, 4 . 1 8 Mr. maseres’s Method of 
vv , t > 4 
i-. 250,000,000,000,* — + .140,025,000,000, X j 
v 6 v % 
-.097,656,450,000, xpr + .074,768,066,406, X jr 
V 10 
-.060, 562, 133, 788, xj^ + .050,889,015,196, x s - 
— .043, 878, 793, 714, xjtx + See. The co-efficients of 
thefe terms decr'eafe fo flowly (efpecially after the firft 
twelve or fourteen terms) that, when the verfed line v is 
very nearly equal to the right fine s (as is th e cafe when the 
arch through which the heavy body defeends is nearly 
equal to 90°, or the arch of a W'hole quadrant of a circle) 
it would be neceffary to compute a vaft number of the 
terms of the feries in order to obtain its value exadt to 
feven or eight places of figures ; and, when v is quite 
equal to s (as is the cafe when the arch, through which 
the defeent is made, is exadtly equal to 90°) the compu- 
tation of the value of the feries to that degree of exadt- 
nefs in that diredt manner becomes wholly impractica- 
ble. But by the help of the differential feries above- 
mentioned its value may be found, even in this cafe, to 
that degree of exadtnefs without much difficulty ; more 
efpecially if we compute the firft twelve terms of the 
feries in the common way, and then apply the differen- 
tial feries to the inveftigation of the remaining part of it 
in the fame manner as in the laft example. This we 
lhall now proceed to do. 
5 
Art. 
