224 SPECIAL PHYSIOLOGY 



longus the long arm is 36 cm. and the short arm 4.8 cm. Reducing 

 these to per cent, ratios we have: For the biceps, which we will 

 designate as b, 16.6 per cent, leverage; for the brachialis anticus, 

 which we will designate as a, 13.6 per cent, leverage; and for the 

 supinator longus, which we will designate as s, 13.3 per cent, leverage. 



But there is another important consideration: Fick has demon- 

 strated that when the fibres are parallel the strength of two muscles 

 is proportional to the areas of their cross-sections (Hermann's Hand- 

 buch der Physiologic, i. p. 295). The average ratio of the diameter 

 of the three muscles in question is 4 : 2 : 1, respectively. This means 

 that with the same leverage the biceps would lift four times as much 

 as the brachialis anticus and that the brachialis anticus would, with 

 the same leverage, lift four times as much as the supinator longus. 



We have now discussed the relation of these three factors as to 

 leverage and as to relative power exerted. 



As to leverage one may say: The power of the three muscles 

 varies in proportion to biceps leverage (bl), brachialis anticus 

 leverage (a/), supinator longus leverage (si), respectively; or, mathe- 

 matically expressed, P varies as bl : al : si or varies as 16.6 : 13.6 : 13.3. 

 As to cross-section one may say: The power varies in proportion to 

 the respective cross-sections ($), or P varies as bs : as : ss= 16 : 4 : 1. 

 Now when any function varies with two or more variable factors, 

 its variation when influenced by the action of all of these factors at 

 once would be represented by the product of the several variables. 

 Then the power varies as the leverage times the cross-section of each 

 of the muscles when all act together; or, expressed mathematically, 

 P varies as b(lXs) : a(lXs) : s(lXs). 



&(/Xs) = 16.6Xl6=265.6, or 79.7 per cent, of the total power ex- 

 erted; a(lXs) = 13.6X4= 54.4, or 16.3 per cent, of the total power 

 exerted; s(lXs) = 13.3X1 = 13.3, or 4.0 per cent, of the total power 

 exerted; total = 333.3, or 100.0 per cent. 



But the weight supported by the action of these muscles is 10 kilos. 

 If the biceps does 79.7 per cent, of the total work, it would support 

 7.97 kilos. What would be tension upon the tendon of the biceps 

 when it is supporting 7.97 kilos at the end of its lever? One need 

 only to use the 16.6 per cent, leverage (7.97 -^ 16.6 per cent.) to find 

 that the tension would be 47.8 kilos. A similar process shows that 

 the approximate tension upon the tendon of the brachialis anticus 

 is 12 kilos, and upon the tendon of the supinator longus 3 kilos. 



b. The amount of contraction of a muscle bears a fairly con- 

 stant ratio to the resting length of the muscle. This law of muscle 

 physiology was discovered and demonstrated by Ed. Fr. Weber 

 (Mechanik der menschlichen Gehwerkzeuge, 1851) and was cited 

 by Strasser (Funktionellen Anpassung der Quergestreiften Muskeln, 

 1883) as an example of the adaptation of muscle tissue to the mechan- 

 ical requirements of the body. Weber showed that the maximum 



