C is 7 3 
XIV. A Method of finding the Value of an infinite Series oj 
decreafing Quantities of a certain Form , vehen it con- 
verges too Jlowly to be fummed in the common Way by 
the mere Computation and Addition or Subtraction of 
fome of its initial Terms. By Francis Maferes, Ff quire , 
F. R. S. Curfitor Baron of the Exchequer. 
Read Feb. 13, A RTIGLE Iff Let a , b, c, d, e,f g, h, &c. 
ad infinitum , reprefent a decreafing pro- 
greffian of numbers, fo that b fhall be lets than a, and 
c than b, and d than c, and fo on of the following num- 
bers, ad infinitum. 
And 2 dly, let thefe numbers be fo related to each 
other, that they not only fhall form a decreafing progref- 
fion themfelves, but that their differences, a— b, b—c , 
c-d, d-e, e—ff-g,g-h, See. fhall alfo form a decreafing 
progreffion, fo that b—c fhall be lefs than a-b, and c-d 
than b—c , and d—e than c—d, and fo on of the following 
differences; and likewife, that the differences of thefe 
differences (which may be called the fecond differences of 
the original numbers a, b, c, d, e, f g, h, 8cc. fhall form 
a decreafing progreffion ; and that the differences of thole 
fecond differences, or the third differences of the original 
B b a numbers 
