, p, ,, and for their denominators any assigned quantities ql, q2, q 2, The partial fraction b n /a n corresponding to the n th convergent can be found from the relations pn = anpn -I +bnpn -2 1 qn = anq,i l +bngn-2; and the first two partial quotients are given by b l =pi, a1 = ql, 1)102=1,2, a1a2 + b2= q2.
Un, and ql, q2, q3,
X=~-ql +~-qi +...
The mathematical importance of this function called the potential is that it is a scalar quantity, and the potential at any point due to any number of point charges ql, q2, q3, &c., distributed in any manner, is the sum of them separately, or qi/xl+q2/x2+q3/x3+&c. =F (q/x) =V (17), where xi, x2, x 3, &c., are the distances of the respective point charges from the point in question at which the total potential is required.
(iv.) If P and Q can be expressed in the forms pL and qL, where p and q are integers, R will be equal to (p-kq)L, which is both less than pL and less than qL.