OF ARTS AND SCIENCES. 415 



The small cylindrical magnet was carefully measured by means of a 

 dividing-engine. 



For the diameter, I found 



North end. Mean of five measurements d = 14.395 mms. 

 Southend. „ „ „ <Z=: 14.399 „ 



Giving as the mean diameter d^ 14.397 „ 



The length was given as the average of five measurements equal 

 to 49.448 mms. 



The wei";ht was 62109,2 milligrams. 



If, now, following Rankiue, we use the weight instead of the mass 

 in determining the moment of inertia, we get 



if I = length of the cylinder and 



r = its radius 



.= ,r(£+'^) = c.3.09.2('--5>i!fl) 



= 13459758.5 mms. mgms. 



We have, then, all the data to get the value of 3IH. w\\\ch is given 

 by Gauss's formula 



J/^=-1^. (A.) 



£•■2(1+0) ^ ' 



M 



To get — , I suspended a small magnet carrying a plane mirror from 



the centre of the apparatus, and measured the deflections produced 

 by the cylindrical magnet described above, when placed at two points 

 to the east and to the west, Usiug both poles in each position gives 

 eight measurements. I also made a few observations with a box 

 compass, but the results were by no means as precise or accurate as 

 those obtained by suspension. 



If, now, cp and qj' are the angular deviations from the meridian 

 produced by the magnet at the distances r and r', and if 



= the coeificient of torsion of the thread, we have 



M »-5 tan ^ - r-i tan 0i , r^x /r. x 



ff='^ ^^ZTV^. (1 + 0). (B.) 



and we easily see that 



H=K/Mff-^-. 



The inclination or dip was determined accoi-ding to the method 

 given by Weber (PoggendorfF's Annal. XC), by the strength of the 

 inductive currents produced in a coil of copper wire, rotated in such a 



