10 Mr. Ivory on a perpendicular Degree at Beachy Head. 



t • " i /ycosu\ , ! , L ',. Mi Me 



Log. sin - = log.( — r ) - i log. (cos A cos A') - — + -y- 



xcos(X-t-V). 



Applying this method to the case of Beachy Head and 

 Dunnose, we have the latitudes as before determined : the 

 chord between them, or y, is equal to 339397*6* feet, or 

 56566'3 fathoms : and, with these data, we get, in the same 

 spheroid as before, 



co = 1° 27' 5"*78, 

 which is 18" more than according to the Survey. 



Now the length of a geodetical line drawn from Beachy 

 Head at right angles to the meridian, and limited by the me- 

 ridian of Dunnose, is 3361 19f feet, or 56020 fathoms. Let 

 A be the amplitude of this arc ; then we get, by the usual 

 method, 



Tan A = cos \ tan w, A = 55' 7"'57. 

 And if we lengthen the arc in the proportion of the amplitude 

 to 1°, we shall get 60973 fathoms for a degree perpendicular 

 to the meridian at the latitude of Beachy Head, which is 200 

 fathoms less than according to the Survey. This result may 

 be verified by comparing it with the length of a perpendicular 

 degree at the given latitude. The expression of this degree is, 



/V /l_(2f_^)sin^A I \2 2/5 



and, by substituting the numbers, the length comes out 60974, 

 only one fathom more than what has been deduced from the 

 measurements in the Survey. 



The difference of longitude we have found is only 1" more 

 than what Dr. Tiarks has assigned (Phil. Trans. 1824) as re- 

 sulting from his chronometrical observations. This is no doubt 

 a great confirmation of the theory, but it has not the weight 

 of a direct experiment; because it is deduced from the ob- 

 served difference of longitude between Dover and Falmouth, 

 by making a proportional allowance, which is a method of 

 proceeding in some degree precarious. As there is no doubt 

 about the accuracy of the observed quantities in the Survey, 

 it might be worth while to compute from the data it contains, 

 by rectifying all the calculations, the difference of longitude 

 between Dover and Falmouth, in order to compare it with the 

 result obtained directly by experiment. 



The main purpose of this> article is now accomplished. It 

 has been clearly proved that the same spheroid which repre- 



* Survey, vol. i. p. 295. f Ibid. p. 297. 



sents 



