142 THE PRINCIPLES OF SCIENCE. 



and we can therefore in a certain sense figure to ourselves 

 elasticity a thousand or a million times greater than any 

 which is sensuously known to us. The waves of the ocean 

 are many times higher than our own bodies ; other waves, 

 we may observe, are many times less ; continue the pro 

 portion, and we may ultimately arrive at waves as small 

 as those of light. Thus it is that from a sensuous basis 

 the powers of mind enable us to reason concerning agents 

 and phenomena different in an unlimited degree. If no 

 hypothesis then can be absolutely opposed to sense, 

 accordance with experience must always be a question 

 of degree. 



In order that an hypothesis may allow of satisfactory 

 comparison with experience, it must possess a certain 

 defmiteness, and, generally speaking, a certain mathe 

 matical exactness allowing of the precise calculation of 

 results. We must be able to ascertain whether it does 

 or does not agree with facts. 



The theory of vortices, on the contrary, did not present 

 any mode of calculating the exact relations between the 

 distances and periods of the planets and satellites ; it 

 could not, therefore, undergo that rigorous testing to 

 which Newton scrupulously submitted his theory of 

 gravity before its promulgation. Vagueness and incapa 

 bility of precise proof or disproof often enables a false 

 theory to live ; but with those who love truth, such 

 vagueness should excite the highest suspicion. The up 

 holders of the ancient doctrine of Nature s abhorrence of 

 a vacuum, had been unable to anticipate the important 

 fact that water would not rise more than 33 feet in a 

 common suction pump. Nor when the fact was pointed 

 out could they explain it, except by introducing a special 

 alteration of the theory to the effect that Nature s ab 

 horrence of a vacuum was limited to 33 feet. 



