308 On the Siemens Mercury Unit of Electrical Resistance. 



of each set of observations, and another at the end. As the tem- 

 perature of the air changed but little during the time of ob- 

 servation, this method is in any case adequate. 



The question arises whether the supposition made in the dif- 

 ferential equation (page 302) is correct, namely that the coeffi- 

 cient of sensitiveness q of the galvanometer is constant, or, in 

 other words, that the damping-ratio is independent of the ampli- 

 tude of the swing. In reference to the instruments the question 

 may be thus stated : — Is the multiplier so broad that a lateral 

 displacement of the needles such as occurs in the vibrations 

 does not alter the moment of rotation which a current in the 

 multiplier exerts upon the needles ? The question could be easily 

 decided. The horizontal component of the terrestrial magnetism 

 made the largest arc equal to about 3°; if the damping in these 

 vibrations were already less than in very small ones, its amount 

 must considerably decrease if recoil-observations were made with 

 the vertical component as the inducing force, in which case the 

 arc of vibration amounts to 7°. Observation gave : — 



Large arc =3°, ratio of damping =1*74430 



= 7°, „ „ =1-74255 



Difference . . . 000175 



Hence if the induction were executed with the vertical compo- 

 nent, a correction would be necessary in our galvanometer which 

 would amount to a quarter of a division in the smaller arc. As 

 the correction must be proportional to the square of the ampli- 

 tude, it can from this be calculated that for the horizontal com- 

 ponent it must amount to about 4oVo> a magnitude so small 

 that it is not worth while to determine it accurately. In the 

 sequel no regard is paid to it. 



As regards the induction on each other of the short currents 

 arising and ceasing in the terrestrial inductor, brief considera- 

 tion will show that it can exert no appreciable influence on the 

 deflections ; for the extra current which accompanies the prin- 

 cipal current causes no change in the velocity imparted, but 

 exhibits its influence solely in a sudden displacement of the needle, 

 as I have shown elsewhere*. From the observations there given 

 we cannot estimate the extra current at more than 1*5 division ; 

 and that produces an error of at most 0*01 division in our larger 

 arc A, which may well be neglected. 



The actual agreement of the three measurements given below 

 quite satisfies expectation. It will be found that they differ 

 respectively from the mean values by 0*14, 04, and 0*11 per 

 cent., which would correspond to a "probable error w in the 

 result of 0*05 per cent. In this indeed are not contained the 

 * Pogg. Ann. vol. cxlii. p. 422. 



