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VOL. LXXVI.] PHILOSOPHICAL TRANSACTIONS. 101 



practicable, in a coarse way, to ascertain the difference of altitude between any 

 two objects that passed the field of view ; on which account, Dec. 30, I began to 

 use an index-board, divided into inches, and marked with numbers, which, being 

 placed behind the rope that moved the telescope, would point out at what altitude 

 a certain index, affixed to the rope, was situated. My tackle of ropes and 

 pulleys was such that, while the telescope traversed an arch of 2°, the mark on 

 the rope passed over about 24 inches of the index-board: but the exact measure 

 was always to be determined experimentally, as it varied according to the situa- 

 tion of the instrument. I perceived immediately that the quantity of rope used 

 in the motion of the telescope would be much better observed by the assistant, 

 if the index were brought within doors near the writing desk: to effect this I 

 used a small cord, which, being led off from the great one, was carried over a 

 pulley into the observatory, so as to pass over a set of numbers, which I now 

 divided into such parts as, in an equatorial situation of the instrument, would 

 give nearly each equal to one minute. 



It would exceed the limits of this paper to enumerate the various trials I made 

 to bring the right ascension to greater perfection ; such as causing the tube some- 

 times to hang inclining or rubbing against a perpendicular plane; at others, 

 drawing it against the same by a small weight, fastened to a cord, passing over a 

 side pulley, &c. I shall also pass over the several changes in the form of the ma- 

 chine showing the polar distance, which, for convenience sake, was soon brought 

 to an index moving over a dial, in the manner of a clock. By way of directing 

 the person who gives motion to the telescope, a small machinery was added, 

 which strikes a bell at each extreme of the breadth of the sweep, and is adjust- 

 able to any required number of turns of the handle. 



In June, 1784, I introduced a small quadrant of altitude, the use of which 

 became soon after of the greatest consequence in determining the value of the 

 numbers of the polar distance piece. Hitherto I had settled this value by caus- 

 ing a star to pass vertically through the field of the finder, which was very accu- 

 rately limited to 2°; but now I found, by many comparisons between the degree 

 determined by the quadrant and by the finder, that I had generally under-rated 

 the value of the numbers. Fortunately so many stars of Flamsteed's catalogue 

 had been taken, that the numbers between their different polar distances were 

 sufficient to recover the value of the degree; but this occasioned a laborious re- 

 calculation of the places of all objects taken in near 300 sweeps. The quadrant 

 being once introduced, I carried the refinements of the determination, in high 

 sweeps where the ropes acted very unequally, so far as to ascertain by it sepa- 

 rately the value of every 20 or 30 minutes throughout the whole breadth of a 

 sweep of 2°, and the numbers were then accordingly cast up by so many different 

 tables calculated on purpose. 



VOL. XVI. Y 



