144 PHILOSOPHICAL TRANSACTIONS. [aNNO 1787. 



Greenwich, to its intersection with the Paris meridian, will then be readily 

 computed, answering to the difference of longitude between the two Observa- 

 tories ; which, as far as can be judged from the map of Kent, corrected for the 

 error in the direction of its meridian, amounts to about 2° 10' 20'', supposing 

 always that no uncertainty remains with regard to the position of the point m near 

 Dunkirk. But here some remarks become necessary, which may probably sug- 

 gest to the Academy of Sciences, that a further investigation of this matter may 

 be needful on their part. 



By referring to the 57th page of the first part of M. Cassini's book (La Me- 

 ridienne verifiee,) it will be seen, that Dunkirk, by one series of triangles, is 

 eastward from the meridian of Paris 1426.53, and by another 1414.29 toises, 

 the mean of which is 1420.41, equal to 1514 fathoms. This difference of 6^ 

 fathoms, or little more than half a second of longitude between the mean 

 and extreme places of m, is certainly very inconsiderable. But in the 6oth page, 

 where, in verifying the meridian of Paris, by the comparison of the angle that 

 Broulezele makes with the meridian of Dunkirk, and the angle of convergence 

 of one meridian to the other, a difference of 21 seconds between 10° 16' I'd" 

 and 10° l6' 34^', is alledged to be almost insensible, we do not think to be a 

 conclusion so unexceptionable. This however is not the only cause of uncer- 

 tainty with regard to the just position of the point m : one of more importance 

 arises, from the difference that is found by two sets of triangles in the angle of 

 intersection of the meridian of Paris, with a line drawn through m from the 

 tower of Dunkirk to that of Calais. 



Thus, by p. 33 and 56 of the first part of M. Cassini's book, Dunkirk being 

 the station, Broulezele makes an angle with the meridian of lO'' 18' 25''' to- 

 wards the south-west : and the angle between Broulezele and Hondscote being 

 78° \V 42", their difference Q7° 53' 17'' is the angle that Hondscote is south- 

 east from the meridian ; therefore the complement of this last angle to 180°, viz. 

 112° 6' 43", is the angle that Hondscote makes with the meridian of Dunkirk 

 produced northward. By p. l66 of the 2d part, Dunkirk being the station, 

 the angle between Hondscote and Mont-Cassel is shown to be 51° 7' 15" ; that 

 between Mont-Cassel and Watten 42° 6' 35"; and by p. 167 that between 

 Watten and Calais is 51° 40' 20". The sum of these 3 angles is 144° 54' 10" ; 

 from which deducting Q']^ 53' 17", the angle that Hondscote is south-eastward 

 from the meridian, there remain 77° O' 53" for the angle of Calais south- 

 westward from it ; and the complement of this angle to 180°, viz. 102° 59' 7", 

 becomes the angle that the meridian of Dunkirk produced northward makes 

 with a line drawn through m to Calais : to which last adding the angle of con- 

 vergence of one meridian to the other 1 ' 50''-i-, corresponding to the distance of 

 1514 fathoms, equal to l' 29"-i- of a great circle, we shall have 103° 0' 5 7 "4- for 



