some observations made with chronometers. 
369 
sin. a 2 , y sin. 
cos. p'®» tan S* 4 cos. «p 9 ’ 
-r, we have £ = sin. \{/, 
and the compression = 2 . sin. J \}/ 3 . 
From e and an arc of the meridian the dimensions of the 
spheroid are readily found ; the angle P, and the length of 
the geodetical line BD, may likewise be determined. The 
geodetical line BD, which is used in the Survey to find the 
degree perpendicular to the meridian, furnishes therefore no 
new datum for determining the dimensions of the parallels ; 
and this line will vary very little for different values of e, 
provided the values of « and ot and one of the latitudes be 
the same, while the other latitude is determined by the above 
equation. But the value of P will be different for every value 
of e ; and the same geodetical line will therefore correspond 
to different values of the difference of longitude according to 
the different compressions which are assumed. It follows 
therefore from all this, that the dimensions of the parallels 
have entirely been derived from the arc of the meridian in 
latitude 50° 41', and the compression resulting from the values 
of <p, <p'. The angle a was observed = 8i° 56' sg'. a 
96 ° 55 ' 58" ; <p is according to Captain Kater = 50° 37' ^'.27, 
and the value of <p', resulting from the addition of the dif- 
ference of latitude of B and D to <p, is = 50°44' 21 ".67. This 
value gives, by the above formula, the compression — - 
nearly the same as found in the Survey. For the compression 
the value of <p' would be 50° 44' 20". 35 for ; qf = 50° 
44'2o".42; f° r 7“ 50 ° 44 ' -79* From what was re- 
marked before, it is clear that x and ol being the same, no 
MDCCCXXIV. 
3 B 
