1889.] A. MakhopadhysLj— Elliptic Functiovs and Mean Values. 199 



killer, &c. and where sucli liigli air temperatures prevail. It is probably 

 the fact that the custom in India of having almost all doors and win- 

 dows constantly open has proved a safeguard against such poisoning in 

 the case of libraries, etc., where mercuric chloride has been and is being 

 used, but it does not appear to be desirable to rely on this fact, and 

 it would be safer to discontinue altogether the use of such an insidious 

 poison as mercuric chloride for the purposes above described. 



X.— (Some Applications of Elliptic Functions to ProUems of Mean Values. 

 (First Paper).— By Asutosh MuKnoPADHTAY, M. A., F. R. A. S., 

 F. R. S. E. 



[Roccivod July 25th ;— Road Augnst 1st, 1888.] 

 (With a Woodcut.) 

 Contents. 



§ 1. Expression for tlie area common to an ellipse and a concentric circle inter- 

 secting it. 



§ 2. Mean value of the common area when the intersecting circle is of variable 

 radius. 



§ 3. Expression for the angle of intersection of the ellipse and the circle. 

 § 4, Mean value of the angle of intersection. 



§ 5. Mean value of the angle of intersection of the lines joining the opposite 

 corners of the figure formed by the intersection of the ellipse and the 

 circle. 



§ 6. Moan value of the arc of the circle intercepted by the ellipse. 



§ 1. Expression for Common Area. 



The object of the present paper is to discuss some problems of 

 Moan Values which are chiefly interesting from the mode in which the 

 application of Elliptic Functions simplifies the calculations. 



In the first place, let us consider an ellipse and a concentric circle 

 intersecting it ; then, if the ellipse be NPA, and the circle ISTPR, the 

 area of the portion common to both the curves may be found as followSi 

 m;;.,the ellipse being 



