42, Mr Webb, The problem of three moments. i [Nove22; 
considered as a conductor, but to complete the investigation it is 
necessary to find the , due to an open circuit, and a number of 
difficulties are introduced. 
By employing a cylinder, whose length is s parallel to the cur- 
rent and is indefinitely great compared with its breadth, we get 
rid of all these difficulties. For since the form of the rest of 
the closed circuit only affects the values of §, in the negligibly 
small portions of the cylinder near the ends, it is reasonable to 
assume that the value of §, derived from any one of these closed 
circuits is the value due to the current in the cylinder alone, and 
this is the value we have used. 
(3) The problem of three moments. By R. R. Wess, M.A. 
This problem originally due to Clapeyron (Comptes Rendus, 
XLV.) seems to be the basis of the practical determination of the 
bending moments in such structures as girder bridges. The 
history of the problem is concisely given in the Proceedings of the 
Royal Society (xvii. 1869—70) and there is no need of reproduc- 
tion here. 
The solution as given by Clapeyron (loc. cit.) proceeds on the 
comparatively simple hypotheses of constant flexural rigidity, 
equal spans, uniform loads, and the same is to be said of the 
extensive solution of the problem of the elastic beam resting on 
any number of supports as given by Bresse in his Cours de 
Mécanique Appliquée (Paris 1859). Rankine (Proceedings, Royal 
Society, XIx. 1870—71) seems to have greatly remedied the defects 
of his predecessors, still his formule are encumbered with double 
integrals, and no serious attempt is made to meet the mathe- 
matical difficulty of discontinuous loading. Weyrauch (Zevtschrift 
fiir Mathematik und Physik, Xvi, X1x, 1873—4) gives general 
formule involving double integrals and meets the case of irregular 
loading with Fourier’s analysis, a proceeding that virtually places 
his results to some extent outside the region of a practical 
computer. 
The object of this note is to give an edition of the problem 
having the advantages of symmetry, while at the same time it 
meets the wants arising from (1) variable flexural rigidity, (2) un- 
equal spans, (3) irregular loading. It will be convenient to firstly 
solve the problem when there is no load, and the rod is merely 
used as a stress transmitter. To fix ideas suppose the unstrained 
rod O... ABC... to pass through smooth rings at... A, B, C..., 
let the shearing stress at any pier P be denoted by P, and P, , fore 
and aft of the pier so that the pressure on this particular support 
will be (P,~P,), let M4, Mz, Mc be the bending moments at 
A, B,C all measured positively in such a way as would in the 
