Moment of Inertia of Magnets. 141 



carried along by the system at the two pressures, then 



^i = J7tw — i and tr, = zir\/ ^ 



or since £ 2 ~ "^i is small compared to either t x or t 2 , 



2fa-fr)K 



/Jo — AN = • 



From this expression and the numbers contained in the table 

 above, we get the following results : — 



Difference 

 of Pressure. 



*„-*!■ 



Moment of 



Inertia of 



Vibrating 



Body. 



Increase of 

 Moment of 

 Inertia for 

 76 cm. Air- 

 pressure. 



Percentage 

 increase of 

 Moment of 

 Inertia for i 

 76 cm. Air- 

 pressure. : 



Cradle ( 710cm. 



Cradle+BarNo.l 70-5 

 Bar No. 1 



•073 



•288 



70-88 

 615*68 

 544-80 



•078 

 •311 

 •233 



•11 



•05 

 •04 



As far as I am aware the only experiments on the effect of 

 the inertia of the air carried by a swinging magnet on its 

 period previously made are those of Lamont (Fogg. Ann. 

 lxxi. p. 124, 1847) . He found that the period of a cylindrical 



magnet 85 cm. long and weighing 8 



is given by 



T(l 



■(l+^ x -00033), 



where T p is the period in air at a pressure of p cm. of mercury, 

 and T is the period in a vacuum. 



The above corresponds to a percentage increase of moment 

 of inertia for 76 cm. of air-pressure of 0'066, which agrees 

 in magnitude with the numbers I have obtained. 



It is thus evident that the inertia of the air appreciably 

 increases the period. This result will not influence the results 

 obtained in the preceding part of the paper, since the bars 

 were all of the same size and did not differ much in moment 

 of inertia. The magnitude of the effect, however, was such 

 as to make it worth while to investigate the effect of the air 

 in the case of the magnets used in the Kew pattern unifilar 

 magnetometer. Since the moment of inertia of the magnet 

 is determined by means of a bar such as those which are being 

 tested, when the effect of the air is neglected the moment of 

 inertia deduced will be too small. The moment of inertia 

 required is that of the magnet together with any air it may 



* This corresponds to a diameter of about 04 cm. 



