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XXYI. — On the Rotatoey Motion of the Heavenly Bodies. By 

 the Rev. W. G. Penny, M. A., Professor of Mathematics in the 

 Catholic University of Ireland, and late Mathematical Scholar in the 

 University of Oxford. 



[Read February 24, 1868.] 



1. The object of the present Paper is, in the first place, to ascertain 

 whether the various disturbing forces which act upon the heavenly bo- 

 dies produce any permanent effect upon their rotation; and, secondly, 

 supposing such an effect to exist in general, to ascertain under what 

 circumstances it will cease to do so — that is to say, what are the con- 

 ditions under which they would rotate permanently without any but 

 periodic changes. 



The inquiry may be of some interest, for two reasons : — First, it has 

 been ascertained that the observed acceleration in the motion of the 

 moon has been only partially accounted for by the diminution of the 

 excentricity of the earth's orbit, to which cause part of it, though not 

 much more than half, is undoubtedly due ; that is, if we calculate 

 what onght to have been the angular distance of the sun and moon at 

 the time of an ancient eclipse — say 2500years ago — it is found that, 

 after making allowance for the acceleration produced by the cause men- 

 tioned, that their angular distance so calculated does not agree with 

 what it was actually observed to have been. Now, such an error might 

 be produced either by an error in the supposed velocity of the moon, or 

 of that of the sun, i. e. of the earth ; but both these have been care- 

 fully examined, and found to be inadequate to explain the phenomena. 

 There is, however, a third cause which would give rise to the same dis- 

 crepancy between theory and observation — namely, an error in the mea- 

 sure of time — just as an error in a ship's longitude at sea might be 

 caused by an error in the rate of the chronometer. Just so an error in 

 the angular distance of the sun and moon a certain number of years ago 

 might be caused by an error of any one of the three elements which 

 enter into it — the length of the year, the length of the month, and the 

 length of the day; and so it is evident that, if the length of the day has 

 undergone any sensible alteration since the date of the eclipse above 

 spoken of, the real length of time that has elapsed since then must be 

 different to what would be supposed if the length of the day had re- 

 mained invariable ; and thus the relative positions of the sun and moon 

 would also be different. Accordingly, it was suggested by M. Delaunay 

 that possibly the length of the day — or, in other words, the velocity of 

 the earth's rotation — had varied. 



In the next place, the moon, and it is said satellites generally, turn 

 always the same face towards their primaries ; that is, they rotate about 

 their axes in the same time that they perform a revolution about 

 their primary. And it has been asked whether there is any cause for 

 this ; in other words, whether the body about which they revolve exerts 

 any influence upon them which would affect the rotatory motion, so as 



E. I. A. PEOC. VOL. X. 2D 



