406 Dr. C. Chree. Collimator Magnets and the 



"Whence 



o% 4 - Siii = i (y ~ z) tan u, 8u 2 - 8u B = \(y+ #) tan u, 



hu '4 - 811 1 = ^ - 5) tan w'j oV 2 - 6V 3 = ^ (?/ + 2) tan m'. 



The mean results from the thirty-nine absolute determinations of 

 horizontal force made with the Kew unifilar in 1892, were as follows : — 



<k 4 - Siii Sit 2 - 8113 6V 4 - 811 1 811'. 2 - 6V 3 . 



10' 22". 27' 29". 3' 1". 8' 25". 



Also, approximate!} 7 , 



u = 15° 30', v! = 6° 30'. 



Thence we have — 



From observations at 30 cm. From observations at 40 em. 



?/ + 2 = 5 x 3-606 x 0-00799 = 144 cm., I # + z = 6*6 x 8*777 x 0*00245 = 0*143 cm., 

 ^-;=5x 3606 x 0*00302 = 0054 „ ! y-z = 6*6 x 8*777 x 0*00088 =0*052 „ 

 whence whence 

 y = 0*099 cm. z = 0*045 cm. y =■■ 0*098 cm. z = 0*045 cm. 



If the hypotheses on which the calculations are based are incorrect, 

 the agreement between the two sets of values found for y and z is cer- 

 tainly remarkable. 



I repeated the calculations for the data from the same unifilar in 

 1893, and again the two sets of values for y and z were in excellent 

 agreement, the means being 



y = 0*095 cm., z = 0*039 cm. 



§ 42. Consequences of Asymmetry. — Using the first approximation 

 formula, we have of course when we neglect 8r 2 and 6V 2 



8iii + 8u 2 + 8u s + = 0. 



Thus to estimate the size of the error we must go as far as squares 

 and products of small quantities, replacing (10) by 



8u = - 3?- 1 tan u&r + J tan u8u 2 - dr^&u&r - 3r" 2 tan u8r 2 . . . (11). 



Substituting the first approximation value for 8uj8r in the small 

 terms in the usual way, we find 



81c = - Sr~ l tan u8r + § tan u (3 tan% + 4) r~ 2 8r 2 (12). 



Taking r = 30, and ascribing to 8?* in succession the values corre- 

 sponding to the four positions, I find on reduction 



Su = i(Sui + &u 2 %-8u a + &u i ) = ^tanw(3tan^ + 4)(y 2 + 2 ) ... (13).* 



* The method followed above has the advantage of leading directly to the value 



