

ELEMENTARY PRINCIPLES OF MECHANICS. 423 



In all levers are distinguished, the arm of the power and the arm 

 of the resistance. The 



former is the distance Fig. 176 



comprised between the 

 power and the ful- 

 crum, P F, Figs. 174, 

 175, and 176; and 

 the latter is the dis- 

 tance W F, or that 



between the weight ^ rw 



and the fulcrum. * 



When, in the lever of . LeV er of the third kind, 



the first kind, the ful- 

 crum occupies the middle, the lever is said to have equal arms ; but if 

 it be nearer the power or the resistance, it is said to be a lever with 

 unequal arms. 



The length of the arm of the lever gives more or less advantage to 

 the power, or the resistance, as the case may be. In a lever of the 

 first kind, with equal arms, complete equilibrium would exist, provided 

 the beam were alike in every other respect. But if the arm of the 

 power be longer than that of the resistance, the resistance is to the 

 power as the length of the arm of the power is to that of the arm of 

 the resistance; so that if the former be double or triple the latter, the 

 power need only be 'one-half or one-third of the resistance, in order 

 that the two forces may be in equilibrium. A reference to the figures 

 will exhibit this in a clear light. The three levers are all presumed 

 to be of equal substance throughout, and to be ten inches, or ten feet, 

 in length. The arm of the power, in Fig. 174, is the distance P F, 

 equal to eight of those divisions ; whilst that of the resistance is W F, 

 equal to two of them. The advantage of the former over the latter is, 

 consequently, in the proportion of eight to two, or as four to one ; in 

 other words, the power need only be one-fourth of the resistance, in 

 order that the- two forces may be equilibrious. In the lever of the 

 second kind, the proportion of the arm P F of the power is to that of 

 the resistance, W F/ as tenthe whole length of the lever to two ; 

 or five to one ; whilst, in the lever of the third kind, it is as two to 

 ten, or as one to five; in other words, to be equilibrious, the power 

 must be five times greater than the resistance. We see, therefore, 

 that in the lever of the second kind, the arm of the power must neces- 

 sarily be longer than that of the resistance, since the power and the 

 fulcrum are separated from each other by the whole length of the 

 lever ; hence this kind of lever must always be advantageous to the 

 power; whilst the lever of the third kind, for like reasons, must always 

 be unfavourable to it, seeing that the arm of the resistance is the 

 whole length of the lever, and, therefore, necessarily greater than that 

 of the power. 



It can now be understood why a lever of the first kind should be 

 most favourable for equilibrium; one of the second for overcoming re-, 

 sistance ; and one of the third for rapidity and extent of motion : for 

 whilst, in Fig. 176, the power is moving through the minute arc at P, 



