369 

 with its mean ; but as this mean is itself affected with an error 



= — _, the value thus computed must be multiplied by 

 V ' n 



V 



n 



n + 1 



" My first examination was made in 1830. The instru- 

 ment had then seven wires, and its eye-piece gave a power of 

 130. It was, however, far inferior in sharpness of definition 

 to the one which it replaced ; that was 104, and was removed 

 because it was unprovided with means of attaching a dark 

 glass for sun observations. 



" The stars chosen, observed almost in every case on the 

 same nights, except the excess of the second, were 



a Lyra, 8 = + 38°. 38' . . . No. wires, 120 

 j3Aquihe, + 5°. 59'. . . „ „ 167 

 a 2 tf - 13°. 4' .. . „ „ 122 



Giving the equations 



(0M041) 2 = u 2 + y 2 x 1-63878 + z 2 x 1-76856 



(0 s -0959) 2 = v? + y 2 x 1-01097 + z 2 x 2-29065 



(0 s - 128 1) 3 = u 2 + i/ 2 x 1-05385 + z 2 x 7-14595 



These give 



u = + s - 0445 ; y = ± S -0619 ; z = + 5 -038l. 



In my case, therefore, the ear could estimate the twenty- 

 third part of a. second, and its precision was to that of the eye 

 as 7 :5. 



" With this ratio of y to z, the two real roots of the 

 equation of minimum are, the positive = tang. 37°. 55'; and 

 the negative (belonging to a sub-polar transit) = tang. 66°. 47'. 

 Therefore, stars passing at those zenith distances should be 

 used at Armagh to obtain the exactest determination of time. 

 In such an examination we must be careful to use observa- 

 tions made under conditions as nearly the same as possible. 

 For instance, they must be all day or all night ones, as the 



