482 PHILOSOPHICAL TRANSACTIONS. [aNNO 1681. 



moon, and for adjusting the time, having observed Jupiter till 6^' 3"^ in the morn, 

 at the height of 36°, as well with a telescope of 20 feet as with one of 3, which 

 is remarkable, because Jupiter is wont to disappear in the crepuscule some minutes 

 after sun-rising. 



Twelve Problems in compound Interest and Annuities, resolved by Adam Martin- 

 dale, Philos. Collect. N*' 1, p. 34. 



Twelve problems in compound interest and annuities, expressed in symbols, 

 to be resolved by logarithms, and distinguished into three ranks, whose symbols 

 are thus to be understood : 



Principal 1 



Rate, viz. 1 1. with its rate j-Common to all the 3 ranks. 



Time J 



Amount or aggregate "^ C ^ 7 



Sum of principal and arrearages \ proper to •< ^ r Rank. 



Difference of principal and worth J t 3 3 



Their capitals stand for the logarithms of the number signified by the small 

 letters. 



D signifies data, or given ; Q quaestitum, Prob. problem. Res. resolution. 

 The first rank touching compound interest for a single sum of money. 



1 prob. D. p, r, t. Q. a? Res. R^ X P = A. 



2 prob. D. a, r, t. Q. p ? Res. A — R* = P. 



3 prob. D. p, a, t, Q. r ? Res. — - — = R. 



4 prob. D. p, a, r. Q. t. Res. ^~~^ = t. 



R 



The second Rank, concerning Annuities in Arrear at Compound Interest, grounded 



upon these tivo Axioms. 



1 . The annuity and rate of interest being given, the principal correspondent 

 to the annuity is in effect given also, being easily found out by the Rule of 

 Three, thus; 



As the Interest of any principal, ex. gr. of 1, 10, 100, &c. is to that prin- 

 cipal : : so the annuity or pension, to its principal. 



2. The sum of the principal and the arrearage of all the payments being found, 

 the arrearages alone may be obtained, by subtracting the principal from that 

 sum. 



