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 

 heat 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. 

 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, 



