Galvanometers^ and on the Rigidity of Silk Fibre. 49 



which we may, without appreciable error, assume to be 

 the torsion of the fibre, as the angle turned through by the 

 mirror is so small as to be negligible ; in the last part the 

 ordinates have the same meaning, but the abscissae indicate 

 time. This second part of the curve shows the rate at which 

 the fibre takes a set under the torsional stress ; the part of this 

 curve below the zero-line shows the working out of the set 

 after the fibre was untwisted. The length of the fibre in this 

 experiment was 8*5 centim. and the average thickness about 

 0*0015 centim. 



When a galvanometer is made sufficiently sensitive for the 

 fibre to play an important part in directing the needle, the set 

 of the fibre due to continued deflection always produces an 

 apparent change of zero which, in exact measurements, it is 

 somewhat difficult to properly allow for. Except, however, 

 in very special cases, as, for instance, in taking deflections 

 with a Thomson's " dead-beat " galvanometer in a weak 

 magnetic field, the error is small, and it is not in any way 

 capricious. It is important to bear in mind, however, that 

 for very sensitive galvanometers to be used as deflectional 

 instruments the suspension should be of considerable length, 

 such, for example, as is provided in the Thomson's astatic 

 galvanometer. 



From the data given above we may very easily form an 

 estimate as to when the rigidity of a silk fibre comes to be an 

 important factor, affecting the sensibility of a galvanometer. 

 If C be the current flowing through the galvanometer, K a 

 constant depending on the coils, I and V the field at the upper 

 and lower needles respectively, m and m! the magnetic mo- 

 ments of these needles, t the torsional rigidity of the fibre, 

 and 6 the deflection, we have 



c = K |Im-IW ta re V 



(, m + m (m + m) cos u J 



When the needle system is perfectly astatic, m=m', and this 

 reduces to rT— V *() *\ 



C=K | V-tan 6+ ^—A 5 

 L 2 2ra cos 6 J 



and for small deflections this may, without great error, be 

 written rT— T' * "i 



From this equation we see that the fibre becomes important 

 when — is not small compared with I— F. Now in a very 



sensitive instrument it is not unusual for I— V to be reduced 

 Phil. May. S. 5. Vol. 23. No. 140. Jan. 1887. E 



