462 Dr. Herschel’s Catalogue of One Thoufand 
accurately limited to two degrees ; .but now I found, by many 
companions between the degree determined by the quadrant 
and by the finder, that I had generally under-rated the value of 
the numbers. Fortunately fo many fears of Flamsteed’s Cata- 
logue had been taken, that the numbers between their different 
polar diftances were fufficient to recover the value of the degree ; 
but this occafioned a laborious re- calculation of the places of 
all objedts taken in near 300 fweeps. The quadrant being once 
introduced, I carried the refinements of the determination, in 
high fweeps where the ropes adled very unequally, fo far as to 
afeertain by it feparately the value of every 20 or 30 minutes 
throughout the whole breadth of a fweep of two degrees, and 
the numbers were then accordingly caft up by fo many different 
tables calculated on purpofe. 
Being {fill difappointed in many inftances, when, on a're- 
view of a nebula whofe place I had before determined, I pern 
ceived a difference of 4 or 5 minutes in polar diftance, I began 
at laft inti rely to new model the machinery of the polar diftance 
piece, and on Sept. 24, 1785, completed one with the follow- 
ing capital improvements. My former piece {hewed a fet of 
numbers whole value differed in every fituation of the telefcope, 
and therefore required different and very extenfive tables to caft 
them up in degrees and minutes. This {hews at once both 
the degree and minute of the polar diftance of every celeftial 
objeft, without requiring any tables to caft up numbers. In 
the next place, the confiderable inaccuracy arifing from the 
unequal tenfion of the great ropes, and their expanfion or con- 
traftion by moifture or drynefs, is in tire ly taken away ; for 
now my index cord is contrived fo as to go off from the front 
t)f the telefcope itfelf, in the direction of a tangent to the arch 
it deferibes when moving; by which means this cord will even 
ferve 
