![volcanoes; I understood the motions of the earth and its
relations with the stars, and, just as if the earth had been
turned round before my eyes that I might be made to admire
Thy greatness, O my God! I saw all countries with their
various inhabitants, and their different customs, I saw every
variety of my species, and a voice said to me: 'Like thyself, all
these men are the image of the Creator; like thyself, they are
ever journeying towards God, and conscious of their
progress!' The thickness of the forests, the depth of the seas
could not hide anything from my eyes; I had power to see
everything, to admire all, and I was happy in my happiness,
in the happiness of the dear objects of my tender love. Our
joys were in common. We felt ourselves united by our former
affections which had now become much more deep, and by
the love of God: we drew happiness from one and the same
source; we were but one, we each and all enjoyed this
happiness, which was far too great to be expressed. I am
silent now, that I may feel it more deeply."[22]
It is easy for us to verify to ourselves the fact that men who are
condemned by nature to a premature death, are endowed with a
great serenity of mind. This moral condition is, in our opinion, an
indication that they have the presentiment or even the anticipated
possession of the new life which awaits them after death. Why are
consumptive people so gentle and sensitive? We believe it is
because, being already half out of this world, they are partially
endowed with the moral attributes of superhuman beings. They are,
as it is well known, always confident in their destinies, they make
projects of happiness, and for the future, when their last hour is
striking, they feel hope and joy when the by-standers are thinking of
their burial. It is customary to explain this anomaly by saying that
persons in consumption do not understand the gravity of their
illness, but we believe that they have, on the contrary, a confused
notion of their state, that nature reveals to them the approach of an
existence of cloudless happiness, and that it is this secret conviction](https://image.slidesharecdn.com/80258-250323050531-c9279af1/85/Business-Statistics-using-Excel-2nd-Edition-Glyn-Davis-34-320.jpg)
![which gives them hope and confidence in the future. The future
which they foresee is not of this world, but the future of the
heavens. This applies not to consumptive persons only. Every man
destined to die young seems to be marked with that inner stamp of
the soul which lends him now a gentle and charming melancholy,
anon vivacity or sensibility which his parents admire, and which is
too often only an indication that he is not to remain with them. The
charming qualities of many young people are often only the
precursors of their death.
"When they have so much intellect, children have brief lives," says
Casimir Delavigne. "Whom the gods love, die young," said the
Greeks.
Let us, then, not fear death; but await it, not as the end of our
existence, but as its transformation. Let us learn by the purity of our
life, by our virtues, by the culture of our faculties, by our knowledge,
by the exercise of the religion of our ancestors, to prepare ourselves
for the critical moment of that natural revolution which shall usher
us into a blessed sojourn in the ethereal spheres on the day after
death.
FOOTNOTES:
[22] Quoted by M. Pezzani, in his "Pluralité des
Existences de l'âme," pp. 261-263.](https://image.slidesharecdn.com/80258-250323050531-c9279af1/85/Business-Statistics-using-Excel-2nd-Edition-Glyn-Davis-35-320.jpg)
![our world in the disposition and the motions of the stars within
them. The universe is composed of the agglomeration of them all.
You know all this, but there is one fact which, as it is the result of
recent discoveries, you may not be aware of; it is, the great variety
of disposition or of physical aspect presented by certain stars, in
which a kind of overturn of that which constitutes nature on our
globe has taken place. While they remain similar to our world in the
order of their movements, certain stars differ widely in the forces
which govern nature in them.
Theophilus. Pray explain your meaning.
The Author. While our solar system is governed by a single central
star, there are stellar systems which are governed by two, three, and
even four suns. It is evident that worlds which have two or three
centres of light and heat must present physical and mechanical
peculiarities of which we have no idea. There are also other
differences proper to many of the stellar worlds. The light of our sun
and of the greater number of the stars is constant: it never
undergoes either augmentation or diminution. But this is not the
case with many of those distant suns which we call stars. We see
their light alternately fade and revive; sometimes they shine brightly,
then become almost imperceptible, and anon brilliant again. Some of
them become altogether extinct. The decrease in lustre of several
stars has been noted by different astronomers.[23]
Stars which have been observed in other times no longer exist.[24]
Others have suddenly appeared, shone with excessive lustre, and at
the end of some years have been seen no more.
These successive augmentations and diminutions of luminous
brilliance are not uncommon in the stars with which we are
acquainted. According to M. Flammarion,[25] star ο of the Whale
varies very much in luminous intensity and the constellation itself
frequently disappears. Star χ of the Swan passes from the fifth to
the tenth size under our eyes, the thirtieth star of the Hydra, which
is of the fourth size, almost always disappears at intervals of 500](https://image.slidesharecdn.com/80258-250323050531-c9279af1/85/Business-Statistics-using-Excel-2nd-Edition-Glyn-Davis-41-320.jpg)
![days. These variations must, as M. Flammarion observes, produce
strange results. To-day, the radiant star is shedding floods of light
and fire upon the planets which it governs, and the soul of that
planet is warmed by its burning rays. A few months later, without
the least cloud in the sky, the shining of the sun becomes fainter,
and then, by degrees, the obscurity increases, until at length the
planet is plunged into thick darkness. When the diminution of the
light of the sun is periodical, this universal night lasts for a fixed
time, at the end of which the light returns, if not, the darkness is
dispersed after varying periods. The light grows, little by little, until
at length the radiant star reappears in all its primitive brightness.
The fine days, the glorious light returns, until the moment when the
same fading recommences and the darkness sets in once more.
Can we picture to ourselves the strange alterations which nature
undergoes in regions which are subjected to torrid heat and glacial
cold by turns? I am convinced that the glacial period which
geologists have defined in the history of our globe, during which an
extraordinary and sudden lowering of the temperature caused the
death of multitudes of living beings, and covered Europe with
glaciers from the mountains—was caused by a momentary
weakening of the intensity of the sun's light. When it resumed its
ordinary brightness, the sun dispersed the ice which had covered the
earth with a death mantle.[26]
I have said that there are double stars, that is to say, worlds
illuminated by two suns, and sometimes even by three or four. It is a
strange fact that in almost every instance one of these suns is white,
like ours, but the second is coloured, blue, red, or green. In the
constellation Perseus for example, a double star can be distinctly
seen by the aid of a good telescope. The star η is in fact
accompanied by a second, which makes part of the same solar
system. Now, this second star is blue. In the constellation Ophiochus
there is a similar system of double stars, one of which is red and the
other blue. The same peculiarity exists in the constellation of the
Dragon. In a double star of the constellation of the Bull, there is a](https://image.slidesharecdn.com/80258-250323050531-c9279af1/85/Business-Statistics-using-Excel-2nd-Edition-Glyn-Davis-42-320.jpg)
Business Statistics using Excel 2nd Edition Glyn Davis
- 1. Download the full version and explore a variety of ebooks or textbooks at https://ebookultra.com Business Statistics using Excel 2nd Edition Glyn Davis _____ Tap the link below to start your download _____ https://ebookultra.com/download/business-statistics-using- excel-2nd-edition-glyn-davis/ Find ebooks or textbooks at ebookultra.com today!
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- 5. Business Statistics using Excel 2nd Edition Glyn Davis Digital Instant Download Author(s): Glyn Davis ,Branko Pecar ISBN(s): 9780199659517, 0199659516 Edition: 2 File Details: PDF, 16.70 MB Year: 2013 Language: english
- 7. business statistics using Excel®
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- 9. business statistics using Excel® Second edition Glyn Davis & Branko Pecar 1
- 10. 1 Great Clarendon Street, Oxford, OX2 6DP, United Kingdom Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries © Glyn Davis and Branko Pecar 2013 The moral rights of the authors have been asserted First Edition copyright 2010 Impression: 1 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by licence or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this work in any other form and you must impose this same condition on any acquirer British Library Cataloguing in Publication Data Data available ISBN 978–0–19–965951–7 Printed in Italy by L.E.G.O. S.p.A.—Lavis TN Links to third party websites are provided by Oxford in good faith and for information only. Oxford disclaims any responsibility for the materials contained in any third party website referenced in this work.
