THE DEDUCTIVE METHOD. 541 



And only when the induction which furnished the 

 premisses to the Deductive Method rested upon such 

 instances, has the application of such a method to the 

 ascertainment of the laws of a complex effect, been 

 attended with brilliant results. 



2. When the laws of the causes have been 

 ascertained, and the first stage of the great logical 

 operation now under discussion satisfactorily accom- 

 plished, the second part follows ; that of determining, 

 from the laws of the causes, what effect any given 

 combination of those causes will produce. This is a 

 process of calculation, in the wider sense of the term ; 

 and very often involves processes of calculation in 

 the narrowest sense. It is p. ratiocination; and when 

 our knowledge of the causes is so perfect, as to ex- 

 tend to the exact numerical laws which they observe 

 in producing their effects, the ratiocination may 

 reckon among its premisses the theorems of the 

 science of number, in the whole immense extent of 

 that science. Not only are the highest truths of 

 mathematics often required to enable us to compute 

 an effect, the numerical law of which we already 

 know; but, even by the aid of those highest truths, we 

 can go but a little way. In so simple a case as the 

 celebrated problem of three bodies gravitating towards 

 one another, with a force directly as their mass and 

 inversely as the square of the distance, all the re- 

 sources of the calculus have not hitherto sufficed to 

 obtain anything more than an approximate general 

 solution. In a case a little more complex, but still 

 one of the simplest which arise in practice, that of the 

 motion of a projectile, the causes which affect the 

 velocity and range (for example) of a cannon-ball may 

 be all known and estimated ; the force of the gun- 



