MATHEMATICAL SECTION. 135 
above and infinite relatively to orders below. A volume is inte- 
grated from surfaces, a surface from lines, and a line from points. 
Each integral is infinite relatively to the magnitudes from which 
it is integrated. As momentum is integrated from motion-genera- 
ting force, it is infinite relatively thereto. Momentum may also be 
dissipated by infinitesimal decrements; and it is possible that mo- 
mentum is always thus dissipated and re-integrated whenever 
motion is communicated from one body to another; but the prin- 
ciples of mathematics are equally consistent with the hypothesis 
that actual contact sometimes occurs, in which case motion is di- 
rectly. and instantaneously transmitted without dissipation or re- 
integration. Granting that infinitesimal time requires infinite force, 
momentum satisfies that condition. 
This paper gave rise to considerable discussion, in which Messrs. 
Taytor, Hitt, KuMMELL, and Leravour maintained the legiti- 
macy of the notion of infinitesimals as real elements out of which 
quantity is built up; Messrs. E:xiorr, DooLitrrye, and FarquHaR 
took the opposite ground, preferring the Newtonian view of the 
Calculus; while Mr. Curistixn, while preferring the infinitesimal 
method, maintained that no evaluation of continuous quantity, in 
terms of units as it must necessarily be, could ever be precise or 
entirely satisfactory, to however small a compass the uncertainty be 
reduced. Mr. CurisTIE also pointed out some paradoxes to which 
the usual definitions of curves and tangents appeared to lead. 
Mr. Exiorr then exhibited some tables to serve as a perpetual 
calendar, and gave a full explanation how by means of them the 
day of the week corresponding to that of the month for any year, 
New or Old Style, B. C. or A. D., could be found. 
5tH MEETING. May 23, 1883. 
The Chairman presided. 
Twenty members and guests present. 
The appointment of the committee called for under the new 
Standing Rule relating to papers read before Sections of the 
Society was considered. Mr. Tayntor moved that the committee 
consist of the Chairman and Secretary and a third member to be 
