102 Capt. Kater/s experiments for determining , &c. 
j. z 2 + V x n + v z 2 + v z " 2 + v z 2 + v z'" 2 + v 
> d! rid 1 d“ 7i"d" d u ‘ ri"d“ * 
VI, by comparing the first of these equations successively 
with the second arid third, and bringing the terms containing 
v to the same side, we obtain 
__ fz* z 1 2 z i . z " 2 \ _ / 2 i_ I _i__\ _\f_ \ 
^ irf' n’d d"*~n"d"j ' \rf" n"d" d' * ?i'd' ) \d‘ 
z ' 2 . z " 12 \ / i i i , i \ 
n'd d"‘ * ri"d'") ' \d"‘ n m d‘“ d' ■ rid') 
This equation contains only the squares of the values of 
% with known coefficients ; and if we substitute % — d', z — d" 7 
and z*-^d" t for z\ z", and z ,n , respectively, we shall obtain an 
equation in the form ez t -\-fz=g, whence z z=±\/ (g-\-±f 2 ) 
