TRAINS OF REASONING. 



H5 



§ 6. We can now understand how 

 an experimental may transform itself 

 into a deductive science by the mere 

 progress of experiment. In an ex- 

 perimental science, the inductions, as 

 we have said, lie detached, as a a 

 mark of 6, c a mark oi d, e a. mark of 

 /, and so on : now, a new set of in- 

 stances, and a consequent new induc- 

 tion, may at any time bridge over the 

 interval between two of these uncon- 

 nected arches ; b, for example, may 

 be ascertained to be a mark of c, 

 which enables us thenceforth to prove 

 deductively that a is a mark of c. 

 Or, as sometimes happens, some com- 

 prehensive induction may raise an 

 arch high in the air, which bridges 

 over hosts of them at once : b, d, f, 

 and all the rest, turning out to be 

 marks of some one thing, or of things 

 between which a connection has 

 already been traced. As when New- 

 ton discovered that the motions, 

 whether regular or apparently ano- 

 malous, of all the bodies of the solar 

 system (each of which motions had 

 been inferred by a separate logical 

 operation from separate marks) were 

 all marks of moving round a common 

 centre, with a centripetal force vary- 

 ing directly as the mass, and inversely 

 as the square of the distance from 

 that centre. This is the greatest 

 example which has yet occurred of 

 the transformation, at one stroke, of 

 a science which was still to a great 

 degree merely experimental, into a 

 deductive science. 



Transformations of the same nature, 

 but on a smaller scale, continually 

 take place in the less advanced 

 branches of physical knowledge, with- 

 out enabling them to throw off the 

 character of experimental sciences. 

 Thus with regard to the two un- 

 connected propositions before cited, 

 namely, Acids redden vegetable blues, 

 Alkalies make them green ; it is re- 

 marked by Liebig, that all blue 

 colouring matters which are reddened 

 by acids (as well as, reciprocally, all 

 red colouring matters which are ren- 

 dered blue by alkalies) contain nitro- 



gen : and it is quite possible that 

 this circumstance may one day furnish 

 a bond of connection between the two 

 propositions in question, by showing 

 that the antagonistic action of acids 

 and alkalies in producing or destroy- 

 ing the colour blue is the result of 

 some one, more general, law. Al- 

 though this connecting of detached 

 generalisations is so much gain, it 

 tends but little to give a deductive 

 character to any science as a whole ; 

 because the new courses of observa- 

 tion and experiment, which thus en- 

 able us to connect together a few 

 general truths, usually make known 

 to us a still greater number of uncon- 

 nected new ones. Hence chemistry, 

 though similar extensions and simpli- 

 fications of its generalisations are 

 continually taking place, is still in 

 the main an experimental science, 

 and is likely so to continue unless 

 some comprehensive induction should 

 be hereafter arrived at, which, like 

 Newton's, shall connect a vast num- 

 ber of the smaller known inductions 

 together, and change the whole 

 method of the science at once. Chem- 

 istry has already one great generalisa- 

 tion, 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 en- 

 abling us to a certain extent to fore- 

 see the proportions in which two 

 substances will combine, before the 

 experiment 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 pre- 

 viously obtained by experiment 



§ 7. The discoveries which change 

 the method of a science from experi- 

 mental to deductive mostly consist in 

 establishing, either by deduction or by 

 direct experiment, that the varieties 

 of a particular phenomenon uniformly 

 accompany the varieties of some other 