- 11. Preface Aims of the book Ithaslongbeenrecognizedthatthedevelopmentofmodularundergraduateprogrammes coupled with a dramatic increase in student numbers has led to a reconsideration of teaching practices. This statement is particularly true in the teaching of statistics and, in response, a more supportive learning process has been developed. A classic approach to teaching statistics, unless one is teaching a class of future professional statisticians, can be difficult and is often met with very little enthusiasm by the majority of students. A more supportive learning process based on method application rather than method derivation is clearly needed. The authors thought that by relying on some commonly available tools, Microsoft Excel 2010 in particular, such an approach would be possible. To this effect, a new programme relying on the integration of workbook based open learning materials with information technology tools has been adopted. The current learning and assess- ment structure may be defined as follows: (a) To help students ‘bridge the gap’ between school and university (b) To enable a student to be confident in handling numerical data (c) To enable students to appreciate the role of statistics as a business decision-making tool (d) To provide a student with the knowledge to use Excel 2010 to solve a range of statistical problems. This book is aimed at students who require a general introduction to business statistics that would normally form a foundation-level business school module. The learning mate- rial in this book requires minimal input from a lecturer and can be used as a self-instruc- tion guide. Furthermore, three online workbooks are available; two to help students with Excel and practise numerical skills, and an advanced workbook to help undertake facto- rial experiment analysis using Excel 2010. The growing importance of spreadsheets in business is emphasized throughout the text by the use of the Excel spreadsheet. The use of software in statistics modules is more or less mandatory at both diploma and degree level, and the emphasis within the text is on the use of Excel 2010 to undertake the required calculations. How to use the book effectively The sequence of chapters has been arranged so that there is a progressive accumulation of knowledge. Each chapter guides students step by step through the theoretical and spreadsheet skills required. Chapters also contain exercises that give students the chance to check their progress.
- 12. Hints on using the book (a) Be patient and work slowly and methodically, especially in the early stages when progress may be slow. (b) Do not omit or ‘jump around’ between chapters; each chapter builds upon knowledge and skills gained previously. You may also find that the Excel applications described earlier in the book are required to develop applications in later chapters. (c) Try not to compare your progress with others too much. Fastest is not always best! (d) Don’t try to achieve too much in one session. Time for rest and reflection is important. (e) Mistakes are part of learning. Do not worry about them. The more you repeat something, the fewer mistakes you will make. (f) Make time to complete the exercises, especially if you are learning on your own. They are your best guide to your progress. (g) The visual walkthroughs have been developed to solve a particular statistical problem using Excel. If you are not sure about the Excel solution then use the visual walkthrough (flash movies) as a reminder. Preface vi
- 13. Brief contents How to use this book xiv How to use the Online Resource Centre xvi 1 Visualizing and presenting data 1 2 Data descriptors 58 3 Introduction to probability 107 4 Probability distributions 135 5 Sampling distributions and estimating 185 6 Introduction to parametric hypothesis testing 243 7 Chi-square and non-parametric hypothesis testing 296 8 Linear correlation and regression analysis 343 9 Time series data and analysis 406 Glossary 468 Index 477
- 14. Detailed contents How to use this book xiv How to use the Online Resource Centre xvi 1 Visualizing and presenting data 1 Overview 1 Learning objectives 2 1.1 The different types of data variable 2 1.2 Tables 3 1.2.1 What a table looks like 4 1.2.2 Creating a frequency distribution 6 1.2.3 Types of data 10 1.2.4 Creating a table using Excel PivotTable 11 1.2.5 Principles of table construction 21 1.3 Graphical representation of data 21 1.3.1 Bar charts 22 1.3.2 Pie charts 27 1.3.3 Histograms 31 1.3.4 Histograms with unequal class intervals 40 1.3.5 Frequency polygon 42 1.3.6 Scatter and time series plots 47 1.3.7 Superimposing two sets of data onto one graph 51 Techniques in practice 54 Summary 56 Key terms 57 Further reading 57 2 Data descriptors 58 Overview 58 Learning objectives 59 2.1 Measures of central tendency 59 2.1.1 Mean, median, and mode 59 2.1.2 Percentiles and quartiles 63 2.1.3 Averages from frequency distributions 67 2.1.4 Weighted averages 77 2.2 Measures of dispersion 80 2.2.1 The range 82 2.2.2 The interquartile range and semi-interquartile range (SIQR) 82 2.2.3 The standard deviation and variance 83 2.2.4 The coefficient of variation 88
- 15. 2.2.5 Measures of skewness and kurtosis 89 2.3 Exploratory data analysis 94 2.3.1 Five-number summary 94 2.3.2 Box plots 96 2.3.3 Using the Excel ToolPak add-in 100 Techniques in practice 102 Summary 104 Key terms 105 Further reading 105 3 Introduction to probability 107 Overview 107 Learning objectives 107 3.1 Basic ideas 107 3.2 Relative frequency 109 3.3 Sample space 112 3.4 The probability laws 114 3.5 The general addition law 115 3.6 Conditional probability 117 3.7 Statistical independence 120 3.8 Probability tree diagrams 123 3.9 Introduction to probability distributions 124 3.10 Expectation and variance for a probability distribution 127 Techniques in practice 131 Summary 133 Key terms 133 Further reading 133 4 Probability distributions 135 Overview 135 Learning objectives 135 4.1 Continuous probability distributions 136 4.1.1 Introduction 136 4.1.2 The normal distribution 136 4.1.3 The standard normal distribution (Z distribution) 140 4.1.4 Checking for normality 149 4.1.5 Other continuous probability distributions 153 4.1.6 Probability density function and cumulative distribution function 154 4.2 Discrete probability distributions 155 4.2.1 Introduction 155 4.2.2 Binomial probability distribution 155 Detailed contents ix
- 16. 4.2.3 Poisson probability distribution 165 4.2.4 Poisson approximation to the binomial distribution 173 4.2.5 Normal approximation to the binomial distribution 175 4.2.6 Normal approximation to the Poisson distribution 180 4.2.7 Other discrete probability distributions 182 Techniques in practice 182 Summary 183 Key terms 183 Further reading 184 5 Sampling distributions and estimating 185 Overview 185 Learning objectives 185 5.1 Introduction to the concept of a sample 186 5.1.1 Why sample? 186 5.1.2 Sampling terminology 187 5.1.3 Types of samples 188 5.1.4 Types of error 192 5.2 Sampling from a population 193 5.2.1 Introduction 193 5.2.2 Population versus sample 194 5.2.3 Sampling distributions 194 5.2.4 Sampling distribution of the mean 194 5.2.5 Sampling from a normal population 198 5.2.6 Sampling from a non-normal population 204 5.2.7 Sampling distribution of the proportion 210 5.2.8 Using Excel to generate a sample from a sampling probability distribution 212 5.3 Population point estimates 217 5.3.1 Introduction 217 5.3.2 Types of estimate 218 5.3.3 Criteria of a good estimator 218 5.3.4 Point estimate of the population mean and variance 218 5.3.5 Point estimate for the population proportion and variance 222 5.3.6 Pooled estimates 224 5.4 Population confidence intervals 225 5.4.1 Introduction 225 5.4.2 Confidence interval estimate of the population mean, µ (σ known) 226 5.4.3 Confidence interval estimate of the population mean, µ (σ unknown, n < 30) 228 5.4.4 Confidence interval estimate of the population mean, µ (σ unknown, n ≥ 30) 232 5.4.5 Confidence interval estimate of a population proportion 235 Detailed contents x
- 17. 5.5 Calculating sample size 237 Techniques in practice 239 Summary 241 Key terms 241 Further reading 242 6 Introduction to parametric hypothesis testing 243 Overview 243 Learning objectives 243 6.1 Hypothesis testing rationale 244 6.1.1 Hypothesis statements H0 and H1 244 6.1.2 Parametric versus non-parametric tests of difference 246 6.1.3 One and two sample tests 246 6.1.4 Choosing an appropriate statisitcal test 247 6.1.5 Significance level 248 6.1.6 Sampling distributions 248 6.1.7 One and two tail tests 249 6.1.8 Check t-test model assumptions 250 6.1.9 Types of error 251 6.1.10 P-values 251 6.1.11 Critical test statistic 252 6.2 One sample z-test for the population mean 253 6.3 One sample t-test for the population mean 257 6.4 Two sample z-test for the population mean 261 6.5 Two sample z-test for the population proportion 266 6.6 Two sample t-test for population mean (independent samples, equal variances) 269 6.7 Two sample tests for population mean (independent samples, unequal variances) 274 6.7.1 Two sample tests for independent samples (unequal variances) 274 6.7.2 Equivalent non-parametric test: Mann–Whitney U test 279 6.8 Two sample tests for population mean (dependent or paired samples) 279 6.8.1 Two sample tests for dependent samples 279 6.8.2 Equivalent non-parametric test: Wilcoxon matched pairs test 283 6.9 F test for two population variances (variance ratio test) 285 6.10 Calculating the size of the type II error and the statistical power 290 Techniques in practice 292 Summary 294 Key terms 294 Further reading 295 Detailed contents xi
