1 .200 1
Utah 1853 3 1858 1 .333 1 .333 1 .333 1
Washington 1855 2 1861 2 .100 . . . . 1 .500 1
Nebraska 1858 2 1862 1 .500 . . . . 1 1.000 1
Dakota 1861 1 . . . . . . . . . . 1 1.000 1
Colorado 1863 1 . . . . . . . . . . 1 1.000 1
Nevada 1863 1 . . . . . . . . . . 1 1.000 1
At large 1837 330 . . 139 .421 156 .473 35 .106 40
Unknown 1803 26 . . . . . . . . . . . . . . . .
Total 4,626 2,020 210 294
The Totals in the column of Cadets admitted, graduated, and failed to graduate,
for each State and Territory, and for the country at large, are obtained from Tables
prepared by Capt. Boynton, in his “History of the United States Military Academy.”

The per centage of graduates, failures, c., is calculated from the totals thus
obtained. The minute accuracy of the results is slightly effected by the difficulty of
assigning the twenty-six Cadets admitted, whose place of residence was unknown,
to their respective States. The column of Cadets to which each State and Territory is
entitled in the apportionment of members of Congress under the Census of 1860, is
official so far as States not involved in rebellion are concerned; the latter is given
according to the Census of 1850.
OPINIONS OF COL. THAYER AND OTHERS.
On the recommendations of the Board of Visitors as to the conditions of
admission to the United States Military Academy at West Point.
Extract from a letter of Col. Sylvanus Thayer, Superintendent of the United
States Military Academy, from 1816 to 1831.
“The Extracts from the Report of the Visitors at West Point, for 1863, I have read
with the highest satisfaction, not to say admiration. The subject of the admission of
Cadets, their number, age, attainments, and mode of appointment, is discussed in
the most complete and able manner, ne laissant rien a desirer, as far as I can see.
I am naturally the more pleased from finding my own views so perfectly reflected in
many important particulars. The only difference I notice is the small addition to my
standard of attainment for admission. I not only agree to that, but would raise the
standard as high as Congress would be willing to adopt. The higher the standard,
the more perfect will be the test of capacity. The subject, as you may well suppose,
is not a new one with me. More than forty years ago I made my first effort to have
the mode of appointment by nomination, done away with, and admission by open
competition adopted. My last effort before the late one, was made in 1858, while I
was in command of the Corps of Engineers, during the absence of Gen. Totten. At
the same time, I recommended a higher standard of attainment, a Board of
Improvement, and some of the other changes comprised in my “Propositions,” but
with little expectation, however, that my solitary voice would be heeded. After long
despairing, I am now encouraged and cheered. Admission by competitive
examination, open to all, may not be attained as soon as we wish, but come it must
at no distant day. Let every future Board of Visitors recall the attention of the
Government to your excellent Report; no new arguments are needed, and let all the
publications devoted to the cause of education, agitate the question unceasingly.”
We have been favored with the perusal of the “Propositions,” referred to
in Col. Thayer’s letter, and submitted by him to the Secretary of War, in
1863, with “Suggestions for the Improvement of the United States Military
Academy.” So far as the Visitors go, their views, and those of Col. Thayer,
are almost identical, but Col. Thayer’s communication to the Secretary
includes many other suggestions relating to the instruction, discipline, and
administration of the institution, which we hope will be adopted by the
Secretary, and embodied in the Regulations.

