Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 2.djvu/21

Sect. I the right line SMMM in X, and SX will be the true ratio of the reitance to the gravity, which was to be found. From this ratio the length DF is to be collected by calculation; and a length, which is to the aumed length DP, as the length DF known by experiment to the length DF jut now found, will be the true length DP. This being known, you will have both the curve line DraF which the body decribes, and alo the velocity and reitance of the body tn each place.

But yet that the reitance of bodies is in the ratio of the velocity, is more a mathematical hypotheis than a phyical one. In mediums void of all tenacity. the reitances made to bodies are in the duplicate ratio of the velocities. For by the action of a wifter body, a greater motion, in proportion to a greater velocity, is communicated to the ame quantity of the medium, in a les time; and in an equal time, by reaon of a greater quantity of the diturbed medium, a motion is communicated in the duplicate ratio greater; and the reitance (by Law 2 and 3.) is as the motion communicated. Let us therefore ee what motions arie from this law of reitance.