- 18. 7 Chi-square and non-parametric hypothesis testing 296 Overview 296 Learning objectives 296 7.1 Chi-square tests 297 7.1.1 Chi-square test of association 298 7.1.2 Chi-square test for independent samples 303 7.1.3 McNemar’s test for matched (or dependent) pairs 307 7.1.4 Chi-square goodness-of-fit test 312 7.2 Non-parametric (or distribution-free) tests 318 7.2.1 Sign test 318 7.2.2 Wilcoxon signed rank sum test for dependent samples (or matched pairs) 324 7.2.3 Mann–Whitney U test for two independent samples 331 Techniques in practice 338 Summary 340 Key terms 341 Further reading 341 8 Linear correlation and regression analysis 343 Overview 343 Learning objectives 343 8.1 Linear correlation analysis 344 8.1.1 Scatter plots 344 8.1.2 Covariance 347 8.1.3 Pearson’s correlation coefficient, r 348 8.1.4 Testing the significance of linear correlation between the two variables 353 8.1.5 Spearman’s rank correlation coefficient 356 8.1.6 Testing the significance of Spearman’s rank correlation coefficient, rs 358 8.2 Linear regression analysis 362 8.2.1 Construct scatter plot to identify model 364 8.2.2 Fit line to sample data 364 8.2.3 Sum of squares defined 369 8.2.4 Regression assumptions 370 8.2.5 Test model reliability 372 8.2.6 The use of t-test to test whether the predictor variable is a significant contributor 374 8.2.7 The use of F test to test whether the predictor variable is a significant contributor 378 8.2.8 Confidence interval estimate for slope β1 382 8.2.9 Prediction interval for an estimate of Y 383 8.2.10 Excel data analysis regression solution 385 8.3 Some advanced topics in regression analysis 390 Detailed contents xii
- 19. 8.3.1 Introduction to non-linear regression 390 8.3.2 Introduction to multiple regression analysis 397 Techniques in practice 401 Summary 404 Key terms 405 Further reading 405 9 Time series data and analysis 406 Overview 406 Learning objectives 406 9.1 Introduction to time series data 407 9.1.1 Stationary and non-stationary time series 407 9.1.2 Seasonal time series 409 9.1.3 Univariate and multivariate methods 409 9.1.4 Scaling the time series 410 9.2 Index numbers 411 9.2.1 Simple indices 412 9.2.2 Aggregate indices 415 9.2.3 Deflating values 416 9.3 Trend extrapolation 419 9.3.1 A trend component 420 9.3.2 Fitting a trend to a time series 420 9.3.3 Types of trends 423 9.3.4 Using a trend chart function to forecast time series 424 9.3.5 Trend parameters and calculations 426 9.4 Moving averages and time series smoothing 430 9.4.1 Forecasting with moving averages 431 9.4.2 Exponential smoothing concept 436 9.4.3 Forecasting with exponential smoothing 438 9.5 Forecasting seasonal series with exponential smoothing 445 9.6 Forecasting errors 450 9.6.1 Error measurement 450 9.6.2 Types of errors 453 9.6.3 Interpreting errors 455 9.6.4 Error inspection 456 9.7 Confidence intervals 458 9.7.1 Population and sample standard errors 458 9.7.2 Standard errors in time series 459 Techniques in practice 463 Summary 465 Key terms 466 Further reading 466 Glossary 468 Index 477 Detailed contents xiii
- 20. How to use this book Learning objectives Each chapter opens with a series of learn- ing objectives outlining what you can expect to learn as you progress through the chapter. These also serve as helpful recaps of impor- tant concepts when revising. Step-by-step Excel guidance Excel screenshots are fully integrated throughout the text and visually demonstrate the Excel formulas, functions, and solutions to provide you with clear step-by-step guidance onhowtosolvethestatisticalproblemsposed. Example boxes Detailed worked examples run throughout each chapter to show you how the theory relates to practice. The authors break concepts down into clear step-by-step phases, which are often accompanied by a series of Excel screenshots, enabling you to assess your progress. Note boxes Note boxes draw your attention to key points, areas where extra care should be taken, or certain exceptions to the rules. Interpretation boxes Interpretation boxes appear throughout the chapters, providing you with further explanations to aid your understanding of the concepts being discussed. »Learning objectives« On successful completion of the module, you will be able to: » understand the concept of an average; » recognize that three possible averages exist (mean, mode, and median) and calculate them using a variety of graphical and formula methods in number and frequency distribution form; » recognize when to use different measures of average; » understand the concept of dispersion; » recognize that different measures of dispersion exist (range, quartile range, SIQR, standard deviation, and variance), and calculate them using a variety of graphical and formula methods in number and frequency distribution form; » recognize when to use different measures of dispersion; » understand the idea of distribution shape, and calculate a value for symmetry and peakedness; Figure 2.4 Example 2.4 To illustrate the use of the Select Formulas > Select Insert Function method consider the prob- lem of calculating the mean value in Example 2.1. In Figures 2.1 and 2.2 the mean value is located in cell E12. To insert the correct Excel function into cell E12 we would click on cell E12 and then Select Formulas > Select Insert Function as illustrated in Figures 2.3 and 2.4. Note According to Table 2.3, a number of claims corresponding to ‘one’ occurs three times, which will contribute three to the total, ‘two’ claims occur four times contributing eight to the sum, and so on. This can be written as follows: Mean( (3*1) + (4*2) +.........+ (1*10) 3 + 4 + 4 + 5 + X) = 5 5 + 7 + 5 + 3 + 3 + 1 = 206/40 = 5.15 As already pointed out, as we are dealing with discrete data we would indicate a mean as approximately five claims. Equation (2.3) can now be used to calculate the mean for a fre- quency distribution data set: X fX f = ∑ ∑ (2.3) ❉ Interpretation Twenty five percent of all the values in the data set are equal to or below 430 miles, while 75% are equal to or below 470 miles. »Learning On successf d Examp To illustrate t lem of calcu Note times, whic to the sum, ❉ Interpr below 430 m
- 21. Exploring the Variety of Random Documents with Different Content
- 24. CHAPTER THE TWENTIETH. PRACTICAL RULES RESULTING FROM THE FACTS AND PRINCIPLES DEVELOPED IN THIS WORK.—THE ENNOBLING OF THE SOUL BY THE PRACTICE OF VIRTUE, BY SEEKING TO KNOW, THROUGH SCIENCE, NATURE AND ITS LAWS.—THE RENDERING OF PUBLIC WORSHIP TO THE DIVINITY.—THE MEMORY OF THE DEAD TO BE RETAINED.—WE OUGHT NOT TO FEAR DEATH.—DEATH IS ONLY AN UNFELT TRANSITION FROM ONE STATE TO ANOTHER, IT IS NOT A TERMINATION, BUT A METAMORPHOSIS.—THE IMPRESSIONS OF THE DYING.—THEY WHOM THE GODS LOVE DIE YOUNG.—REUNION WITH THOSE WHO HAVE GONE BEFORE. E will conclude our work by laying down certain practical rules which result from the facts and the principles that have been explained in its course. Since man can raise himself to the range of a superhuman being only when his soul has acquired the necessary degree of purification in this life, it is evidently his interest to apply himself to the culture of his soul, to preserve it from every stain, to keep it from falling. Be good, generous, and compassionate; grateful for benefits, accessible to the suffering, the friend of the oppressed. Console those who suffer and who weep. Practise every form of charity. Endeavour to raise your thoughts above terrestrial things. Strive against those material instincts, which are the stigmata of human existence. Aspire to the good and the beautiful. Live in the most elevated spheres, those which are the least bound to lower things. It is only thus that you can elevate and ennoble your soul, and render it fit to enjoy the higher existence which awaits it in the ethereal spheres. For, if your soul be vicious and corrupt, if, during all your terrestrial life, you have been sunk in material interests, exclusively given up to purely physical occupations and enjoyments,
