Royal Society, 5S1 



coming more restricted as the order rises. The iiitegrable cases are 

 very numerous and vary considerably in form ; and, as each distinct 

 form requires a variation in the process, they are distributed into 

 classes. In each class, a few particular examples, derived from the 

 general cases, are given. 



By means of the general theorem, the equation 



may be integrated in the most general case, or when the coefficients 

 are any functions of x, having, however, certain relations between 

 them. 



Several theorems of the form ifnpu^pirn-iu, where p^D+Q, 

 *»=D'^ + AnD+B„, or similar to it, are given. They are not found 

 without difficulty ; are much more restricted in their application 

 than the general theorem ; and lead to but few results ; but they 

 are deserving of notice on the ground that they may possibly suc- 

 ceed in a particular case when all other methods fail. 



A few general examples of a class of equations, the solution of 

 which is attended with considerable difficulty, are next given. These 

 are of the forms, 



and others varying a little from them. 



The concluding part of the paper is occupied with the transfor- 

 mation and application of one or two of the general theorems which 

 have been given by the author in the Cambridge Mathematical 

 Journal, New Series, vol. iii., from which a few examples, more or 

 less particular, have been derived. 



March 1, 184-9 " Minute Examination of the Organ of Taste 



in Man." By Augustus Waller, M.D. Communicated by Richard 

 Owen, Esq., F.R.S. 



The author commences by describing his mode of observation, 

 which differs from that followed by previous observers. It consists 

 in removing from the living tongue one of the papillae, and imme- 

 diately subjecting it to examination. He then proceeds to describe, 

 — 1st, the epithelium; 2nd, the fungiform papillae; 3rd, the conical 

 papillae ; and ^th, the inferior surface with its mucous glands, &c. 



1. The epithelium is of two kinds ; the flat plates with a central 

 nucleus, which are mostly found clothing the stem and other regions 

 of the fungiform papillae ; and the globular cells which compose 

 most of the external parts of the processes of the conical papillae. 



2. The fungiform papillae are found to consist of numerous small 

 cones seated on a common stem. These secondary cones, already 

 described by Albinus, are completely hidden by a common invest- 

 ment of epithelium which fills up the irregular spaces between them. 

 Each of these cones contains capillary vessels, which, at the apex of 

 the cone, either form a simple loop or a complex coil which is covered 

 only by epithelian scales of the most attenuated nature. The author 

 states that in these capillary vessels the motion of the blood may be 

 observed for several seconds after the removal from the living body, 



2 M2 



