124 THE PRINCIPLES OF SCIENCE. 



observation will become perceptible or great under ex 

 treme circumstances. When the variable in our empirical 

 formula is small, we are justified in overlooking the exist 

 ence of higher powers, and taking only two or three of 

 them. But as the variable increases, those higher powers 

 gain in importance, and in time will yield the principal 

 part of the value of the function. 



This is no mere theoretical inference. Excepting the 

 few great primary laws of nature, such as the law of 

 gravity, the conservation of energy, &c., there is hardly 

 any natural law which we can trust in circumstances 

 widely different from those with which we are practically 

 acquainted. From the expansion or contraction, fusion 

 or vaporisation of substances by heat at the surface of the 

 earth, we can form a most imperfect notion of what would 

 happen near the centre of the earth, where the pressure 

 must almost infinitely exceed anything possible in our 

 experiments. The physics of the earth again give us 

 a feeble, and probably often a misleading, notion of a body 

 like the sun, in most parts of which an almost incon 

 ceivably high temperature is united with an inconceivably 

 high pressure. If, as is probable, there are in the realms 

 of space many nebulae consisting of incandescent and 

 unoxydized vapours of metals and other elements, so 

 highly heated perhaps that chemical composition is out 

 of the question, we are hardly able to treat them as 

 subjects of scientific inference. Hence arises the great 

 importance of any experiments in which we can investi 

 gate the properties of substances under extreme circum 

 stances of cold or heat, density or rarity, intense electric 

 excitation, &c. It should be observed that this insecurity 

 in extending our inferences wholly arises from the purely 

 approximate character of our measurements. Had we 

 the power of appreciating indefinitely small quantities, 

 we should by the principle of continuity discover some 



