166 KEASONING. 



producing or destroying the color blue, is the result of some one, more 

 general, law. Although this connecting of detached genei'alizations is so 

 much gain, it tends but little to give a deductive character to any science 

 as a whole ; because the new courses of observation and experiment, which 

 thus enable us to connect together a few general truths, usually make 

 known to us a still greater number of unconnected new ones. Hence 

 chemistry, though similar extensions and simplifications of its generaliza- 

 tions are continually taking place, is still in the main an experimental sci- 

 ence; and is likely so to continue unless some comprehensive induction 

 should be hereafter arrived at, which, like Newton's, shall connect a vast 

 number of the smaller known inductions together, and change the whole 

 method of the science at once. Chemistry has already one great generali- 

 zation, which, though relating to one of the subordinate aspects of chemical 

 phenomena, possesses within its limited sphere this compi-ehensive charac- 

 ter; the principle of Dalton, called the atomic theory, or the doctrine of 

 chemical equivalents : which by enabling us to a certain extent to foresee 

 the proportions in which two substances will combine, before the experi- 

 ment has been tried, constitutes undoubtedly a source of new chemical 

 truths obtainable by deduction, as well as a connecting principle for all 

 truths of the same description previously obtained by experiment. 



^^-— § 7. The discoveries which change the method of a science from experi- 

 r mental to deductive, mostly consist in establishing, either by deduction or 

 \ by direct experiment, that the varieties of a particular phenomenon uni- 

 lyformly accompany the varieties of some other phenomenon better known. 

 Thus the science of sound, which previously stood in the lowest rank of 

 merely experimental science, became deductive when it was proved by ex- 

 periment that every variety of sound was consequent on, and therefore a 

 mark of, a distinct and definable variety of oscillatory motion among the 

 particles of the transmitting medium. When this was ascertained, it fol- 

 lowed that every relation of succession or co-existence which obtained be- 

 tween phenomena of the more known class, obtained also between the 

 phenomena which correspond to them in the other class. Every sound, 

 being a mark of a particular oscillatory motion, became a mark of every 

 thing which, by the laws of dynamics, was known to be inferable from 

 that motion ; and every thing which by those same laws was a mark of any 

 oscillatory motion among the particles of an elastic medium, became a mark 

 of the corresponding sound. And thus many truths, not before suspected, 

 concerning sound, become dedacible from the known laws of the propaga- 

 tion of motion through an elastic medium; while facts already empirically 

 known respecting sound, become an indication of corresponding properties 

 of vibrating bodies, previously undiscovered. 



But the grand agent for transforming experimental into deductive sci- 

 ences, is the science of number. The properties of number, alone among 

 all known phenomena, are, in the most rigorous sense, properties of all 

 things whatever. All things are not colored, or ponderable, or even ex- 

 tended ; but all things are numerable. And if we consider this science in 

 its whole extent, from common arithmetic up to the calculus of variations, 

 the truths already ascertained seem all but infinite, and admit of indefinite 

 extension. 



These truths, though aflSrmable of all things whatever, of course apply 

 to them only in respect of their quantity. But if it comes to be discovered 

 that variations of quality in any class of phenomena, correspond regularly 



