VOL. XLl.] PHILOSOPHICAL TRANSACTIONS. 4lp 



it necessary to verify the sides, at least at every second degree, by measuring 

 the principal base twice over with due care; which might have been done, and 

 therefore should have been done, in a matter of so much nicety, as an attempt 

 to find the difference between 2 degrees so near one another, under the same 

 meridian. 



To show what bad consequences may arise from small errors committed in 

 observing the angles of several triangles, Mr. Olaus Hiorter, a curious and 

 ingenious friend of Mr. Celsius, has taken the pains to form the triangles of 

 M. Cassini between Bourges and CoUioure; so that the distance between their 

 parallels shall be considerably lessened; and yet the base in Roussillon, found 

 by computation, shall not, after due correction, differ sensibly, if at all, from 

 the same actually measured. In consequence of this, Mr. Celsius concludes 

 with observing, that the distance between the Royal Observatory, and the 

 perpendicular to the meridian of Collioure, deduced from the triangles of Cas- 

 sini, corrected after Mr. Hiorter's Method, &c. will amount to but 358,980 

 toises. This, divided by the mean difference of their latitudes, 6° ig' 1 1'', 

 will give 56,803 toises, for the length of a degree, one with another, between 

 Paris and Collioure, which is less than the length of a mean degree found by 

 M. Picard, and pretty near the truth : so that the degrees decrease as you go 

 towards the equator ; and consequently the earth is higher at the equator than 

 at the poles, as Sir Isaac Newton and Mr. Huygens believed. 



The distance of the parallels of Paris and Collioure, by this method, is in- 

 deed less than that computed by M. Cassini; but this cannot reasonably be 

 complained of, since these computed measures of M. Cassini seem very capa- 

 ble of being lessened ; and it is no more than what M. Cassini himself has 

 done to the measures published by his father, which he has shortened by 325-^ 

 toises. But however that matter be, whether this particular correction of M. 

 Cassini's distance, and consequently length of a mean degree, be admitted or 

 not, Mr. Celsius is fully persuaded, on the whole, that he has made it plain to 

 every unprejudiced reader, that these two sets of observations in France, are 

 not taken with such a degree of exactness, as to be depended on, in deter- 

 mining so nice a matter, in dispute for 50 years, as the true figure of the earth; 

 which was the thing proposed to be done by them. 



Concerning a Place in New- York Jbr measuring a Degree of Lalittuie. By 

 Mr. J. Alexander. N° 457, p. 383. > 



The mention of the French endeavours, to discover the figure of the earth 

 by observation, put Mr. A. in mind, that a very exact observation for that 



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