INVESTIGATIONS IN PHYSICAL ASTRONOMY, 



PRINCIPALLr RELATIVE TO 



THE MEAN MOTION OF THE LUNAR PERIGEE. 



By the Rev. JOHN BRINKLEY, D. D. F. R. S. M. R. I. A. 



AND ANDREWS' PROFESSOR OF ASTRONOMY IN THE UNIVERSITY OF DUBLIN. 



Read April 91. 1817. 



THE difficulties that occur relative to the investigation of the mean 

 motion of the apsids of the lunar orbit are well known. Two cir- 

 cumstances have principally led me to offer to the Academy the 

 following paper on this subject. It affords me an opportunity of 

 introducing a peculiar method of integration which I hope soon to 

 illustrate more folly elsewhere. This method is I think deserving 

 of the attention of mathematicians, and as applied to the integra- 

 tion of the equation of the lunar orbit affords very convenient results. 

 The other circumstance alluded to, was a desire to improve a parti- 

 cular step that appeared defective in the lunar theory as given by 

 several authors, and recently by M. Laplace. These circumstances 

 and some deductions that offer themselves in the following investi- 

 gation will be best understood by a brief detail relative to this subject. 



VOL. XIII. F 



