of Iron and German Silver. 489 



moment, which is called the galvanometer -function, by /(</>), it 

 can be shown that 



/(<^) =/ (O)cos 0(1 + fl sin 02 + i sin </)4 + c sin <^^ + . . . ), 



where a, b, c, . . . are constants. The smaller the angle 0, the 

 more rapidly convergent is this series; and in observations in 

 which remains always small, we may content ourselves with 

 the first two terms, so that we have 



/(^)=/(0)cos^(l+flsin^^)* (7) 



If we connect the galvanometer with the conduction to the 

 middle of the bar, the thermo-current (whose intensity may be i) 

 deflects the needle from the plane of the meridian to an angle 0; 

 and for this new position of rest the following equation holds : — 



if{(f)) = Tm sin <f>, 



m being the magnetic moment, T the horizontal component of 

 the earth^s magnetism. With the aid of equation (7) we find 

 from this : — 



._ Tm tan , . 



^~7(0) l + asin02 (^) 



But, on the other hand, the intensity of the thermo-current is 

 also proportional to the difference between the temperatures of 

 the middle of the bar and the points A (fig. 5), the latter of 

 which have the temperature of the surrounding air. Hence, if 

 we denote by W the resistance of the whole circuit, by V^ and 

 U (as before) the temperature of the middle of the bar and the 

 surrounding air, then 



^=%^l (9) 



where a denotes the electromotive force which corresponds to a 

 temperature- difference of 1° C. From (8) and (9), therefore, if 



* The quantity /(O) is the torsion-moment exerted upon the needle in 

 the plane of the meridian hy the multiplier when it is traversed by the unit 

 of current. In the previously mentioned memoir (Pogg. Ann. vol. cxxxvii. 

 p. 134) it is denoted by D. There it was found that 



/(0) = 2-8884^ ^W 



in which L denotes the length of the needle, h the specific resistance, and W 

 the total resistance of the galvanometer-wire. For the above-mentioned gal- 

 vanometer it was found from direct observations that/(0) = 48*09 . m ; while, 



millimetres 

 according to the formula given,/(0) = 47'41 . mif A; = 219274 ^ — ' 



Probably the value of k on which the calculation is based is somewhat too 

 great. 



