296 



A. TANAKADÂTE 



.5 and .71 so that -it-y- hîvs a maximum between a/h = .5 and .71 for 

 any ratio of c/b. Hence "bW/lx^ can always be made to vanish by 

 takino- a, and a, on both ;^ides of the maximum. The \'alaes of -^rH- 



^ ' Ö.T- 



are graphically represented in B'ig. 9 for c/b = 1, 2, 3, cc. 



At first these curves are in the order 1, 2, 3 &c, counting 

 from above, but afterwards when they become distinctly asymptotic 

 their order liecomes reversed. This is indeed aj^parent from the 

 equation. 



An indefinite number of proper values for a^ and «a i^i'iy ^e got 

 by the following simple construction. Draw any horizontal line 

 cutting any particular curve in the points p, q ; the a;-coordinatcs of 

 these points at once give a special pair of suitable values a^ and a,. In 

 the case of simple coils p and q coincide at the top of the curve, 

 which is the case already di^^cussed. 



§ III. Internal Coils for Measuring Large Differences 

 of Potential and Small Currents. 



We are now in a position to consider the dimensions Avhich 

 ought to be given to the internal coils spoken of in page 279 as 

 necessary for the measurement of large differences of potential and 

 small currents. For examining the above curves we see that l^Q/'bx'^ 

 becomes very small when a/b is more than 3. Also putting (B) in 

 the form 





popi \ PÖ pi / PoPi \ p' pi / 



and considering 7) and S as \'ariables we may regard the action as due to 

 two e(|uivalent "Electro-magnetic strips."* The coils are shown in the 



* See my paper on the ' Electio-maguetic Decliuometer ' published in the Proceediugs of 

 the Royal Society of Ediuburgb (Vul. XII. P. 544 188,'— 4) or Eigakiikyôk\vai Zassi (Vol. IF. P. 84). 

 iu whicli curves are shown very similar to those just giveu. 



