Moment of Inertia of Magnets. 145 



From these results it would appear that if the correction for 

 the air effect varies with the period, the experiments are not 

 of sufficient accuracy to detect it, at any rate over the range 

 employed. Neither do they indicate clearly that there is 

 any change with the size of the box containing the vibrating 

 system, at any rate nothing of the same order as the change 

 in the logarithmic decrement. Hence the mean o£ all the 

 observations will be taken when calculating the correction to 

 be applied to the moment of inertia of the dummy as deduced 

 from observations of period with and without the inertia-bar 

 made at ordinary atmospheric pressure. 



Since it is the apparent moment of inertia of the magnet 

 swinging in air which is required when determining H, no 

 correction is required to eliminate the effect of the air 

 carried by the magnet itself. When, however, the inertia- 

 bar is used with the magnet in determining the moment 

 of inertia of the magnet^ the inertia of the bar is really 

 greater than that calculated from its dimensions, on account 

 of the air which it carries along with it as it swings. To 

 obtain the moment of inertia of the air carried by the bar, 

 we have to take the difference between the corrections for the 

 dummy together with the bar and that for the dummy alone. 

 Hence the moment of inertia of the bar must be increased by 



0*271 orm.-cm, 2 Jn the case of a brass bar 10 centimetres long 



... 

 and 1 centimetre in diameter, which will have a moment of 



inertia of about 550 grm.-cm. 2 , the correction amounts to 



0049 per cent. That is, the calculated value of the moment of 



inertia of the magnet determined with such a bar, without 



taking any account of the air effect, will be 0"049 per cent, too 



small. If the horizontal component of the earth's field has 



the value 0*18, this corresponds to an error in H given by 



H = 0'000044 c.G.s. or 4*4 7 . 



The above correction only applies to the form of magnet 

 used in the particular pattern of unifilar, and of which the 

 dimensions are given in lig. 2. 



It will be noticed that when used in the instrument em- 

 ployed for comparing the moments of inertia of the bars, the 

 correction to the moment of inertia of the bar 1 due to the 

 air effect was 0'233 grm.-cm. 2 ; while when this bar is used 

 with the dummy magnet, the correction comes out as 0*271 

 grm.-cm. 2 A difference in the two cases is to be expected 

 owing to the great difference in the shapes of the carriages 

 which support the bar in the two cases, which will certainly 



Phil Mag. S. 6. Vol. 10. No. '55. July 1905. L 



