516 WEBER ON THE MEASUREMENT 



moreover. 



ddr, ddr, ^ , ddr, , , ddr, 



dr ds~ ds,dsl ds, 



ddr.. ddr., , „ , ddr.. , , ddr., 



,J =uu , J' + 2uu' -1 — ^ + u' u' , ,'' , 



df- ds- ds,ds,l "V 



ddr,,, ddr,,, , . , ddr,,, , ,ddr„, 



III _ „. .. Ill ^ 2uv; -3 — -Jii-r + u' u' '" 



~d¥~ - "' " ds,f ^ '"■'"' ds„ ds,; ^""^ ds,;-' ' 



ddr,,,, ddr,.,, , . , ddr,,,, , , ,ddr„„ 



dr ds,,' ds„ds; ds;^ 



From the four last equations we get immediately — 



, ddr, , ddr, ddr, , , ddr, 



ds,ds; dt ' ds,' ds;' 



, ddr,, ddr,, ddr,, , , ddr,, 



ds,d s,; dt' d s^ d s,;' 



, ddr,,, ddr,,, ddr,,, , , ddr,,, 



2UU'-: j^= + — T-^ - UU -j-^ - U' U' -j—^, 



ds,a s,; at' a s„- d s,;' 



— 2uu, , , 

 d s„ d s; 



Now the differential coefficients -T—g^, -7— g", —, — IP, ~. — ^ have 



d s,' d s,' d s,,' d s,,' 



the same value, which is dependent merely upon the position 



and form of the^?'s^ conducting wire, and which we shall denote 



by - , g -. This applies also to the differential coefficients -7—7^, 



Gi S (I S I 



-z — i^, -^ — ;", —^ — T^' all of which denote the same magnitudes, 

 ds,;^' ds,;^' ds,'^ ' ^ ' 



which are dependent merely upon the position and form of the 



second conducting wire, and which for brevity we shall denote by 



■7-75. On summation, bearing this in mind, we have 



\d s,d s; d s, d s,; d s„ ds,; d s„ d */ / 



_d dr, d dr„ d d r,„ d d r„„ 

 ~ ~dF ~ "dW ^ ~df- dt^ ' 



But from the first four equations, after they have been squared, 

 we have 



