THE LEVER AND MUSCULAR MECHANISM. 



13 



Whence is produced : 



F 

 F' 



01) 



c ' 



Fio. 5. 



That is to say, that the forces are to each other inversely as the arms of their lever : 

 great force, small lever-arm, and, reciprocally, large lever-arm, small force. 



Again, the intensity of the forces varies according to their degree of inclina- 

 tion. The three following cases may present themselves : 



1st. The force makes a right angle with the lever-arm. 



It acts then with its maximum of intensity. This is, in fact, the case where 

 the lever-arm is the most considerable; it is measured by the distance of the 

 point of application of the 

 force to the jjoint of relation. 



2d. The force makes an 

 acute angle (Fig. 5). 



Let the force F act upon the 

 lever AOB. If it acted perpendic- 

 ularly, its lever-arra would be AO. 

 Now, OA is > than OC, as oblique 

 upon AFviiih reference to the per- 

 pendicular OC, arm of the lever of 

 F. Thus a certain part of the force 

 employed in repelling the fixed 

 point is lost for the movement of 

 the point A. This is seen by de- 

 composing F into two forces, AE 

 and AD, acting upon the point 

 A, following the directions indi- 

 cated. AD is the quantity em- 

 ployed to repel the fixed point. 



It may be conceived that the more the angle formed by the force with its 

 lever-arm is acute, the greater will be the increase of AD at the expense of AE, 

 and the force utilized for the movement will thus be less. The disposable force 

 will be null if F becomes parallel to the arm of its lever. 



3d. The force makes an obtuse angle (Fig. 6). 



In this case the arm of the lever OC is smaller than if F were perpendicular to OA, since it 

 would be OA itself. Thus a certain 

 ^jart of F is lost in drawing A tow- 

 ards AD at the expense of the 

 movement. The more the inclina- 

 tion of F is obtuse, the more the 

 component AD will increase rela- 

 tively to the component AE, alone 

 useful for the movement. The 

 parallelism of F with its arm would 

 cause, as in the preceding case, total 

 annulment of AE, without there 

 being any possible movement. 



Thus it results from the 

 preceding remarks that every 

 time a force is not perpen- 

 dicular to its lever-arm, a ^ g 

 part of its intensity will be 



attracting or repelling the point of support according to the nature of the angle 

 formed. - , . , 



