408 



Dr. C. Chree. Collimator Magnets and the 



magnets' centres y, measured as in § 40, we can find its value if we 

 know the circumstances of the case. Thus suppose the magnet to have 

 a moment 840 and to weigh, with lens and scale, 30 grams ; then at 

 a place where g (gravity) is 980, and the vertical magnetic force is 

 0*44, we have 



-y = (840 x 0*44)-^ (980 x 30) - 0*013 cm., approx. j 



The value thus found for y is not only much less numerically, but 

 even opposite in sign to the value calculated for the Kew collimator 

 magnet in § 41. There is nothing surprising in this, because the per- 

 fect symmetry which our last calculation assumes in the magnet and its 

 appendages is a remote probability. For instance, the lens and scale 

 of the magnet, in the only case where I had them weighed, differed by 

 nearly half a gram. If other things were symmetrical this alone 

 would remove the C.G. nearly 0*08 cm. from the symmetrical position. 



Mechanical asymmetry might arise in many other ways. The 

 magnet itself, for instance, might be slightly conical. 



It is also at least conceivable that magnetic asymmetry may exist. 

 If a magnet were conical, or had one end tempered differently from 

 the other, I see no reason to expect its "poles " to be equidistant from 

 the middle point of its length. 



§ 44. Whilst numerous causes may contribute to the asymmetrical 

 displacement denoted by y, the first mentioned appears the most 

 interesting. Not merely is it, as we have seen, unavoidable, but it 

 varies if either m or the vertical force alters. 



The vertical force on the earth's surface varies from about + 0*6 to 

 — 0*6 C.G.S. unit. Thus if the typical magnet above considered were 

 adjusted so as to be horizontal under the one limiting force, it would 

 have to be shifted about - 034 cm. in its stirrup to become horizontal 

 under the other. 



The shifting in the stirrup entailed by this variable cause of 

 asymmetry slightly affects the moment of inertia. For instance if the 

 symmetrical magnet considered above, for which y = 0*013 cm. at 

 Kew, were used in a tropical station where the vertical force vanished, 

 y should be reduced to 0, and the consequent change in moment of 

 inertia would be 



SK = -30(0-013) 2 = - 0-005 C.G.S. unit, approx. 



The mean K in Table I is 2711/7T 2 , or 274 approximately; and with 

 these values 



8K/K = - 2 x 10- 5 , approx. 



Supposing no allowance made for this, the consequent error in X 

 would be 



SX = - X x 10" 5 . 



