410 



the whole mass will be supported, whilst in 

 B it will fall over on the side of II . 



A Fig. 210. B 



MOTION. 



In the third order of lever the power acts 

 between the prop and the resistance (fig. 213), 



Fig. 213. 



B 



In most animals moving on solids, the centre 

 is supported by variously adapted organs; 

 during the flight of birds and insects it is 

 suspended ; but in fishes, which move in 

 a fluid whose density is nearly equal to their 

 specific gravity, the centre is acted upon 

 equally in all directions. 



The lever. Levers are commonly divided 

 into three kinds, according to the relative po- 

 sitions of the prop or fulcrum, the power, and 

 the resistance, or weight. The straight lever of 

 each order is equally balanced when the power 

 multiplied by its distance from the fulcrum 

 equals the weight, multiplied by its distance, 

 or P the power, and W the weight, are in 

 equilibrium when they are to each other in the 

 inverse ratio of the arms of the lever, to which 

 they are attached : the pressure on the fulcrum 

 however varies. 



In straight levers of the first kind, the ful- 

 crum is between the power and the resistance, 

 as in Jig. 211, where F is the fulcrum of the 



Fig. 211. 



lever A B ; P is the power, and W the weight 

 or resistance. M"e have P : W : : B F : A F, 

 hence P. AFrsW. BF, and the pressure on the 

 fulcrum is both the power and resistance, or 

 P+W. 



In the second order of levers (Jig. 212) the 

 resistance is between the fulcrum and the 

 power ; and, as before, P : W : : BF : AF, but 

 the pressure of the fulcrum is equal to W P, 

 or the weight less the power. 



Fig. 212. 



where also P : W : : BF : AF, and the pressure 

 on the fulcrum is P W, or the power less the 

 weight. 



In the preceding computations the weight of 

 the lever itself is neglected for the sake of sim- 

 plicity, but it obviously forms a part of the 

 elements under consideration, especially with 

 reference to the arms and legs of animals. 



To include the weight of the lever we have 

 the following equations : P. AF+AF. AF= 

 W. BF+BT. J BF ; in the first order where 



AF and BF represent the weights of these 

 portions of the lever respectively. Similarly, 



in the second order P. AF = W. BF+AF- ^ 

 and in the third order P. AF=W. BF+BT. 



BF 



2 



In this outline of the theory of the lever, the 

 forces have been considered as acting ver- 

 tically, or parallel to the direction of the force 

 of gravity. 



The head moving backwards and forwards 

 on the atlas acts on the principle of the 

 first kind of lever, the fulcrum being placed 

 between the power and the resistance. The 

 tibia resting on the astragalus acts on the prin- 

 ciple of the second order of lever, when the 

 heel is raised by the tendo Achillis, the re- 

 sistance being between the power and the 

 fulcrum, or between the heel and the toes. 



In lifting a weight by the hand and bending 

 the elbow-joint, as in.fig. 214, in which p the 

 power, or biceps muscle is inserted at a between 

 the fulcrum f, and the resistance w or b, we 

 act on the principle of the third order of lever. 



In the latter case, however, the power, in- 

 stead of acting vertically, is applied obliquely, 

 and the lever, instead of simply resting on the 

 fulcrum, turns upon a point at./", Jig. 214. 

 Instead, therefore, of estimating the values of 

 p and w as before, according to their reciprocal 

 distances from the fulcrum, we resolve each of 

 them into two other forces by perpendiculars 

 drawn from the fulcrum f to the directions of 

 the forces p and w. Thus, in Jig. 214, p will 

 not be to w as b f to af, but as the perpen- 

 diculars from /on the vertical line through/) 

 to that on a c the direction of the insertion of 

 the muscle. 



The pulley. The principles of the simple 

 pulley are introduced into the mechanism of 

 animals for the production of motion, and to 

 change the directions of the motions of several 

 organs in reference to that of the tendons 