In addition to the modifications suggested by Col. Thayer, we should like
to see the theoretical course at West Point reduced to two years; and
Special Courses, or Schools of Application and Practice established for the
Engineer, Artillery, Cavalry, and Infantry service, open only to those who
should show natural aptitude, and the proper amount of acquired
knowledge, whether graduates of the scientific course of West Point, or any
State scientific or classical school, in a competitive examination. In each of
these courses or schools, there should be a graduation, and promotion, in
the particular service, according to merit. Our whole system of military
instruction should terminate in a staff school, open only to those who, in
addition to the knowledge required for graduation in at least two of the
above special courses, should have had at least three years actual
experience in service. While members of the Staff School, these candidates
for the Staff Corps, should, if called for by the State authorities, assist
without compensation, in conducting Military Encampments of the Officers
of the State Militia, like those held every year in Switzerland, and
corresponding to what is known in this country to Teacher’s Institutes. The
graduates of the Staff School, should constitute the Staff Corps, from which
all vacancies in the higher offices of the Regular Army should be filled, and
all appointments to new regiments be made.
Extract from a letter of Gen. H. K. Oliver.
I have read with the utmost care, the Extract from the Report of the Board of
Examiners of the Military Academy at West Point, for the year 1863, and most
heartily concur in the views therein set forth, and especially in that portion of it,
which recommends a competitive examination of candidates for admission. In all its
relations it is right. In fact it stands out prominently as the only proper mode of
admittance.
My intimate acquaintance with the Academy, having attended the examination in
1846, by invitation, and again in 1847, as Secretary of the Board of Visitors for that
year, enables me to speak with reasonable authority. These visits afforded me
opportunities, which I improved to the utmost, and most minutely, to become
intimately well informed of the effect of the prevailing method of selection, and of its
practical results upon character and scholarship after admission, as well as to know,
with what degree of fidelity, the institution was answering the intent of its founding,
and the just expectation of the country; and I was then satisfied, and subsequent
observation has confirmed me in my opinion, that whatever of deficiency prevailed,
was traceable to the method of admission. Faithful teachers and faithful teaching will
achieve great results, but they can not make good, incompetent natural
endowments, nor infuse vigor and life into sluggish natures. I sincerely hope that
the Government will feel the force of your views, and comply with your most
commendable recommendations.

Resolution adopted by the American Institute of Instruction at the Annual
Meeting in August; 1863.
Whereas, the security and honor of this whole country require in the military and
naval service the right sort of men with the right sort of knowledge and training;
and whereas, the military and naval schools established to impart this knowledge
and training will fail in their objects, unless young men are selected as students of
the right age, with suitable preparatory knowledge, with vigor of body, and aptitude
of mind, for the special studies of such schools; and whereas, the mode of
determining the qualifications and selecting the students, may be made to test the
thoroughness of the elementary education given in the several States, therefor
Resolved, That the Directors of the American Institute of Instruction are
authorized and instructed to memorialize the Congress of the United States, to
revise the terms and mode of admission to the National Military and Naval Schools,
so as to invite young men of the right spirit, and with vigor and aptitude of mind for
mathematical and military studies, who aspire to serve their country in the military
and naval service, to compete in open trial before intelligent and impartial examiners
in each State, without fear or favor, without reference to the wealth, or poverty, or
occupation, or political opinions of their parents or guardians, for such admission,
and that in all cases the order of admission shall be according to the personal merits
and fitness of the candidate.”
Extract from letter of Prof. Monroe, St. John’s College, Fordham, N.Y.
I rejoice that some one has taken hold of this subject at last. It needs only to be
understood to be adopted; for I can not see from what quarter any opposition to it
can arise. You rightly observe that “all the educational institutions of the several
States” are interested in this mode of appointment. Great Britain, France, and many
of the Continental States admit to their military schools the most competent young
men who present themselves, and the method is found to be as economical as it is
equitable. Long years of winnowing is saved to the Government; for the subjects
who present themselves are, of course, the most capable. For several years I was a
witness of the beneficial effects produced on youth in France by the stimulation of
their energies in order to undergo an examination for admission into the military or
naval schools. Our present mode of appointment appears to be an anomaly; for
while monarchies find it expedient to adopt a less exclusive mode of sustaining their
military organizations, we still cling to one founded on patronage and prerogative.
Many of our young men in different colleges and educational institutions have a
taste and vocation to the military profession, and have an equal right to compete for
a place in the only fields where such a taste can be gratified—viz., in the army and
navy. These careers should then be open to them. There is danger and want of
policy in suppressing the legitimate aspirations of young men in a nation which is,
say what we can, passionately fond of military glory.
Extract from the Report of the Board of Visitors of the U.S. Military
Academy at West Point for 1864.
The main features of the Report of the Visitors for 1863 we most cordially
approve, especially its recommendations of competitive examination, and raising the

