( 796 ) 



On the otlici' luiiid liowever : 



^ z= Uió — ü, yO° — ('p ^(- ^1 = cot ( w -f ~Y 



where - is half of the break uf the isotliermal lines at the boundary 



line OG. 



The immediate conclusion is therefore : 



^ =<r/( y + — jcoU/) (J) 



From this equation the required proportion may be at once dedu- 

 ced when (f represents the direction of the plate and the value of e 

 has been ascertained. 



Moreover it will be easy to tiud the maximum of e — and thus 

 reduce the errors of investigation to the lowest figures. Suppose 



A^— , the above stated formula, after a few goniometrical trans- 



formations becomes : 



(A—l)sin2(p 



Hi -7 = 



(yl+1) — {A—\)cos2(p 



ds ^ . 

 This tuiiction will be a maxinuim for -— := 0, i. e. 



(Up 



ds _ 2 |(^' — 1) cos 2(p — {A—iy\ _ 

 d^~ {A'-irl) — {A'—l)cos2^~' 



The maximum condition then becomes : 



cos ZfC rr: ^ , 



and the appertaining maximum break e in the isothermal lines is 

 then expressed by : 



ia - = "^^-^ ^ (B) 



In cases where the difference between j/P., and j/;.^ is vei'y small 

 — and observation teaches that this is usually the case — the 

 notation may be : 



« P-, — ^„ 

 <<7— = -i 1 (C) 



For practical i)iirposes therefore, the theoretical maxinuini c/) = 45° 

 may be taken as fairly accurate, so that then the twin plate with 



