4 jo Mr . wales on the Refoluhon 
Thus far this matter has been carried by former writers ; but 
thofe who may be at the trouble of confulting them will find 
that I have not copied their methods : on the contrary, thefe 
which are given here are more plain and obvious than theirs are, 
and the operations confiderably fhorter. What follows has not, 
I believe, been adverted to by any before me. 
£ x A M P L E IV. 
Let the equation a rifing from the proportion a : b-\-x . i - c * 
:: c%/ i —x z : cT be taken, which is the refult of an inquiry 
into the fituation of that place on the furface of the earth, 
confidered as a fpheroid, which is at the greatefl diflan ce from 
a given one, fuppofe London- In this inquiry a and h were 
put to rep relent- the fine and coline of the latitude of the given 
place (in the fpheroid) ; c for , the ratio of the axes ; and# 
for the fine of the diflance of the required place from the oppo- 
fite pole (in the fpheroid alfo). The equation, which is of 
four dimenfons with all the terms, is manifeftly acx~ 
b+x . i e x %/ 1 — x % , or — — x.. — ; in which it 
ac ac 
t 1 ■ ’ ■ 
is evident from tab. I. that the difference between the tangent 
and the produdt of the fine into a given quantity is known. 
In order, therefore, to find the value of x, compute^, and 
- — f , arid find the logarithm of the latter. Now, becaufe the 
elliptic meridian differs but little from a circle, the place fought 
will not be far from the antipodes of the given one, and its 
diflance from the oppofite pole may therefore be eflimated at 
