53.2 Mr. D. D. Heath on a passage in 



what he found in an author whom he trusts. Not having access 

 to Mayer, I will speak of the argument as his own. 



I cannot persuade myself that it is not vague, incorrect, and 

 inconsistent. If, however, it had appeared in any transactions 

 or other work addressed to the learned, I should not have med- 

 dled with it : they can take care of themselves. But where it 

 is, it comes with the authority of a teacher, and its doctrine will 

 be quoted in all the drawing-rooms in London, and I hope in 

 all the schools in the kingdom. Therefore I think that, if ques- 

 tionable, it ought to be questioned, and an explanation called for. 



My first difficulty is in ascertaining what is meant to be 

 asserted. The statement at the end, that " the heat produced 

 by the friction of the millstones of a tide-mill is produced at 

 the expense of the earth's rotation/'' paralleled as it is with 

 " the heat of another mill turned by a mountain stream " — 

 which is indisputably derived from the work done by, and there- 

 fore is entirely " at the expense of the sun's radiation/'' — leads 

 to the inference that the thing spoken of is all the heat produced 

 everywhere by the tidal action ; and that it is conceived that this 

 heat, estimated in its dynamical equivalent, would on an average 

 be found to be at all events not greater than the contemporaneous 

 loss of vis viva of rotation. 



But the most elementary consideration of the matter shows 

 that this is not so. The heat developed at each point is practi- 

 cally ascertained by the strength of the current (i. e. of the rela- 

 tive velocity of the water), and the coefficient of friction ; . and as 

 the velocity of the current is sensible and the supposed retarda- 

 tion of rotation is quite insensible in thousands of years, it is 

 quite indifferent to the calculation whether there is a retardation 

 or not. When Professor Tyndall drops his leaden ball from the 

 top of his lecture-room, it is mathematically correct to state that 

 the earth moves, or tends to move, upwards to meet it with an 

 equal momentum*, and that the collision will generally cause a 

 loss of motion and of vis viva in the earth as well as in the ball : 

 but if the same experiment happened to be performing simulta- 

 neously at his antipodes, the earth's motion would be neutralized. 

 His formula, that " the heat generated increases as the square of 

 the velocity/' is strictly true only in the latter case; but the 

 error in the former is infinitesimally small ; for though the mo- 

 mentum of the earth is equal to that of the ball, its loss of vis 

 viva is immeasurably less. And in like manner, even if every 

 tidal motion over the whole ocean were checking the rotation, 

 the whole mass of the water is so small that the loss of vis viva 

 and production of heat would be rightly calculated from the loss 



* Mr. Grove, by the way, does not seem to be aware of this elementary 

 doctrine (Correlation of Forces, 4th ed. p. 20). 



