GAUSS AND WEBER ON TERRESTRIAL MAGNETISM. 81 



of r is obtained by calculation from the experiments of deflec- 

 tion. 



2nd. From the experiments of vibration the value of the time 

 of vibration t is found : having thus the values of r and ty it is 

 only required, for the purposes of the travelling observer, to 

 calculate 1 



for this value is proportional to the number, which expresses the 

 absolute terrestrial magnetism, and consequently suffices for the 

 comparison of the absolute intensity of all places where such 

 experiments may be performed. Such a comparison is usually 

 the only object sought by the travelling observer. It may some- 

 times, however, be desirable to obtain not only comparisons of 

 the absolute intensity at various places, but the absolute inten- 

 sity itself; the apparatus may be lost on a voyage, and be re- 

 placed by a new one ; and it then becomes necessary, in order 

 to compare the two series of results obtained with instruments 

 which cannot be compared together, to calculate the moment 

 of inertia of the magnet bar, the time of vibration of whicli 

 had been obsei'ved, and to extract its square root. The product 



of the quantity ■ into the square root, and into the number 

 t Y r 



TT = 3*14159. ..gives a number expressing the earth's magnet- 

 ism in absolute measure. 



On this account it is advantageous that the bar should be 

 an accurate parallelopiped, because in such case the moment 

 of inertia can be deduced for the present purpose directly 

 from the weight p, the length a, and the breadth b of the 

 bar. For it is well known that the square a^ + A^ of the 

 diagonal of the superficies of the parallelopiped, multiphed 

 by the mass p of the weight, and divided by 12, gives the mo- 

 ment of inertia sought, in the case in which the bar shall have 

 been suspended by the centre of that superficies. Consequently 

 in the equations (VII.) and (VIII.) 



C = 9-8696.. -^l±i!.» 

 12 ^ 



If we compare the observations above mentioned with these 

 formulae, it will be seen that the following quantities have been 

 directly measured, and the following values found for them : 



VOL. II. PART V. F 



