80 GAUSS AND WEBER ON TERRESTRIAL MAGNETISM. 



most probable values of those quantities. These rules are as 

 follows. 



From the quantities Rq, ii„ Rc^, etc., Vq, v,, v^, etc., M'e must 

 calculate the following expressions : 



tang Vq tang Vi tang v, 



"W "^ R:' ii:' 



tang Vq tang v, tang v, _ ., 



-Ro^ + ~R^ "^ i«/ + " 



, _J_ I _i L etc. = B" ■ 



+ /? 1° + R'^ • 



J^ 1 



Rq Aly ^12 



thence we shall have the most probable value of 

 AB' - A'B 



L = h 



B" - B 



m 



M _ , A'B' - AB" 



From this, and equation (I.) 



we obtain 



M^—a/vC (VII.) 



= T\/V' ("^"^'^ 



The experiments M'ith the small measuring ap})aratus may be 

 calculated according to these laws and formula:, and the absolute 

 magnetism of the bar and that of the earth determined. 



4. Calculation, according to the above rules, of the observa- 

 tions made with the small measuring apparatus. 



The experiments were, 1 st, those of deflection, which gave the 

 values of Uq — u^, Wj — w/, ii, — ui, tiJ' — u!", u^" — «,'", 

 Uq" — Uq", and the corresponding values of R, viz. Rq, i?j, i?.^ 

 R^ 7?i, Rq. We calculate from these the values of Vq, v^, v^, cor- 

 responding to Rq, i?i, Ri ; and hence the values of -^4, A', B, B', B", 

 which are simple functions of the six quantities, Vq, v^, v., ; R^, 

 R^, Ro. And lastly, the value of r is deduced fi-om the quan- 

 tities A, A', B, B', B", of which it is a function. Thus, the value 



