198 Mr. C. W. Merrifield on the Geometry of 



excess, a white bulky precipitate was produced which rapidly 

 contracted in volume and became crystalline; after standing 

 twelve hours it was filtered and washed with a solution of chlo- 

 ride of ammonium and ammonia (the chloride of ammonium is 

 absolutely necessary). The precipitate was perfectly white, and 

 remained so after ignition, when it weighed 8-67 grs. =4'33 

 MnO ; it was decomposed and examined, it did not contain a 

 trace of nickel. 



The ammoniacal solution was treated by sulphuretted hy- 

 drogen, and the sulphide converted into oxide by roasting with 

 a little carbonate of ammonia. It weighed 5*57 grs. 

 Taken. Obtained. 



MnO . . . 4-11 4-33 



NiO ... 5-63 5-57 



I probably drove off a little sulphuric acid on igniting the 

 sulphate of manganese. I have obtained more accurate results 

 with the manganese since. 



In operating with cobalt and manganese in the same manner, 

 I obtained a slight excess of manganese, and the salt was slightly 

 pink, but on repeating the operation the separation was complete. 

 I took 3'22 grs. of oxide of manganese, and obtained 3" 15 grs. 

 free from cobalt. 



XXII. On the Geometry of the Elliptic Equation. 

 By Charles W. Mekrifield, Esq.'^ 



IT is now some years since Mr. John Riddle (of the Nautical 

 School, Greenwich Hospital) remarked, that if circles on a 

 sphere be projected on Mercator's chart, their projections are 

 rectified by the elliptic integral 



^(l-sin^^sinSi/,)-^^. 



This observation has led me to a geometrical exhibition of the 

 elliptic equation 



cos ^0= cos ^1 cos ^2 + sin ^i sin ^^(l — sin^ 6 sin^ ^)^, 

 and at the same time of its corresponding transcendental equation 



F(^,0o)=F(^, 02) -F(^, (/>.), 

 which seems to me to be sim])lcr than anything which has yet 

 been given on the subject. My investigation has also presented 

 me with Lagrange's modular scale, as the mere consequence of 

 passing from the pole or centre of the sphere to the circum- 

 ference of the circle in the stereograph ic projection. 



* Communicated by the .\uthor. 



