MUSCULAR CONTRACTION 5 



student who is familiar with the expression for maximum work 

 done by a gas in changing its volume. The condition for 

 maximal work done by a gas in expanding from v to v' is first, 

 that the internal pressure P should be opposed at each stage by 

 an external pressure F—dp differing from it by an infinitesimal 

 amount. Then, if the process be carried out so slowly that the 

 gas is not allowed to gather momentum and dissipate part of 

 its energy as heat 



W= r FJv 



In order to realise the total amount of potential energy liberated 

 in contraction, one must imagine that the tension of the muscle 

 does work at every stage against a load differing by an in- 

 definitely small amount from the tension it exerts. Since the 

 energy released at each infinitesimal step is the product of the 

 force into the distance, the total energy is the sum of a series of 

 products Tdl ; expressed analytically : 



W= r T.dl 



(E being the extended length and C contracted length of the 

 muscle.) 



In this form it is not possible to evaluate W directly, since 

 we do not know what function T is of L. But the integral 

 formula at once suggests that the potential energy of the 

 contractile mechanism is represented by the area of a curve 

 expressing the relation of tension to length in the unstretched 

 muscle. We have therefore to construct a tension-length 

 indicator diagram for the muscular machine analogous to the 

 familiar pressure- volume indicator of the heat engine. 



The accompanying diagram (Fig. i) will explain to the 

 reader unfamiliar with the notation of the calculus the way in 

 which W is calculated. OC is the contracted, OE the extended, 

 length of an unstretched muscle. Ti is the initial tension of 

 the muscle, T2, T3, T4, etc., the tensions exerted when the 

 muscle has been allowed to shorten by equal steps A^- The 

 average tension between Ti and T2, T2 and T3, etc., are 

 represented by ^1, toy ^3, etc. In contracting through the 

 first step A^ the work done (force X distance) is hAh in 



