Jan. 15, 1885] 



NA TURE 



243 



of the United Kingdom," from which Columns I. and V. 

 of the following table have been for the most part taken. 



Since the amounts of coal used are very large, and 

 great accuracy cannot be expected in inquiries of this 

 nature, it is convenient to take as the unit of our calcula- 

 tions 1,000,000 tons of coal instead of our ordinary unit, 

 the ton. This unit may be expressed in several different 

 ways : a cubic yard of anthracite weighs about 2700 lbs., 

 and of bituminous coal from 2090 to 2400 lbs., hence on 

 an average a cubic yard of coal weighs a ton ; and our unit 

 of 1,000,000 tons is a cubxal block of coal 100 yards each 

 way, or a bed of coal a mile square and a foot thick. 

 Column I. in the following table gives the annual output 

 of coal since 1854, and the total output during the thirty 

 years, which amounts to ;, 245, 100,000 tons. 



A few comparisons may enable the mind to grasp the 

 real meaning of these enormous figures. It was calculated 

 by Sir Henry Bessemer that the output of coal, 154,000,000 

 of tons for the single year 1881, would suffice to build 55 

 Great Pyramids, or to rebuild the Great Wall of China, 

 and to add a quarter to its length ! In 1883 the output 

 was i6j, 800,000 tons, which would form a column a mile 

 ind nearly 164 feet high ; or would build a wall 

 from London to Edinburgh 400 miles long, and 45 feet 

 9 inches high and thick, or another round the world 

 24,000 miles long, and 5 feet 1 1 inches high and thick : or, 

 if the Straits of Dover are 21 miles across and 600 feet 

 deep, would make an embankment across them 22 yards 

 wide : while the total output for the 30 years would build 

 a round column 9 feet 4 inches in diameter, which would 

 reach 240,000 miles high, the distance of the moon. 



The numbers show considerable fluctuations — as might 

 be expected from the variety of accidental circumstances, 

 such as new inventions, the mean annual temperature, and 

 the state of trade, which affect the amount of coal used — 

 but, on the whole, a very rapid increase ; the output for 



1875 being double of that for 1854, and that for 1883 

 double of that for 1862. 



If we assume that the increase in annual output would 

 be constant were it not for accidental circumstances, we 

 can represent the actual numbers, with fair accuracy, by 

 an arithmetical series of which the first term is 64-7, and 

 the last 151-7, the increase in annual output being 3, and 

 the total amount 3246 (Column II.). Further it has been 

 shown that the coal still available in 1884 is 144,700,000,000 

 tons, and we may assume that the output in 1884 will be 

 at least as great as that in 1883, or 163,800,000 tons. 

 Hence, if the output of coal continues to increase at the 

 rate of 3,000,000 tons annually, our supply will last for 261 

 years, or will be exhausted about A.D. 2145. 



But this calculation is open to several objections, and 

 the numbers as shown by Prof. Stanley Jevons may bear 

 a much more serious significance. 



It is improbable that the annual difference should 

 always remain the same, and in fact, in the calculated 

 series (Column 1 1.), while all the early terms are higher 

 than the real outputs, the later terms are lower, showing 

 that the difference itself probably increases. If we calcu- 

 late the series backwards we have no output at all about 

 21 years before 1854, a result we cannot agree with, and 

 for all years before 1833 a negative output, a result we 

 cannot understand. Hence it is probable that the results 

 may be better expressed by another kind of series. 



Theory and experience show that the same causes 

 always produce the same effects, unless fresh circum- 

 stances intervene to modify the effects produced. Thus 

 the population of England, which was about 9,000,000 in 

 1801, became 18,000,000 in 185 1, or doubled in 50 years ; 

 hence, if no new causes intervene, we should expect it to 

 double again in the next 50 years, or to become 36,000,000 

 in 1901. This is usually expressed by saying that social 

 statistics in general show uniform multiplication in uniform 

 periods, or obey the compound-interest law, or form a 

 geometrical series. As an example of this law let us 

 examine a little more closely the population of England 

 and Wales. The increase for each 10 years since 1 801 is 

 itself perpetually increasing, or the numbers must be ex- 

 pressed by a geometrical series of which the ratio is 

 nearly ri47, and not by an arithmetical scr>: . 



1 No 1 

 1S11 



1821 



184 I 

 I8 5 I 



Calculated 



147 



8S9 

 IO -20 



IK70 

 13 42 



15 39 

 17-65 

 2024 



2 V22 

 26-63 



From the dependence of the numbers representing the 

 annual output of coal upon the number of inhabitants, it 

 might be expected that they also can be expressed by a 

 geometrical series, and this has been shown by Prof. 

 Stanley Jevons to be the case. According to his calcula- 

 tions the ratio of the series is about 1-035, or t' le rate °f 

 increase of the output is about 3i per cent per annum, and 

 it may be assumed for the reason before given that the 

 sum of all the outputs is likely to be more approximately 

 correct than the single output for 1854 The annual out- 

 puts calculated from these data are given in Column III., 

 and show a fair approximation to the actual numbers, 

 though the first term is rather low, and the last six terms 

 are nearly as much above the true results as those in the 



