ch. ix.] PHILOSOPHY AS AN ORGANON. 237 



imparted by systematic instruction is quite incontestable. 

 Doubtless it is by long-continued practice that men learn to 

 paint pictures, to mould statues, and to compose oratorios or 

 symphonies. But it is none the less probable that Mozart 

 and Beethoven would have accomplished comparatively little 

 without the profound study of harmony; and in painting 

 and sculpture the " originality of untaught geniuses " is, not 

 unjustly, made a subject for sarcasm. It is therefore useless 

 for Macaulay to remind us that men reasoned correctly long 

 before Bacon had drawn up his elaborate canons of induc- 

 tion ; or for Comte to appeal to rhetoric, grammar, and 

 aesthetic art in support of the opinion that we need no 

 general doctrine of logic. 



To take a concrete example, — if, as in Borda's experiment, 

 you make a simple pendulum oscillate thirty hours in an 

 exhausted receiver, by diminishing the friction at the point 

 of support, and proceed to infer that with the total abolition 

 of friction and atmospheric resistance the pendulum would 

 oscillate for ever, it may not be essential to the validity of 

 your inference that you should understand the character of 

 the particular logical method which you are employing. 

 Nevertheless it cannot but be of advantage to you to know 

 that you are using the " method of concomitant variations," 

 and to understand on general principles the conditions under 

 which this method may be employed and the precautions 

 required in order to make it valid. For want of such general 

 knowledge of method, even trained physicists not unfre- 

 quently make grave errors of inference, applying some 

 powerful implement of research in cases where interfering 

 circumstances, not sufficiently taken into account, render it 

 powerless. Thus the method just alluded to, of varying the 

 cause in order to observe and note the concomitant variations 

 of the effect, is a very powerful instrument of induction ; 

 but in order to use it effectively, we need to bear in mind 

 two things. First, we need to know the quantitative relation 



