4*0 Mr. Pond on the different methods of 
new result of the position of the star : and of the totality of 
these results is the catalogue ultimately formed. 
In a paper which I had the honour of communicating 
to the Society, in the year 1816, I have given several 
examples of the manner in which the index error of the 
mural circle is calculated, though I did not at that time 
explain the principle or advantages of this method. In the 
printed Greenwich observations will be also found the com- 
putations of this index error for every month. 
I should observe, that when the greatest possible accuracy 
is required, the whole of the observations should be re-com- 
puted from the catalogue now supposed to be in its most 
perfect state, except the extremely small improvement it may 
receive from this process. And thus/ by continued observa- 
tion and approximation, may the relative places of the stars 
be assigned to a very unexpected degree of accuracy. Now, 
though a continuation of this process has an evident tendency 
to improve the catalogue, as far as concerns the relative 
distances of the several stars to each other, yet it can have 
no effect in correcting any common error that may exist from 
a false assumption either of the zenith or the pole. I will 
endeavour, therefore, to explain the next part of the process, 
which is to determine the common error in polar distance. 
It is to be presumed that the pole star forms one of the stars 
of which the intended catalogue is composed, and it should be 
observed most assiduously, both above and below the pole. 
These observations are to be treated as if appertaining to 
different stars, and the place of each determined in the 
catalogue, by applying the same index error as that em- 
