INTRODUCTION 67 



tially by hooking the muscle to a very strong spring balance) the force 

 being exerted can be determined. The use of these data depends on the 

 questions being asked. One could ask for the total energy being ex- 

 pended, in which case a simple multiplication of the force and the distance 

 through which it moved (the contraction) gives the external work clone 

 by the muscle. This doesn't answer the entire question, because there are 

 quite obviously three energies to be reckoned with: 



(a) the external work done, 



(b) the work done in maintaining the readiness of the muscle, and 



(c) the energy dissipated, as in heat, for there is always some in- 

 efficiency in any machine, even the human one. 



There are still other questions. An important one derives from reason- 

 ing that the total external work done isn't always the important thing — 

 some situations might be better described in terms of the rate at which 

 work is being done, for that measures the extent of the immediate avail- 

 ability of the energy. In this case, as shown in an introductory physics 

 course, the rate can be computed from the product of the (assumed 

 constant) force and the velocity of contraction of the muscle. From this 

 rate of doing work the energy expended is computed by first multiplying 

 each rate by the duration of its persistence, and then adding the products, 

 in the same way that an electric company computes the electrical energy 

 we have used by adding the products obtained by multiplying the various 

 rates by the duration of use of each. The formula can be stated as 



B = f - Pv, 



where R is the rate of energy E expended in a time t if a pull (or force) 

 P is accomplished with a contraction velocity v. (These symbols are 

 chosen to conform to practice in muscle research laboratories.) 



By studying a number of muscle preparations from different sources, 

 it has been found, empirically, by A. V. Hill (one of the pioneers of 

 biophysics and of muscle research) that a generalization can be made: 



(P + a)v = constant. 



Here a is a factor whose existence is readily rationalized. It is the internal 

 force expended to make the muscle contract, and therefore the product av 

 is the rate at which work is done to contract the muscle itself. The 

 magnitude of a can be determined from heat measurement, to be dis- 

 cussed later. This term is entirely similar to the corresponding correc- 

 tion to the ideal gas law. 



PV = constant 



