propofid trigonometrical Operation. 2 1 1 
Tome remarks on that column of it, which contains the fum of 
the three equations, or difference between the degree of the 
meridian and the correfponding degree of the great circle per- 
pendicular to it, which is the mod troublefome to compute, but 
muft be found before the degree of longitude can be obtained. 
The firft part of M. Bouguer’s equation confifts of T 7 ths of 
the difference between the degree of the meridian at the equa- 
tor and that at the pole, viz. 545.12 fathoms, to be conftantly 
added. Secondly, |ths of the increment of the correfponding 
degree of the meridian above that at the equator, to be fub- 
t rafted ; and, thirdly, -P 5 ths of a third proportional to the 
excefs of the degree at the pole above that at the equator as 
radius, and the fine of the correfponding latitude, to be added. 
Now it will be found, that this laff part of the equation 4^ ths, 
if uniformly applied, would have produced abfurd refults at 
the 75th degree of latitude, that is to fay, the degrees of a 
great circle would there have become greater than the degree 
at the pole. The equation yt^ths or |th would in like man- 
ner have produced abfurd refults between the 79th and 80th 
degree. Even ths will not go on further than the 85th; 
and the higheft equation that will go through the whole qua- 
drant, uniformly applied, muft not exceed T 8 T 0 - parts of the 
third proportional. M. Bouguer himfelf had found this, and 
accordingly had applied the equation with a certain modifica- 
tion or abatement, which neverthelefs he makes no mention of 
in his book. Seeing, therefore, that the degrees of a great 
circle perpendicular to the meridian differ moft from thofe of 
latitude about the tropics, I have, at the 20th degree, applied 
the equation yLths or parts, and made the divifor increafe 
by unity for each degree of the quadrant above that point to 
the pole, where it becomes T 8 T °o P arts * Below the 20th degree 
the 
