394 Dr. C. Chree. Collimator Magnets and the 



Thus we have XX' in (9) as against X 2 in (4) ; but this only means 

 that the X appearing in (4) is in reality a mean between the values 

 possessed by the horizontal force during the vibration and deflection 

 experiments. 



In actually comparing the result of an absolute horizontal force 

 observation with the magnetogram one measures the curve ordinates 

 at the mean times of the two experiments — times separated usually by 

 thirty or forty minutes — and takes the mean of the two ordinates as 

 corresponding to the X deduced from (4). 



Again, the K appearing in (4) is really taken from a table which 

 allows for variations of temperature, and the same is true of r. 



§ 27. The first difference of real significance is that (9) contains 

 1 + Pr -2 , while (4), on the other hand, has (1 - Pr -2 ) -1 . Supposing X 

 measured as usual to five significant figures, this becomes objectionable 

 when the value of X is affected by so much as 5 x 10 -6 C.G.S. unit. 



The limiting value of Pr -2 for which the substitution is justifiable is 

 given by 



X(l-P 2 r-^= X-5xl0- 6 , 

 or, approximately, P/'~ 2 = 10~ 3 (10/X) i . 



This gives — 



For X = 0-18, P/- 2 = 0-0074, approx., 

 X = 0-36, Pr- 2 = 0-0053 „ . 



The mean value found for Pr ~ 2 , when P is positive, in Table I is just 

 in excess of 0-0074, and values in excess of 0*0053 are very common. 

 Thus the employment of (1 - Pr -2 ) -1 in (4) is, to say the least of it, 

 frequently unjustifiable. 



As regards the possible size to which the error in question might 

 attain, we should have in the case of the largest P given in Table II 



for X = 0-18, error 0*00006, 

 X = 0-36, „ 0-00011. 



§ 28. The second difference of note between (4) and (9) is that 

 (1 + qt' + q't' 2 + 2/xr" 3 ) -1 occurs in the former as against 



l-qt' - q't' 2 - 2/xV- 3 



in the latter. 



Overlooking for the present a possible difference between /x and //, 

 we see that objection arises when 



(^' + 2 7' 2 + 2p- 3 ) 2 



ceases to be negligible. 



So far as the +erm in fx is concerned there is no cause for apprehen- 

 sion, as 0*0006 would be an exceptionally large value for 2/a?-~ 3 . 



