WEBER ON A TRANSPORTABLE MAGNETOMETER. 5 77 



If the mass of the cylinder were concentrated m its axis, its mo- 

 ment of inertia would be 



^Pp = 109091000. 



If the cylinders revolved only round theu' own axis, their mo- 

 ment would be 



r^p = 529000. 



Their moment in the above experiments is to be taken as equal 

 to the sum of 



^ Pp + r^p = 109620000. 



Whence therefore the moment of inertia of the oscillating bar 

 may be obtained from the equation 



TT^ K TT^ (K + K') 



MT = 



t' 



where K' signifies the known, and K the desired moment of 

 inertia, t' the time of vibration with a weight, and t the time of 

 vibration without a weight, consequently 



K = 49103000. 



In these expei'iments the needle was suspended to a thread in 

 which the force of torsion was so small as to be insensible. The 

 same series of experiments was repeated with the needle sus- 

 pended by a wire in which the force of torsion was much gi'eater ; 

 the result was almost the same as before, namely, 



K = 49044000. 



Finally, in order to furnish a check, the deflecting bar was 

 weighed, and its length and radius were exactly measured : 



Weight y = 66670">s 

 Length I = 93^'^'42 

 Radius / = 5'»™'45, 



whence its moment of inertia may be calculated. Supposing 

 perfect internal homogeneity, 



K = T2 ^^y + i r'^p' = 489S2000. 



The accordance of all these experiments sufficiently shows that 

 the moment of inertia of even such small bars may be detei-- 

 mined with great precision. 



