AIMS, ETC., OF SCIENTIFIC THOUGHT, 101 



between exactness and universality. It is found that the deviation, if 

 it exists, must he nearly proportional to the area of the triangle. So 

 that the error in the case of a triangle whose sides are a mile long 

 would be obtained by dividing that in the case I have just been con- 

 sidering by four hundred quadrillions ; the result must be a quantity 

 inconceivably small, which no experiment could detect. But between 

 this inconceivably small error and no error at all, there is fixed an 

 enormous gulf the gulf between practical and theoretical exactness, 

 and what is even more important, the gulf between what is practically 

 universal and what is theoretically universal. I say that a law is 

 practically universal which is more exact than experiment for all cases 

 that might be got at by such experiment as we have. We assume 

 this kind of universality, and we find that it pays us to assume it. 

 But a law would be theoretically universal if it were true of all cases 

 whatever; and this is what we do not know of any law at all. 



I said there were two ways in which a law might be inexact. 

 There is a law of gases which asserts that when you compress a perfect 

 gas the pressure of the gas increases exactly in the proportion in which 

 the volume diminishes. Exactly; that is to say, the law is more accu- 

 rate than the experiment, and experiments are corrected by means of 

 the law. But it so happens that this law has been explained; we 

 know precisely what it is that happens when a gas is compressed. 

 We know that a gas consists of a vast number of separate molecules, 

 rushing about in all directions with all manner of velocities, but so that 

 the mean velocity of the molecules of air in this room, for example, is 

 about twenty miles a minute. The pressure of the gas on any surface 

 with which it is in contact is nothing more than the impact of these 

 small particles upon it. On any surface large enough to be seen there 

 are millions of these impacts in a second. If the space in which the gas 

 is confined be diminished, the average rate at which the impacts take 

 place will be increased in the same proportion ; and, because of the 

 enormous number of them, the actual rate is always exceedingly close 

 to the average. But the law is one of statistics ; its accuracy depends 

 on the enormous numbers involved ; and so, from the nature of the case, 

 its exactness cannot be theoretical or absolute. 



Nearly all the laws of gases have received these statistical expla- 

 nations; electric and magnetic attraction and repulsion have been 

 treated in a similar manner ; and an hypothesis of this sort has been 

 suggested even for the law of gravity. On the other hand, the man- 

 ner in which the molecules of a gas interfere with each other proves 

 that they repel one another inversely as the fifth power of the dis- 

 tance; so that we here find, at the basis of a statistical explanation, a 

 law which has the form of theoretical exactness. Which of these 

 forms is to win ? It seems to me, again, that we do not know, and that 

 the recognition of our ignorance is the surest way to get rid of it. 



The world, in general, has made just the remark that I have attrib- 