- 25. which make you the fellow of the animals; if your heart has been hard, your conscience dumb, your instincts low and evil, you will be condemned to recommence a second existence on the earth. Once, or many times again you will have to bear the burthen of life on this disinherited globe, where physical suffering and moral evil have taken up their abode, where happiness is unknown, and unhappiness is the universal law. There is another motive for our careful cultivation of the faculties of the soul, and for our constantly purifying ourselves by the practice of good. Noble and generous persons, elect souls, are, as we have said, the only ones capable of communicating with the dead, with the beloved beings whom they have lost. If, therefore, we be stained with moral evil, we shall not receive any communication, any succour from the beings who have left us, and whom we loved. This is a powerful motive for our constant striving towards perfection. One of the most effectual means of perfecting and ennobling the soul, of raising it above terrestrial conditions, and bringing it near the higher spheres, is science. Study, labour to learn of nature, to comprehend the plans and the phenomena which surround you, to explain to yourselves the universe of which you form a portion, and your soul will grow in strength and wisdom. It is very sad to contemplate the shameful ignorance in which almost all humanity is sunk. The population of our globe numbers 1,300,000,000, and of all this multitude hardly 10,000,000 can be said to have studied the sciences, and really cultivated their minds. All the rest of mankind are abandoned to an intellectual passiveness, which almost reduces them to the level of the animals. The earth is but a vast field of ignorance. As far as knowledge is concerned, almost all men die as they were born, they have not added a single idea, a single branch of knowledge to those which their parents—themselves ignorant— have inculcated in their youth. Nevertheless, thanks to the labours of some few men of uncommon mind and energy, the knowledge we possess at the present time is immense, we have made great progress in the study of nature and its laws.
- 26. We understand the mechanism and the regulation of the universe, we have learned to reject the fallacious testimony of our senses, we have discerned the courses of the different stars, which look so much alike, when they shine in the firmament by night. We know that the sun is motionless in the centre of our world, and that a company of planets, among which the earth figures, revolve around him, in an orbit whose mathematical curve has been precisely fixed. We know the cause of the days and nights, as well as that of the seasons; we can predict almost to a second the return of the stars to a certain point of their orbit, their meetings, eclipses, and occultations. The globe which we inhabit has been surveyed and explored with care which has hardly missed a nook of it. We know the causes of the winds and of the rains, we can point out the exact course of the sea-currents, and foretell the hour and the height of the tides all over the globe. We know why glaciers exist at the northern and southern extremities of the earth, and why other glaciers crown the great mountain heights. The movements of the earth, which formerly produced chains of mountains, and which at present occasion volcanic eruptions and earthquakes, are quite comprehensible to us. The composition of all the bodies which exist on the surface, or are hidden in the depths of the earth, has been fixed with certainty. We know what air contains, and what water is composed of. There is not a mineral, not a particle of earth to which we cannot assign its composition. More than that, we can tell what is the composition of the soil of the planets, and of their satellites, those stars which roll at incalculable distances above our heads, and which we can reach only with our eyes. Science has performed this miracle, the chemical analysis of bodies which it cannot touch, and which it can only see across millions of miles in space. We have studied, classified, demonstrated all the living beings, animals and plants which people the earth. There is not an insect hidden in the grass of the fields which has not been described, which has not had its just place in creation assigned to it; there is
- 27. not a blade of grass which has not been reproduced by the pencil of the naturalist. Beyond all this, science has penetrated far beyond the reach of our vision. It has invented a marvellous instrument which has unveiled an entire world to our astonished gaze, a world whose existence we never should have suspected without its aid. The world thus revealed to us is that of infinitely little things. We know that myriads of living creatures, both animals and plants, exist in a drop of water; that those creatures, in all their prodigious littleness, have a complete existence, and are as well organized as those of great size which are analogous to them, and that the physiological functions of all these imperceptible beings are fulfilled as perfectly as our own. Just as we have penetrated into the life of infinite littleness, so we have pierced the depths of celestial space, and scrutinized with our eyes the magnified image of the stars which revolve at an incalculable distance above us. The telescope shows us the surface of the moon, the depths of its ravines, and the rough serrated edges of its enormous mountains, furrowed with deep circular crevasses. We can cast our eyes over the lunar disc as if it were a distant landscape of our own globe. We can even, thanks to the magnifying powers of the telescope, form an idea of the aspect of the surfaces of those planets which are almost lost in the infinite distances of the heavens. After this faint and incomplete sketch of that which human science has been able to accomplish, it might be supposed that every inhabitant of the earth is impatient to make all this knowledge his own, that every one must desire to fill his mind with its treasures. Alas! the great majority of the human species is ignorant of even the elements of all this. Take away the ten millions of individuals, to whom we have already alluded, and who, numerically, are hardly to be counted in considering the population of the globe, all people imagine that the earth is a flat surface which extends to the limits of the horizon, and is covered with a blue cupola, called heaven. If you assert that the earth revolves, they laugh, and point to the
- 28. motionless earth, and the sun which rises on the right hand and sets on the left, a manifest proof that the sun comes and goes. The poets will have it that the sun rises from his bed in the morning, and returns to it in the evening. People believe that the stars which shine by night, in the celestial vault, are simply ornaments, an agreeable spectacle, made to please our eyes, and that the moon is a beacon. Nobody inquires into the causes of the rain or fine weather, of heat or cold, of the winds or the tides. Every one shuts his eyes to natural phenomena, so as to avoid the trouble of explaining them. Nature is a shut book for the majority of mankind, who live in the midst of the most curious and various phenomena, but who occupy themselves in eating and drinking, and trying to harm their fellows. It is a sorrowful spectacle to behold humanity thus preoccupied by its more material necessities, and utterly without interest in any mental exertion, and one grieves to think that such is the condition of almost all the inhabitants of the globe. How far is he superior to the great mass of his fellows, who has cultivated his mind, enriched it with various and useful ideas, and appropriated to himself at least one branch of the varied tree of the exact sciences. What breadth and power must be acquired by a mind thus fortified! Strive, O my reader, to study and to learn. Initiate yourself into the secrets of nature, try to understand all that surrounds you, the universe and its infinite productions, admire the power of God in learning the wonders of His works. Then shall you not approach the tomb with your soul void as on the day of your birth. At the supreme hour of death you will be wise, instructed, and, finding yourself nearer to the sublime essence of superhuman beings, you will be eager to follow them into the ethereal spheres. In order to elevate and perfect the soul, it is not sufficient only to apply ourselves to the practice of moral virtues and to learning; we must also endeavour to understand God, the Author of the universe. Therefore, let men enter into the temples, and prostrate themselves before God according to the forms and rites of worship in which they have been reared. All religions are good, and ought to be respected,
