4/0 Mr. wales on the Refolution 
Tims far this matter has been carried by former writers ; but 
thole 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. 
EXAMPLE IV. 
Let the equation arifing from the proportion a : h + x . i - c z 
:: cs/i. — x z : c r x 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 greateft diftance from 
a given one, fuppofe London. In this inquiry a and b were 
put to reprefent the fine and cofine of the latitude of the given 
2 O Q 
: place (in the fpheroid) ; c for the ratio of the axes ; and x 
for the fine of the diftance of the required place from the oppo- 
site pole (in the fpheroid alfo). The equation, which is of 
four dimenfions with all the terms, is manifeftly acx — 
b + x 
x %/ 
l~c 2 b . ,. t . 
— x . = — ; ill which It 
ac ac 7 
is evident from tab. I/that the difference between the tangent 
and the produfl of the fine into a given quantity is known. 
In order, therefore, to find the value of x, compute—, and 
l — and 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 
diftance from the oppofite pole may therefore be eftimated at 
39 ° 5 ' ; 
