1887.] Mr Basset, On the Application of Lagrange’s Hquations. 135 
November 28, 1887. 
THE following were elected Fellows: 
C. Chree, M.A., King’s College. 
G. H. Bryan, B.A., Peterhouse. 
J. R. Vaizey, B.A. 
The following communications were made to the Society: 
(1) On the interaction of zinc and sulphuric acid. By M. M. 
Pattison Murr, M.A., and R. H. Aprg, B.A. 
An experimental investigation of the nature of the products of 
the interaction of zinc, sulphuric acid, and water, and of the in- 
fluence on the chemical change in question of temperature, changes 
in the relative masses of the reacting bodies, and the presence of 
traces of foreign metals in the zinc used. 
(2) On the Application of Lagrange’s Equations to the Motion 
of a number of Cylinders in a Liquid when there 1s Circulation. 
By A. B. Basset, M.A. 
1. Ina previous communication to the Society, I showed how 
Lagrange’s equations might be employed to obtain the motion of a 
number of perforated solids in a liquid when there is circulation, 
and I proved that the modified Lagrangian function was 
REE CAG EA IN ee Jv ce (1), 
where J is the kinetic energy due to the motion of the solids 
alone, w is any one of the component velocities of the solids, ¥ 
is the generalised component of momentum corresponding to w of 
the cyclic motion which remains after all the solids have been re- 
duced to rest, & is the kinetic energy due to the cyclic motion alone, 
and V is the potential of the impressed forces. 
If we endeavour to calculate the right-hand side of (1), in the 
case of the two-dimensional motion of a number of cylinders in an 
infinite liquid when there is circulation round some or all the 
cylinders, it will be found that some of the terms become infinite. 
In order to avoid this difficulty, we must describe an imaginary 
fixed circular cylinder in the liquid, the radius of whose cross 
section is a very large quantity c, and then calculate the value of 
L, for the space contained between the moving cylinders and the 
outer one, omitting all the terms which vanish when c becomes 
infinite. It will then be found on substituting the value of Z thus 
obtained in Lagrange’s equations and performing the differentia- 
tions, that all the terms which become infinite with c disappear, 
and we thus obtain the equations of motion of the cylinders. 
VOL. Vi. PL I, 10 
