18 LORD ROTHSCHILD 



of bull spermatozoa, as the free energy transferred during anaerobic 

 fructolysis is 47.3 kcal/mole, which even the most confirmed optimist 

 would agree is more than the terminal phosphate bond energy of 2 

 moles of ATP. As a matter of fact, it would be very silly of bull sper- 

 matozoa to use all the free energy of fructolysis to synthesize ATP, 

 because it they did, the reaction 



Fructose + 2P, + 2ADP ^ 2 lactate" + 2ATP + 2H+ 



would be in equilibrium, and the net rate of fructolysis would be 

 zero. Paradoxically, therefore, it is useful and necessary to "waste" 

 some of the free energy of fructolysis. I referred to calculations of 

 sperm energy expenditure as an amusement, and I must confess to 

 having experienced a feeling of mild amusement when finding that, 

 in spite of being so different in regard to their motility parameters 

 and metabolism, a bull and a sea urchin spermatozoon expend the 

 same amount of energy, 2 X 10~ 7 erg per second (Rothschild, 1961). 

 Such calculations are of questionable value because we do not know 

 the effect on sperm A's energy expenditure of a nearby sperm B, 

 whether it is motionless or not. The total energy dissipated by two 

 spermatozoa beating in phase may be less than if they are out of 

 phase, though even this is not certain because Taylor's analysis of 

 this problem (1951) applied to infinitely wide waving parallel sheets, 

 which are not the same as parallel cylinders, let alone nonparallel 

 ones. Even if the problem is simplified in the following way, no an- 

 swer is available from our hydrodynamic advisers, though perhaps 

 Dr. Carlson will be able to dispel some of the gloom which surrounds 

 the following apparently simple problem. Suppose an inertialess rod, 

 or better still an inertialess rigid metal strip, oscillates in a viscous 

 medium with fixed frequency and amplitude. One can measure how 

 much energy is needed to make the strip behave in this way. Now 

 suppose one puts into the medium another, stationary strip, free to 

 oscillate, of the same size, fairly near the oscillating one, for ex- 

 ample one strip length away. How much more energy has one got 

 to pump in to keep the first strip oscillating in the same way as be- 

 fore the other, stationary strip was put in? This is, of course, a grossly 

 oversimplified system, both as regards strip density, separation, and 

 behavior, in comparison with the one in which we are really in- 

 terested. Yet the hydrodynamagician cannot answer the question. 



