Professor Leslie on Electrical Theories, 
vious that the particles of air which surround A, being repelled 
perpendicularly by its surface, and also by each other, will flow 
equally in all directions. The particle projected to B will pro- 
ceed, without deviating from the straight line ; but a particle 
wh : ch receives a lateral impulse, will be perpetually deflected 
from its course by the attraction of B, and will therefore de- 
scribe a curve that is concave towards A B. Suppose the par- 
ticle has arrived at D, and that T D is there the direction of its 
motion ; let the repulsion of A be to the attraction of B as AD 
to DE, then AE will denote the joint action of A and B. It 
is evident, that, when AD is less than DB, that is, when D lies 
between A and the middle perpendicular CO, DE will be much 
less than DB, or AE will make a considerable inclination with 
AB on the side O. Produce TD to G, and draw GH parallel 
to AE, such that DG shall be to GH as the velocity of 
the particle at D is to the velocity which the joint actions of A 
and B would, in a given instant, impress upon it: DH is the 
direction that will result, and G D H the angle of deflexion. 
Let the particle move through the space D d in the same in- 
stant, and if the repulsion at A decreases in the simple ratio of 
the distance, while neither the quantity nor direction of B's at- 
traction varies, the angle DAE will receive an increment 
DAE Sin. "yL But when BD acquires the position B d, the 
attraction D E will be increased, and also become less oblique 
to A D ; on both accounts, therefore, the angular increment will 
D d 
be greater than DAE Sin. and this quantity will be 
much increased, if, what is most probable, the forces vary more 
rapidly. 
The elementary deflexion GDH is DEASin. 
G H 
GD’ 
but if the particle, in describing A D, received impulses equal 
to that at D, DG would be to GH, as the time elapsed in de- 
scribing A D is to the given instant in which D d is described ; 
but since the velocity of the particle increases, this ratio will be 
that of A D to D a smaller portion than D d. Consequently, 
even on this supposition, the curve will bend more slowly from 
the initial tangent than the line AE. But the impulses which 
the particle receives, diminish fast in its progress from A ; and 
