Wherein a Is the length of any Arch which you^efrgn fliall 
be the Integer or Unity in your Meridicmal Parts, ( whether 
it be a Minute, League or Degree, or any other.) S the Co- 
fine of the Middle Latitude, and s the Sine of half the diffe- 
rence of Latitudes; But the Secants being the Reciprocals 
of the Co- fines, -i will be equal to -^putting / for the Sd- 
cant of the Middle Latitude; and — into-L will be = 
a S ar 
This multiplied by — that is by -^^, will give the fe- 
%SS irrrr 
'cond ftep : and that again by i^^, the third flcp : and fo 
forward till you have compleated as many Places as you 
defire. But the Iquares of the Sims being in the fame ratio 
with the Verfed fmes of the double Arches, we may inftead 
of ~ alTume for our MultipHcator — , or the Verfed- 
^SS 3 V 
fine of the difference of the Latitudes divided by thrice 
the Verfed-fine of the ium of the Co-latitudes, &c. which 
is the utmoft Compendium I can think of for this purpofe, and 
the fame feries will become. 
— 5>nto , + — + _ 
Hareby we are enabled to eflimate the default of the me- 
thod of making the Meridian line by the continual additi- 
on of the Secants of aequidifferent Archs, which as the dif 
ferences of thofe Arches are fraaller, does flill nearer and 
nearer approach the Truth. If we afTume, as Mr. Wright 
did, the Arch of one Minute to beUnity, and one Minute 
to be the common difference of a rank of Arches: It will 
be in all cafes, As the Arch of one Minute, to its Chord; : 
So the Secant of the Middle Latitude, to the firft flepof our 
feries. This by reafon of the near equality between ^ and 
2 s, which are to one another in the ratio of Unity to 
I—- o,oooooooo352j^64577i3, &c, wilhnot differ from the 
Secant 
