Royal Society. 363 



remaining integrals deduced. The set of " normal elements " thus 

 obtained coincide with those given by Jacobi (in a memoir in Crelle's 

 Journal, vol. xvii.). In the problem of rotation, the algebraical solution 

 of the three assumed integrals for y^, y.., y-, depends upon that of an 

 equation of the fourth degree. It is therefore impracticable to 

 exhibit the principal function in an explicit form. In this respect 

 the result arrived at resembles that obtained by Mr. Cayley in a 

 totally different way ; Mr. Cayley having shown that the solution of 

 the problem is reducible to quadratures, assuming the algebraical 

 solution of a certain system of equations of the same form as those 

 to which the author of the present investigation is conducted. (Camb. 

 and Dub. Math. Journ. vol. i. p. 172.) 



Methods are then indicated by which, when one system of "normal 

 elements " is given, other systems may be found. 



The practical value of " normal solutions " of the system (I.) de- 

 pends chiefly upon the simplicity of the corresponding formulae for 

 the variation of elements, the theory of which is intended to form 

 part of the subject of the following sections. 



March 2. — Professor Graham, V.P., in the Chair. 



The following Papers were read : — 



1. "On the Growth of Land Shells." By E. J. Lowe, Esq., 

 F.G.S., F.R.A.S. &c. 



Perhaps the following observations on the growth of land shells 

 may contain sufficient information to prove interesting to the Royal 

 Society. Before describing them, however, a few introductory re- 

 marks will be necessary. Every individual experimented upon has 

 been kept in confinement since the day it was hatched. Each 

 species has been placed in a separate box (filled with soil to the 

 depth of three inches), and care has been taken to feed the Mollusca 

 every other day, the food chiefly consisting of the leaves of the 

 lettuce and cabbage. In very dry weather the soil has been moistened 

 ■with rain-water about once a week ; in the box containing Helix 

 pomatia small lumps of chalk have been mixed with the soil. 



The species experimented upon were : — 



Helix aspersa 



— caperata 



— hispida 



— nemoralis 



— po.aatia 



— rotundata 



— virgata 



The facts arrived at are, — 



1st. The shells of Helicidae increase but little for a considerable 

 period, never arriving at maturity before the animal has owce become 

 dormant. 



2nd. Shells do not grow whilst the animal itself remains dor- 

 mant. 



3rd. The growth of shells is very rapid when it does take place. 



Zonites cellarius 



— lucidus 



— nitidulus 



— radiatulus 

 Bulimus obscurus 

 Clausilia nigricans 

 Pupa umbilicata 



