369 
with its mean; but as this mean is itself affected with an error 
= wa the value thus computed must be multiplied by 
if (22) 
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, 6=+ 38°.38'... No. wires, 120 
B Aquile, DO ote 55 ea 6 
a’ VF es Base 55 9» 122 
Giving the equations 
(01041)? = u? + y? x 1°63878 + 2? x 176856 
(0°-0959)? = u? + y® x 1:01097 + 2? x 2°29065 
(01281)? = u? + y® x 105385 + 2? x 714595 
These give 
u=+0° 0445; y=+0°0619; 2z=+ 0°0381. 
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 asub-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 
‘ 
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