age and qualifications of candidates for admission. The only student who obtained
his appointment through competitive examination (introduced into his district by the
member of Congress upon whose recommendation he was appointed from the
common schools 15 of New York) graduated at the head of his class this year.
The beneficial effect on schools, as regards both pupils and teachers, of
throwing open appointments in civil, as well as in military and naval service,
to competition, and giving them to the most meritorious candidates, on
examination, is thus commented on in the Report of the Queen’s
Commissioners on the Endowed Schools of Ireland:
This measure has received the unanimous approval of our body, who regard it as
an effectual method of promoting intermediate education. The experience already
obtained respecting the operation of public and competitive examinations, so far as
they have hitherto been tried, leaves no doubt on our minds that the extension of
this system would, under judicious management, produce very beneficial effects,
both in raising the standard of instruction, and in stimulating the efforts of masters
and of pupils. The educational tests adapted for examinations for the public service
would be, in our opinion, of all others the most general in their character, and
therefore, those best calculated to direct the efforts of teachers to that course of
mental discipline and moral training, the attainment of which constitutes, in our
opinion, the chief object of a liberal education. The experience of the civil service
commission has shown the shortcomings of all classes in the most general and most
elementary branches of a literary and scientific education.
These views are strongly corroborated by the testimony, appended to the Report,
of prominent teachers and educators consulted on the subject:
Prof. Bullen, in the Queen’s College, Cork, remarks:—“No movement ever made
will so materially advance education in this country as the throwing open public
situations to meritorious candidates. It has given already a great impulse to schools
and will give greater. The consequence of throwing the civil service open to the
public is already beginning to tell—although only in operation a few months, it has
told in a most satisfactory manner in this city; and, from what I can see, it will have
the happiest results on education generally.”
Prof. King, Head Master of a Grammar School at Ennis, writes:—“These
examinations have already caused improvements in my own school by inducing me
to give instruction in branches which I had never taught before.”
The Dean of Elphin, the Archdeacon of Waterford and the Bishop of Doun,
advocate the measure on the ground of its tendency to produce competition
between schools, and to stimulate private enterprise. The Bishop of Cashel “thought
that this competition would be more valuable than the endowment of schools giving
education gratuitously.”
In confirmation of the above views, and as an illustration of the benefits likely to
accrue both to the cause of education and to the public service from the extension
of the system of competitive examinations, we may add that, at the late competitive
examination for certificates of merit held by the Royal Dublin Society Mr. Samuel
Chapman, who was educated solely by the Incorporated Society, as a foundation

boy, obtained the first place and a prize of £5. In consequence of this success the
Bank of Ireland immediately appointed him to a clerkship. Mr. Chapman was
originally elected to the Pococke Institution, from a parish school, by a competitive
examination; and on his leaving the Santry school Prof. Galbraith appointed him his
assistant in Trinity College, in consequence of the skill in drawing which he
exhibited, and his knowledge of mathematics, as proved by his final examination.
III. COMPETITIVE EXAMINATION AT WEST
POINT.
DEBATE IN THE UNITED STATES SENATE, MAY 18TH, 1864.
The Bill making appropriation for the Military Academy being under
consideration, Senator Anthony, of R. Island, remarked on the following
amendment:
And be it further enacted, That hereafter, in all appointments of cadets to the
Military Academy at West Point, the selections for such appointments in the several
districts shall be made from the candidates according to their respective merits and
qualifications, to be determined under such rules and regulations as the Secretary of
War shall from time to time prescribe.
This, Mr. President, is substantially the proposition which I offered at the
last session; and although I was not so fortunate as to obtain for it the
assent of the Senate, mainly from an apprehension of practical difficulties in
carrying out what is admitted to be a desirable reform if it could be
effected, yet the general expression of Senators was so much in favor of the
principle, and I have been so much strengthened in my views on the
subject by subsequent reflection and examination, that I am emboldened to
renew it.
I differ entirely from those who are fond of disparaging the Military
Academy. It has been of incalculable service to the country; it is the origin
and the constant supply of that military science without which mere
courage would be constantly foiled, and battles would be but Indian fights
on a large scale. Not to speak of the Mexican war, throughout the whole of
which West Point shone with conspicuous luster, it is safe to leave the
vindication of the Academy to the gallant and able men who have illustrated

