LOCOMOTION AND TRANSPORT. 



more uniformly diffused ; and the extent of the diffusion which 

 may be thus effected, compatibly with the same degree of inter- 

 course, will be, to use an arithmetical phrase, in the direct 

 proportion of the square of the speed of locomotion. 



24. The common average of the speed of diligences in France and 

 other parts of the Continent is two leagues, or about five miles, an 

 hour. The speed of stage-coaches in England, before the esta- 

 blishment of railways, did not average eight miles an hour. 

 According to the principle just explained, it would follow that the 

 same degree of intercourse could be kept up in England in a space 

 of sixty-four square miles, which in France could be maintained 

 only within twenty-five square miles. Since the establishment of 

 railways the average speed upon these lines of communication, on 

 most parts of the Continent and in America, is fifteen miles an 

 hour. By this improvement, so far as it has been carried, as 

 compared with diligences, the area of practical communication, or, 

 what is the same, of the diffusion of the population compatible 

 with a given degree of intercourse, has been augmented in the 

 ratio of the square of five to the square of fifteen ; that is, in a 

 ratio of twenty-five to two hundred and twenty-five. In other 

 words, the same degree of intercourse can 1;3 maintained by means 

 of the present railways within an area of two hundred and twenty- 

 five square miles, as could be previously maintained by diligences 

 within an area of twenty -five square miles. 



But in England, where the average speed of railway transit is 

 much greater, this power of diffusion is proportionally increased. 

 Assuming the average speed on English railways at twenty-five 

 miles an hour, which is less than its actual amount, the power of 

 intercommunication thus obtained will bear to that obtained on 

 the Continent of Europe where railways are in operation, the 

 ratio of the square of twenty-five to the square of fifteen ; that 

 is, of six hundred and twenty-five to two hundred and twenty- 

 five, or of twenty-five to nine. 



Thus, the English railways afford the same facilities of commu- 

 nication within an area of twenty-five square miles as is afforded 

 by the continental railways within an area of nine square miles ; 

 and thus, by augmenting the speed from fifteen to twenty-five 

 miles an hour, the practical convenience to the public is aug- 

 mented in the ratio of twenty-five to nine, or very nearly as three 

 to one. 



25. The importance of good internal communications in military 

 affairs has long been acknowledged. By the possession of such 

 means of transport as may enable a body of troops, with their 

 arms and ammunition, to be transported promptly and rapidly 

 from one part of the country to another, the standing army, 



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