508 irHlLOSOPHICAL TRANSACTIONS. [aNNO l/CO. 



/ But botli these operations are an immediate consequence from the proposi 

 tion in spherical trigonometry, usually delivered under the name of the 4th 

 axiom, which is this : that the square of the radius is to the rectangle under the 

 sines of the sides containing any angle, as the versed sine of that angle is to 

 the difference between the versed sines of the third side, and of the difference 

 between the sides containing the angle. 



Hence Dr. P. institutes a rather long and laboured geometrical dissertation, 

 to show how the set of tables in question are, or might have been constructed. 



LXXXII. Of the Plants Halesia and Gardenia. In a Letter from John Ellis, 

 Esq. R. R. S.y to Philip Carteret fVebb, Esq., F. R. S. p. 929. 



The intent of this letter is to exhibit the characters of two new genera of 

 plants, growing in Mr. Webb's garden, which Mr. Ellis calls after Dr. 

 Hales of Teddington, and Dr. Grarden, of Charlestovvn, South Carolina.* The 

 first of these is thus described by Dr. Garden, when he sent the specimens and 

 seeds. 



" This beautiful tree grows commonly along the banks of Santee river, and 

 rises often to the size of middling mulberry-trees. I have seen it sometimes 

 more southerly, near the small rills of water ; but of a much smaller size than 

 that which grows on Santee. The wood is hard and veined ; the bark is of a 

 darkish colour, with many irregular shallow fissures. The leaves are ovated 

 and sharp pointed, with the middle depressed, growing alternately on short 

 footstalks. The flowers hang in small bunches all along the branches, each gem 

 producing from 4 to 8 or 9 flowers, bell-shaped, and of a pure snowy whiteness. 

 As they blow early in the spring before the leaves appear, and continue for 2 or 

 3 weeks, they make a most elegant appearance. They are followed by pretty 

 large four-winged fruit, which likewise hang in bunches, each containing 4 ker- 

 nels that are very agreeable to the taste." 



This tree is mentioned by Catesby, vol. i. p. 64, and called Frutex padi foliis 

 non serratis, fioribus monopetalis albis, campaniformibus, &c. &c. 



Mr. E. had not heard that it was cultivated in England, till about 4 years 

 before, when the Doctor sent him over from Carolina a large parcel of the seeds, 

 which he distributed among many curious gardeners, and others : but he could 

 not find any one that it had succeeded so well with as Mr. Gordon, gar- 

 dener at Mile-end. a man who seems to be possessed of a knowledge peculiar to 

 himself, in raising all the rarer and most difficult exotics from seeds, layers, or 

 cuttings. He informs Mr. E. that it stands our winter in the open air, without 

 shelter. 



* It is the Halesia Tetraptera o[Linneu$, 



