37. IF this lever be set into any other position (as in fig. 31.) then the weight, which is raised highest, will outweigh the other. Here, if the point F be raised higher than E, the perpendicular C K will be longer than C I: and therefore the weights would equiponderate, if the weight at F were less than the weight at E. But the weight at F is equal to that at E; therefore is greater, than is necessary to counterbalance the weight at E, and consequently will outweigh it, and draw the beam of the lever down.
38. IN like manner in the case of the steelyard (fig. 32.) if the weights at E and F are so proportioned, as to equiponderate, when the points E and F are horizontally situated; then in any other situation of this lever the weight, which is raised highest, will preponderate. That is, if in the horizontal situation of the points E and F the weight at F bears the same proportion to the weight at E, as C I bears to C K; then, if the point F be raised higher than E (as in fig. 32.) the weight at F shall bear a greater proportion to the weight at E, than C I bears to C K.
39. FARTHER a lever may be hung upon an axis, and then the two arms of the lever need not be continuous, but fixed to different parts of this axis; as in fig. 33, where the axis A B is supported by its two extremities A and B. To this axis one arm of the lever is fixed at the point C, the other at the point D. Now here, if a weight be hung at E, the extremity of that arm, which is fixed to the axis at the point C; and another weight be hung at F, the extremity of the arm, which is fixed on the axis at D; then these weights will equiponderate, when the weight at E bears the same proportion to the weight at F, as the arm D F bears to C E.
40. THIS is the case, if both the arms are perpendicular to the axis, and lie (as the geometers express themselves) in the same plane; or, in other words, if the arms are so fixed perpendicularly upon the axis, that, when one of them lies horizontally, the other shall also be horizontal. If either arm stand not perpendicular to the axis; then, in determining the proportion between the weights, instead of the length of that arm, you must use the perpendicular let fall upon the axis from the extremity of that arm. If the arms are not so fixed as to become horizontal, at the same time; the method of assigning the proportion between the weights is analogous to that made use of above in levers, which make an angle at the point, whereon they are supported.