1887.] Library. 151 



9. On the Differential Equation of a Trajectory. — By Asutosh 

 Mukhopadhyaya, M. A., F. R. S., F. R. S. E. — Communicated by 

 the Hon. Dr. Mahendralal Sarkar, C. I. E. 



(Abstract.) 



This paper is devoted to a consideration of Mainardi's problem of 

 determining the oblique trajectory of a system of confocal ellipses. 

 Mainardi's result, which, is reproduced by Boole in his Differential 

 Equations, pp. 248 — 251, comes out in a very complex form ; it is, how- 

 ever, shewn in the present paper that the co-ordinates of any point 

 on the trajectory may be represented by the remarkably simple pair of 

 equations 



x = a cos cf> cos h n (Ax <f>) 

 y — b sin cf> sin h n (\x<f>) 

 where a, b are the semi-axes of the ellipse, n the tangent of the angle of 

 intersection, A an arbitrary constant, and <£ a variable parameter ; an 

 elegant geometrical interpretation of these equations, by means of a 

 hyperbola, is added. 



The paper will be printed in the Journal, Part II, for 1887. 



The subject of conversation by the Philological Secretary — 

 " The International Congress of Orientalists at Vienna, held in 1886," — 

 was postponed. 



Library. 



The following additions have been made to the Library since the 

 meeting held in April last. 



Transactions, Proceedings and Journals, 

 presented by the respecting Societies and Editors. 



Baltimore. Johns Hopkins University, — American Chemical Journal, 



Vol. IX, No. 1, February, 1887. 

 . t . — . . American Journal of Philology, Vol. VII, No. 4, 



December, 1886. 



. . Circulars— Vol. VI, No. 56, March, 1887. 



-. Studies from the Biological Laboratory, — Vol. 



Ill, No. 9, February, 1887. 

 Batavia. Bataviaasch Genootschap van Kunsten en Wetenschappen, — 

 Notulen, Deel XXIV, Aflevering 4. 