- 29. because they permit us to pay the homage of gratitude and heartfelt submission to the Author of nature. The Christian religion is good, because it is a religion. The religion of Mahomet is good, because it is a religion. For the same reason Buddhism and Judaism are good, and the religion of the wild Indians who worship the sun in the depths of their forests. The fourth practical rule which we derive from the principles and theories which we have laid down, is that the remembrance and commemoration of the dead should be preserved. Let us not efface from our hearts the memory of those whom death has snatched from us. To forget them is to cause them the most cruel anguish, and to deprive ourselves of the aid and guidance which they can give us here below. The ancients sedulously kept up the memory of the dead. They did not put the idea of death away from them with terror, like the modern peoples; on the contrary, they loved to invoke it. Among the Greeks and Romans the cemeteries were places of meeting, used for festivals and promenades. The Orientals of our days preserve this ancient tradition. Their cemeteries are perfectly kept gardens, whither festive crowds resort on festal occasions. They visit the relatives and friends who are buried in the shrubberies and the flower-beds, and revel in the pleasures of life amid the pretty dwelling-places of the dead. In Europe we know nothing of this wholesome philosophy. But we may remark, that peasants, unlike dwellers in cities, who are not brought into familiar daily contact with nature, are far from shunning the idea of death, or avoiding the cemeteries where their relatives and friends rest. They recall the remembrance of their dead, they speak to them, they question them, they consult them, as though they were still seated by the family fireside. The custom of funeral repasts, which dates from the time of primitive man, is still observed in several countries. On returning from the cemetery the company seat themselves before a well-
- 30. spread table, in the house of the deceased, and wish him a happy journey to the land of shadows. In our cities, it is "the people" who hold it a duty to carry flowers to the graves of their relatives. Among the higher classes of society people hold themselves exempt, in general, from this pious care, and they are wrong. Piety towards the dead, and reverent commemoration of them, are prescribed by the laws of nature. Finally, we would impress upon the reader, as a consequence and a practical rule resulting from all that has gone before, that he ought not to fear death. Let him regard with firm heart and tranquil eye that moment which all men dread so much. We have said that death is not a conclusion, but a change, we do not perish, we are transformed. The grub which seems to die, enclosed within a cold shell, does not die, but is born again, a brilliant butterfly, to flutter joyously in the air. Thus it shall be with us. Though our miserable frames remain on earth, and restore their elements to the common reservoir of universal matter, our souls shall not perish. They shall be born again, brilliant creatures of the celestial ether. They shall leave a world in which pain and evil are the constant law, for a blessed domain where every condition of happiness shall be realized. Why, then, should we dread death? If we do not desire it, we ought at least to await it with hope and tranquillity. Death must unite us to those beings whom we have loved, whom we do love, and whom we shall love for ever. What an immense source of consolation during the remainder of our life! What a store of courage for the terrible moment of our own end! The beloved dead, who have never ceased to be present to our memory, have done us the sad, supreme service of softening the anguish of death to us. The sadness of our last moments will be calmed by the thought that they are awaiting our coming, that they are ready to receive us on the threshold of the other life, that they are gone before to lead us into the new domain of existence beyond the tomb! The fear of death, which is so prevalent among men generally, loses its intensity when the last hour has come. Those who are accustomed to witness death know that the last agony is rarely
- 31. severe. He who dies after a long and honourable existence knows at that solemn moment that he is going to a new and better world. He is happy, and his words and looks express happiness. The only thought which makes him sorrowful is the grief which his loss must occasion to those whom he loves and is about to leave. The observations which follow have been made by persons accustomed to observe the dying. But deaths occasioned by maladies which destroy consciousness, or reason, or speech, must not be included in these observations. In order to judge of the thoughts which occupy the dying we must consider those who preserve the integrity of their intellectual faculties until their latest breath. They always die calmly. Consumptive patients, the wounded, those who die from an affection of the stomach or of the intestinal tube, of those slow fevers which consume the strength without impairing the intellectual faculties, these generally remain in the full possession of their intelligence to the last, and die with great tranquillity, even satisfaction. In almost all these cases death is preceded by a gradual decline of strength and sensation, so that the individual has hardly any consciousness of the change he is about to undergo, and looks forward to the moment of death with perfect indifference. There is a period, which frequently lasts for several hours, during which, life having completely left the body, it is already a corpse which is under the eyes of the spectators, and yet that corpse still moves and speaks. But the soul which survives in the body, really dead, is not the soul of the terrestrial man, but of the superhuman being. The dying person has the consciousness, and perhaps even the prevision of the ineffable happiness which awaits him in that new world upon whose threshold he is standing, and he expresses his happiness by his words and looks. In a sigh of supreme joy he exhales his last breath. This extraordinary state, in which the dying are partly on earth, and partly in the new world to which they are destined, explains the touching eloquence, the sublime words which sometimes come from their feeble lips. An uneducated poor man will express himself upon his death-bed with eloquence
- 32. incomprehensible to those who are listening to him. It also explains the prophecies, justified by subsequent events, which have been uttered by the dying. They have a knowledge of things of which, in their ordinary condition as belonging to the human species, they could not possibly have had any notion. Therefore, we ought to treasure up their last words with pious care, and scrupulously fulfil the wishes which they express. In Moldavia, when a peasant has escaped death in a severe illness, after having been on the brink of the grave, his friends press around his bed to ask him what he had seen in the other world, and what news he has for them from their dead relatives. Then the poor invalid interprets his visions for them as well as he can. A modern writer, who has left some small books on spiritualist philosophy, M. Constant Savy, relates in his "Pensées et Méditations," an extraordinary dream which he had when he was, apparently, at the point of death. We transcribe this curious and interesting document from M. Pezzani's work:— "I felt very ill," writes Constant Savy, "I had no strength, it seemed to me that my life was making efforts to resist death, but in vain, and that it was about to escape. My soul detached itself little by little from the matter spread all over my frame; I felt it retiring from all those parts with which it is so intimately united, and, as it were, concentrating itself upon one single point, the heart, and a thousand obscure, cloudy thoughts about my future life occupied me. Little by little nature faded from before me, taking irregular and strange forms, I almost lost the faculty of thinking, I only retained that of feeling, and this feeling was all love, love of God and of the beings whom I had most cherished in Him; but I could not manifest this love; my soul, withdrawn to one single point in my body, had almost ceased to have any relation with it, and could no longer command it. My soul experienced some distractions still, caused by the pain of the body, and the grief of those who surrounded me, but these distractions were
- 33. slight, like the pains and the perceptions which caused them. My life was now attached to matter by one only of the thousand links which had formerly bound it, and I was about to expire. "Suddenly, no doubt to mark the passage from this life to the other, there came a thick darkness, to which succeeded a brilliant light. Then, O my God! I saw Thy day, that daylight I had so much desired! I saw them, all assembled together, those beings whom I had so dearly loved, who had inspired me during my life in this world after they had left me, and who had seemed to me to dwell in my soul, or float about me. They were all there, full of joy and happiness. They were waiting for me, they welcomed me with delight. It seemed to me that I completed their life and that they completed mine! But what a difference was there in the happiness I now felt from the sensations of the world I left! I cannot describe them! They were penetrating without being impetuous; they were mild, calm, full, unmixed, and yet they admitted the hope of a yet greater happiness! "I did not see Thee, my God! Who can see Thee? But I loved Thee more than I had loved Thee in this world! I comprehended Thee better, felt Thee more strongly, the traces of Thee which are everywhere, and on everything, appeared more plain and bright to me, I experienced such admiration and astonishment as I had never hitherto known, I saw more distinctly a portion of the wonders of Thy creation. The bowels of the earth hid no more secrets from me, I saw their depths, I saw the insects and other creatures which dwell in them, the mines known to men, and undiscovered by them, the secret ways and channels of the earth. I reckoned its age in its bosom as one counts that of a tree in the heart of its trunk; I saw all the water-courses which feed the seas; I saw the reflux of these waters, and it was like the motion of the blood in a man's body; from the heart to the extremities, from the extremities to the heart; I saw the depths of the
