418 t'HILOSOPHICAL TUANSACTION8. [aNNO 1/40. 



fereiice of latitude between Paris and CoUioure, are, in tlie first place, that 

 though 5 stars were observed at Collioure and Paris, yet one only was made use 

 of, viz. Capeila. That the difference of latitude by Capella is 6° 18' 57". If 

 Lucida Lyra had been used, the difference would have been but 6° 17' T' ; but 

 by the right shoulder of Auriga, 6° 1 9' 25". Hence arises the uncertainty or 

 difference oil' 18" between the greatest or least of their observations ; that 

 the late M. Cassini makes the difference 37" less than M. Cassini, who accounts 

 for this difference from the observations being taken by an ordinary instrument ; 

 but the instrument is the same which was used to take the altitude of the pole 

 of Amiens, which was very near that found by Mr. Picard. 



As to the trigonometrical operations for finding the distance of places, M. 

 Celsius thinks they labour under considerable uncertainties ; not only on ac- 

 count of the many difficulties they met with, viz. the mountainous countries, 

 want of proper signals, &c. so that convenient triangles could not be formed ; 

 but add to all these, that several of the triangles had but two angles observed, 

 and some of these angles too acute ; whence, as M. Cassini himself very justly 

 observes, in his examination of Snellius and Riccioli's observations, great errors 

 may arise. M. Picard thinks all angles less than 20° ought to be avoided ; as 

 also that the triangles should be contrived so as to have sides of a due length, 

 neither too great nor too small. Then follow 16 triangles, wherein one or more 

 of these inconveniencies are to be found. 



It may be said, the whole of these observations and measures of M. Cassini 

 seem to be sufficiently confirmed, if not ascertained ; since the principal base 

 in Roussillon was found, when computed, to differ but 3 toises from the same 

 as it was actually measured ; and that, after some due corrections, it was made 

 to agree with the greatest exactness. M. Celsius replies, why are we not told 

 what those corrections were, that we may see whether they were really neces- 

 sary or no? Why were they not taken notice of in the calculations of each 

 triangle ? Besides, the real length of the base, or the fundamental line in 

 Roussillon, is not fully ascertained, it not being measured more than once ; 

 whereas that at Dunkirk, and that of M. Picard, were measured twice ; and 

 there was more reason for doing so here than at Dunkirk, on account of the 

 uneven and almost ever-changing shore in Roussillon, from the restless over- 

 flowing sea. 



The great number of the triangles, joined with the numerous small errors 

 of the angles, is another ground of uncertainty; for the errors in the angles, 

 though small, may make the distance of the parallels, of the two extreme 

 places, greater than it ought to be; and yet the principal sides, that is, those 

 that are made bases to the following triangles, continue the same. This made 



