To ascertain how far this is consistent with the theorem of “the parallelogram of forces,” let a line P O be drawn upon the upright board to which the wheels are attached, from the point P upward, in the direction of the thread C P. Also, let lines be drawn upon the board immediately under the threads P M and P N. From the point P, on the line P O, take as many inches as there are ounces in the weight C. Let the part of P O thus measured be P _c_, and from _c_ draw _c a_ parallel to P N, and _c b_ parallel to P M. If the sides P _a_ and P _b_ of the parallelogram thus formed be measured, it will be found that P _a_ will consist of as many inches as there are ounces in the weight A, and P _b_ of as many inches as there are ounces in the weight B. In this illustration, _ounces_ and _inches_ have been used as the subdivisions of _weight_ and _length_. It is scarcely necessary to state, that any other measures of these quantities would serve as well, only observing that the same denominations must be preserved in all parts of the same investigation. (78.) Among the philosophical apparatus of the University of London, is a very simple and convenient instrument which I constructed for the experimental illustration of this important theorem. The wheels M N are attached to the tops of two tall stands, the heights of which may be varied at pleasure by an adjusting screw. A jointed parallelogram, A B C D, _fig. 9._, is formed, whose sides are divided into inches, and the joints at A and B are moveable, so as to vary the lengths of the sides at pleasure. The joint C is fixed at the extremity of a ruler, also divided into inches, while the opposite joint A is attached to a brass loop, which surrounds the diagonal ruler loosely, so as to slide freely along it. An adjusting screw is provided in this loop so as to clamp it in any required position. In making the experiment, the sides A B and A D, C B and C D are adjusted by the joints B and A to the same number of inches respectively as there are ounces in the weights A and B, _fig. 8._ Then the diagonal A C is adjusted by the loop and screw at A, to as many inches as there are ounces in the weight C. This done, the point A is placed behind P, _fig. 8._, and the parallelogram is held upright, so that the diagonal A C shall be in the direction of the vertical thread P C. The sides A B and A D will then be found to take the direction of the threads P M and P N. By changing the weights and the lengths of the diagonal and sides of the parallelogram, the experiment may be easily varied at pleasure.