280 
MR. LUBBOCK’S RESEARCHES 
in the case of comets, not only on account of their great eccentricity, but also 
on account of their small density, in the same manner as a flock of any light 
substance is wafted by the gentlest wind and prevented from reaching the 
ground. The eccentricity of the orbit of the comet of Halley in 1759 is 
known with great accuracy, and as its perturbations have been calculated with 
t 
great care by MM. Damoiseau and de Pontecoulant, the eccentricity which 
it should have in 1835, when it will again visit this part of space, unless it be 
affected by a resisting medium, is also known with great precision. It is 
scarcely probable, however, that any change will be perceptible in one revolu- 
tion, even if the cause exists ; but the succeeding revolutions of this body will 
no doubt throw light upon this question. The ratio of the change of the semi- 
major axis to the change of the eccentricity, due to the action of the resisting 
medium, is known, being a function of the eccentricity, and independent of the 
constant, which depends upon the density of the medium ; this ratio therefore 
may also tend to elucidate the question, if it can be determined by observation 
with sufficient accuracy. 
Let x', y ', z' be the co-ordinates of any point P corresponding to the elemen- 
tary portion of the surface ds, and referred to axes passing through the centre 
of gravity and revolving with the body in motion. 
Let P be the point of which the co-ordinates are x', y\ z\ A P the direction 
of the normal at the point P, B P perpendicular to the axis of instantaneous 
rotation, and cutting it in B, and C P the direction of motion of the point P. 
I suppose the resistance of the medium to create a force proportional to 
v 2 cos A P C d s, acting in the direction of the normal A P upon the point P, v 
being the velocity of the point P. 
Suppose the straight line MO PL to : N 
p 
revolve about an axis passing through O, 6 A 
and perpendicular to it, and in the direc- i R 
tion LN, the action of the resisting medium will be in the direction N L, on 
one side only of the line O L, upon all the points P between O and L, and 
upon all the points between M P it will be in the contrary direction R M, and 
on the other side of the line. 
