Permanent Magnets. 183 



sion was thus quite long and was but little exposed to the 

 action of the heat. The bulb of the thermometer was close to 

 the magnet. In the side of the box was another opening, covt 

 ered with glass, through which a mirror attached to the mag- 

 net was observed, and the time of vibration thus determined. 

 The temperature of the space in which the magnets swung was 

 kept quite constant at 11° C. or 99° C, by passing a current of 

 cold water or steam through the space between the two parts 

 of the double box. For the lower temperature city water was 

 used direct from the faucet. 



The magnets and the mirror used in observing their vibra- 

 tions were weighed. The lengths of the magnets were meas- 

 ured at the ordinary temperature of the room, 18° C. The 

 corrected lengths for 11° and 99° C. were obtained by the fol- 

 lowing formulae : 



L 11= :L (I — 7X0-000011), 



L 99 =L(1 + 81X0-000011), 

 in which L n and L 99 are the lengths at the temperatures indi- 

 cated by the subscripts, L is the observed length, and 0-000011 

 is the coefficient of linear expansion of untempered steel. The 

 moments of inertia for the magnets at each temperature were 

 calculated as follows : 



L 1X 2 +b" 



hi 

 W ' 



in which m is the mass of the magnet and b its thickness. The 

 mass of the mirror and of the appliances by which it was fas- 

 tened to the magnet was 0-4245 grms., and calling its radius of 

 gyration 0*2 cm the moment of inertia due to it was 0*0170, 

 which was added to that of the magnets. No correction was 

 made for the rest of the suspending apparatus ; its mass was 

 always less than 0*10 grms., and it consisted principally of a 

 piece of fine wire about 25 cm long ; and its radius of gyration 

 was exceedingly small, being a fraction of the diameter of the 

 wire. The silk suspension was about 3'5 meters long. No 

 allowance was made for the effect of torsion, as the magnet 

 could be turned 360° without producing enough difference in 

 azimuth to be detected by a telescope and scale at a distance of 

 3 meters. The formulae for the magnetic moments are: 





T 2 TT ' 99 — T 2 H ' 



in which V denotes the total moment of inertia of the system 

 at the temperature indicated ; T, the period of a complete 

 vibration ; and H, the horizontal intensity of the earth's mag- 

 netic force. H was taken as equal to 0*2. It has been deter- 



