AS A MENTAL OPERATION 13 



just mentioned its combining power. By bringing in- 

 ductive facts under principles it enables us to reach 

 further than induction, as in the case of the nature of 

 heatP Thirdly, it gives us a greater power of discovering 

 causation beyond experience, and that in two ways. 

 Sometimes we start from the effect and deduce its cause, 

 sometimes from the cause and deduce its effect : that is, 

 deduction is either analytic or synthetic. Sometimes, | 

 again, it may consist wholly of facts without causes, j 

 In short, deduction is full of variety. But, as we are 

 now about to treat it, it is no longer the simple deduc- ^ 

 tion of pure mathematics, but is interlaced with physical 

 experience and induction in such a way as to produce 

 a mixed method. 



The superiority of mixed method comes out conspicu- 

 ously in mixed mathematics, where deduction has more 

 empirical materials than in the pure mathematics of num- 

 bers and figures. For example, Galileo, as we have seen, 

 had a genius for observation and experiment. But no 

 amount of experience and induction could tell him that 

 a projectile moves in a parabola, because the curve in 

 which it moves is beyond experience. How then did he 

 make this discovery ? By combining the empirical and 

 deductive methods. He had induced that a body falls 

 in a straight line by gravity with a uniform acceleration, 

 so that the space is as the time squared. He had 

 experienced that a projectile is emitted in a straight 

 line, with what he concluded to be a uniform velocity 

 as the time. But this empirical knowledge could not 

 tell him in what line a projectile moves under the com- 

 bined action of both forces. He knew, however, by the 

 composition of forces, and by the Greek laws of conic 

 sections, that a body having a uniform velocity as the 

 time, and a uniform acceleration as the time squared, 



