I9I2] William N. Berg 109 



If in I c.c. of muscle there are 5 X lo^*' rods, the lateral area of 

 each of which diminishes from 4.8 /a^ to 2.8 /^^ when the muscle con- 

 tracts, the total reduction in area is 5 X 10^" X 2 /x,2__io^i fx^ = 

 lO'^ cm. 2 (i ju. = 0.001 mm.). The calculations will be simplified 

 if it be assumed that the increase in surface tension is instantaneous, 

 giving the contracting muscle the largest surface tension during the 

 entire contraction phase. Then since 

 surface energy liberated = diminution in area X surface tension, 



(e.,s) (c..^) {^) 



the energy liberated is 1000 X 85 ergs. Let it be assumed that all of 



this is transformed into external work — lifting a weight — and that 



the resultant heat arises from the activity of a different mechanism ; 



in short, that the muscle is an engine having an efficiency of 100 



per Cent. How great a weight will this i c.c. of muscle lift? Since 



there are 800 layers of rods, and each layer shortens by 3 /-i during the 



contraction (see Plate i herewith), the muscle shortens by 2400 /a 



or 2.4 mm., lifting a mass of W grams 2.4 mm. The energy (ergs) 



expended in lifting a mass of W grams thru the distance D (cm.) 



is PF X ■C' X 981 ergs, since gravity = 98i dynes. Therefore the 



8s,ooo 

 85,000 ergs will hft ^^3^ = 361 grams. 



According to Zuntz (1. c, p. 23) i gram of muscle substance 

 can do 0.002 kilogram-meter of work in one contraction under 

 favorable conditions. If this muscle shortened 0.24 cm. as the 

 above muscle did, it would lift a trifle more than 800 grams. Bern- 

 stein^^ mentions 600 grams at least, as the pull of i cm.^ of frog 

 muscle in an isometric contraction. Insofar as i cm.^ of many 

 kinds of muscle can support without lengthening (but not lift) 

 several kilograms — about 6 kilograms for human, and probably 

 more for certain types of insect muscle — the above figure of 361 

 grams, as the weight a muscle could lift, is small, especially when it 

 is borne in mind that it is an improbable maximum. 



The foregoing discussion may be summarized as f oUows : 



I. Too often there is a general lack of definiteness in the mathe- 



" Bernstein, J. : Arch. f. d. ges. PhysioL, 1905, 109, 326. 



