with the Flow of Electricity in a Plane. 387 



§ 16. For the case when both poles are at the same distance 

 from the sides of the strip, or a=b, this becomes 



C7T 2<27T V 



IT/CO n 



2s . , TTC 



— sinn tt- 



7Tp 2s 



( ctt zair y 

 cosh cos \ i 

 ■■■'■• •«,' )k- < 12 > 

 1— cos / J 



and if they are also both in the middle of the strip, it simplifies 

 to 



^log^sinh^), (2/ 



which is just half (2), as it ought to be. I write out this par- 

 ticularly, because this case has been already studied by Stefan, 

 and experimentally verified by von Obermayr ( Wien. Akad. 

 Ber. 1869, vol. lx. part 2. p. 245). Stefan, it seems, wrote the 

 expression he obtained thus (merely altering his letters), 



si — — — 



and this is identical with (2)'. 



§ 17. It seems as if expressions like the above might pos- 

 sibly be employed in obtaining the values of certain continued 

 products. Thus to take (12) as an example. 



The direct geometrical product for this case, occurring in (/3), 

 is the root of 



£_. 2a . 2s — 2a . 2s. 2s. 2s + 2a . As — 2a . 4s . 4s . 4s + 2a . 6s — 2a . 



p 2 . ~ 77 -2 



where Jcs±2a is an abbreviation for 1 + 



(&s±2a) 5 



Now one portion of this we know (cf. § 10), 



{(*+ A)( 1+ AX 1+ &)■■■}-£ -*£)"«* ^ 



"c 2 

 and as A 2 -^ equals the square of the rational part of the quan- 

 tity inside the brackets of (12), it follows that the square of 

 the irrational part is equal to the remaining factors of the above 

 product. It may be written 



cosh cos smJr — 



•=i+ i. 



_ Zair 



1 — cos snr — 



s s 



=( i+ £>( i+ (^) 



merely putting s instead of 2s, and a instead of 2a. 



