EXAMPLES OF THE FOUR METHODS. 307 



of the precession of the equinoxes resulted as a residual phenomenon, from 

 the imperfect explanation of the return of the seasons by the return of the 

 sun to the same apparent place among the fixed stars. Thus, also, aberra- 

 tion and nutation resulted as residual phenomena from that portion of the 

 changes of the apparent places of the fixed stars which was left unaccounted 

 for by precession. And thus again the apparent proper motions of the stars 

 are the observed residues of their apparent movements outstanding and 

 unaccounted for by strict calculation of the effects of precession, nutation, 

 and aberration. The nearest approach which human theories can make to 

 perfection is to diminish this residue, this caput mortuum of observation, 

 as it may be considered, as much as practicable, and, if possible, to reduce 

 it to nothing, either by showing that something has been neglected in our 

 estimation of known causes, or by reasoning upon it as a new fact, and on 

 the principle of the inductive philosophy ascending from the effect to its 

 cause or causes." 



The disturbing effects mutually produced by the earth and planets upon 

 each other's motions were first brought to light as residual phenomena, by the 

 difference which appeared between the observed places of those bodies, and 

 the places calculated on a consideration solely of their gravitation toward the 

 sun. It was this which determined astronomers to consider the law of gravi- 

 tation as obtaining between all bodies whatever, and therefore between all 

 particles of matter ; their first tendency having been to regard it as a force 

 acting only between each planet or satellite and the central body to whose 

 system it belonged. Again, the catastrophists, in geology, be their opinion 

 right or wrong, support it on the plea, that after the effect of all causes now 

 in operation has been allowed for, there remains in the existing constitu- 

 tion of the earth a large residue of facts, proving the existence at former 

 periods either of other forces, or of the same forces in a much greater de- 

 gree of intensity. To add one more example : those who assert, what no 

 one has shown any real ground for believing, that there is in one human 

 individual, one sex, or one race of mankind over another, an inherent and 

 inexplicable superiority in mental faculties, could only substantiate their 

 proposition by subtracting from the differences of intellect which we in 

 fact see, all that can be traced by known laws either to the ascertained 

 differences of physical organization, or to the differences which have ex- 

 isted in the outward circumstances in which the subjects of the comparison 

 have hitherto been placed. What these causes might fail to account for 

 would constitute a residual phenomenon, which and which alone would be 

 evidence of an ulterior original distinction, and the measure of its amount. 

 But the asserters of such supposed differences have not provided them- 

 selves with these necessary logical conditions of the establishment of their 

 doctrine. 



The spirit of the Method of Residues being, it is hoped, sufiiciently in- 

 telligible from these examples, and the other three methods having already 

 .been so fully exemplified, we may here close our exposition of the four 

 methods, considered as employed in the investigation of the simpler and 

 more elementary order of the combinations of phenomena. 



§ 6. Dr. Whewell has expressed a very unfavorable opinion of the utili- 

 ty of the Four Methods, as well as of the aptness of the examples by which 

 I have attempted to illustrate them. His words are these :* 



* Philosophy of Discovery, pp. 263, 264y 



