27ri 



pear to be inaccurate. Added to this is the circumstance, that M. 

 Liouville has not effected the exhibilion of any forinulse analogous 

 to the ordinary formulae of the Differential Calculus, such as Tay- 

 lor's Theorem. 



" The objects of the present memoirs are, 1. The completion of 

 the science as regards its elementary theorems, by the exhibition 

 of one general form, and the deduction of all other forms from it : 

 2. The application of the general theorem to a variety of cases ana- 

 logous to those dealt with in the common differential analysis : 

 and, 3. The demonstration and application of theorems of expan- 

 sion, not subject to failure for particular values of the variable. To 

 complete the subject, a vast deal more is required ; but the author 

 hopes, by the present essay, and another which he intends shortly 

 to present to the Society, that the study of this important calculus 

 will be excited ; and confidently anticipates the consequent improve- 

 ment and extension of its processes." 



Monday IQth December 1839. 



Sir T. M. BRISBANE, Bart. President, ia the Chair. 



The following donations were presented : — 

 Journal of the Asiatic Society of Bengal, No. 85, for January 1839. 



— By the Society. 

 Transactions of the Meteorological Society, vol. i — By the Society. 

 Comptes Rendns Hebdomadaires des Seances de I'Academie des 



Sciences (1839, 2"^ Semestre). Nos. 20, 21, 22 — By the 



Society. 



The following communications were read : — 



1. Experiments on the Development and Growth of the Sal- 

 mon, from the exclusion of the ovum to the age of two 

 yeai-s. By Mr Shaw, Driunlanrig. Communicated by 

 James Wilson, Esq. 



The author, in this paper, gives an account of the continuance 

 and confirmation of his experimental observations on the growth 

 of salmon fry, as formerly communicated to the Society. He con- 

 siders the objections made to his artificial ponds, in so far as they 

 were supposed to afford an insufficient supply of food, to be with- 

 out reasonable foundation, as these ponds actually abound with the 

 ordinary insect food of fishes, and the young broods themselves 



