perpendicular to the Meridian. 1 93 



As in this instance we have the rectilineal distance of the 

 stations, or the chord y between them, we must find by the 



formula sin -f- =s -£- = ~—\ whence /3 = 47' 50"*94. With 



2 la 2;> A ■ 



this value of ]3, and the values of m and *' noted above, the 

 difference of longitude will be found, by the formula (B), equal 

 to 48' 57"*05. From this we get 47' 47"*03, for the amplitude 

 of the perpendicular arc at Carangooly, and 60866 fathoms, 

 for the perpendicular degree, very little different from 60865*2, 

 the length on the surface of the spheroid at the latitude of 

 Carangooly. 



But if the measurements made in England and India are 

 all represented by the same spheroid, Why should not the 

 case be the same in France ? We have a great tendency to 

 infer uniformity in the works of Nature, which principle is in 

 reality the foundation of every physical inquiry. And if the 

 public were put in possession of the extensive operations that 

 have been executed in France and the north of Italy, for de- 

 termining an arc of the mean parallel, there can be little doubt 

 that we should be able to prove that all the degrees of the pa- 

 rallel are equal, and agree in their length with the dimensions 

 of the spheroid we have been considering. But at present we 

 cannot draw our arguments from so rich a source, and we 

 shall be content with examining a single instance taken from 

 the great meridional measurement of France. 



The length of an arc drawn perpendicular to the meridian 

 of Dunkirk from La Rogiere, in latitude 44° 34' 36"*6 is, ac- 

 cording to the survey, 27534*6 toises *. This length is a de- 

 duction from actual measurement, and is independent of any 

 hypothesis about the figure of the earth. The arc is 29345*2 

 fathoms ; and, by proceeding as in the example of Dover, we 

 get = 28' 55"*95, and the difference of longitude =40' 33"*21. 

 In order to find the amplitude of the arc, we must know the 

 latitude of the point where it cuts the meridian. Now, ac- 

 cording to the survey, the small arc of the meridian, between 

 the foot of the perpendicular and the parallel of La Rogiere, 

 is = 114*3 toises = 121*7 fathoms, making 7"*2 of difference 

 of latitude. The latitude of the foot of the perpendicular is 

 therefore, 44° 34' 43"*8; whence we get the amplitude = 

 28' 53"* 18, and the length of the perpendicular degree = 

 60953 fathoms, exactly the same as on the surface of the 

 spheroid at the latitude 44° 34' 43"*8. 



In this last instance, as well as in all the others, the degree 

 perpendicular to the meridian measured on the earth's surface, 



* Sate Metrique t vol. iii. p. 268. 



New Series. Vol.4. No. 21. Sept. 1828. 2 C is 



