77 6 
MR. A. McAULAY OH THE MATHEMATICAL 
Add to 3rd term of 46 (10) 
||(4 + K) ds .(1^)* 
46 (11) Unaltered .(15). 
In place of 46 (12) 
K = - Is, ts= 0.. . • . (16). 
Add to right of 46 (13) 
j](- m,/d$ + Sdjvy ds - *' + fs (u P ') . (17). 
Add to right of 46 (14) 
||Sd d V4c?s — || (i'YiV^ds + |Sp'</>/ (i'dp ). . . . (18). 
47 (15), 49 (17), 50 (26) Unaltered . . . . . . . . . . (19). 
Add to right of 49 (18) and 50 (27) 
- <f> sl ' (i'YiY') ..(20). 
Besides the equation (f> s 'i' — 0, we here have 
l<f>s (i'dp%+f+ = ° .( 2i )> 
the suffix e + f + indicating two or more superficial regions bounded by the curve. 
49 (19), 49 (20), 50 (28), 50 (29) Unaltered .(22). 
In place of 49 (21) and 50 (30) 
e s = [d^Ja + i.(23). 
49 (22), 50 (31) Unaltered .(24). 
49 (23), (24), (25) Unaltered .(25), 
[since all the new terms added to 46 (14) are clearly accounted for by P,,. It will 
be observed that this statement is true of any term of L not involving a velocity, i.e., 
of any term which merely contributes to the potential energy]. 
57 (1) Unaltered .(26). 
