467 
are corrected or not ; but for fnch ns are fcrupulous to fractional 
parts of fathoms, thefe may fatisfy themfelves with great 
facility and exactnefs, by attending to and proportioning by 
the common tabular differences, as in the following example 
of the application of the correction to oblique degrees, in the 
latitude of Greenwich 51 0 28" . 
Obliquity, 
Original 
tabular 
difference. 
Supp. 
correc- 
tion. 
Corrected 
difference. 
Corrected 
degree. 
r 
Application of the 
correction to the 
degrees of great 
circles, fituated 
obliquely to the s 
meridian, in the 
latitude of Green- 
wich. 
0 y 
45 0 
33 45 1 
‘ 5 / 
22 20 1 
67 30 j 
11 r 5 1 
78 45 J 
0 0 1 
90 0/ 
Fath. 
204.45 
78.24 
66.33 
44 * 3 2 
x 5-56 
Fath. 
- 1.65 
-0.63 
- 0.54 
-0.36 
— 0.12 
Fath. 
4 - 202.80 
{+ } ”- 61 
{+ } 65 '79 
{ 4 } 4 3 - 9 6 
{;} . 5-44 
Fath. 
6 1070.20 
f 60992.63 
1 61 147.85 
J 60926.84 
L 61213.64 
f 60882.88 
1 61257.60 
j 60867.44 
[ 61273.04 
Here it is to obferved, that half of the correction is con- 
ftantly to be applied at the 45th degree of obliquity; and fince 
the differences between the terms in the progreflion equally- 
removed on either tide from 45 0 , are always equal to each other, 
it follows, that the corrected differences are to be applied with 
the contrary lign, thole between 45 0 and the meridian being in 
diminution, and thefe between 45 0 and the eaft or weft points 
being in augmentation of the length, till, in the firft cafe, 
the degree becomes equal to that of latitude ; and in the laft 
to that of a great circle perpendicular to the meridian. 
The Table of Companion, p. 227. is no where affeCled by 
the alteration which has been the fubjeCt of this dilcuffion, 
except in the two laft lines from the bottom, as adverted to 
among the errata fubjoined to this fupplement. 
This intimation of M. Bouguer’s miftake in exprefiing his 
formula in words, was accompanied with the converfion of 
that 
