146 REASONING. 



it tends but little to give a deductive character to any science as a 

 w^hole ; 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 general- 

 izations are continually taking place, is still in the main an experimen- 

 tal science ; 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 generalization, which, though relating to one of the 

 subordinate aspects of chemical phenomena, possesses within its limited 

 sphere this comprehensive character ; 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 experiment has been_ tried, con- 

 stitutes 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 ex- 

 perimental to deductive, mostly consist in establishing, either by de- 

 duction or by direct experiment, that the varieties of a particular 

 phenomenon unifonnly accompany the varieties of some other phe- 

 nomenon better known. Thus the science of sound, which pre-^dously 

 stood in the lowest rank of merely experimental science, became de- 

 ductive when it was proved by experiment that every variety of sound 

 was consequent upon, 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 followed that every relation 

 of succession or coexistence which obtained between phenomena of the 

 more known class, obtained also between the phenomena vvhich cor- 

 responded to them in the other class. Every sound, being a mark of 

 a particular oscillatory motion, became a mark of everything which, by 

 the laws of dynamics, was known to be inferrible from that motion ; 

 and evei'ything which by those same laws was a mark of any oscilla- 

 tory motion, became a mark of the corresponding sound: And thus 

 many truths, not before suspected, concerning sound, became deduci- 

 ble from the known laws of the propagation of motion through an elas- 

 tic medium ; while facts already empirically known respecting sound, 

 became an indication of corresponding properties of vibrating^ bodies, 

 previously undiscovered. 



But the grand agent for transforming experimental into deductive 

 sciences, is the science of number. The properties of nujnbers, alone 

 among all known phenomena, are, in the most rigorous sense, jiroper- 

 ties of all things whatever. All things are not colored, or ponderable, 

 or even extended ; 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 infi- 

 nite, and admit of indefinite extension. 



These truths, although afiirmable of all things whatever, of coiirse 

 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, corre- 



