46 



Prof. Maxwell, On Approximate Multiple [Mar. 12, 



The equations to "be satisfied in order that equation (1) may 

 be satisfied for any function of x, y and z of not more than seven 

 dimensions are 



+ QP +12Q +8i2 =8, 



2F/ + 8^2^ + 8Er^ = |, 

 2P/ + 8(52* + 8jS/ = |, 

 2P/ + 8Q2^ + 8i?r« = ^, 



4^g« + 8i2r« = ^, 



The solution of these equations gives two systems of values: 



Second System. 



First System. 

 1 - / 5\i 



Pi 

 1 



i.-K""(S)']- 



p, = 0-969773, 

 q^ = 1-119224, 

 r, = 0-652817, 

 0, = - 2-856446, 

 P, = 1106789, 

 Q^ = 0-032304, 

 Pj = 0-478508, 



Pa 



?2 



'ii\r 



.15, 



P2 = 2-638430. 

 ^2 = 0-602526. 

 r^ = 0-855044. 

 0^ = - 7-999462. 

 p^ = 0-000513. 

 Q, = 1-238514. 

 i?, = 0-094777. 



