463 



above general theorem of definite integration. Of the Notes by 

 which the paper is accompanied, the first discusses the connexion 

 between the author's symbol and Cauchy's, and contains two 

 theorems, one exhibiting the general solution of linear differential 

 equations with constant coefficients, the other the general integral of 

 rational fractions. Both these theorems involve in their expression 

 the symbol 6. The second Note is devoted to the interpretation of 

 some theorems for the evaluation of multiple integrals, investigated 

 in the closing section of the paper. 



May 14, 1857. 



General SABINE, R.A., Treas. and V.P., in the Chair. 

 The following communications were read : 



I. "On the Organization of the Brachiopoda." By ALBANY 

 HANCOCK, Esq. Communicated by T. H. HUXLEY, Esq., 

 F.R.S. Received April 24, 1857. 



(Abstract.) 



In the present memoir the author states at length, and fully illus- 

 trates by figures, the conclusions to which he has been led by a long 

 series of researches into the anatomyof theBrachiopoda; investigations 

 which have been conducted with a special reference to the discrepant 

 opinions maintained by Prof. Owen and the older writers on the one 

 hand, and by Prof. Huxley and himself on the other. Some of the 

 points in dispute have already been discussed in a paper read before 

 the British Association at Cheltenham, and in the present memoir 

 the author not merely reiterates the statements which he then made, 

 but gives a detailed account of the whole organization of the Bra- 

 chiopoda based upon his dissections of the following species : Wald- 

 heimia australis, W. Cranium, Terebratulina caput-serpeniis, R/iyn- 

 chonella psittacea, Lingula anatina, and another species of Lingulu. 



The Brachiopoda are divisible into two groups, according as the 

 valves of their shells are articulated or not. Waldheimia is the type 

 of the former group, Linyula of the latter. 



