BY SUEFACES OF A HYPOTHETICAL CLASS INCLUDINO I’UE KI>IJl*SOnj. II 
hence the second and third terms of (13.) destroy one another; also \y^k=<p{li), and 
by (11.) ; thus (13.) becomes, finally, 
an 
Wh „ Wh 1 ,,, 
^(/0-w-^ = 0, ox-^=-<p{h). 
It follows that the equation Tyf[h) will be satisfied if f{h) be determined by the 
equation 
that is, if , r 
which is the theorem in question. This demonstration might have been given at the 
beginning of the investigation, and the theorem might have been made the foundation 
of the whole. But as there is nothing on the face of the assumed differential equations 
(•5.), art. 3, to suggest the possibility of satisfying the condition Dy(A)=0, the whole 
process would then have acquired the character of a verification^ rather than of a demon- 
stration following the natural order of discovery, in which latter form I wished it to 
appear. 
