[ 305 ] 



XXXVI. On the Moon's Libration. 

 By W. R. Birt, F.R.A.S., F.M.S. 



To the Editors of the Philosophical Magazine and Journal. 



Gentlemen, 



MAY I trespass on your kind indulgence for a portion of 

 your columns to rectify a mistake into which, as it ap- 

 pears to me, Mr. Proctor has fallen in preparing his work on 

 the Moon, recently published, or at least to supply an omission ? 

 In his preface he says, "In Chapter III. I give amongst other 

 matters a full explanation of the effects due to the lunar libra- 

 tions. I have been surprised to find how imperfectly this inter- 

 esting and important subject has been dealt with hitherto. In 

 fact I have sought in vain for any discussion of the subject with 

 which to compare my own." If Mr. Proctor confines his atten- 

 tion to the effects (I have italicized the word in my quotation) 

 of libration only, the portion of the work which treats of them 

 is not entirely original as he would indicate, inasmuch as the 

 operation of libration in producing the elliptical motion of the 

 point of intersection of the moon's first meridian and equator 

 round the centre of the apparent disk was shown by me in 

 Appendix II. of the Report of the Lunar Committee of the Bri- 

 tish Association for the Advancement of Science in 1866 ; but 

 if Mr. Proctor alludes to the subject of libration generally, then 

 it would appear that he has entirely overlooked the investigation 

 of Encke in the Berliner Astronomisches Jahrbuch fiir 1843, 

 pp. 283-293. It is the method of Encke that enters as an ele- 

 ment into the computation of points of the first order ; and if I 

 remember rightly, Mr. Proctor has not made the slightest allu- 

 sion either to these points or to the method of computing libra- 

 tion, these omissions constituting defects in his work which we 

 should hardly expect to find in a writer of his ability. The fol- 

 lowing quotation from the Appendix before mentioned will show 

 that Mr. Proctor has merely worked out the principle which I 

 set forth in 1866 (Report Brit. Assoc. 1866, pp. 231-233); it 

 should be read in connexion with that portion of his work con- 

 tained in pp. 173-199:— 



" Application of the foregoing investigations to the motion on the 

 apparent disk of the point at which the Equator intersects the 

 First Meridian. 



" It now remains to inquire how the point of intersection of 

 the moon's equator and first meridian will be affected by the 

 changes in latitude and longitude which the centre of the appa- 

 rent disk is perpetually undergoing ; for as only the latitude and 

 longitude of this single point are determined by the formulae for 



Phil. Mag. S. 4. Vol. 46. No. 306. Oct. 1873. Y 



