XXXVI1 
of an orbit, and the equable description of areas, under oné 
common formula, namely, the following : 
dp dp 
DP Gauiiaig Putt 
from the general expression of a central force, namely, from 
the equation 
const, 
ap... 6 
which asserts merely the coawality of the vector p and the 
force = or the existence of one common line along which 
this vector and this force are (similarly or oppositely) directed. 
Since the suggestion above acknowledged was made, Sir 
William Hamilton has proposed to himself to express by an 
equation, on the principles of the method of vectors, the pro- 
blem of any number of bodies attracting according to New- 
ton’s law : and has arrived at the formula 
da bi’ m + Am 
OP dai Aw) ds oa 
rh may also be thus written, 
d’a m! 
= =—ow V¥$—(a—a)*}’ (8) 
and from which he has deduced anew the known laws of the 
centre of gravity, of areas, and of the vis viva, under the 
forms : 
d\? 
(<) Z.ma = 0; (c) 
d da da 
d=" -m(« dé de a) =0; (P) 
d — m(da\?_ a mm’ : 
23a) ta=7EGsa HS 
aisthe vector and m the mass of one body ; a’ and m’ ofanother; 
