764 



/ ÖA óix du dX , - 



= i rf,.(,iA;. + ;A«) + è U-^ + ^ .- - X 2„ . . (4) 



§ 2. We MOW liave to substitute in (4) for i and j^ values that are 

 exact including terms of tlie lirst order. We iind tiieni from (2) by 

 omittina; all terms of higher orders than the second. This gives us 



— cg,,W Ay„li) = «ï.v(i) and — cg,,W Ly,.p) = xlj^l 

 When <j ^ r ^ 4 this becomes 



A;i r= ^ or and Aji = ^' or . . . (5) 



a c 



In these equations pj and (>, represent positive constants; the right 

 member of the first equation is dilferent from zero only in the 

 interior of a sphere of radius R^ and the righthand member of the other 

 equation is different from zero only in a sphere of Radius R,. 

 From (5) we have 



^ = ^- — and f^ = -- . — (6) 



Of J'j OC T-j 



Each equation (6) is valid only at a point outside the sphere the 

 radius of which occurs in it; within that sphere is 



A = '^(3fi,^-V) andft = ^(3«,= -^,=) . . . (6a) 

 be DC 



We now substitute this in the righthand member of (4). Within the 



tirst sphere that second member becomes 



tu.tu, to, to, r, /dr. or, dr,dr.\ _ 



when we put 



XQji^" xu^R,^ 

 to, = and to, =; . 



6c ' ÖC 



111 the intei'ior of the second sphere we find in the same way 

 — R^,. Outside both spheres the right member of (4) will be 



Considering (6) we thus find outside both spheres 



(o,a>, rF,.,dS, rR,,d8. fQ^dS 

 r,r, J im' J éitr J iJir 



