412 Mr. Pond on the different methods of 
error of the clock in this case, answers to the index error of 
the circle, and is investigated in precisely the same manner. 
An approximate catalogue is first assumed; and here, as with 
the circle, the observation of each star serves a double pur- 
pose : in the first place, in common with all the rest, it is 
employed to determine the error of the clock ; and the error 
thus found is applied to the observation of the star. In 
this case, the right ascension of the star is supposed to 
be known ; in the second part of the process, the star is 
considered as a planet, or unknown object, and its right 
ascension found by the usual rules, and recorded as a single 
result ; and from the totality of these results is the right 
ascension ultimately obtained. 
Should the deduced right ascensions differ materially from 
those originally assumed, the improved catalogue must be 
substituted for the approximate one, and the whole process 
recomputed. In this substitution, however, some judgment 
and discretionary power must be exercised ; for should the 
assumed or approximate catalogue be very exact, and the 
subsequent observations few or inaccurate, it is evident that 
the new catalogue might be less correct than the assumed 
one; this, however, does not arise from any defect in the 
method, but is the inevitable .consequence of any attempt to 
improve good observations by bad ones. As a practical 
illustration of this remark, I might add, that having myself 
assumed an approximate catalogue, so exact as that of Dr. 
Maskelyne, it happens that at this moment, in the case of 
some stars which have not been very frequently observed, I 
have great doubts whether the new determination is more 
