of Edinburgh^ Sessio7i 1865-66. 565 
external unit of matter placed at a distance r from its centre is 
represented by 
Integrating between the limits 0 and a (a<Cf) for a, we have the 
attraction of a uniform sphere on an external point. Forming 
the equation of fluid equilibrium on the supposition that such a 
spherical portion ceases to exert molecular force, we find the ex- 
pression for the pressure in the fluid at a distance r from the 
centre of the bubble. This contains the following new functions 
to(r)=yrc?r frdr ff)(r)dr, 
and X W = f<\> (r) c?r, 
but, from the manner in which they appear in the final expression, 
it is impossible to determine the relative importance of the terms 
containing them. 
We see, however, that the terms in to, which are multiplied 
by the curvature, become somewhat less as the radius of the bubble 
diminishes — so that the calculated pressures given above are pos- 
sibly too large. 
4. On some G-eometrical Constructions connected with the 
Elliptic Motion of Unresisted Projectiles. By Professor 
Tait. 
In “ Tait and Steele’s Dynamics of a Particle,” chap, iv., a 
number of geometrical constructions are given, some possibly for 
the first time, connected with the motion of projectiles in para- 
bolic paths in vacuo. I have recently been led to remark that 
most of these propositions still hold when we substitute, for the 
uniform action of gravity in parallel lines, the action of gravity 
supposed to be directed to the earth’s centre, and to vary inversely 
as the square of the distance from that point. My excuse for 
bringing so simple a matter before the Society is, that the proposi- 
tions are in themselves curious and elegant, and that I am not 
aware of their having been before mentioned. A very few ex- 
amples will suffice to indicate the change of form required by the 
more general assumed conditions. The following may be taken 
for this purpose : — 
