220 PHILOSOPHICAL TRANSACTIONS. [aNNO ]685. 



The author being, by these observations, confirmed in his resolution of ad- 

 hering to bare sights, with his naked eye, without glasses ; and having satisfied 

 Mr. Halley as to the certainty and accuracy thereof (far beyond what Mr. 

 Halley could expect ;) thought fit in the first place (after his Machina Coelestis) 

 to publish these, for the satisfaction of others, to preserve the just reputation 

 of his observations before published, which Mr. Hook had endeavoured to 

 render suspected. 



He therefore gives, first, his obversations of the year 1679, beginning from 

 Jan. 8, N. S. where his Machina Coelestis ended ; and so onwards till May 26, 

 when Mr. Halley arrived. And therein, among others, the transit of some 

 stars, and the occultatiou of some others, by the moon : March 25, March 30. 

 From thence, to June 18, is an account of all his observations made with Mr. 

 Halley, with their success. And thence to Sept. 26, the fatal day when his 

 observatories, with all their furniture, were destroyed ; which concludes the ob- 

 servations of that year. 



After these observations, of the year 167Q, are 27 letters which had passed 

 between the author and several other learned men, relating to the controversy 

 between him and Mr. Hook, about the use of telescopic sights ; in which 

 letters are contained the whole particulars of this notable controversy. 



With regard to the subject of diagonal divisions, he observes, that the divi- 

 sion of an angle into equal parts by straight diagonals, obliquely cutting concen- 

 tric arches in the limb, would require, in mathematical rigour, that the concen- 

 tric circles be set at somewhat unequal distances ; and in small instruments, 

 where the breadth of the divided limb is a considerable part of the radius, as -j-, 

 or tV of it> 3"d ^he angle to be so divided, of a considerable size, suppose 10 

 minutes or more, it may require some little difference of intervals. But where 

 the instrument is large, as here, 6, 8, or 10 feet radius, and the breadth of the 

 limb to be divided, but narrow, as here about half an inch, and (as here) the 

 angle to be so divided but 5 minutes ; the true intervals according to mathe- 

 matical rigour, are not to be distinguished by the clearest sight from equal 

 distances ; for no sense can distinguish the one from the other. And if there 

 had been any diflference ; the author had sufficiently provided for it, by per- 

 forming the same divisions by straight lines from the centre also. The com- 

 putation of Dr. Wallis, to which the letter refers, is to be seen at large in the 

 Philosophical Transactions, N° 111.* On this principle the author makes a 

 calculation, by which it appears that the differences are far too small to be in 

 any way distinguished. 



* Volume 2, p. 189, of this Abridgment. 



