transit instrument at the Cambridge Observatory. 421 
would be o ».4288 (= o*.2 x 2144) ; which not being found 
to agree with the observed error (or rather the difference 
of its observed passage and its computed right ascension ) , 
showed that the difference of the errors of the clock had 
been wrongly, or partially, assigned. 
If we suppose the difference of the errors of the clock to 
arise from two causes — the want of horizontality and the de- 
viation of the transit from the plane of the meridian, then, 
calling the latter deviation H, we have, instead of the former, 
these equations : 
— 4.721 -f 6 = 1.39 H .185 Z 
— 4.854 + 6 = .73 H + .7 Z 
to which a third similar equation must be added for a Urs. maj. 
If from such three equations we determined H and Z, we 
might proceed as before, and examine, by means of a fourth 
star, whether it were nec-essary to suppose the existence of a 
third cause (an error in the line of r.(dliiiiation for instance) 
to account for the differences in the clock’s error. 
If C should denote the error of collimation, dt the error of 
time, c the colatitude of the place of observation, ^ the star’s 
north polar distance, the general form of the equations for 
determining H, Z, &c. is 
7 < I Tx COS. (c — I ry Sin. (c I C 
d ^ -f- S = H + Z . k . 
sin. ' sin. s ' sin. 
In this way we might consider the subject in all its gene- 
rality (as foreign writers express themselves) ; and from 
observations alone, arrive at a knowledge of the defects of 
the instrument. And this mode of considering the subject is 
" not without its use, since it may be applied to recorded and 
ancient observations ; as Bessel has done in the case of 
