TRAINS OF REASONING. 165 



sciences which can be made Deductive, and those which must as yet re- 

 main Experimental. The difference consists in our having been able, or 

 not yet able, to discover marks of marks. If by our various inductions we 

 have been able to proceed no further than to such propositions as these, a 

 a mark of J, or a and h marks of one another, c, a mark of J, or c and 4 

 marks of one another, without any thing to connect a or b with c or d; we 

 have a science of detached and mutually independent generalizations, such 

 as these, that acids redden vegetable blues, and that alkalies 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 proposi- 

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

 knowledge, has not yet thrown off this character. There are other sci- 

 ences, however, of which the propositions are of this kind : a a mark of h, 

 h a mark of c, c of d, d of e, etc. Jn these "sciences we can mount the lad- 

 der 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 al- 

 though even d, our only direct mark of e, may not be perceptible in those 

 objects, but only inferable. Or, varying the first metaphor, we may be 

 said to get from a to e underground : the marks h, c, d, which indicate the 

 route, must all be possessed somewhere by the objects concerning which 

 we are inquiring ; t)ut 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 may transform itself 

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

 mental science, the inductions, as we have said, lie detached, as, a a mark of 

 ft, e a mark of d, e a mark oif, and so on : now, a new set of instances, and 

 a consequent new induction, may at any time bridge over the interval be- 

 tween two of these unconnected ai'ches ; 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 comprehensive induc- 

 tion 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 Newton discovered that the motions, whether regular or apparently 

 anomalous, 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 

 varying 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 gi"eat de- 

 gree 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, without 

 enabling them to throw off the character of experimental sciences. Thus 

 with regard to the two unconnected propositions before cited, namely, 

 Acids redden vegetable blues. Alkalies make them green ; it is remarked by 

 Liebig, that all blue coloring matters which are reddened by acids (as well 

 IS, reciprocally, all red coloring matters which are rendered blue by alka- 

 ies) contain nitrogen : and it is quite possible that this circumstance may 

 me day furnish a bond of connection between the two propositions in 

 question, by showing that the antagonistic action of acids and alkalies in 