- 34. volcanoes; I understood the motions of the earth and its relations with the stars, and, just as if the earth had been turned round before my eyes that I might be made to admire Thy greatness, O my God! I saw all countries with their various inhabitants, and their different customs, I saw every variety of my species, and a voice said to me: 'Like thyself, all these men are the image of the Creator; like thyself, they are ever journeying towards God, and conscious of their progress!' The thickness of the forests, the depth of the seas could not hide anything from my eyes; I had power to see everything, to admire all, and I was happy in my happiness, in the happiness of the dear objects of my tender love. Our joys were in common. We felt ourselves united by our former affections which had now become much more deep, and by the love of God: we drew happiness from one and the same source; we were but one, we each and all enjoyed this happiness, which was far too great to be expressed. I am silent now, that I may feel it more deeply."[22] It is easy for us to verify to ourselves the fact that men who are condemned by nature to a premature death, are endowed with a great serenity of mind. This moral condition is, in our opinion, an indication that they have the presentiment or even the anticipated possession of the new life which awaits them after death. Why are consumptive people so gentle and sensitive? We believe it is because, being already half out of this world, they are partially endowed with the moral attributes of superhuman beings. They are, as it is well known, always confident in their destinies, they make projects of happiness, and for the future, when their last hour is striking, they feel hope and joy when the by-standers are thinking of their burial. It is customary to explain this anomaly by saying that persons in consumption do not understand the gravity of their illness, but we believe that they have, on the contrary, a confused notion of their state, that nature reveals to them the approach of an existence of cloudless happiness, and that it is this secret conviction
- 35. which gives them hope and confidence in the future. The future which they foresee is not of this world, but the future of the heavens. This applies not to consumptive persons only. Every man destined to die young seems to be marked with that inner stamp of the soul which lends him now a gentle and charming melancholy, anon vivacity or sensibility which his parents admire, and which is too often only an indication that he is not to remain with them. The charming qualities of many young people are often only the precursors of their death. "When they have so much intellect, children have brief lives," says Casimir Delavigne. "Whom the gods love, die young," said the Greeks. Let us, then, not fear death; but await it, not as the end of our existence, but as its transformation. Let us learn by the purity of our life, by our virtues, by the culture of our faculties, by our knowledge, by the exercise of the religion of our ancestors, to prepare ourselves for the critical moment of that natural revolution which shall usher us into a blessed sojourn in the ethereal spheres on the day after death. FOOTNOTES: [22] Quoted by M. Pezzani, in his "Pluralité des Existences de l'âme," pp. 261-263.
- 36. EPILOGUE. IN WHICH WE SEEK FOR GOD, AND IN OUR SEARCH, DESCRIBE THE UNIVERSE. HE author now asks his reader's leave to relate a conversation which took place between himself, and a friend named Theophilus, to whom he had confided the manuscript of "The Day After Death," in order to obtain his opinion and impressions of the work. He will allow the interlocutors to express themselves in the ordinary form of dialogue. Theophilus, (who comes into the Author's study, and lays the manuscript upon the table). I have read your work, and I will tell you presently my impressions of the details, but I must in the first place point out the great deficiency of the book. The Author. What is wanting in it? Theophilus. God. The Author. But—— Theophilus. (Interrupts him.) You are going to remind me that you frequently mention the sacred name, that Providence, the Author of nature, the Creator of the worlds, and so on, are words you
- 37. constantly employ. That is true, but it is equally true that you restrict yourself to these vague expressions, that you say nothing about the person of God, that you assign to Him no place in the world which you range over in company with more or less spiritualized souls. Why this reserve? Since you tell us that entirely spiritualized souls inhabit the sun, why do you not tell us where your system places God, the sovereign master of those souls! What is your motive for leaving aside a question of such great importance? The Author. I have several. In the first place, I have everybody's motive. The idea of God which must be formed in order to place Him in harmony with the boundless immensity of this universe which is His work, so far surpasses the limit of the human intellect, it is so overwhelming to our mind, that we stop, powerless and even frightened at our boldness, when we venture to ask ourselves, what is God? Theophilus. Nevertheless, I am surprised at your hesitation. When a system of the universe is to be constructed, one does not pause in the task, and I can hardly believe that when you venture, as you do, to place on the ladder-steps of your theory all the elements of the solar world—the planets and their satellites, stars and asteroïds, plants, men and animals, creatures visible and invisible, bodies and souls, matter and spirit—you have not assigned a place to the Creator. Have you classified everything in this immense edifice of the worlds, except its Sovereign Architect? The Author. No, my friend, you are not mistaken; God has His place in my system. Theophilus. Why, then, have you not said so! Why have you kept silence on this point? The Author. My book contains so many daring assertions, I have already exposed myself so fully to the animosity of both the learned and the ignorant, that I feared to furnish an additional pretext to their diatribes.
- 38. Theophilus. That is not a reason. If you dread discussion and fear detraction, why do you take up your pen at all? You were at liberty to keep your ideas on the origin and the destiny of man to yourself, but, when you decided on submitting them to the public, you became bound to explain all your mind on the subject. If you believe in your system, you must explain it without any reserve. The Author. Your words are wise, and I ought therefore to bow to them, and follow your imperative advice. Nevertheless I cannot make up my mind to do so, absolutely. I am going to propose a middle course to you. In confidence, and between ourselves, I will explain my ideas about God to you, I will tell you in what part of the immense universe I place this dazzling personality. If the idea seems to you absurd, untenable, or even too hazardous, you will frankly tell me so, and thus duly warned, I will keep my theory to myself; if not —— Theophilus. (Interrupting him.) An excellent plan. There can be no objection to that. Go on, I am listening. (At this point, Theophilus seats himself, his elbow resting on a book, and a cigar in his mouth, and composes himself to listen, with an expression of grave attention, dashed with suspicious severity, suitable to the arbitrator in a literary and philosophical matter.) The Author. You want to know, my dear Theophilus, where I place God? I place Him at the centre of the universe, or, I had better say, at the central focus, which must exist somewhere, of all the stars which compose the universe, and which, carried along by a common motion, circulate in concert around this central focus. Theophilus. Forgive me, but I do not seize your meaning exactly. The Author. You will understand it presently. Remember, to start from, that I place God at the common focus of the actual motion of the entire universe. But, where is the common focus? In order to know that, we must first of all know the universe, and all the order of its movements. Theophilus. All that is explained in the course of your work.
