390 



Dr. C. Chree. Collimator Magnets and the 



Also it must be remembered that in equatorial regions X may be double 

 the value assumed in Table X, and that SX in this case varies directly 

 as X. • 



§ 22. The number of instances where two observations had been 

 made of jx were fewer ; I examined forty-one of these in all. 



Eepresenting by fy, and 8/x" the mean of the semi-differences between 

 the two observed values and the mean probable error respectively, I 

 found 



= 0-198, S//' = 0-134. 



The corresponding probable error in X, treating r as 30 cm., is, 

 irrespective of sign, 



BX = X(l+cosec?0(30)- 3 x 0-134, 

 = 5 x 10~ 6 X (1 + cosec u), approx. 



This is troublesome to deal with ; because cosec u depends both on X 

 and on the magnetic moment. As a first approximation we have in 

 fact 



cosec u = Xx 30 3 /2m. 



To get an idea of the probable error arising from error in f±, suppose 

 X = - 18, as at Kew, and m — 840, as in the average new collimator 

 magnet. This gives 



cosec u = 3, approx. 



SX = 0-000004, approx. 



Thus when there are two observations of /x the probable error will in 

 the average case fail to affect the last significant figure, supposing X 

 measured as usual to 1 x 10~ 5 C.G.S. 



Of course in a good many individual cases the probable error in fju, 

 determined from two observations, was sufficient to affect the last 

 significant figure at Kew. More often than not /x has been derived 

 from a single experiment, and in the majority of such cases we should 

 conclude that the probable error was large enough to affect the last 

 significant figure in X, measured at Kew. Owing to the occurrence 

 of a term 



- r~ 2 X cosec u EE - X 2 /2m 



in the expression for 8X/8p, we see that where X is large, and m is 

 small, error in /x may be very much more serious than in the case we 

 have selected for numerical treatment. 



§ 23. The influence of errors in q and q' on X is difficult to present 

 clearly, as it depends both on the difference and the mean of the 

 temperatures t and t' existing during the vibration and deflection 

 experiments. If t and t' are equal, it does not matter — the funda- 



