from the measurement of an arc of the meridian , &c. 501 
From this equation we get d — Cos . 7( , v;,sin ~) ■ 
And from equation 9 we get p — — ; and since 
at the equator the degree of longitude, and the perpendicu- 
lar degree are equal, then 0 = r+T^i ’ 
and this reduced we shall have df = p'. Cos. where d! and 
p' are in the same latitude. Hence d': p'\ : Cos. 7 : rad . . . (20) 
I shall now proceed to determine the compression at the 
poles from the foregoing three sections of the arc; and 
comparing each, first with the French degree in latitude 
47°3° / 46 // , equal 60779 fathoms; then with the English degree 
in latitude 52 0 2' 20", which is 60820 fathoms ; and lastly with 
the Swedish degree in latitude 66° 20' 12," when it is 60955 
fathoms. 
With respect to the French degree, as there appears much 
irregularity in the different sections of the arc between Dun- 
kirk and Montjouy, I have used that between the Pantheon 
at Paris, and Eveaux, as given by De Lambre in the Base 
du Systeme Metrique, as it appears to be the most consistent. 
This degree is 57066 toises, equal to 60798 fathoms. But 
their measurements being all reduced to the temperature of 
32 0 of Fahrenheit’s thermometer, the above degree will 
require a deduction of 19 fathoms nearly, to make it what it 
would have measured by the brass standard at the tempera- 
ture of 62°, which is our standard temperature. Hence, 
60779 fathoms is the degree in latitude 47°|Jo' 46" to com- 
pare with the Indian measurements. 
Let this degree be denoted by m‘ ; and its latitude, 
47° 30' 46" by 7 ; and let the degree 60472,83 fathoms be 
m, and its latitude 9° 34' 44" be /. Then by equation t, 
