LENGTH OF A DEGREE.] 



ASTRONOMY. 



921 



tions, extending the whole length of a kingdom, is effectec 

 by a series of triangulations in the following manner : 

 In the figure (Fig. 7), the length of the meridian A r is 

 required ; and for this purpose we select certain stations 

 A, B, C, D, <fec. , as clock-towers or 

 elevated objects. Conceive these 

 to be joined as in the figure, anc 

 thus to form a series of triangles, 

 as A B C, B C D, C D E, &c. 



If we know all the sides and a! 

 the angles of these different tri- 

 angles, as well as the angle formed 

 with the meridian A TO n, with the 

 side A B, we can conclude easily the 

 lengths of the different parts, A TO, 

 m n t n p, of this meridian. In fact, 

 in the triangle A B TO, we know the 

 side A B, and the two adjacent 

 angles A B TO, B A m, whence we 

 can readily find the side A TO, which 

 forms the first portion of the meri- 

 dian, as well as B TO, and the angle B TO A. In the tri- 

 angle TO C n we know the side C m, which is the differ- 

 ence between B C and B m, and the two adjacent angles 

 m C n, C TO n, the second being equal to B m A, pre- 

 viously determined. We arrive at the same conclusion 

 with tie side TO n, which forms the second portion of the 

 meridian, and at the same time the side C n, and the 

 angle C n TO. In the same manner the triangle D np will 

 show us the third part of the meridian, and by this pro- 

 ceeding we have determined all the parts of the meridian 

 of the point A. 



But we do not require a measurement of all the sides 

 it will be necessary only to measure a certain part 

 termed the base. Suppose that the side A B be the part 

 measured, then the triangle A B C is entirely known, 

 since we know one side and the three angles, and we can 

 find the lengths of the two sides, A C, B C. In the same 

 manner, the knowledge of the three angles of the triangle 

 H C D, and of the side B C, that we find, permits the 

 determination of the length of each of the two sides B D 

 and C D ; and proceeding in this manner, we find all the 

 sides and angles of all the triangles as well as if we had 

 measured these lines directly. 



In determining an arc of the meridian, we know well 

 the point of departure, but we do not know where the 

 second extremity is situated. We can find, it is true, 

 after having determined conformably to what precedes, 

 the length of the portion F r of the side F G, by measur- 

 ing the distance F r ; but besides that this often presents 

 great practical difficulties, it will frequently happen that 

 the point r would not be favourably placed for erecting 

 an instrument such as a repeating circle or theodolite. 

 We have also sometimes occasion to know the latitude of 

 the point r, as well as that of the point A, in order to 

 deduce the angle included between the verticals drawn 

 through the two points. To attain this, we observe the 

 latitudes of the two extremities F G of the side on which 

 the point r is situated ; we can easily compute the lati- 

 tude of the point r, by the knowledge that we have ascer- 

 tained of the distances comprised between this point r 

 and the two points F G. Having the length of the line 

 F G, relatively to the dimensions of the earth, we can 

 admit that in going from F to G, along the line F G, the 

 latitude varies proportionally to the distance passed over 

 on this line. 



MERIDIAN OF FRANCE. One of the greatest measure 

 meuts of an arc of the meridian was that performed at 

 the end of the last century, by the celebrated astronomers 

 Delambre and Mechain. The arc which they measured 

 took its departure at Dunkirk and across France at its 

 greatest length, terminating in Spain, near Barcelona, 

 the Pantheon, at Paris, forming the summit level. Part 

 of this survey is contained in the following figure ; the 

 base line, on which the success of the whole measurement 

 depends, was measured with every possible precaution by 

 means of rods of platinum, and was found to be 6075-98 

 metres. The angles of the triangles were measured by 

 means of the repeating circle, and the lengths of the 

 vul J. 



different sides of the triangles were successively deter- 

 mined by the method before mentioned. 



Fig. 8. 



J 

 1 



chatOlon 



In order to have some independent check on the re- 

 sult, a second base was measured near Perpignan ; that 

 is, near the southern extremity of the series of triangles. 

 The length of the second base, reduced to the level of the 

 sea, was found to be 6006-25 metres. In comparing the 

 length thus obtained to that of this same base, deduced 

 from the successive calculations, we have not found a 

 greater difference between the two results than 10 inches 

 8 lines (cent, metres, 288). So small a difference on a 

 length of more than 6,000 toises, is surprising, especially 

 when we consider the immense distance which separates 

 the base of Melun and Perpignan, a distance of more than 

 450,000 toises. This certainly shows that the operations 

 tad been executed with great care. 



The results arrived at by these measurements showed at 

 once, that the value of a degree was different at the 

 equator and the poles, being least at the equator, and 

 greatest near the poles. 



From a judicious combination of the observations at 

 all the stations, Bessel deduces the following elements of 

 ;he earth's figure : 



Equatorial diameter, 41847199-9966 feet, or 7925-606 

 miles. 



Polar diameter, 41707314-3324 feet, or 7809-113 

 miles. 



Which shows an ellipticity of gj^jth. 



The following are the principal results on which the 

 above elements are founded, viz. : 



6u 



