40G USE OF THE GALVANOMETER 



and rational. Its results, therefore, cannot be more erroneous tnan 

 the measurements on which they are based." 



The principle of this method is closely allied to that on which the 

 use of the compass of sines is based. There is, however, a difference 

 between the two methods. In measuring- with the compass of sines, 

 the magnetic needle maintains constantly the same angle with the 

 spiral; and as the point of suspension of the needle turns with the 

 spiral the torsion of the thread is eliminated, and at the same time 

 the great advantage is gained of allowing the needle any eccentric 

 position in respect to the centre of the graduated circle without 

 injury to the results. 



In the galvanometrical method described in this paper, the needle 

 makes the same angle with the coils only while it is deflected by the 

 currents to be measured. Before and after the action of these cur- 

 rents it makes a different angle with the spiral, or none at all. On 

 this account it is necessary that its axis, the prolongation of the 

 thread, should pass through the centre of the graduation, so that the 

 angles read off by the needle may be really those which it makes 

 with the spiral, or with the magnetic meridian. The small size of 

 the graduated circle on ordinary galvanometers renders it very diffi- 

 cult to hit this coincidence exactly, and this method of measurement 

 is. therefore, inferior in accuracy to that with the compass of sines. 



It may be objected that, as recourse must be had to rotation, it 

 would be better to use the galvanometer at once as a compass of 

 sines. If the former instrument were made on the same principle, and 

 as accurately as the latter, this would certainly be preferable; but 

 even the best galvanometers are only tolerable measuring instruments, 

 and the small increase in accuracy which might perhaps be gained by 

 this process is no equivalent for the trouble of turning the spiral at 

 each measurement. Besides this, there are many investigations 

 which, without requiring great accuracy, make it very desirable to 

 be able to follow the variations in the force of the current from in- 

 stant to instant. This cannot be done more conveniently or certainly 

 than by a previously-constructed scale of intensity. 



Appendix. — In the foregoing paper the principle of the new method 

 was illustrated, for the sake of clearness, by a geometric construction. 

 It may be more concisely demonstrated in the analytical way, as fol- 

 lows: Let the successive angles between the magnetic meridian and 

 the spiral, with the same intensity /of the current, be represented 

 by + m", -j- m', 0, — m n — m in • • • • and the corresponding angles 

 between the magnetic needle and the spiral by n", n\ n, n n n ln 

 The needle will assume, with the different values of the first angle, 

 such a position that /, multiplied by an unknown function/ of the last 

 angle, will be equal to a magnitude, M, proportional to the terrestrial 



* This assumes that the torsion of the thread and the influence of the ends of the wire have 

 been eliminated in the way indicated in the note on page 39'J. 



