EVIDENCE PKOVING THE STATEMENT OF THE CASE 43 



It is like attempting to solve the problem : if one 

 purchases 100 cheeses for 100, how many watches 

 can one purchase for one shilling? Nay, more, what 

 is there in Nature which can be expressed in the terms 

 of a distance squared ? Space is continuous, it cannot 

 be squared. The surface of an object existing in space 

 can be squared, but only in the same sense can it be 

 done in Nature as we count the squares on a chess- 

 board. Given so many areas of eight, and repeat those 

 areas eight times, or add them together eight times, 

 and we have 64 areas. Now let us amplify the idea. 

 Suppose we could ascertain how many molecules, that 

 is the exposed surface of those molecules, there are in 

 each square, and suppose each square contained the 

 same number of molecules, then it would be the 8# 

 number of molecules multiplied eight times, or added 

 together eight times = 64$ molecules. And this is 

 the only way Nature recognizes mathematics. 



Illustrations might be multiplied to almost any extent. 

 Thus to multiply specific heat by atomic weight is like 

 multiplying three pint measures by three pounds weight. 

 The natural answer is always readily given by experi- 

 ments. If we take the contents of three pint measures 

 and three pound weights and try to multiply them 

 together we fail. If we try to conceive what is meant 

 by the square of a second ( 2 ), again the mind fails. Truly 

 does Dr. Lodge, an eminent mathematician, state, " The 

 height fallen by a dropped body is not proportional to 

 the time simply, but to what is rather absurdly called the 

 square of the time, i.e. the time multiplied by itself." 1 



When we see the ^ 2 , or whatever the symbol may 



i "Pioneers of Science," Prof. 0. Lodge, F.R.S., 1893, p. 82. 

 The italics are ours. 



