376 
MONDAY, JANUARY 28, 1861. 
James Hentuorn Topp, D. D., President, in the Chair. 
Reap a letter from George M. Miller, Esq., announcing a donation of 
some osseous remains and antiquities, found in the works of the Great 
Southern and Western Railroad, near the King’s-Bridge Terminus. 
Parke Neville, Esq., C.E., presented an ancient sword, spear-head, 
and some human remains, found under the street opposite to St. Bride’s 
Church. 
It was moved by the Rev. 8. Haughton; seconded by the Rev. 
Joseph Carson, D. D., and 
Resotvep,—That it be recommended to the Council to lay a Report 
before the Academy with respect to the Cunningham Fund, including, — 
1. A history of the fund from its origin to the present time; 
2. A list of the recipients of the proceeds of that fund, and Cunning- 
ham Medallists; with a statement of the purposes for which they re- 
ceived such fund or medal: and that the Council be requested to lay 
before the Academy its views with respect to the best mode of ap- 
propriating the Cunningham Fund in future. 
MONDAY, FEBRUARY 11, 1861. 
James HentHorn Topp, D. D., President, in the Chair. 
James Foulis Duncan, M. D., Wyville Thomson, LL. D., and David 
Walker, M. D., were elected members of the Academy. 
The Rey. Ropert Carmicwazt, F.T.C. D., read a paper— 
ON THE GENERAL THEORY OF THE INTEGRATION OF NON-LINEAR PARTIAL 
DIFFERENTIAL EQUATIONS. 
A cometets theory of the genesis and solution of non-linear partial 
differential equations of the second and higher orders, in two or more 
independent variables, has been long a desideratum; and any conside- 
rable addition to our knowledge in this department of science can only 
be expected from the combined labours of those who have devoted some 
attention to this branch of the Integral Calculus. The following paper 
is intended as a small contribution towards the formation of such a 
theory. The solutions of non-linear partial differential equations are 
sought in the form of what are denominated ‘complete primitives,’ ex- 
hibiting arbitary constants, as contradistinguished from ‘ general primi- 
tives,’ exhibiting arbitrary functions. It is allowed that solutions in 
the latter form are more general; but then they are theoretically unat- 
tainable, unless in certain cases which, the equations being linear, admit 
of symbolic treatment, or which are susceptible of reduction by methods 
not universally applicable. The importance of the subject, partly in 
