AS A MENTAL OPERATION 21 



tions either from facts to causes, or from causes to facts, 

 or first one and then the other, because analysis is the 

 ground of synthesis. The truth is that the explanatory 

 method is various, being sometimes from facts to causes, 

 and sometimes from causes to facts. Sometimes, again, 

 the premisses are hypothetical ; but sometimes they are 

 sound principles, as in Newton's Principia. 



Besides the mathematical, the empirical, and the ex- 

 planatory, Mill has yet a fourth method, the verificatory 

 method, which consists of principles, or sometimes hypo- 

 theses, followed by deductions and verifications. It is 

 another species of mixed induction and deduction, and a 

 famous example is supplied by the discovery of the planet 

 Neptune from the deflection of the planet Uranus from its 

 orbit round the sun. Herschel in 1781 had found Uranus 

 empirically by observing it through the telescope, and at 

 least two of its satellites. But Neptune was afterwards 

 discovered deductively. The law of gravitation, thanks 

 to Newton, had become a principle so firmly established 

 that it could be used to explain the deflections of planets 

 from their orbits by their gravitation to one another. 

 Thus some of the deflections of Uranus were explained 

 by its gravitation to Jupiter and Saturn. But there re- 

 mained other deflections on this or that side of its orbit. 

 It was therefore inferred that, as deflections are caused 

 by gravitation in the direction of deflection, and as 

 Uranus deflects in a given direction, it must be gravi- 

 tating to an unknown planet in the direction of deflec- 

 tion. So far deduction. Then came verification. 

 Adams and Leverrier, having each calculated the direc- 

 tion, the planet, since called Neptune, was actually 

 observed through the telescope in that direction. Thus 

 deduction was verified empirically. 



When we consider our liability to error both in 