the annals of the war that is now raging. Nor have its indirect advantages
been less marked than its direct. It has kept alive a military spirit, and kept
up a good standard of military instruction in the volunteer militia. It
furnished, from its graduates who have retired from the Army, scores of
men who rushed to the head of our new levies, who organized and
instructed them, inspired them with confidence, and led them over many a
bloody field to many a glorious victory. Large numbers of our best volunteer
officers owe their instruction indirectly to West Point.
To say that no course of military instruction can make a pupil a military
genius, can create in him that rare quality that takes in at a glance, almost
by intuition, the relative strength of great masses opposed to each other,
and that power of combination which can bring an inferior force always in
greater number upon the severed portions of a superior force, is very true.
To discard military education on that account would be like shutting up the
schools and colleges because they can not turn out Miltons and Burkes and
Websters. Education does not create, it develops and enlarges and inspires
and elevates. It will make the perfect flower, the majestic tree, from the
little seed; but it must have the seed. And what I desire is that the
Academy at West Point should have the best seed; that its great resources,
its careful culture, its scientific appliances, should not be wasted on second-
rate material. The Academy has never had a fair chance; the country has
not had a fair chance; the boys have not had a fair chance. This is what I
want them all to have, and especially the country. I desire that the Academy
shall begin, as it goes on, upon the competitive principle. As all its standing,
all its honors, are won by competition, so should the original right to
compete for them be won. I would give all the youth of the country a fair
chance; and, more desirable than that, I would give the country a fair
chance for all its youth. I would have the Academy filled up by those young
men who, upon examination by competent judges, should be found most
likely to render the best service to the country; to make the best officers;
whose qualifications, physical, intellectual, and moral, whose tastes and
habits, should seem to best fit them for military life.
But, it is objected, no such examination would be infallible. Of course it
would not be. No human judgment is infallible. Our deliberations are not
infallible; but therefore shall we not deliberate? The decisions of the
Supreme Court are not infallible; therefore shall we abolish the court?
A Senator. The Senator from New Hampshire would say yes.

Mr. Anthony. I know the Senator from New Hampshire [Mr. Hale] would
say “Yes.” He would abolish both the Academy and the Court, and I can well
suppose that the policy which would abolish the one might abolish the
other. But although such an examination would not be infallible, it would, if
properly organized and properly conducted, accomplish much toward the
reform which all admit to be desirable, if it be practicable. It can not be
doubted that the young men who would come out best from such a trial
would, as a body, be superior to those who are selected upon mere
personal preferences, and these preferences generally not for themselves,
but for their parents; not for their own qualifications, but as a recognition of
the political services of their fathers.
But, again, it was objected when I made this proposition a year ago that
it was not equal; because, in giving to any given place of examination,
some young men would have further to travel than others! If this objection
had not been gravely made by men for whom I have the highest respect I
should be tempted to call it puerile. A boy asks the privilege of going a
hundred miles to the place of examination, and is told that he can not have
it because another boy will have to go two hundred miles, and another but
fifty, and it is not equal! The fact that either of them would go five hundred
miles on foot for the opportunity of competition is not taken into the
account. On the same principle our elections are not equal, for one man
must travel further than another to reach the polls. For a boy who can not
obtain the means to travel from his home to the place of examination—and
there will be very few such of those who would be likely to pass high in the
examination—the plan proposed would be no worse, certainly, than the
present system; for those who have the means the difference in travel is
too small an item to enter into the account.
No plan can be made perfectly equal. Shall we therefore refuse to make a
large advance toward equality? Certainly the system which invites a
competition from all who are in a condition to avail themselves of it is more
equal than that which excludes all competition. But although equality in the
advantages of the Academy is very desirable, and although the amendment
proposed would be a long step in that direction, it is not for that reason that
I urge it. It is not to give all the young men an equal chance for the
Academy, it is to give the Academy a chance for the best young men; and
although even under this system the best young men will often fail of
success, it can not be doubted that many more of them will enter the
service than under the present system.

