426 



MUSCULAR MOTION. 



happens, that the muscle is inserted at the most favourable angle: it is 

 generally much smaller than a right angle. Reverting to the deltoid, 

 this muscle is inserted into the humerus at an angle of about ten de- 

 Fig. 179. 



Action of the Biceps. 



A. The os humeri. B. The ulna. C. The radius. D. The biceps. 



into the radius. 



E. Insertion of the biceps 



grees. Now, a power acting obliquely upon a lever, is to one acting 

 perpendicularly, as the sine of inclination, represented by the dotted 

 line F s, Fig. 177, to the whole sine P P. In the case of the deltoid, 

 the proportion is as 1,736,482 to 10,000,000. Wherefore, if the 

 muscle had to contract with a force of one hundred and eighty pounds, 

 owing to the disadvantage of its insertion near the fulcrum, it would 

 have, from the two causes combined, to exert a force equal to 1,058 

 pounds. 



Again, the direction in which the fibres are inserted into the tendon 

 has great influence on the power developed by the muscle. There are 

 few straight muscles, in which all the fibres have the same direction as 



the tendon. Fig. 180 will exhibit the 

 loss of power, which the fibres must 

 sustain in proportion to the angle of 

 insertion. The fibre t F would, of 

 course, exert its whole force upon the 

 tendon, whilst the fibre t 90, by its 

 contraction, would merely displace the 

 tendon. Now, the force exerted is, 

 in such case, to the effective force, 

 that is, to that which acts in moving 

 the limb, as the whole sine F is to 

 the sines of the angles at which the 

 fibres join the tendon represented by 

 the dotted lines. Borelli and Sturm 

 have calculated these proportions as 



follows: At an angle of 30, they are as 100 to 87; at 45 as 100 to 

 70; at 26 as 100 to 89; at 14 as 100 to 97; and at 8 as 100 to 99. 

 The largest angle, formed by the outer fibres of the deltoid, is esti- 

 mated by Haller at 30: the smallest about 8. If this disadvantage 



Fig. 180. 



70' 



Insertion of Fibres into Tendon. 



