568 Royal Society. 



has usually been established, either by the calculus of variations, or 

 by a process of elaborate expression of the actual result in terms of 

 definite integration with respect to a subsidiary variable. Mr. De 

 Morgan, after some remarks upon the manner in which certain 

 proofs of the necessity of the criterion fail, gives a very simple ele- 

 mentary proof founded upon the following theorem. If U be any 

 function of .r, y, p, &c., — as far say as s, for an instance, — then 



(U'),=u;, (u'),=u;, (U'),=u;+u,. 



(U'),=U,' + U,, (U') =U,,' + U„ (U'),=U/ + U„ (U'),=U,. 



Mr. De Morgan takes it to liave been hitherto unnoticed that the 

 formulae Vp— V,' + V/'— ..., V,— V,' + .... .so much used in this sub- 

 ject, are, when V is integrable, nothing but the dilFerential coefficients 

 oi/Vdx, with respect to y, p, &c. 



[But since the paper was communicated, Mr. De Morgan has found 

 the above theorem, and its consequences, in a memoir by M. Sarrus, 

 apparently belonging to the Journal de I'Ecole Polytechnique, and 

 printed in 1824. No notice is taken of this method by MM. Ber- 

 trand, Binet, or Moigno, who have written on the subject since 

 M. Sarrus.] . 



ROYAL SOCIETY. 

 [Continued from p. 508.] 



April 3, 1851. — Lieut.-Colonel Sabine, V.P. & Treas. in the Chair. 



A paper was read, entitled " Observations upon Appendicularia 

 and Doliohim." By Thomas H. Huxley, Esq. Communicated by 

 E. Forbes, Esq., F.R.S. 



This is a description of two Ascidian genera which possess very 

 considerable interest : Doliolunt, as forming a link between the 

 Pyrosomata and SalpcE ; and Appendicularia, as representing in a 

 permanent form the larval state of the Ascidians, long ago described 

 by M. Milne-Edwards. 



Appendicularia, which has been also imperfectly described under 

 the names of Oihopleura and Venillaria, is in fact an ascidian pro- 

 vided witli a long vibratile iin or tail, by the aid of which it swims 

 freely about. 



That it is an adult form is shown by the existence of a well- 

 developed testis, but the author leaves undecided the nature of the 

 female organs. 



On the other hand it seems doubtful whether Doliolum is truly an 

 independent form, or whether it is not rather a detached " zooid " 

 of the genus Atiche?iia. 



April 10. — Sir Philip de Malpas Grey Egerton, Bart, in the Chair. 



The reading of Dr. Hofmann's paper " On the Molecular Consti- 

 tution of the Organic Bases," commenced at the previous meeting 

 (April 3), was concluded. 



In a former paper* the author advanced a general theory regard- 



* Phil. Trans., part i. p. 93, 