Nor will the advantages of this competition be confined to those who
reach the prize for which so many will struggle. An incalculable although an
incidental benefit will accrue to the thousands whose youthful hearts will be
stirred by an honorable ambition, and who will cultivate their minds by
liberal studies and develop their physical power by manly exercises in the
struggle upon which the humblest may enter, and in which the proudest can
obtain only what he fairly earns. Under the present system the Academy
wastes full half its strength upon boys who never ought to be admitted, and
whose natural incapacity derives but little benefit from the partial training
that they receive there. Under the system proposed, the Academy would
exert its influence upon thousands of the brightest and most aspiring boys
all over the country, stimulating them to the pursuit of such studies and to
the formation of such habits as, if they fail to carry them to West Point, will
help to conduct them to usefulness and honor in whatever path of life they
may choose.
But, again, we are met with the objection that this proposition is
impracticable, that it looks very well on paper, but that it can not be carried
into effect. Let us see. It is quite safe to conclude that what has been done
can be done, and that what wise and judicious people do, and persist in
doing after experiment, is proper to be done. What is the most warlike
nation of Europe? What nation of Europe has carried military science to the
highest degree? What nation of Europe has the greatest genius for
organization? You will say the French. Let us see what is their system .
I read from the report of the Commission appointed by Congress in 1860 to
visit the Military Academy at West Point, and report upon the system of
instruction; a commission of which you, Mr. President, [Mr. Foot,] were a
member:
Among the European systems of military education that of France is preëminent.
The stimulating principle of competition extends throughout the whole system; it
exists in the appointment of the student, in his progress through the preliminary
schools, in his transfer to the higher schools, in his promotion to the Army, and in
his advancement in his subsequent career. The distinguishing features of the French
system are thus described by the British commissioners.
“1. The proportion, founded apparently upon principle, which officers educated in
military schools are made to bear to those promoted for service from the ranks.
2. The mature age at which military education begins. 3. The system of thorough
competition on which it is founded. 4. The extensive State assistance afforded to
successful candidates for entrance into military schools whenever their
circumstances require it. * * * * * *

Admission to the military schools of France can only be gained through a public
competitive examination by those who have received the degree of bachelor of
science from the lycées or public schools, and from the orphan school of La Flèche.
A powerful influence has thus been exercised upon the character of education in
France. The importance of certain studies has been gradually reduced, while those
of a scientific character, entering more directly into the pursuits of life, have been
constantly elevated.
The two great elementary military schools are the School of St. Cyr and the
Polytechnic School. These, as well as the other military schools, are under the
charge of the Minister of War, with whom the authorities of the schools are in direct
communication. Commissions in the infantry, cavalry, and marines can only be
obtained by service in the ranks of the army, or by passing successfully through the
School of St. Cyr, admission to which is gained by the competitive examination
already referred to.”
Again, the Commission say, speaking of the School of St. Cyr:
The admission is by competitive examination, open to all youths, French by birth
or by naturalization, who, on the 1st of January preceding their candidature, were
not less than sixteen and not more than twenty years old. To this examination are
also admitted soldiers in the ranks between twenty and twenty-five years, who, at
the date of its commencement, have been actually in service in their regiments for
two years.
A board of examiners passes through France once every year, and examines all
who present themselves having the prescribed qualifications.
A list of such candidates as are found eligible for admission to St. Cyr is submitted
to the Minister of War. The number of vacancies has already been determined, and
the candidates admitted are taken in the order of merit.
Twenty-seven, or sometimes a greater number, are annually, at the close of their
second year of study, placed in competition with twenty-five candidates from the
second lieutenants belonging to the army, if so many are forthcoming, for admission
to the Staff School of Paris. This advantage is one object which serves as a stimulus
to exertion, the permission being given according to rank in the classification by
order of merit.
In regard to the Polytechnic School, the Commission say:
Admission to the School is, and has been since its first commencement in 1794,
obtained by competition in a general examination, held yearly, and open to all. Every
French youth between the ages of sixteen and twenty (or if in the army up to the
age of twenty-five) may offer himself as a candidate.
This is the system which was organized by Carnot and adopted and
extended by Napoleon. Under this system the French army has attained its
perfection of organization, its high discipline, its science, its dash, and its
efficiency.

