258 



Mr. W. H. L. Russell on 



[Jan. 19, 



AB. The outer flat copper case. 



C. Plate of amalgamated lead held in grooves in the cap D and the 

 slip E. 



E shows the hole in the cap through which the solution is intro- 

 duced, and by the introduction of a glass tube through this hole the 

 state of the charge is seen by observing the colour ; the interior surface 

 of the case forms the negative, and the amalgamated lead the positive 

 electrode. 



January 19, 1882. 



THE PRESIDENT in the Chair. 



The Presents received were laid on the table and thanks ordered for 

 them. 



The following Papers were read : — 



I. "On certain Definite Integrals." No. 10. By W. H. L. 

 Russell, F.R.S. Received December 31, 1881. 



Let a + ciq% + a 2 x 2 + a s x 5 + a 4 x 4: = x + /3 (fi + vx + px 2 ) + 7 (/m + vx + px 2 ) 2 . 

 Then we find the condition 



8a 1 <x 4 2 + a 3 3 — 4a 3 a 3 a 4 = 0, 

 together with the equations — 



ry^ 2 =a 4 , 2a 4 y=pa%, f3v-\-2>yfiv=a 1 , 



when there are three equations connecting the five quantities /3, 7, /u, 



v, p. 



Under these conditions we shall have — 



Jb Jfi+vb+pb V 4p(z — jui) + v 



: . . . (220). 



In the same way, if 



a Q + OqX + «2 a ' 2 "1" a 3 x * + + a ^ + ^6^ 6 



=x+j3(fi+vx+ px 2 ) + 70 + f« + />£ 2 ) 2 + 8 (/* + va> + />a? 2 ) 3 , 

 we have similarly — 



I cZaJe fl o +ffl i a! + fl 9« a +«3a :8+fl 4 a; * +0 6* s+fl e* e = I - . (221). 



J5 J m+ v5+p5 2 V / 4 /C ,( _ ytt ) + i ,2 



There will be six equations connecting the quantities a v a 2 , a 3 , a 4 , 



