- ( 2^9 ) 
■ T ""'^ S + p + p-+ 7S' + ^ , «^'^ 
wherein as the differences of Latitude are fmaller. fewer fleps 
will fuffice. And if the Equator be put for the' Middle La- 
titude, and confequently S = R, and j to the fine of the Lati- 
tude^the Meridional parts reckoned from the Equator willbs 
which is coincident with Dr. WaUis% folution in Numb. 176» 
And this tzmQ Series y being half the Logarithm of the ra^io 
oi R-\-s toK — /, that is^ of the Verjed-fines of the diftances 
from both Poles, does agree with what Dr. Barr&w h^d 
fliewn in his XL Le5irure, 
The fame ratio oi t to t may . be exprefl^d alfo. by that 
of the Sum of the Co-fines of the tvpo Latitude Sy to the fine of 
their difference : As like wife by that of the Sme of the Sum of the 
two Latitudes, to the difference of then Co. fines : Or by that of 
tht Verfed-fine of the Sum of the Co-latitude Sy to the dtffmnce of 
the fines of the Latitudes Or as the [ame difference of the fines 
of the Latitudes ^to the Verfed-fine of the difference of the Latitudes ^ 
all which are in the fame rittio of the Co- fine of the Middle 
Latitude, to the Sine of half the difference of the Latitudes. 
As it were eafie to demon ftrate, if the. Reader were not 
fuppofed capable to do it himfeif, upon a bare infpedion of a 
Sheme.duly reprefenting thefe Lines. 
This variety of Expreffion: of the fam€- r^fw T thought 
not fit to be omitted, becaufe by help of the rationality of 
the Sine of %o^\ in all cafes where, the Sum or difference of 
the Latitudes is 5 o^V 90^' j ^ 2 or 150 degrees, foms 
one of them will exhibit afimple feriesy wherein great part 
of the Labour will be faved: And befides 1 am willing to 
give the Reader his choice which of thefe. equipollent me^ 
thodsto make ufe of ^ but for his exercife ihall leave the pro- 
fecution* of them, and, the icon^fmdia arifing, therefrom , to 
his own induftry. Contenting my felf to confider only ths 
former, which for all ufes leems the rpofl convenient,, whe- 
ther we d^^ign to make the whole lMei:idian;Xine3; or . any 
par: thereof,. 
