( 107 ) 



A. Ti {113,-1 — ni.2). 



This difference was repeatedly determined for one of the central 

 lines, the one chosen being the central line of the middle screen, so 

 as to make the deviation errors for the other lines as small as 

 possible. In these measnrements allowance is made for the sinking 

 of the volumenometer as a whole when water is admitted; the 

 distances through which it sank were measured each time by focus- 

 sing a second telescope of the cathetometer upon a mark on the 

 volumenometer. 



Further, let the indices e and ƒ of /?o, /?!,/?., etc., indicate whether 

 they represent the corresponding angles when the volumenometer 

 jacket is empty or when it is full of water, and just as with ^, let 

 us write i\^, i\^, etc., and ;\^, 1\^, etc., for the various values of 

 i\ and r.,; we then get for the distance measured with the jacket 

 empty e. g. 



.1 (^?ie - ihe) = A ni.2 I {r,, — rj + (r,, — r,,) ] - A {a, - a,) 

 and when it is full 



A (/?)ƒ — ^2f) = A Wi.2 {r\\ — r2l) -f- A «32 (ri2 — ?'22) — A («1 — «2). 



Taking the measured distances ^ (/?ie — /?2e) and A{^[f— ^2/) in 

 pairs and subtracting the one from the other ^ve obtain the following 

 equations in which V is the difference thus obtained. 



Foi 1 

 n)2 == —. r ^1.2 



A «3.2 — n\9 



F,2 1 



ri2 ■= f- T-22 



A «3.2 — Wi.o 



F23 1 



^22 ^^^ ~~ -~ 4" ^32 



A 713 2 — Wi 2 



Fat 1 

 ^32 ^^^ r ^'-is • 



A «3.2 — ?il.2 



Substituting in these equations the value of ;'3.2 which is directly' 

 measured at ??«,, we obtain in succession values for ?'.^j, etc., and 

 from these the optical deviations are calculated. For example for 

 m^ from 



A («1.2 — 1) ft[ 4" Ar[2{n3,2 — "1.2)' 



The numbers thus obtained are giveji in Tab. Ill, col. Ill (p. 111). 



§ 4. Control measurements. 



Partly to verify the results obtained and partly to control the 

 proper temperature equilibrium between the various mercury filled 

 parts of the apparatus, control measurements were carried out as 



