156 A. Mukhopadhay — On Parabolas. [JuNB, 



district about 1870 1 have taken great interest in sucli matters. But 

 I never could find out that any natives knew anything about them or 

 ever saw any of them. During this last touring season I have discover- 

 ed that they are to some extent known. They are noted as being made 

 of the very best copper obtainable. 



*' The people here call them Kurabhau (or it may be Kuruphau ?) 

 and they believe they fall from the sky during the thunderstorms. 

 They are occasionally ploughed up and brought to the Sonars and brass 

 workers, who purchase them at 12 annas to 1 rupee per ser, and melt 

 them up. An old Kasera of Chiebli, before me to-day, told me he has 

 seen 15 or 20 of them, but never knew they were of value." 



The following papers were read : — 



1. A list of the Ferns of Simla, in the N. W. Himalayas, between 

 levels of 4,600 and 10,600 feet.— By H. F. Blanford, Esq., F. R. S. 



2. Notes on some Indian Chiroptera. — By W. F. Blanford, Esq., 

 F. R. S. 



3. On new or little known butterflies from the Indian Region. — By 

 L. DE Nic'eville, Esq., F. E. S. 



These papers will be published in full in the Journal, Part II. 



4. On the Differential Equatioii of all Parabolas. — By Babu Asutosh 

 MuKHOPADHYAT, M. A., F. R. A. S., F. R. S. E. 



(Abstract.) 

 The object of the author in the present paper has mainly been the 

 discussion of the differential equation of all parabolas, which, it is be- 

 lieved, is geometrically interpreted here for the first time. The paper 

 is divided into four sections, of which the first is introductory, giving 

 the easiest method of deriving the differential equation of all parabolas 

 from the integral equation of the conic, and explaining the exact mean- 

 ing of the process of geometrically interpreting differential equations. 

 The second section is devoted to a full exposition of Transon's Theory 

 of Aberrancy ; in addition to the ordinary terms, angle of aberrancy, 

 axis of aberrancy and centre of aberrancy, three new terms are in- 

 troduced, namely, the radius of aberrancy, being the distance between 

 the given point on the curve and the corresponding centre of aberrancy, 

 the index of aberrancy, being the reciprocal of the radius of aberrancy, 

 and the aberrancy curve, being the locas of the centre of aberrancy. A 

 lemma is then proved, establishing a relation between the angle includ- 

 ed by the normal and central radius vector at any point of a conic, 

 the radius of curvature of the conic at that point, and the radius of curva- 

 ture at the corresponding point of the evolute. The well-known value of 

 the angle of aberrancy is then easily obtained, and expressions are also 



