312 THE BORDERLAND OF SCIENCE. 



risen to 5,000,000? half a century hence to 10,000,000? 

 and so on. It is clear, at least, that if changes such as 

 these take place in the rate of increase, we have greatly 

 over-estimated in the above calculations the probable 

 duration of our coal supply. 



Mr. Stanley Jevons, in discussing the subject nine 

 years ago, took the increase of increase into account 

 with very startling results. He said: 'We, of course, 

 regard not the average annual arithmetical increase of 

 coal consumption, but the average rate per cent, of 

 increase, which is found by computation to be 3-26.' 

 Now, to illustrate the difference between this method 

 and the other, we shall not take the actual figures, 

 which are inconvenient for ready computation. Instead 

 of doing so, we shall compare two simple progressions. 

 One is the series 100, 110, 120, 130, 140, 150, and so 

 on, increasing by ten at each step ; the other is a pro- 

 gression increasing at the rate of ten per cent., and runs 

 thus: 100, 110, 121, 133 (not counting fractions), 

 146, 161, and so on. It will be observed that the cor- 

 responding terms of the two series differ more and 

 more from each other as we proceed : the difference is 

 but one at the third term, and amounts to eleven at the 

 sixth. It would be found to increase marvellously with 

 a few more steps. Now, the ' difference between Mr. 

 Stanley Jevons's method and Mr. Hull's is precisely 

 analogous; only that whereas the rate per cent, just 

 considered is ten, it is in the actual case about three 

 and a quarter. 



The fact really is, that the rate of increase corre- 



