VOL. LX.] PHILOSOPHICAL TRANSACTIONS. 83 



phicai Society, held at Philadelphia, for promoting useful Kriowledge. By 

 fVm. Smith, D.D., John Lukens, Esq., David Rittenhouse, M.A., and Mr. 

 Owen Biddle. Communicated by Ben. Franklin, LL.D., F.R.S. p, 304. 



These gentlemen had the same telescopes now as before, in the transit of 

 Venus, viz. the college reflector, with DoUond's micrometer ; used by Dr. Smith, 

 with a magnifying power of 200, to observe the contacts. 2. A refractor of 42 

 feet, magnifying 140 times, used by Mr. Lukens. 3. Mr. Rittenhouse's refrac- 

 tor, with about the same power, used by himself. Mr. Biddle had no telescope; 

 but was very serviceable in the other parts of the observation. 



The first external contact was observed to the same instant by all the three 

 observers, who had no communication with each other, the two refractors being 

 out of doors, and the reflector within the observatory; and the contacts noted, 

 as at the transit of Venus, by signals given to persons set at the windows of the 

 observatory, to count the clock. )t «r ik - ' 



■ The contacts were as follow: 1769, Nov. 9, apparent time. 

 At 1^ 35"" 17* first external contact, by all the three observers. 



1 36 35 first internal contact, by Dr. Smith and Mr. Rittenhouse. ' 



2 36 33 first internal contact, by Mr. Lukens. 



The sun's diameter, per micrometer 35' 20".24 



Mercury's diameter taken backwards and forwards several times, and 



the sum halved, gave only 8.22 



By the contacts of Mercury at Philadelphia and Norriton, they get the latter 



55» of time west of the state-house observatory ; the same they made by the 



eclipses of Jupiter's satellites. 



XLIII. Investigations of Twenty Cases of Compound Interest. By J. Robertson, 



Lib.R.S. p. 508. 



The late Wm. Jones, Esq. f.r.s., among the variety of mathematical matters 

 to which he gave attention, considered the business of compound interest fully, 

 and did, many years ago, cause to be engraved on a copper- plate, more cases in 

 interest than had been exhibital before that time : several copies of impressions 

 from that plate were distributed among his friends; to whom it appeared that he 

 had treated this subject in a more extensive manner, than had been done by other 

 mathematicians. . ^ 



The theorems, or rules, for the cases of compound interest, without their in- 

 vestigations, were inserted by Mr. Jones, in ttie quarto edition of logarithms, 

 published by Gardiner ; and the rules were also communicated to Mr. Dodson, 

 who published them, by Mr. Jones's leave, with examples to illustrate the use of 

 his antilogarithmic tables: but the investigations of these theorems not having 



M 2 '■'■:' ■■ -■■■ "-■•'' • '^■" 



