5fi DR. R. A. SAMPSON ON A 



Sin= ... --59583H, 



.- - '8019054,- -222246q,', -V* = + '595833q B , 

 ... + '595833^ 



and the rest zero. 

 For the second lens, the subsequent normal scheme OV-.F 7 is 



{g f ,h f ; VI'} = {I, +713667; * ,1} 



and by (17) of the Memoir, tbis gives for the second lens from O a ...F' 7 the terms 

 in q: 



The preceding normal scheme O ...O rt is 



{g,h; k,l} = { + '140346, + 3'389017 ; -'007760, +6'937860}. 



We see, by referring to the equations (17) of the Memoir already quoted so 

 frequently, that in order to get <S,G, S 2 G, S 3 G, we must form gS,y 6 + kS,^ e (s - 1,2,3) 

 with these values of g, h, k, I, and multiplying them respectively by 



g 1 = + '019697, 2gk = - '002178, k 2 = + '000060, 



gh = + '475635, gl+hk = + '947402, kl = - '053838, 



= +1T485436, 2M = +47'025051, P = +48'133901, 



take the sums. The values of gS,y^ + kS^ are 



Coefficient, q . Coefficient, q a 2 . 



* = 1 -'167242 -'022260 



2 ..... +'059679 * 



3 ..... * * 



the resulting values are 



Coefficient, q 6 . Coefficient, q a 2 . 



<! i G =- -'003424 -'000438,5 



-'023006 -'010587,6 

 + '885540 -'255667,4. . . . (31) 



