1886.] Mr M*Connel, On Lagrange’s Equations of Motion. 27 
the second law of motion. But on examination this proof turns 
out to be quite invalid. He obtains* an equation of the form 
d (at dT d (aT ar 
which is established by the remark that the change of kinetic 
energy must be equal to the work done by the forces, 
Moreover he says that p,=~r,5¢; from both of which state- 
ments it is evident that p,, p,... are the displacements which 
actually occur under the action of the forces V,, V, ... in time ot. 
So the p’s are not independent of the W’s nor of the wW’s, he 
cannot equate all the p’s to zero except p,, and he is not justified 
in deducing that the coefficient of p, on the one side is equal to that 
on the other. 
November 8, 1886. 
Mr TROTTER, PRESIDENT, IN THE CHAIR. 
Mr W. F. Sheppard, B.A., Trinity College, and Mr F. H. 
Neville, M.A., Sidney College, were elected Fellows. 
Mr H. F. Reid was elected an Associate. 
The following communications were made to the Society. 
(1) On the Celom and body-canity of Peripatus and the Arthro- 
poda. By ApAm Sepewick, M.A., Trinity College. 
It is well known that the vascular system of the Arthropoda is 
in direct communication with the body-cavity, and that the vessels 
are, for the most part, very rudimentary. In fact the blood is 
driven by the heart or dorsal vessel into the body-cavity and 
returned directly through the lateral cardiac ostia into the heart. 
In no other group of animals, so far as I know, does this direct 
communication exist between the heart and the pericardium +}. 
* § 561, equations (7) and (8). 
+ This important Arthropodan character has so far escaped the notice of mor- 
phologists: at least I have never seen it mentioned in any of the books. My 
attention was first called to it by Professor Ray Lankester. 
