TRAINS OF REASONING. 115 



thing to connect a or b with c or d: we have a science of detached 

 and mutally independent generalizations, such as these, that acids 

 redden vegetable blues, and that alkalis color them green ; from 

 neither of which propositions could we, directly or indirectly, infer 

 the other : and a science, so far as it is composed of such propositions, 

 is purely experimental. Chemistry, in the present state of our knowl- 

 edge, has not yet thrown oft" this character. There are other sciences, 

 however, of which the propositions are of this kind : a a mark of Z», i a 

 mark of c, c of d, d of e, &c. In these sciences we can mount the 

 ladder from a to e by a process of ratiocination ; we can conclude 

 that a is a mark of e, and that every object which has the mark a has 

 the property e, although, perhaps, we never were able to observe a 

 and e together, and although even d, our only direct mark of e, may 

 be not perceptible in those objects, but only inferrible. Or varying 

 the first metaphor, we may be said to get from a to e underground : the 

 marks b, c, d, which indicate the route, must all be possessed somewhere 

 by tlie objects concerning which we are inquiring ; bat they are below 

 the surface : a is the only mark that is visible, and by it we are able 

 to trace in succession all the rest. 



§ 6. We can now understand how an experimental transforms itself 

 into a deductive science by the mere progress of experiment. In an 

 experimental science, the inductions, as we have said, lie detached, 

 as, a a mark of 6, c a mark of <Z, e a mark oif, and so on : now, a new 

 set of instances, and a consequent new induction, may at anytime 

 bridge over the interval between two of these unconnected 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 some- 

 times happens, some grand comprehensive 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 connexion has already been traced. As when New- 

 ton discovered that the motions, whether regular or apparently anom- 

 alous, of all the bodies of the solar system, (each of which motions had 

 been infeiTed by a separate logical operation, from separate marks,) 

 were all marks of moving round a common centre, with a centripetal 

 force varying directly as the mass and inversely as the square of the 

 distance from that centre. This is the greatest example which has yet 

 occun-ed of the transformation, at one stroke, of a science which was 

 still to a gieat degi-ee merely experimental, into a deductive science. 



Transfonnations of the same nature, but on a smaller scale, contin- 

 ually take place in the less advanced branches of physical knowledge, 

 without cna1)ling them to throw off the character of experimental 

 sciences. Thus with regard to the two unconnected propositions be- 

 fore cited, namely, Acids redden vegetable blues, Alkalis make them 

 green ; it is remarked by Liebig, that all blue coloring matters which 

 are reddened by acids (as well as, reciprocally, all red coloring matters 

 which are rendered blue by alkalis) contain nitrogen : and it is cjuite 

 possible to conceive that this circumstance may one day funiish a bond 

 of connexion bet^vcen the two propositions in question, by showing 

 that the antagonist action of acids and allcalis in producing or destroy- 

 ing the color blue, is the result of some one more general law. 

 Although this connecting of detached generalizations is so much gain, 

 T 



