440 
Proceedings of the Royal Society 
between irregular prominences on the surface of the foetal ovary. 
The irregularities of the surface of the foetal ovary are produced 
by the expansion of egg clusters upwards under the germ epithelium. 
When the walls of furrows and depressions come in contact, egg 
clusters are formed by the embedding of germ epithelial corpuscles in 
that situation, just as in other situations. Egg clusters are formed 
in connection with the germ epithelium lining the furrows and 
depressions. Among the germ epithelium corpuscles lining the 
furrows, &c., we find large primordial ova, and corpuscles in all 
stages of development into the same, just as in other situations 
among the ordinary germ epithelial corpuscles. 
At the age of six years the epithelium on the human ovary con- 
sists of very small flat hexagonal-shaped corpuscles, measuring 
- 3 " 2 l o~o of an inch. The corpuscles are seen dividing. This 
layer can be stripped off without difficulty. At the age of twelve 
Ihe epithelium has little difference in appearance from the above, 
the small size of the epithelial corpuscles being remarkable. 
The epithelium is beautifully seen in old cats, and must be 
regarded as homologous with the peritoneal epithelium. In old 
cats the epithelium on the surface of the ovary consists of very 
small distinct cells, measuring from ygVoth to g-J^th inch, with 
granular oval nuclei. 
4. Mathematical Notes. By Professor Tait. 
{Abstract.) 
(1.) On a singular Theorem given by Abel. 
The theorem in question, in its simplest form, is 
Abel’s proof of it involves the properties of the gamma-function, 
and requires that f'(f) should be capable of development in powers 
of £. ( (Euvres , I. 27.) 
Independently of the interesting kinetic application for which it 