- 39. The Author. No, my friend, you are mistaken. In my work I have spoken of the solar system only, and a very incomplete and insufficient idea would be gained of the universe by contemplating that system alone. We must not, as is too often done, confound the world and the universe. The world is our world, that is to say, the solar system, of which we form a part; the universe is the agglomeration of all the worlds or systems similar to our world, or solar system. In the manuscript which you have just read, I have only been able to expound one little corner, one insignificant fraction of the universe. Theophilus. You call the solar world a little corner. The Author. Yes. Our whole solar system, the sun, with its immense following of planets and asteroïds, with the satellites of those planets, with the comets which from time to time come sweeping on, to fall into the burning furnace of the radiant star, all that, compared with the universe, is no more than an ear of corn in a huge granary, than a grain of sand upon the shore, than a drop of water in the ocean. The terrible vastness of the universe is such that it is absolutely inaccessible to our measurement, and it is for us the image of the infinite, or the infinite itself. Now, my friend, attend to me. Most certainly God, as to His nature, is absolutely inconceivable by our minds. His essence escapes us, and always must escape us. We can only affirm that He is infinite in His moral perfections, and in His intellectual power. But if, on the one hand, God is The Infinite in the moral order, and if, on the other hand, the universe is The Infinite in the physical order; if one is The Infinite in spirit, and the other is The Infinite in extent, these two ideas, although in themselves inaccessible to human intelligence, are nevertheless of the same order, and may be regarded in contiguity. It is then possible, without laying one's self open to the charge of presumption or absurdity, to place the Infinite, which is called God, in the Infinite which is called the Universe, in other words, to locate the person of God at the common focus of the worlds which compose the Universe.
- 40. Theophilus. Your reasoning is just. But you must prove, or, if you prefer the phrase, you must teach me that the universe is truly The Infinite by its extent. I could not admit that assertion without very convincing evidence. The Author. Very well. Lend me your best attention, and excuse me if my demonstration resembles a lecture on astronomy. I have said that our solar system is only a little corner of the universe. When you look at the vault of the sky on a bright clear night, you see it thickly strewn with stars, which, you will at once acknowledge, it would be impossible to count. But all that you see with the naked eye is next to nothing. Take a good telescope, and direct it to any part of the sky. There where a moment before you saw nothing, you will now discern legions of stars, bright spots will come out upon the darkness of space, like diamonds upon the velvet lining of a casket, each of them a star, exactly like those which we see at night in the sky. And now, let me ask you, do you know what a star is? Theophilus. Yes, I know from your manuscript, and I had already known, that the stars which we see by night, but which the greater light of the sun hides from us in the day-time, are self-luminous orbs, each the centre of attraction and the lamp to the particular world it lights, and which revolves around it. As a whole company of planets, satellites, asteroïds, and comets revolve round our sun, receiving heat, motion, and light from that great central orb, so, the stars dispersed throughout space, communicate motion and activity to a vast aggregate of planets and satellites. These planets, which revolve round the stars, constitute stellar worlds, analogous to our solar world. We cannot see the planets, which accompany these stars, by reason of their smallness, and the prodigious distance between us and them, beyond the reach of the most powerful telescopes; we only see the suns which govern them, i.e., the stars. But the existence of the fixed stars, like our sun, implies the existence of planets revolving around them. The Author. Perfectly correct. Thus, our solar world is not unique, it is only one member of the family of stellar worlds, which resemble
- 41. our world in the disposition and the motions of the stars within them. The universe is composed of the agglomeration of them all. You know all this, but there is one fact which, as it is the result of recent discoveries, you may not be aware of; it is, the great variety of disposition or of physical aspect presented by certain stars, in which a kind of overturn of that which constitutes nature on our globe has taken place. While they remain similar to our world in the order of their movements, certain stars differ widely in the forces which govern nature in them. Theophilus. Pray explain your meaning. The Author. While our solar system is governed by a single central star, there are stellar systems which are governed by two, three, and even four suns. It is evident that worlds which have two or three centres of light and heat must present physical and mechanical peculiarities of which we have no idea. There are also other differences proper to many of the stellar worlds. The light of our sun and of the greater number of the stars is constant: it never undergoes either augmentation or diminution. But this is not the case with many of those distant suns which we call stars. We see their light alternately fade and revive; sometimes they shine brightly, then become almost imperceptible, and anon brilliant again. Some of them become altogether extinct. The decrease in lustre of several stars has been noted by different astronomers.[23] Stars which have been observed in other times no longer exist.[24] Others have suddenly appeared, shone with excessive lustre, and at the end of some years have been seen no more. These successive augmentations and diminutions of luminous brilliance are not uncommon in the stars with which we are acquainted. According to M. Flammarion,[25] star ο of the Whale varies very much in luminous intensity and the constellation itself frequently disappears. Star χ of the Swan passes from the fifth to the tenth size under our eyes, the thirtieth star of the Hydra, which is of the fourth size, almost always disappears at intervals of 500
- 42. days. These variations must, as M. Flammarion observes, produce strange results. To-day, the radiant star is shedding floods of light and fire upon the planets which it governs, and the soul of that planet is warmed by its burning rays. A few months later, without the least cloud in the sky, the shining of the sun becomes fainter, and then, by degrees, the obscurity increases, until at length the planet is plunged into thick darkness. When the diminution of the light of the sun is periodical, this universal night lasts for a fixed time, at the end of which the light returns, if not, the darkness is dispersed after varying periods. The light grows, little by little, until at length the radiant star reappears in all its primitive brightness. The fine days, the glorious light returns, until the moment when the same fading recommences and the darkness sets in once more. Can we picture to ourselves the strange alterations which nature undergoes in regions which are subjected to torrid heat and glacial cold by turns? I am convinced that the glacial period which geologists have defined in the history of our globe, during which an extraordinary and sudden lowering of the temperature caused the death of multitudes of living beings, and covered Europe with glaciers from the mountains—was caused by a momentary weakening of the intensity of the sun's light. When it resumed its ordinary brightness, the sun dispersed the ice which had covered the earth with a death mantle.[26] I have said that there are double stars, that is to say, worlds illuminated by two suns, and sometimes even by three or four. It is a strange fact that in almost every instance one of these suns is white, like ours, but the second is coloured, blue, red, or green. In the constellation Perseus for example, a double star can be distinctly seen by the aid of a good telescope. The star η is in fact accompanied by a second, which makes part of the same solar system. Now, this second star is blue. In the constellation Ophiochus there is a similar system of double stars, one of which is red and the other blue. The same peculiarity exists in the constellation of the Dragon. In a double star of the constellation of the Bull, there is a
- 43. red sun, and a blue sun. There are double solar systems red and blue; such are the constellations Hercules and Cassiopœia. Other double solar systems are yellow and green, and sometimes yellow and blue. In all the worlds which are illuminated by these coloured suns, the effect of light must be very strange. No painter could represent them, and indeed we, who know only the white light of our own sun, cannot form any idea of them. Theophilus. These features of the stellar worlds are very interesting, and I am glad to learn them. But are we not straying from our subject? The Author. No. After having made you understand that the solar system which we inhabit is only a member of an immense family of other solar worlds, only a small fraction of the universe, I wished to show you by the diversity of those worlds, the facility with which nature varies the forces and the physical conditions proper to the stellar worlds, and consequently the living and inanimate types which make a portion of these different stellar worlds. Now that you understand the prodigious diversity of the solar worlds which compose the universe, I will go on to our principal object. I have not lost sight of my intention of proving to you that the universe has no limits, that in its extent it is really the Infinite. I am now approaching this great question. By the consideration of the stars, I am going to bring out into relief the immeasurable vastness of the universe. Let me speak, first, of the appalling distances which separate the stars from the earth, and the figures will show you that on that side we fall into the Infinite, and then I will speak of the numbers of the stars which people space; and on this side also the abyss of the Infinite will yawn before us. First, as to the distances which separate the stars from the earth, from whence we may logically infer the distances which separate these stars from one another. The distance between the earth and the sun is 38,000,000 leagues, and this shall be our unit, our standard of measurement, by which to estimate the distance of the stars.
