196 



DISCOVERY 



/ Principt della Meccanica alia luce della Critica. By 

 Giuseppe Casazza. (Societa Editrice Dante 

 Alighieri di Albreghi, Segats & C, I-. 8.50.) 



The Physiography of the McMurdo Sound and Granite 

 Harbour Region. By Griffith Taylor, D.Sc, 

 F.R.G.S., etc., C. S. Wright, O.B.E., M.C., and R. E. 

 Priestley, M.C. British (Terra Nova) Antarctic 

 Expedition of 1910-13. (Harrison & Sons, Ltd.) 



The Natural History of Wichen Fen. Part I. Edited by 

 Prof. J. Stanley Gardiner, F.R.S., and A. G. 

 Tansley, F.R.S. (Bowes & Bowes, 35. 6d.) 



Scientific Method. By A. D. Ritchie. (Kegan Paul, bs.) 



The Phase Rule. By A. C. D. Rivett. (Oxford I'ni- 

 versit}' Press, los. 61^.) 



Dreams of an Astronomer. By Camille Flammarion, 

 Translated from the French by E. E. Fournier 

 d'Albe. (T. Fisher Unwin, los. 6d.) 



Petrology for Students : An Introduction to the Study of 

 Rocks under the Microscope. By Alfred Harker, 

 M.A., LL.D., F.R.S., F.G.S. Sixth edition, revised. 

 (Cambridge University Press, 85. 6rf.) 



The Properties of Engineering Materials. By W. C. 

 Popplewell and H. Carrington. (Methuen, 28s.) 



Six Great Scientists. By Margaret Avery'. (Methuen, 

 25. 6d.) 



Correspondence 



AXIAL ROTATION 



To the Editor of Discovery 



Dear Sir, 



I was much interested in Mr. J. Marshall's letter 

 upon Axial Rotation in the May Discovery ; it is a 

 difficulty which I have often met with in others during 

 my many years' experience of teaching astronomical 

 science. 



In the first place Mr. Marshall has not got hold of the 

 idea of the laws that govern lunar rotation, because he 

 states that it seems to him that the moon must turn the 

 same face to the earth if its period be what it is, or 

 28,000,000 years. 



The moon-earth system is one that is bound together 

 by tidal attraction, and this same force is tending to 

 drive the moon farther and farther from the earth, which 

 state of affairs is gradually slowing down the earth, but 

 at the same time is speeding up the moon. The day will 

 therefore come in the dim future when those who are then 

 living will see the other side of the moon. 



Mercury is almost certainly bound to the sun by the 

 same tidal forces, but it is far more likely that Venus has 

 a rotation period not verj- different from our own. 



I think that by the aid of the diagram I have prepared 

 Mr. Marshall's difficulty will vanish and he will see that 

 in the various cases he mentions axial rotation is taking 

 place. 



We will first of all suppose the figure to be a section 

 of the earth-moon system. Let the circle abed be the 

 earth, and let i, 2, 3, 4 be four positions of the moon. 

 Also let e be the centre of the moon, and / be the centre 



of the earth, and let A be a point on the moon's surface 

 where the line ef cuts the moon i. 



Now if the moon simply revolved upon its orbit without 

 rotation upon an axis, wg see that the line ef will have 

 shifted to hk, which must be parallel to ef when the moon 

 arrives at 2. Therefore the point A will no longer be 

 opposite the earth, but will be 90 degrees from the earth. 



Now we know from observation that this is not the 

 case, the point A must be opposite the earth whenever 

 the moon may be upon its orbit, and therefore A is not 

 on the line hk, but is on the line tnf ; and thus the moon 

 must have rotated through 90 degrees on its own axis, 

 and so on for any other position. 



We can thus show that a rotation of 180 degrees has 

 taken place when the moon gets to 3, and 270 degrees 

 when the moon arrives at 4 ; and therefore one complete 

 rotation when the moon arrives back at i. 



The reason why a lunar observ-er at A will not see the 

 earth rise and set is not because the moon has no rotation, 

 but because the revolution and rotation are equal, owing, 

 as we said above, to tidal attraction. 



Now let the diagram illustrate the seconds dial of a 

 clock, and it can be sho%vn that if the disk did not rotate 

 as well as revolve, it would break away from the hand. 



In the diagram the hand is at 30 seconds when the disk 

 is at position i ; and therefore the pivot of the hand is at 

 f on the line yfaAe. 



By the time the hand gets to 45 seconds the point A 

 is on the line bfdm and not on the line hmk ; therefore A 

 has rotated tlirough 90 degrees ; and so on for any other 

 position. 



Mr. Marshall can employ the same diagram to work out 

 his problem of a cricket ball on a string, and also the ball 

 placed at the end of a railwav turntable. 



I am, sir, yours, etc., 

 12, RoTHSAY Gardens, John L. A. Sillem. 



Bedford. 

 April 30, 1923. 



