3 
XXXIX 
- Make now, to distinguish between the length and direction 
of the vector, 
a=n r=V7(—a), @=- 71; (6) 
we shall have 
da = r-di + dros, (7) 
and because r and dr are scalar (or real) quantities, 
a.da = r%.de —7.dr, da.a = deur —r.dr; (8) 
- 
therefore 
| B.dt = 3(a.da — da.a) = z (e.de— dee) = re. de, (9) 
observing that the equation 
’ = — 1 givese.ds + diuc = 0. (10) 
The fundamental equation (1) of the problem becomes, by 
(6) and (9), 
dda M .:dem: 
aide 7a dtp? (ty) 
(in which last member the order of the factors is not indiffe- 
rent), and therefore gives, by integration, since (3 as well as M 
is constant, 
# - 3 = const. ; (12) 
or, as we may also write it, 
, OE Be, de = 0. (13) 
We have, consequently, by (6) and (4), 
Sir aM ware Sab: (14) 
and finally, by (3), 
* — (22 
ae +cat 2r = 2p, (15) ifp= a} (16) 
