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MATHEMATICS: J. K. WHITTEMORE Proc. N. A. S. 
Sevier al samples so treated worked successfully, and the fact that it was 
found impossible with U. S. Government 600 minute charcoal suggests 
that it was due to action of some sort between the hydrocarbons present 
and the gas. The fact that McBain's work^ with hydrogen shows a dual 
action, and that work done later by others^ on other gases points to a 
single action, suggests that while surface condensation is likely to explain 
the major action in both cases, that in the case of hydrogen there must be 
something else at work as well ; either the hydrogen is dissolved or possibly 
combines with hydrocarbons unsaturated at this liquid air temperature. 
It is difficult to draw a distinct dividing line between the two, but the latter 
view is the one taken. 
The deposit of inactive carbons on the active base, is according to this 
theory, much more effective in deactivating for nitrogen, since, interfering 
with surface condensation, it interferes with the whole effect, this not being 
the case for hydrogen which has a dual nature. The observations bear 
this out. 
The decided drop in the initial end of the curves in figure 1 at the be- 
ginning of the work with hydrogen, which does not appear in the nitro- 
gen curves of figure 2, again shows a difference in the adsorption of these 
two gases, possibly resulting from an increased fineness of the division of 
the material with which the hydrogen unites. Further work with other 
gases will be undertaken. 
The author is greatly indebted to Dr. Harvey B. Lemon for valuable 
advice and suggestions in connection with this work. 
1 These Proceedings, 5, July 1919, pp. 291-295. 
2 Phil. Mag. London, Ser. 6, 18, 1909 (916). 
3 Miss Homfray, Zs. Phys. Chem., 74, 1910 (129). 
THE STARTING OF A SHIP 
By James K. Whittemore 
Department of Mathematics, Yale University 
Communicated by L. B. Mendel. Read before the Academy, November 11, 1919 
In this paper we give first the results of a mathematical discussion of 
the motion of a particle under the action of tangential forces depending 
only on the velocity of the particle.^ In the following paragraphs we 
suggest applications of these results to marine engineering and to the study 
of the law of resistance of liquids. 
We consider a particle, P, moving in any path under the action of forces 
whose components along the tangent to the path depend on the velocity 
of the particle alone. We denote the time by t, the distance covered in 
the time t by x, the velocity at the start by , at any time t by v, and the 
acceleration along the tangent by a. By hypothesis, a = F(v). Con- 
cerning F{v) we assume 
