1888.] Library. 185 



always intersects it ; tlie result is expressed in terms of the perimeter of 

 the ellipse, and, therefore, involves the complete elliptic integral of the 

 second kind with the eccentricity for modulus. In the third section is 

 obtained an expression for the angle of intersection of the circle and the 

 ellipse. The fourth section furnishes the mean value of this angle of in- 

 tersection ; the result is found to depend on two complete elliptic integrals 

 of the first and third kind, with the eccentricity for the modulus ; the 

 parameter is easily found to be the square of the tangent of the angle 

 which the line joining a focus with an extremity of the minor axis, 

 makes with that axis. The fifth section contains the calculation of the 

 mean value of the acute angle included between the lines joining the 

 opposite corners of the curvilinear quadrilateral formed by the inter- 

 section of the ellipse with the concentric circle of variable radius ; the 

 result involves the complete elliptic integral of the first kind with the 

 eccentricity for modulus, and is also shown to be expressible in terms of 

 the axes and the differential co-efficient of the perimeter with respect 

 to the eccentricity. The sixth and last section gives the average length 

 of the arc of the circle intercepted by the ellipse ; the mean value is 

 found to vary as the minor axis. 



The paper will be published in full in the Journal, Part II for 1888. 



LlBI^ARY. 



The following additions have been made to the Library since the 

 meeting held in July last. 



Tl\ANSACTIONS, Pl^OCEEDINGS AND JOURNALS, 

 presented by the respective Societies and Editors. 

 Bombay. Bombay Anthropological Society, — Journal, Vol. I, No. 4, 



1888. 



. The Indian Antiquary,— Vol. XVII, Part 208. May, 1888. 



Calcutta. Indian Engineering, — Vol. IV, Nos. 1 — 4. 



' . Meteorological Observations recorded at seven stations in 



India, corrected and reduced. January to April, 1888. 



. The Indian Engineer,— Vol. V, Nos. 12—15. 



Copenhagen. K. Nordiske Oldskrift-Selskab, — Aarboger, II Roekke, 



3 Bind, Heft I. 

 Edinburgh. The Scottish Geographical Society, — Magazine, Vol. IV, 



No. 6, June, 1888. 



