144 Mr Love, Note on Kirchhoff’s theory of the [Nov. 28. 
The last three articles have been worked out for the sake of 
giving examples of the application of Lagrange’s equations; but it 
would not be difficult to develope the subject of the last article 
considerably further. If, for example, we desired to investigate the 
motion when the circulations have different values «, «’; the current 
function due to the cyclic motion might be determined by writing 
down the current function due to two vortices of circulations «, x’ 
situated at A and B respectively, and determining by means of 
dipolar co-ordinates another function yy, such that the sum of all 
three functions is constant at the surfaces of the two cylinders. 
Another problem of the same class is obtained by considering 
the conjugate functions, 
E+ w= log {(w + zw) —eF}/c*. 
If a is positive the curve = — a is a lemniscate consisting of two 
detached ovals. The current functions for the motion of cylinders 
whose cross sections are these curves have been given by myself*, 
but in applying these formule to two detached cylinders, it would 
be necessary to suppose them either rigidly connected together, or 
connected by a rod lying in the plane of the motion and passing 
through the foci, upon which the cylinders can slide. 
(3) Note on Kirchhoff’s theory of the deformation of elastic 
plates. By A. KE. H. Love. 
THE theory here called Kirchhoff’s is that worked out for 
Kirchhoff by his pupil Gehring, and will be found in No. XXX. 
of the Vorlesungen iiber Mathematische Physik, and in §§ 64 sq. 
of Clebsch’s Theorie der Hlasticitdt fester Korper. The object of 
this note is to call attention to some points in which the theory 
of the internal equilibrium of an element of the plate appears 
to be deficient in rigour, and at the same time to make it some- 
what more lucid. 
Objections have been raised to Kirchhoff’s theory by M. 
Boussinesq on the grounds, (1) that it is obscure, (2) that it is 
founded on kinematical considerations which are only approxi- 
mately true, and (8) that it is only capable of giving a first 
approximation. I shall shew that, by a necessary modification 
of the kinematical equations referred to, the equations derived 
therefrom can be made strictly accurate, and shall explain how 
the equations of equilibrium of an element may be made correct 
to any desired order of approximation. The criticisms of M. 
* Quart. Journ. Vol. xx. pp. 242-246. 
