32 PHILOSOPHICAL TRANSACTIONS. [aNNO 1786. 



that the dependance was wholly on the screw divisions, when it came out of Mr. 

 Tompion's hands. This one may reasonably infer from the observations them- 

 selves ; for the first observation, set down as taken with this instrument, being 

 on the 29th of October, 1676, it was not till the llth of September, 1677, 

 that the column which contained the check angle by diagonal lines was filled up ; 

 and there was also a space of time, antecedent to that last-mentioned, wherein 

 no observations are recorded as taken with this instrument, in which time the 

 diagonal divisions might be put on ; and this will be put beyond a doubt, as he 

 says expressly, that finding, in the year \677i that the threads of the screw had 

 worn the border of the limb, he divided the limb into degrees himself, and drew 

 a set of diagonal divisions ; and then comparing the two sets of divisions toge- 

 ther, he sometimes found them to differ a whole minute ; therefore, for correc- 



* tion thereof, he constructed a new table for converting the revolutions and parts 

 of the screw into degrees, minutes, and seconds ; and which he applied in the 

 observations taken in 1678. However, notwithstanding this correction, in 

 looking over the observations noted down as deduced each way, I often find a 

 difference of half a minute ; not unfrequently AO" ; but in an observation of 

 the moon, of the Qth June, 1687, I find a difference of 55^'', which on a radius 

 of 6 feet 9 inches amounts to more than -^V part of an inch. 



In the year 1689, Mr. Flamsteed completed his mural arc at Greenwich ; and 

 ■ in the Prolegomena before mentioned, he makes an ample acknowledgement of 

 the particular assistance, care, and industry of Mr. Abraham Sharp ; whom, in 

 the month of August, 1688, he brought into the observatory, as his amanuensis; 

 and being, as Mr. Flamsteed tells us, not only a very skilful mathematician, but 

 exceedingly expert in mechanical operations, he was principally employed in the 

 construction of the mural arc ; which in the compass of 14 months he finished, 

 so greatly to the satisfaction of Mr. Flamsteed, that he speaks of him in the 

 highest terms of praise. This celebrated instrument, of which he also gives the 

 figure at the end of the Prolegomena, was of the radius of 6 feet 74- inches ; 

 and, in like manner as the sextant was furnished both with screw and diagonal 

 divisions, all performed by the accurate hand of Mr. Sharp. But yet, whoever 



• compares the different parts of the table for conversion of the revolutions and 

 parts of the screw belonging to the mural arc into degrees, minutes, and seconds, 

 with each other, at the same distance from the zenith on different sides ; and 

 with their halves, quarters, &c. will find as notable a disagreement of the screw- 

 work from the hand-divisions, as had appeared before in the work of Mr. Tom- 

 pion : and hence we may conclude, that the method of Dr. Hook, being exe- 

 cuted by two such masterly hands as Tompion and Sharp, and found defective, 

 is in reality not to be depended on in nice matters. From the account of Mr. 

 Flamsteed it appears also, that Mr. Sharp obtained the zenith point of the in- 



