1887.] A. Mukhopadhyaya— On Mongers Equation. 185 



(Catalogue, page 195, Plate IV, 2). 



No. 15. 



Kumara Gupta Mahendra. 



Lion-Trampler type, var. a. Obv. design as described in catalogue. 

 Legend ' Sri Sikye Devata.' The ' Sri Si — ' are plain, but I am not 

 sure of the remaining letters. At first I read ' Sri Sinna,' but this 

 seems hardly tenable. 



Rev. legend, ' Sri Mahendra Sinha,' Lion to r. monogram 8a. 



The obv. legend is new. 



(Catalogue, page 196.) 



No. 16. 



Uncertain, probably Chandra Gupta II, Lion-Trampler type. 



The obv. and rev. devices agree with var. 8 of Chandra Gupta II, 

 (Catalogue, page 184). The only legible character in the obv. legend 

 is « ka.' 



No trace of rev. legend. Lion to left. Monogram 196. 



5. On the Couplets, or " Baits," on the Coins of Shah Nuru-d-din 

 Jahangir, the son of AJcbar. — By C. J. Rodgers, Esq. 



The paper will be published in Part I of the Journal. 



6. On Monge's Differential Equation to all Conies. — By Babu Asu- 

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

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



(Abstract.) 

 This paper, which is devoted to a consideration of Monge's differ- 

 ential equation to lines of the second order (noticed by Boole at the 

 end of the first chapter of his " Differential Equations "), is divided 

 into six sections. The first section gives a short historical introduction ; 

 the second section treats of the easiest way of deriving the Mongian 

 equation from the equation of the Conic ; the differential equations of 

 all parabolas, all circles, and all Conies referred to co-ordinate axes 

 through the centre, are easily obtained incidentally. The third section 

 shews how the Mongian equation can be completely integrated by 

 ordinary methods, a problem which does not appear to have been solved 

 before. The fourth section shews how the same equation may be inte- 

 grated by means of an integrating factor ; and, this process furnishes an 

 immediate proof of a theorem by Professor Michael Roberts, relating 

 to a second integral of the Mongian equation. The fifth section fur- 

 nishes an easy proof of the permanency of form of the Mongian equa- 

 tion, as well as of several other differential equations whose geometrical 



