54 



THE GEOLOGIST. 



There are certain views put forward which, unless I am mistaken, are 

 opposed to the known facts of physical astronomy, and although my mathe- 

 matics are rather rusty, I think I am justified in the following criticisms. 

 At p. 442 you speak of effects which changes in the sun's mass would pro- 

 duce in its attraction upon the earth. But would not any matter either 

 dissipated from or deposited on the sun, continue to attract the earth 

 equally before and after dissipation or deposition, the centre of attraction 

 being in every case the centre of gravity of that matter the sun and 

 the earth, and the whole quantity of matter continuing constant. JSTor can 

 it be supposed that the position of the centre of gravity could be sensibly 

 altered by such changes. 



At p. 443 you refer to Tyndall's expression that the moon " skids the 

 earth." He is considering her tide- generating influence, and shows that 

 she must retard the earth's rotation, but you have spoken, unintentionally 

 no doubt, as if this action had an effect on the orbital motion. Now it is 

 a well-known principle of mechanics, that the motions of rotation and trans- 

 lation are independent of each other ; although they may have been origi- 

 nally both given by the same impulse. 



Unless I am wrong, there is a mistaken idea which runs through por- 

 tions of your articles in ISTos. h /2, 73. You appear to suggest that with a 

 larger extent of orbit there would be greater velocity of the earth in her 

 orbit, and that the effect of a diminished orbit through the action of a re- 

 sisting medium would be to lessen the velocity in the orbit. One passage 

 in which this idea is presented is this, " if we consider the effects of a 

 higher orbital velocity, we shall find it would give rise probably to a 

 larger extent of orbit." 



Now it is usually considered (I may say proved) that the reverse is the 

 case. This may be deduced from Kepler's third law, that the squares of 

 the periodic times of the planets are proportional to the cubes of their 

 mean distances,— a law which is proved, from mechanical considerations, 

 to be true of all cases of planetary motion. 



Suppose, for simplicity's sake, that the orbit may be considered a circle 

 for one revolution, which, with the rarity of the cosmical ether and small- 

 ness of the ellipticity, is sufficiently true for the purpose. 



Expressed symbolically, let T be the periodic time ; a, mean distance : 



. • . T 2 oc a 3 



But in the case of a circular orbit, the velocity (V) is constant : 



. • . TV = 2ira 

 m 2ira 



. T = -r 

 ••• (^) 2oc « 3 



...Voc JL 



. ■ . As the distance of a planet from the sun is increased, the velocity in 

 the orbit will be diminished, and vice versa. 



Hence, paradoxical as it might appear, the effect of a resisting medium 

 by causing the planets to fall towards the sun, and so diminishing their 

 mean distances, is to increase the orbital motion of the heavenly bodies 

 {vide Pratt's 'Mechanical Philosophy,' p. 600). Any changes of the velocity 

 of rotation would be wholly independent of these effects. 



Believe me, my dear Sir, faithfully yours, 



O. Fishek. 



Elmsteady Colchester, 2nd January, 1864. 



