94 Observations on the Measurement of 



supposed to exceed Major Lambton's estimite by more 

 than 5,?2 toises ; and it is extremely difficult to speak with 

 certainty to quantities so small as this. 



The same observer also t^ieasured one degree perpendi- . 

 cular to tlie meridian, by means of a largo side of one of 

 his triangles cutting the meridian nearly at right angles, 

 and of which he observed the azimuth ai the two ex- 

 treiiiilies. The data from which his results may be verified 

 are these : 



Leuiiih of ihe chord of the long side in English feet 

 AB = 29l 197,20. 



Azimuth of the eastern extremity A equal to S7' O' l",54 

 NW. [ 



Azimuth of the western exlrcmitv B equal to 267" lO' 

 44",07 iSW. 



North latitude of A 12' 32' l<2'\'27 

 North latitude of B 12' 34' 38",&0, 



With these data in the triangle formed bv the long side, 

 the meridian at B, and the perpendicular from B on the 

 meridian at A, we have the choid of this last arc equal to 

 2905-15,8 feet, and the arc itself 290848,03 feet. By ap- 

 plying ihe method of M. Delambre, we find the azimuth 

 of the exlremiiy B less by 2" than it was observed to be; 

 so that we have no reason to suppose a greater error than 

 one second in the observation of each azimuth, and it 

 seems next to impossible to arrive at greater exactness. 



The difference of longitude between the points A and B 

 is 48' 37",36. With this angle and the co-latitude at A, 

 we have in the spherical triangle right angled at the point A, 

 the extent of the normal arc equal to 2867,330 seconds, and 

 dividing its length in feei by this number, we have for the 

 degree perpendicular to the meridian, at the extremity A, 

 CG&dl,eo fathoms, or .')7J06,5 toises. Now these values 

 are precisely what we find on the elliptic hypothesis, with 

 an oblattness of -3^ or -^-j-g- ; and in short, the corre- 

 spondence between the hvpothesis and the measures of 

 Major Lambton is as complete as can be wished. Major 

 Lambton, indeed, finds the degree on the perpendicular 

 too great by 200 fathon)£, but this arises from a mistake 

 in his calculation. 



Lastly, I shall apply the same method, and see how 

 nearly the ellijitic hypoihesis agrees with the last measures 

 taken in France, which merit the higliest degree of con- 

 fidence both with respect to the observers wlio have ex- 

 ecuted it, and the means which they had it in their power 

 to employ. 1 have taken only the arc between Dunkirk 



aiKl 



