134 ROYAL SOCIETY OF CANADA 
3°. Applications of the Integral Calculus: Process of integration. 
Length of an arc of a curve, plane and gauche areas, volumes. Differ- 
entiation and change of variables under the sign Wes eee Study of the 
integral / ? f(x) dx when oneof the limitsorthe function becomes infinite. 
Formula of Green.—Study of functions represented by certain series. 
—Properties of power series. 
4°. Elements of infinitesimal Geometry: “ Infinitesimal properties ” 
of plane and gauche curves (curve envelopes, curvature, torsion). In- 
finitesimal properties of the surfaces; surface envelopes, summary of the 
results on the transformations of contact; developable surfaces, ruled 
surfaces, Meusnier’s theorem; principal sections.—Conjugate lines, 
lines of curvature, asymptotic lines in any curvilinear co-ordinates. 
5°. Elementary Functions of a Complex Variable: Simple alge- 
braic functions; circular and logarithmic functions. 
6°. .Theory of Analytic Functions: Properties of the integral 
fh f(z) dz. Series of Taylor and of Laurent. Poles, essentially 
singular points, residues.—Reduction of the hyperelliptic integrals. 
7°. Differential Equations of the first order: General solutions, 
particular solutions, singular solutions.—Simple types of integrable 
equations. Integrating factor.—Theorem of Briot and Bouquet on the 
existence of the solutions in the cases where the known functions are 
analytic. 
8°. Differential Equations and Systems of Equations of any order: 
General solution, particular solutions, first solutions.—Simple types of 
integrable Equations. Linear Equations. 
9°. Integration of linear partial differential equations of the first 
order. 
10°. Integration of differential equations (partial or total) of the 
first order. 
MECHANICS. 
11°. Statics: Composition of forces applied at a point.—Attrac- 
tion of a spherical homogeneous shell at an exterior or interior point. 
Elementary properties of the potential.—Reduction of forces applied 
to a solid body.—Conditions of equilibrium of a solid body. Applica- 
tions to simple machines.—Funicular polygon. Suspension bridges. 
Catenary.—Principal of virtual work. 
12°. Kinematics: Velocity, acceleration.—Movement of a plane 
figure in its plane. Representation of the movement by the rolling of 
a moving curve on a fixed curve.—Movement of a solid body about a 
fixed point. Representation of the movement by the rolling of a 
