THE MEANING OF PERCEPTION 171 



compare them with, the masses of the same substance at other 

 times and places. And in identifying these chemical substances 

 we make use of measurements of space (colour, specific gravity, 

 vapour pressure, boiling-point, chemical properties in general, 

 which are all consequences of the positions of atoms within 

 molecules and of the movements of the atoms and the molecules), 

 and so on. To save time we may assume that the reader is 

 thoroughly conscientious, and desires to verify these statements ; 

 he will find that the results of the investigation of animate, 

 no less than inanimate, activities all reduce down to observation 

 of motions and measurement of displacements. 



But we shall not, or we shall very rarely, get differential 

 equations like we do when we investigate the ether and elec- 

 tricity and relativity, and so on. We may illustrate this by 

 considering growth. Think of a crystal of salt growing in ideal 

 conditions in a pure solution of sodium chloride: if we know the 

 length of one of its sides we can find its mass, thus : 





Mass=c (length) 3 , 



and the differential equation is - =2cZ 2 (where m=mass, 



dl 



Z=length of a side, and c is a constant depending on specific 

 gravity). Knowing the length of one side of the crystal, we can 

 predict its mass. 



We cannot do this with a growing animal. If it grew like 

 the crystal does, we could use the equations just given to find the 

 weight of the animal from a measurement of its length. We can- 

 not find this, as experiment will show, and all that we can do 

 is to make an empirical equation after we have measured both 

 length and mass. This equation will be : 



Mass=aZ+6Z 2 +cZ 3 -h 



where Z=the length, and some of the constants, a, 6, and c, may 

 be negative numbers. 



Go on now to a study of behaviour, and the same contrast 

 emerges. Nothing in the way of differential equations is ever 

 possible, and we cannot, in general, predict how a normal animal 

 will respond when we attempt to stimulate it to activity of 

 some kind or other. Yet we can think of a series of organic 

 responses which begin by showing a high degree of determinism 

 and end by failing to show any. 