- 44. I do not know, my dear Theophilus, whether you have formed an exact idea of this extent of 38,000,000 leagues, which lie between us and the sun. In general, we can only conceive prodigious distances such as astronomy deals with, by representing them by the interval of time which certain movable bodies known to us would consume in traversing them. Let us then have recourse to comparisons of this kind. A cannon-ball weighing 12 kilogrammes, exploded by 6 kilogrammes of powder, proceeding at a uniform rate of 500 metres a second, would take 10 years to travel from the earth to the sun. Supposing sound to travel at the same rate as on the surface of the air, and at a uniform rate, it would take 15 years to accomplish this journey. If a railway were laid through space between the earth and the sun, a train travelling at express speed, 12½ leagues an hour, would not arrive at its destination until the end of 338 years. This imaginary train, if dispatched from the earth in January, 1872, would arrive at the sun in the year 2210. The light from the sun, which travels 77,000 leagues in a second, takes 7 minutes 13 seconds to reach the earth. Theophilus. The distance between the earth and the sun is, then, 38,000,000 miles—that is our unit of measurement for the distances of the stars. Now let us hear about these distances. The Author. I will deal first with those stars which are nearest to us. One of these is a star in the constellation of the Swan. This star is distant from the earth 551,000 times our unit of measurement, that is to say, that we must multiply 551,000 times the distance of the earth from the sun to represent the distance of the star which we are considering, and yet it is one of the nearest to the earth. If we wish to represent this distance by the time occupied in the transit of light, supposing this light to travel, like that of our sun, 77,000 leagues a second, it would take 9½ years to travel from the star to us. Now, if you wish to know the distance of other stars, and remember that I only speak of the nearest, look at this table, which I found in
- 45. an astronomical treatise: DISTANCE OF CERTAIN STARS FROM THE EARTH. Names of the Stars. Distances from the Earth. Time of transit of light. α Of the Swan 551,000 times 9 years and a half. α Of the Lyre 1,330,700 21 years. α Of the Great Dog 1,375,000 22 years. α Of the Great Bear 1,550,800 25 years. Polar Star 3,678,000 50 years. Thus, the star α of the Lyre is distant from us more than 1,330,000 times as far as the earth is from the sun, and its light takes 21 years to reach us. If, by any celestial catastrophe, star α of the Lyre were to disappear, to be annihilated, we should still see it for 21 years, as its light takes that time to reach us. Theophilus. It is then possible that our astronomers are now observing stars which no longer exist, and are only visible to us because the light which they omitted is still travelling towards the earth. The Author. Just so. But to continue. I have begun with the stars which are nearest to the earth. There are the stars of first and second magnitude. You know, I suppose, the signification of those terms first, second, and third magnitude in astronomy? Theophilus. Yes, I know that the word magnitude is only applied to the luminous appearance of the star, and not to its real bulk. A star of the first magnitude is one which forms part of the group of the most luminous stars; a star of the second magnitude is one which comes next in point of brilliancy. The Author. You must bear in mind that the word magnitude signifies in astronomy the opposite of that which it expresses. The more luminous a star appears to us, the nearer it is to us; the paler and
- 46. less visible, the farther it is away. The brilliance diminishes in proportion as the figure increases. This is an introversion of terms, sufficiently exceptional to be taken note of, and it ought to be remembered, for fear of mistakes. Hitherto we have considered only stars of the first and second magnitudes. Those of the third, fourth, fifth, and sixth, lead us to the contemplation of such immense distances, that the unit which we have adopted, enormous as it is, is no longer of use. The instruments of celestial observation which may be applied to the examination and measurement of stars of the first and second magnitudes, do not serve for stars of the third and following magnitudes, and, because the small visible diameter of those stars make them appear mere specks of light, measuring instruments are equally inapplicable to them. In estimating the distances of the stars after the third magnitude, a method of comparison, based on the amplifying power of the telescopes successively used, is employed. I cannot enter into details of this method, which we owe to Sir William Herschel, but must content myself with explaining its results, which are as follows in the case of stars of the sixth magnitude. From certain stars of that class, light would take 1042 years to reach us: from others it would take 2700. After the sixth magnitude, the stars can only be discerned by the aid of the telescope, and their distances become perfectly stupefying in immensity. Certain of these telescopic stars are so far from the earth, that their light can only reach us in 5000, and even 10,000 years after it leaves the luminous centre. From the stars of the last category (fourteenth magnitude), light would take 100,000 years to reach the earth, supposing it to travel at the same rate as the light of our sun, i.e., 77,000 leagues per second. Theophilus. But, if we are to accept the results of the labours of recent naturalists, man exists on the earth only within 100,000 years, and some of those stars may have been extinct during all that time, so that the human race may have been contemplating stars no longer in being for 100,000 years. To what strange consequences does such a science lead us!
- 47. The Author. Yes, the luminous rays which these stars send us from the deepest depths of space may perhaps be emanations from solar systems no longer in existence. The present shows us only the past. There may be stars so profoundly lost in immensity, that their light has not yet had time to reach us. They exist, but we cannot see them, not because the telescope could not discover them, but because thousands of centuries are required for the journey of their luminous rays to our earth, and those thousands of centuries have not yet elapsed; so that this grand spectacle is reserved, in that awfully remote future, for our descendants. And now, my friend, will you not acknowledge with me, that the universe, considered merely by the distances which separate us from the stars, and the stars from each other, is truly the Infinite? Theophilus. Yes, it is the Infinite which unfolds itself before my eyes. Let me breathe a moment. The Author. If we contemplate the number of the stars, we shall also have the perspective of the Infinite. It is easy to reckon those of the first magnitude, i.e., the nearest to us. They are 20. Those of the second magnitude are 65; of the third, 170. The number of the stars increases as their visibility diminishes, in a very rapid proportion. The number of stars of each class of visibility, in apparent magnitude, is three times greater than that of the stars of the preceding class. There are 500 stars of the fourth, 1500 of the fifth, 4500 of the sixth magnitudes. The stars visible by the naked eye are 6000 in number. A practised eye can succeed in counting the 6000 stars in the two hemispheres. But the telescope enables us to push the numbering of the suns much farther: it opens up to us the depths of the heavens. Instead of the small number of stars which our eyes can see, it shows us a myriad of others, so thickly thronged together that they seem to cover the sky with fine silver sand. Here, for instance (fig. 6), is the aspect which one corner of the constellation of Gemini presents to the naked eye. And here is the same portion of the sky seen by the telescope. By the aid of this wonderful instrument stars of the
- 48. Fig. 6.—A Corner of the Constellation of Gemini. thirteenth and fourteenth magnitudes have been distinguished. The number of stars of the twelfth magnitude is 9,556,000, which, joined to the number of the same stars proper to the preceding categories, gives a total of more than 14,000,000. In the third magnitude, a total number of 42,000,000 of stars is counted. Thus, reckoning those visible to the naked eye, and by the telescope, we have 56,000,000 of suns, and we stop at this number only because the telescope does not enable us to see smaller stars than those of the fourteenth magnitude. But, let the telescope be brought to greater perfection, and the whole region of the sky will be seen to be covered with this silver sand, with this diamond dust, of which each grain is a sun. And such will be the accumulation of these suns, in the depths of space, that nothing will be seen on the field of the telescope but a luminous network, formed by the agglomeration of the suns, which will appear to touch each other.
- 49. Fig. 7.—A Corner of the Constellation of Gemini, seen through the telescope. Theophilus. The Infinite is beginning again. Let me shut my eyes. The Author. Wait, I have not said all, I have only begun. I am coming to the nebulæ. Here, indeed, you may expect to grow giddy. The telescope has dispersed all the theories on which the different explanations of the nebulæ were built, and has shown us that they are collections of stars, which, in consequence of their excessive number, and their closeness to each other, appear to form a whole, a single vague and continuous brightness. But, when their dimensions and distances are amplified by the telescope, this diffused light transforms itself into a brilliant point, analogous to that presented by the sky, tapestried with small stars, in the same telescope. These nebulæ are groups of enormous numbers of stars, and even their nearness to each other is only in appearance. They are, in reality, separated by enormous distances, and it must not be supposed that they are all in the same plane; they belong, on the contrary, to very
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