VOL. LXXVII.] PHILOSOPHICAL TRANSACTIONS. 245 



the angle which the meridian of Paris produced northward from m makes with 

 the line joining Dunkirk and Calais. 



Again, by p. 63 of the 3d part of M. Cassini's book, Dunkirk being the 

 station, the angle that Gravelines makes with the meridian south-westward is 

 72° 11' 48" ; and by p. 12 of the said 3d part, the angle between Watten and 

 N. D. Calais is 5 1° 39' 50" : also that between Watten and Gravelines is 46° 52' O'^ 

 Now the difference between these last two, 4° 47' 50", being added to 

 72° 11' 48'^, we have 76° 09' 38^ and its complement 103° O' 22'', for the 

 angles that the meridian of Dunkirk makes with the line drawn from thence 

 through the point m to Calais : to which last angle adding the former conver- 

 gence 1' 50'''4, we have lOS'^ 2' \2'% for the angle that the meridian of Paris 

 produced northward from m makes with the said line ; but by the former set of 

 angles it was found to be only 103° 0' ^y'^i, the difference being V IS*". 



From M. Cassini's book it appears, that Dunkirk is north from Paris 

 125515.25 toises, which make 133708 fathoms ; and the point m being south 

 from the tower of Dunkirk 351 fathoms, there remains for the distance of m 

 northward from the Royal Observatory 133417 fathoms. Now, with this dis- 

 tance as radius, the value of an angle of l' 15' is 484- fathoms, equal to 4" 34"' 

 of longitude. Thus the point m, instead of being westward from Dunkirk 1514 

 fathoms, wi41, by the last set of angles, only be removed from it \465-l 

 fathoms : therefore the difference between the mean and extreme places of m, 

 in this way of considering it, will amount to 24^ fathoms, about 4 times as 

 much as that resulting from the comparison stated in the 57th page. In the 

 parallel of Greenwich the extreme difference will amount to 58.4 fathoms, or 

 about 54- seconds of longitude, not much more than one third part of a second 

 of time. In this sort of uncertainty, with regard to the precise point m of in- 

 tersection of the meridian of the Royal Observatory of Paris with the line join- 

 ing Dunkirk and Calais, the only thing that can be done on our part, is to con- 

 sider the mean position of m as just, that is, to suppose it to be 1514 fathoms 

 westward from the great tower of Dunkirk, and having connected it with the 

 British triangles, to show then what angle its meridian will make with the line 

 drawn from Dunkirk to Calais. 



General Roy then institutes a comparison of the celestial arc of the meridian, 

 comprehended between the parallels of Greenwich and Perpignan, with the cor- 

 responding portions, measured and computed, of the terrestrial arc of the said 

 meridian, between the point m and Perpignan. In the consideration of this 

 matter it is to be observed, that M. Cassini has divided the celestial arc between 

 the parallel of Dunkirk, or, which is the same thing, between the parallel of 

 M and Perpignan, into 4 principal sections; viz. that from m to Paris, from 

 Paris to Bourges, from Bourges to Rodes, and from Rodes to Perpignan ; as- 