But not the French alone have adopted the competitive system. In
England, all whose traditions are aristocratical, where promotion in the
army has so long been made by patronage and by purchase, the sturdy
common sense of the nation has pushed away the obstructions that have
blocked up the avenues to the army, and have opened them to merit, come
from what quarter it may. In the commencement of the Crimean war, the
English people were shocked at the evident inferiority of their army to the
French. Their officers did not know how to take care of their men, or how to
fight them. And although in the end British pluck and British persistence
vindicated themselves as they always have and always will, it was not till
thousands of lives had been sacrificed that might have been saved under a
better system. No French officer would have permitted that memorable
charge at Balaklava, which was as remarkable for the stupidity that ordered
it as for the valor that executed it, and which has been sung in verses
nearly as bad as the generalship which they celebrate. After the war, the
English Government, with the practical good sense which usually
distinguishes it, came, without difficulty, to the conclusion that merit was
better than family in officering the army, and that it was more desirable to
put its epaulets upon the shoulder of those who could take care of the men
and lead them properly than upon those who could trace their descent to
the Conqueror, or whose uncles could return members of Parliament.
Accordingly, the Royal Military Academy, which had been filled, as ours is,
by patronage, was thrown open to public competition. On this subject I
quote from the very interesting and valuable report of the Visitors of the
Military Academy in 1863:
The same principle was applied to appointments and promotion in the new
regiments called for by the exigencies of the great war in which England found
herself engaged.
Subjects, time, and place of examination were officially made known throughout
the kingdom, and commissions to conduct the examinations were appointed,
composed of men of good common sense, military officers, and eminent practical
teachers and educators. The results, as stated in a debate in Parliament five years
later, on extending this principle to all public schools, and all appointments and
promotions in every department of the public service, were as follows: in the
competitive examinations for admission to the Royal Military Academy candidates
from all classes of society appeared—sons of merchants, attorneys, clergymen,
mechanics, and noblemen, and among the successful competitors every class was
represented. Among the number was the son of a mechanic in the arsenal at
Woolwich, and the son of an earl who was at that time a cabinet minister—the
graduates of national schools, and the students of Eton, and other great public
schools.

On this point Mr. Edward Chadwick, in a report before the National Social Science
Association, at Cambridge in 1862, says:
“Out of an average three hundred patronage-appointed cadets at the Royal
Military Academy at Woolwich, for officers of engineers and the artillery, during the
five years preceding the adoption of the principle of open competition for admission
to the Academy, there were fifty who were, after long and indulgent trial and with a
due regard to influential parents and patrons, dismissed for hopeless incapacity for
the service of those scientific corps. During the five subsequent years, which have
been years of the open-competition principle, there has not been one dismissed for
incapacity. Moreover, the general standard of capacity has been advanced. An
eminent professor of this university, who has taught as well under the patronage as
under the competitive system at that Academy, declares that the quality of mind of
the average of the cadets has been improved by the competition, so much so that
he considers that the present average quality of the mind of cadets there, though
the sorts of attainment are different, has been brought up to the average of the
first-class men of this (Cambridge) university, which of itself is a great gain. Another
result, the opposite to that which was confidently predicted by the opponents to the
principle, has been that the average physical power or bodily strength, instead of
being diminished, is advanced beyond the average of their predecessors.”
I read this also from the same report:
Another result of immense importance to the educational interests of Great Britain
has followed the introduction of these open competitive examinations for
appointments to the military and naval schools, to the East India service, as well as
to fill vacancies in the principal clerkships in the war, admiralty, ordnance, and home
departments of the Government. A stimulus of the most healthy and powerful kind,
worth more than millions of pecuniary endowment, has been given to all the great
schools of the country, including the universities of England, Scotland, and Ireland.
As soon as it was known that candidates, graduates of Trinity College, Dublin, had
succeeded over competitors from Oxford and Edinburg in obtaining valuable
appointments in the East India service, the professors in the latter universities
began to look to their laurels. As soon as it was known to the master of any
important school that some of his leading pupils might compete in these
examinations, and that his own reputation as a teacher depended in a measure on
the success or failure of these pupils, he had a new motive to impart the most
vigorous and thorough training.
Such has been the result in France and in England. We are not without
examples at home. The competitive system has been tried in repeated
instances here in the appointments both to the Military and the Naval
Academy. Several Representatives in Congress, with a conscientious sense
of the responsibility resting upon them, have given their patronage to the
result of general competition, among them the gentleman who so ably
represented, in the last Congress, the district in which I live. The results
have been most satisfactory. Here, again, I will quote from the report of the
Board of Visitors for 1863:

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