557 
of Edinburgh^ Session 1865-66. 
quantities, viz., the Primary, the Function, and the Derivative. 
When the relation between the primary and the function is given, 
the discovery of the derivative belongs to the Differential Calculus. 
When that between the primary and the derivative is given, the 
function is found by help of the Integral Calculus. And the gene- 
ral problem to find the primary when the relation between the 
function and its derivative is given, belongs to a third branch, which 
may be called the Calculus of Primaries. 
It was stated, in the course of the paper, that, by help of well- 
known artifices, problems involving the first derivative or the second 
derivative can be converted into problems of integration, and that 
thus the first two chapters of the Calculus of Primaries are, as it 
were, abstracted ; but that, whenever the order of derivation is 
higher than the second, the equations cannot be transformed so as 
to be rendered integrable. 
The following Gentlemen were duly elected Fellows of 
the Society : — 
Charles Morehead, M.D., F.K.C.P. Lend. 
Professor David Masson. 
David Douglas, Esq. 
The following Donations to the Library were announced : — 
Abstracts of the Proceedings of the G-eological Society of London. 
jNo. 139. 8vo. — From the Society. 
Bulletin de la Societe Imperiale des Naturalistes de Moscou. No. 
2. 1865. 8 VO. — From the Society. 
Sitzungsberichte der konigl. bayer. Akademie der Wissenschaften 
zu Miinchen 1865. II. Heft 1, 2. 8vo. — From the Academy. 
Astronomical, Magnetical, and Meteorological Observations made 
at the Eoyal Observatory, G-reenwich, in the year 1863. 
London, 1865. 4to. — From the Observatory. 
Transactions of the Linnean Society of London. Vol. XXV. 
Part II. 4to. — From the Society. 
List of the Linnean Society of London for 1865. 8vo. — From the 
Society. 
Proceedings of the Eoyal Society of London. Vol. XIV. No. 
79. 8vo. — From the Society. 
Monthly Eeturns of the Births, Deaths, and Marriages, registered 
