6'JO PHILOSOPHICAL TRANSACTIONS. [ANNO 1785. 



the method of correction in other instances, where the value of the correction 

 will be found to be different, according as we begin to collect at the 1st or 2d 

 term. Let the series be ^- — ■§- + -f- — -f + r — & c * sme ^ ne > which came ori- 

 ginally from 5; now if we begin to collect at the 1st term, the series 



becomes — + — — + &c. and for the same reason as before, the correction, 



to be added, is f ; but — - + — + &c. = | of a circular arc (a) of 30° to 



the radius 4V 3; hence the sum required = |A + f If we begin to collect at 



2 2 



the 2d term, the series becomes 2 — -— ; — — — — &c; and the correction to 



2 . 4 5 . / 



be subtracted is f ; for the 2d part of the original series is now — 1 -J- 1 — 1 



+ 1 — &c. which was produced by ■■ ■ , ; but 2 — — — — r^~: — &c. = 



' ' •'14-1+1 2.45.7 



1 + ;a; therefore the sum required = -i -j- -J-a as before. In the same manner 

 we may apply the correction in all other cases. Though, therefore, the series 

 1 — 1 + 1 — 1 -J- &c. or — 1 + 1 — 1 + 1 — &c. have no determinate value 

 in the abstract, yet the given series will fix its value by pointing out the quan- 

 tity from which the series must have been originally produced. 



V. Description of a Plant yielding Asafcetida. By John Hope* M. D., 



F.P^S. p. 36. 



ASAFCETIDA. [FERULA ASSAFCETIDA.] 

 An umbelliferous plant, about 3 feet high, up- ovate, many times pinnate-divided; leaflets cut, 

 right, branchy, glaucous, with yellow (lowers. subacute, subdecurrent ; the common footstalk 

 Root perennial. flat above, with an elevated line running longitu- 



Leaves radical six, procumbent, three-lobed- dinally through the middle. 



* Dr. John Hope was the son of a respectable surgeon at Edinburgh, where he was born in 1725. 

 After the usual grammatical education, he entered on the study of physic at his native place. He 

 afterwards went to Paris, and attended the lectures and demonstrations of the celebrated Bernard 

 Jussieu. Returning from his travels, he obtained the degree of ji. d. from the university of Glasgow, 

 in 1750, and soon after was admitted a member of the Royal College of Physicians at Edinburgh, 

 where he settled for the purpose of engaging in practice. In 1761 he was appointed to die professor- 

 ships of botany and mat. med. vacant by the death of Dr. Alston. His health becoming impaired, 

 he some years afterwards resigned the professorship of the mat. med. but still continued to hold his 

 botanical appointment ; to which was afterwards added the office of physician to the Royal Infirmary. 

 At the time of his death, which happened in November 1780', he held the high office of president of 

 the Royal College of Physicians at Edinburgh, and several years before he had been elected a fellow 

 of the R. s. of London. 



Dr. H. was indefatigable in promoting the progress of his favourite science, botany. With him 

 originated the botanical garden near Edinburgh, planted on a spot, which before was little better than 

 a dreary waste; but which in a few years was stocked with the rarest plants of every clime. The 

 pecuniary supplies requisite for this establishment were obtained from the Sovereign, first during the 

 administration oi Lord Bute ; and (he sum granted for this purpose was afterwards augmented, when 

 the Duke of Portland presided over his Majesty's councils. It was in this garden that Dr. H. reared 



