on Galvanometers. 59 



galvanometers. Prof. A. Gray, in his treatise on i The Theory 

 and Practice of Absolute Measurements in Electricity and 

 Magnetism/ maintains that it is not, for he says (page 31 1) : — 

 " Sensibility is sometimes obtained by the use of astatic 

 galvanometers, but these are rarely necessary and are more 

 troublesome to use than ordinary non-astatic instruments/'' 



This opinion carries special weight as it may be very 

 probably taken as expressing Sir William Thomson's view 

 on this subject, seeing that the usual method adopted by Sir 

 William for measuring small currents is to employ a galva- 

 nometer with a single set of magnetic needles, and to weaken 

 the magnetic controlling field as far as requisite by means of 

 adjustable magnets. Theoretically there is no limit to the 

 sensibility obtainable in this way; but with any strength of the 

 resultant controlling field due to the earth and the adjustable 

 magnets an astatic combination of magnetic needles must 

 give a more sensitive arrangement than a non-astatic one. 

 For let F be the resultant strength of this controlling field, 

 let M be the magnetic moment of a needle within the coil 

 whose magnetic constant is G, and let C x be the current 

 flowing, then, if a be the deflexion, we have for small deflexions 



C,G 



Next, let a needle of moment m be attached to the sus- 

 pended system outside the coil, so as to form an approximately 

 astatic system with the needle inside, then, even if we neglect 

 the action of the coil on the needle outside, an action which 

 of course assists the action of the coil on a needle inside, we 

 have, if C 2 be the current now flowing, 



C 9 GM. 



F(M-m)* 

 Hence, if the deflexions be the same in the two cases, 



M— m 



C 2 — c r 



M 



Now M may be made large, and M — m small, hence C 2 may 

 be a small fraction of C r Consequently for any adjustment of 

 the controlling magnet, the current required to produce a given 

 deflexion can be much diminished by using an astatic combina- 

 tion instead of a non-astatic one. 



But, perhaps, the most important advantage of an astatic 

 over a non-astatic instrument is its much greater freedom 

 from outside magnetic disturbance. In order that Ci, the 



