TRANSACTIONS OF SECTION F. 777 



supply of perishable food articles had aggravated the differences of prices, and it 

 would be dangerous for India and the colonies to depend on increased food .exports, 

 but they must extend other branches of trade. He pointed out that India and 

 the colonies required an immense extension of railways and waterworks. As to 

 India, he said there was one mile of railway to 20,000 people with a revenue of 

 about Is. 6d. ner head per annum, and with the Government expending about as 

 much on extensions. In connection with colonial development he advocated repro- 

 ductive emigration, that every man who had a free passage should be taxed for its 

 repayment, so that the fund should constantly be employed in sending out more 

 ■emigrants, 



6. The Mathematical Theory of Banking. 

 By F. Y. Edgewoeth, M.A., F.8.S. 



The higher mathematics make two contributions to social economy — the cal- 

 •culus of probabilities and what we may, after Jevons, call the calculation of utility. 

 Of these branches the former is more fruitful ; and, as it has been cultivated by the 

 most distinguished mathematicians, so it appears at first sight to belong to the 

 ■same genus as physics. But, when we examine the root and ground from which 

 it springs, the science whose object is the calculation of credibility is found to be 

 nearly as speculative as the other branch of mathematics applied to human affairs. 

 They both are developed from somewhat conjectural first principles, and they 

 yield, for the most part, very hypothetical conclusions. We gather from them, 

 rather appropriate general ideas, than results immediately applicable to practice. 



I. Probability is the foundation of banking. The banker contracts liability to 

 pay amounts which he never could pay if all his creditors should at the same time 

 ■demand full payment. His solvency and profits depend upon the probability that 

 he will not be called on to meet at once more than a certain amount of his lia- 

 bilities. There is involved not only the calculation of averages — which is an affair 

 of arithmetic — but also the doctrine of deviations from an average, of errors, which 

 iias exercised the ablest mathematicians. The general theory is that, when any 

 quantity fluctuates under the influence of a number of independent causes, the 

 values assumed from time to time by the variable quantity occur each with a fre- 

 quency which fulfils a certain mathematical law — the so-called Imo of error. 



The following experiment, which the writer has partially performed, illus- 

 trates the principle. Take at random a hundred digits from the pages of a 

 mathematical table or statistical journal, and add them together. This aggi'egate 

 may be regarded as formed by a hundred independent agencies. Accordingly, 

 sums thus formed will fluctuate about their mean value (450) according to the 

 normal law. The probability of any such sum deviating in excess or defect 

 to the extent of 42 from the mean 450 is about ^. The probability of a devia- 

 tion twice as great is about ^^o' ^°^ the odds are about fifty thousand to one that 

 the limits 576 and 324 will not be passed. It is upon this principle that the 

 •anthropologist, armed with the formulae of Quetelet, could, by inspecting some 

 samples of a new race, determine the probability that there should be found 

 •among a thousand taken at random from them a single six-footer or a dozen 

 whose average height is six feet. Now the variables with which the banker is 

 concerned, such as the amount of notes remaining out in the hands of the public 

 and the demands on the reserve, depend in ordinary times upon a multeity of causes, 

 the fortunes and actions of the bank's numerous customers. Accordingly the 

 theoretical banker, interpreting experience by mathematics, can calculate with 

 nicety the chance that the demands on him in the immediate future will ex- 

 ceed a certain extent. Ideally in the planet Saturn, the banker may determine the 

 probability of demands of different extent, and make such arrangements, that to 

 -demands of different probability may correspond different degrees of facility in 

 meeting them. The use and beauty of this ideal arrangement are somewhat marred 

 when we descend to the affairs of Earth. The fluctuations of banking business 

 are not entu'ely subject to the rules of chance. They have been partly reduced 

 ■to law. There is a tide in the affairs of business men. There are periodical 



