This is an abstract of an investigation which will be published in full in “Thomson and Tait's Natural Philosophy.” It contains the application of Green's wonderful results regarding the potential to the determination of the centre of gravity of a system when there is such a point. Some of the more remarkable propositions, which are thus established are as follows:—

If the action of terrestrial or other gravity on a rigid body is reducible to a single force in a line passing always through one point fixed relatively to the body, whatever be its position relatively to the earth or other attracting mass, that point is called its centre of gravity, and the body is called a centrobaric body.