308 J. LeConte—Horizontal Motions of small 
. 
same however much the film is extended, and the tension at 
any point is the same in all directions.” 
M. Simon (of Metz),* confirmed as they have been e 
experimental researches of Béde,—do not seem to h 1s 
turbed co in the essential validity of the fundamental 
inconsistencies of the theory, revealed in the remarkable post- 
umous memoir of M. G. Wertheim,+ do not seem to have 
attracted the attention which they deserve. The results ob- 
tained by the last mentioned experimenter, Prof. J. P. Nichol} 
regards as invalidating the basis of the mathematical theory, 
and he maintains that the whole subject needs to be re-investl- 
gated under a fuller and wider view of the conditions of the 
physical problem. 
Indeed, it is very evident, that notwithstanding the classical 
researches of Laplace, Gauss and Poisson, and the more recent 
investigations of Dupré and Maxwell, the mathematical theory 
of capillarity presents difficulties which have not yet been fully 
- surmounted. In common with many other problems in molec- . 
ular physics, we here encounter difficulties and uncertainties 
originating in the different physical interpretations of the math- 
ematical processes and their results. They involve the consid: 
eration of the true signification of mathematical results which 
are known to have been reached by processes which are 
not rigorously exact, Many of the differential equations are 
utterly unmanageable and incapable of integration unless cel 
tain assumptions are made. Hence questions arise in relation © 
ao 
* Ann, de Chim, et de Phys., III, vol. xxxii, pp. 5-41, 1851 
+ Ann. de Chim. et de Phys., III, vol. lxiii, pp. 129-201, 1861. __ ; 
¢ Cyc. of the Physical Sciences, Article *Capillarity,” Third Edition, 1868. 
