388 Br. C. Chree. Collimator Magnets and the 



For clearness, I shall in what follows suppose r to be 30 cm., that 

 being the smaller of the two distances now adopted generally. 

 X is deduced by combining the two formulas — * 



v 7r 2 K f _ © , 2[x cosec u ~\ -1 

 mX = -^(l+^- 2 *-^ + Ji-_j (2), 



WX = (l-?j{ 1+^ + ^ + 2^}^;™ (3) 



whence we have — 



X2 = tt 2 K . 2r~ 3 cosec u (1 - P/r^Tr 2 ^ 



( 1 + i - qt - + i cosec u ) ( l + 5 + ^ + 



Suppose SK, Sfi, &c, to represent the errors in the values ascribed to 

 K, ft, &c. Terms in ©, g, q[ in the denominator of the expression 

 for X 2 are always small compared to unity, and may for our present 

 purpose be neglected in the coefficients of S/x, 8q, &c. In this way we 

 easily find for the consequent error 8X in X : — 



SX .SK.^P , (1+ cosec^) t-t , „ t 



......... (5). 



From (5) we see noteworthy differences in the consequences of 

 errors in the different " constants." 



In the case of K it is not the absolute size of the error that counts, 

 but the ratio it bears to the size of K ; while in the case of P, /x, and 

 the temperature coefficients it is the absolute size of the error that 

 counts. In all cases SX increases with X, so that the absolute effect of 

 a given error in any one of the " constants " is greater where the hori- 

 zontal force is large than where it is small. 



§ 20. In estimating the probable errors in the several constants, I 

 have confined my attention to the cases in which the accepted results 

 were based on two, and only two, experiments. 



If 28y be the difference between the values given by two experi- 

 ments for a certain quantity, the probable error in the arithmetic mean, 

 y } of the two determinations is 



8f = 8yx 0-6745. 



In many instances the value of a " constant " was based on only one 

 experiment. In such cases we may reasonably assume that the single 

 experiment was, on the average, neither better nor worse than the 



* Of. Stewart and Gee's ' Elementary Practical Physics,' vol. 2, pp. 298, 307, &c, 

 allowing for difference of notation. 



