84 PHILOSOPHICAL TRANSACTIONS. [aNNO 1770. 



yet been made public, it is apprehended that gentlemen curious in these specu- 

 lations would be pleased to see them. 



In this subject 5 particulars are taken into consideration. 1st. The annuity, 

 rent, or pension ; 2d. The times that annuity, rent, or pension is to continue ; 

 3d. The rate of interest used in the computation ; 4th. The amount of those 

 rents, and their interest, when they are forborn to be received any times after 

 they are due: 5th. The present worth of those rents, some times before they 

 are due; or of a sum to be received before it is due, discount being allowed. 



And the investigations naturally fall under two heads. 1 st. The consideration 

 of amounts. 2dly. The consideration of discounts. Under the first head an 

 equation is to be obtained between the annuity, time, rate and amount, from the 

 known proportion that subsists between sums of money put to interest, during 

 the same length of time, and the amounts of the principal and interest together. 

 Under the 2d head another equation is to be formed between the annuity, rate, 

 time and present worth, from the known proportion that subsists between the 

 sums discounted, and their present worths, when done for the same time. As 

 these equations involve quantities common to both of them, therefore other equa- 

 tions may be thence deduced, containing all the 3 terms before specified. And 

 hence, any 3 of the 5 terms being given, the other 2 are to be found; which 

 admits of 20 cases. 



Some of these cases will produce affected equations, where the index of the 

 highest power of the unknown quantity will be the number of times the rent is 

 to continue, or to be paid : therefore the solution of those cases will be given 

 by a method of approximation, as no better way has yet been discovered for the 

 solution of afFectal equations, in numbers, above the 3d or 4th degree. 



The algebraical investigations are then given ; but it is unnecessary that they 

 Bhould be here retained. 



XL IF. A Copy of a Letter from John Ellis, Esq., F.R.S. to Dr. Lintiteus,. 

 F. R. S., &c. with the Figure and Characters of that elegant American Ever- 

 green Tree, called by the Gardeners the Loblolly-Bay, taken from Blossoms 

 blown near London, and showing that it is not an Hibiscus, as Mr. Miller 

 calls it ; nor an Hypericum, as Dr. Linnceus supposes it ; but a new Genus, to. 

 which Mr. Ellis gives the Name of Gordonia. p. 518. 



We have lately got into a method of cultivating the loblolly-bay, or alcea flo- 

 ridana, &c. of Catesby's History of Carolina, vol. i. tab. 44, p. 44. This tree 

 has lately produced some well-blown flowers, in the botanic garden of Mr. 

 Bewick, at Clapham near London, who sent them to me to examine their cha- 

 racters while fresh : I had by me some dried specimens, which had been sent from 

 our friend Dr. Alex. Garden, of Charlestown. On comparing these with the 



