of adf effect Equations . 475 
two angles are 10.3343832 and 10.0857536, which being re- 
lpeCtively increafed by 9.9208188 and 9.7446275, the two 
conftant logarithms, make 0.2552020 and 9.8304811, which 
are the logarithms of 1.7997079 and .6768323 ; and the dif- 
ference of thefe two numbers' is 1.1228756, which is lefs than 
the difference of the log. co-tangents by .0954226. 
I next aflume the angles 30° and 52° 45' ; and by purfuing 
the fame fteps which have been defcribed above, I find the dif- 
ference of their co-tangents exceeds the difference of the pro- 
ducts by .0028987. Then, as 925239 (the difference of the 
errors.) is to 145' (the difference of fuppofitions), fo is the latter 
error 28987 to 4' 33", which being added to 30°, gives 
30° a! 33^ for the next aifumption of the angle dCl ; but for 
eafe in the computation I fhall take 30° 5' ; in which cafe the 
angle DCI will be 52 0 40' ; and by repeating the operation the 
difference of the co-tangents will be found lefs than the dif- 
ference of the produCls by .0002425. And 51412 (the fum of 
the two laft errors) is to 5' (the difference of the fuppo|hipns) 
as 2425 (the laft error) is to 23"; which being taken 1 Jffim 
30° 5', the laft fuppofition, becaufe it was too great, leaves 
30° 4' 37" for the exaCt value of the angle */CX. 
This equation, like that in the fourth example, when, the 
value of y is properly fubftituted, and the equation reduced in 
the ufual manner, will rife to four dimenfions with all the 
inferior ones ; and it does not appear, that either huygens, 
slusius, Mr. robins, Dr. willson, or P.rofeflbr simson, 
with all their artifice, have been able to deprefs it : but by .this 
method of refolution the point of reflection is found, with the 
greateft exaCtnefs, in much lefs time than this fubftitution and 
reduction can be made. And this example farther fuggefts to 
us, that when the anfw T er is fought by the method now under 
2 con fir 
