the Trigonometrical Operation . iyi 
bad confequence has arifen on that account, there being always 
fuch other checks from the collateral flat ions, as to leave 
nothing doubtful. 
On the whole, although, for the reafons already affigned, we 
have repeated the obfervations feldorner than was at fir ft pro* 
pofed ; yet it will obvioufly appear from the refults, and parti- 
cularly from the near agreement between the meafured and 
computed length of the bafe of verification, that a few very 
good obfervations are greatly preferable to a mean that might 
perhaps have been obtained of many made in a hurry, which 
at beft would have been but indifferent. 
The quantity by which the fum of the three obferved angles 
of fpherical triangles fhould have exceeded i8o° was found as 
follows. 
Becaufe the excefs of the three angles of a fpherical 
triangle above 180° x earth’s radius = its area, therefore 
= excefs above x 8 o° in feconds, if the area and radius 
Earth’s rad. 
are taken in feconds. Now, 60859.1 fathoms being=i° on a 
'■!* 
mean fphere, we get the log. of the feet in a lecondzr 
2.0061743, and twice this, or 4.0123486 is the log. of the 
fquare feet in a fquare fecond. Therefore log. area in feet 
_ 4.01 23486 = log. area in feconds ; and the log. of the earth’s 
radius in feconds being 5.3144251, we have area in feet 
-4.0123486-5.3144251 = log. area in feet- 9.3267737 = 
log. excefs in feconds ; that is to fay, from the logarithm of the 
area of the triangle taken as a plane one , in feet , fubtradl the con - 
flant logarithm 9.32677379 an< ^ the remainder is the logarithm 
of the excefs above 180 0 m feconds nearly . 
