of scientific investigation and observation of nature, and the pushing of hypotheses to their legitimate conclusions by all means which the reasoning powers of man supply, will find their complement, not their contradiction, in the knowledge conveyed by the mission of Him who is both God and man. A grand conception this; one at which the head has no right to sneer, and which the heart receives with joy and with an instinctive persuasion that it must be true.

ROSE CASTLE: Easter 1883.

HARVEY CARLISLE.

a

ESSAYS.

ESSAY I.

THE CONNECTION BETWEEN MECHANICS

AND GEOMETRY.1

THE first step in proving the elementary propositions of mechanics is usually to explain that, for the purposes of demonstration, forces are represented by straight lines; and so simple a step does this appear to be, that it has been complained that students frequently do not perceive that they have passed a distinct boundary-line in their transition from geometry to mechanics. It becomes, therefore, an interesting inquiry, What is the ground of connection between the two sciences? Is it merely conventional, or only partly so, or not at all? Is the substitution of straight lines for forces to be looked upon as an ingenious device, or has it such a natural basis in the reality of

This Essay is a modified reprint of a memoir read before the Cambridge Philosophical Society in the year 1845, and published in the Society's Transactions.'

B