184 A. Mukhopadhdya — O71 Elliptic Functions. [Aug. 



3. The second set of coins consists of 80 Rupees, 79 of which 

 belong to the following emperors of Dehli : — 



No. of specimen. 

 I. AuEANGziB, A. H. 1068— 1118= A. D. 1658— 



1707 ; mint and date illegible ; regnal year 15 1 



IT. Bahadur Shah, A. H. 1118—1124 = A. D. 1707— 

 1712 ; mint : Daru-s-saltanat Lahor ; date : 

 1120, 2 1 



III. Farrukhsiya'r, a. H. 1124— 1131 = A. D. 1712— 



1719; mints: Mustaqira-1-khilafat Akbarabad 

 and Darn-1-khilafat Shahjahanabad ; dates : 

 3131, 7 and — , 5 2 



IV. Muhammad Shah, A.H. 1131—1161 = 1719—1748; 



a, type : Sdhih Qirdn ; mint of all : Darn-1-khila- 

 fat Shahjahanabad ; legible dates 1133, 1136, 



1146, 1149, 1153 IB 



fc, type : Bddshdh Ghdzi ; mint of all, except one, 

 Dar-s-saltanat Lahor, of one, Mnltan ; legi- 

 ble dates : 1134, 1144, 1148, 1152, 1157, 1158 57 

 The remaining coin of the second set belongs to the Sikh Raja 

 Ranjit Singh, dated Samvat 1885 ( = 1828 A. D.) and struck at Amrit- 

 sar. It is, however, a forgery, being copper silvered over. 



The following papers were read : 



1. On the Mother of Jehdngir. — By Mahamahopadhtaya Kaviraja 

 Shyamal Das, M. R. A. S., F. R. H. S. 



2. Note on the Arthuwa (Sanskrit) Inscription. — Bij Mahamahopa- 

 DHYAYA Kaviraja Shyamal Das, M. R. A. S., F. R. H. S., (with an 

 ink impression) . 



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



3. Some Applications of Elliptic Functions to Problems of Mean 

 Values. — By Babu Asutosh Muehopadhyay, M. A., F. R. A. S., F. R. 

 S. E. 



(Abstract.) 

 The present paper is occupied with the discussion of some problems 

 of geometric mean values, which are chiefly interesting from the mode 

 in which the applications of elliptic functions simplify the calculations. 

 The paper is divided into six sections, of which the first gives an ex- 

 pression for the area common to an ellipse and a concentric circle inter- 

 secting it ; the result is expressed as the sum of two inverse-sine- 

 functions. The second section discusses the average value of the area 

 common to an ellipse and a concentric circle of variable radius which 



