41 '2 PHILOSOPHICAL TKANSACTIOXS. [anNO J 76/. 



Is used by that great and able geometrician, in his treatise on the distance of the 

 sun, but founded entirely on the theorems established in that and the preceding 

 tracts of the same author. 



Let TA be a given line. Take Am, so that ta may be to aot, as the rnoon's 

 accelerating attraction to the earth, to the sun's mean disturbance of that attrac- 

 tion. Take ag quintuple of Am. Take ap, such that twice Am may be to ap, 

 as TG to TA. Now it Is proved In the 25th prop, of Dr. Stewart's 4th tract, that 

 the cube of ta is to the cube of tp, in the duplicate proportion of the periodic 

 month to the anomalistic month. Therefore the proportion of ta^ to tp^, and 

 consequently that of ta to tp, is given ; and by division, that of ta to ap is 

 given. Therefore ta being given, ap is given. Now tg : ta = 2Am : ap. That 

 is TA — 5Am : ta = 2Am : ap. Therefore ta X 2Am = (ta — 5Am) X ap. 



•TUa^^e^^^ n.™ TA X AP — 5a/« X AP rr«, ^ ■ „ , 5a»» X AP 



1 heretore 2Am = , That is 2Am ^ , or 



TA ' TA ' 



(2TA + 5aP) X AW rpi ,. • T A X A P 



= AP. That is Am = 



2ta + Sap 



Fig. 1. 



sided as her officiating minister." In 179*. Dr. H. was translated from St. David's to the see of 

 Rochester, with the deanery of Westminster j and in 1802, to the lucrative see of St. Asaph. In 

 1801 he published the first, and in 1803 the last, of 3 octavo volumes of practical mathematics, for 

 the use of students; consisting of Euclid's Elements and Data, with notes, the properties and pro- 

 jection of the sphere, and spherical trigonometry, Archimedes on the mensuration of the circle, a 

 tract on the nature and use of logarithms, &c. Besides these, numerous and important were the 

 writings and labours of Dr. H. in theology, in politics, &c. ; for an ample account of which, and of 

 various other prrticulars of his life and transactions, reference may be had to several memoirs of 

 them, in the Monthly Magazine, anno 1806", vol. xxii. p. 401, and the Gent, Mag. of the same 

 year, vol. Ixxvi. pp. 987. 1057. 1095; but especially the former. 



Dr. H. had gone down to Brighthelmstone, in the latter part of September, chiefly to visit bis 

 very respectable friend Lord Thurlow, who however died two or three days before the doctor's 

 arrival. Dr. H. had not been at that place two weeks before lie was seized with a complaint in the 

 bowels, then frequent in the place, which soon turned to a mortification, and terminated his va- 

 luable existence on the 4th day of his illness. Though Dr. H. had reached the 74th year of his age, 

 the powers both of his body and mind were so vigorous as to promise still a considerable length of 

 years; indeed he was always of a very remarkably active and energetic cast of mind, and firm, com- 

 pact constitution of body. Perhaps no man of the age possessed more of what is termed recondite 

 learning, or was more profoundly versed in classical chronology. As a senator he ranked in the first 

 class : there were few important discussions in tlie house of lords in which he did not participate; 

 especially when the topics related to the hierarchical establishments of the country, or to the French 

 revolution, or to the African slave trade, of which he was a systematic opponent. As an orator, his 

 voice was deep, full-toned and commanding; his enunciation distinct and clear; and his delivery in 

 other respects highly advantageous, abating only for a remarkable mixture of certain guttural sounds, 

 such as are almost peculiar to the inhabitants of the county of Northumberland, occasioned, he used 

 to say, by the circumstance of a nurse from that part of England being long employed in his father's 

 family. 



