516 Mr. T. T. Wilkinson on Mathematics atid Mathematicians : 



told them that he ought to have stated that I had put up all the 

 instruments and drawn the meridian line, and also put the in- 

 stiniment in order when he was at a loss how to do it. Bayly 

 disputed this, so I told him he was at liberty to think as he 

 pleased, but that was a fact which I supposed Mr. Maskelyne 

 would not deny. Wales mentioned the Sieve of Eratosthenes, 

 which led to a deal of conversation. 



" Mem, To call on Carnan on Friday noon.'^ 



Mr. William Bayly was a respectable astronomer and mathe- 

 matician, who filled the office of assistant to the Astronomer 

 Royal, Dr. Maskelyne, for several years. In 1769 he was sent 

 out by the Royal Society to the North Cape, to observe the tran- 

 sit of Venus ; he subsequently accompanied Captain Cook in his 

 second and third voyages, and on the decease of Mr. George 

 Witchell, was appointed as his successor in the mastership of the 

 Royal Naval Academy at Portsmouth. It does not appear that 

 Mr. Burrow ever published anything relating to Euclid^s Porisms, 

 but the following note found in his copy of Dr. Simson's Locis 

 Planis, now in my possession, will show that at the time it was 

 written he had advanced no further in the subject than to be 

 able to transform the enunciation of a Locus into a Local Problem, 

 under the idea that by this process he had obtained the enun- 

 ciation of a Porism. 



" On Porisms. If in the enunciations of the Propositions, 

 which are now in the form of Theorems, the hypothesis was to 

 remain as it is, and instead of saying ' the Locus will be such a 

 line, &c. ;^ if it was required to determine what the Locus 

 would be : — then all this book (Simson's Apollonius de Locis 

 Planis) w ould be exactly in the form of Porisms, except the latter 

 part of each proposition, which shows the composition, or how 

 to determine the Locus. For example, if Prop. VIII. had been 

 in this foi-m : — ^ if from a given point two right lines be drawn in 

 directum, containing a given space, and one of them touch a right 

 line given in position ; required to shew in what line the other 

 point will always fall : ' — this would be in the form of a Porism. 

 In most of the problems in Apollonius de Locis Planis, in Theo- 

 rems, altered as above, instead of right line and circle, &c., sub- 

 stitute Conic Section, &c., and see what would be the result of 

 such an inquiry." (Mech. Mag. No. 1437.) 



His opinions respecting the operose character of Dr. Horsley's 

 restoration of Apollonii Pergai Inclinaiiones Oxonii, 1770, are 

 frequently enforced in his Diaries for 1777-1779, and received 

 an elegant and practical illustration in a Restitution of the Geo- 

 metrical Treatise of Apollonius Pergseus on Inclinations, which 

 he published and dedicated to the Ri^ht Honourable Lord 

 Viscount Townsend in the latter year. The papers on Perfect 



