VOL. XXXIII.] I-HILOSOPHICAL TKANSACTIONS. OS 



to every 20 seconds. Now they allow that J 6 toises on the surface of tlie earth 

 answer to one second in the heavens; and they pretend not to observe nearer 

 than to about 3 seconds, which therefore cannot determine a difference less 

 than 48 toises ; whereas the degrees are only supposed to decrease at most 3 1 

 toises each, from Collioure to Dunkirk. But an error of 8 seconds would 

 make a difference of 128 toises on the surface of the earth; above ten times 

 greater than the difference of degrees in the first supposition, and four times 

 greater than that difference in the last. Besides, the latitude was not observed 

 in the intermediate places between Paris and Collioure, with the abovementioned 

 instrument of 10 foot radius; but they used a quadrant, whose radius was only 

 39 inches, and sometimes an octant of 3 feet radius; and they say themselves, 

 that it is not the observations made at the ends of the meridian that we are to 

 deduce the difference of the length of a degree from, but the altitudes taken 

 at several places between the extremes; and if we grant, that they can take an 

 angle very well to 4 or 5 seconds, with the great instrument, they cannot come 

 nearer than 12 or 15 seconds with the quadrant or octant, which we must de- 

 pend upon for the difference of the measure of degrees : so that on the whole, 

 we are to determine a length of 31 toises, by an instrument which is liable to 

 err above 200. 



But there is another error, which might considerably mislead the French 

 gentlemen, and make the degrees appear longer in the south of France; that 

 is, the error in taking the true height of several mountains in Auvergne, 

 Languedoc, and among the Pyreneans ; for if they have allowed too much for 

 the air's refraction, which, by the observations of travellers, is greater towards 

 the northern regions, and diminishes as we go southward, the heights of those 

 mountains will be taken too little, and their bases consequently longer, which 

 will make the degrees appear greater than they are. 



Now one such mistake, in one degree, will give a difference above twice as 

 great as the supposed difference of degrees in that latitude, which they make 

 of 31 toises. And that there was a mistake of this kind in taking the height 

 of that mountain, Dr. D. shows. 



The vapours, that generally float in the air about the tops of high hills, 

 make it so difficult to take their height exactly, that experiments made with the 

 barometer will, by observing the fall of the Mercury, show the height nearer 

 than any thing else we know of. There were indeed several experiments made 

 with the barometer, where the differences of the height of the Mercury, 

 from the heights at which it stood at the Royal Observatory, are said to answer 

 to so many toises; but of nine observations mentioned by M. Cassini, there are 



