VOL. XLI.] I'HILOSOPHICAL TRANSACTIONS. 4 J 6 



from what it should have been, according to M. Cassini's hypothesis. And if 

 the correction according to Mr. Bradley's theory, were omitted, the difference 

 would have amounted to above lOOO toises : the consequence of which, say the 

 curious observers, is, that the earth is not only flatted towards the poles, but 

 that it is much more so than Sir Isaac Newton or M. Huygens thought it. * This 

 unexpected difference being so very great, made them resolve on a careful, as 

 well as new kind of verification of the whole. In the first place, they repeated 

 their astronomical observations 3 several times, at Tornea and Kittis, with the 

 same instrument, but on another star, viz. i Draconis. The difference of lati- 

 tude between the two places was found to be the same, within 3^^ seconds, with 

 the first. They then not only examined the truth of their meridian line, the 

 exactness of their sector, in the different divisions on the limb, chiefly in the 

 two degrees employed in observing a and i Draconis, but supposed that, in their 

 trigonometrical operations, they had erred in each triangle, by 20 seconds in 

 each of the two angles, and 40 seconds in the third ; and that all these errors 

 tended to diminish the length of the arch ; the calculation, on this supposition, 

 gives but 44tjV toises for the greatest error that could be committed. 



When a particular account of all these observations was read before the Royal 

 Academy of Sciences at Paris, and inquired into ; the main exception taken to 

 them was, that the observers, omitting to make a proof of the line of collina- 

 tion, by means of double observations, with the face of their instrument turned 

 contrary ways, have not duly ascertained the truth of their observations. But 

 this objection was fully answered by M. Maupertius, as Mr. Celsius hopes and be- 

 lieves, to the entire satisfaction of M. Cassini, who made it. He allows M. 

 Cassini had very good reason to mention this, as a thing proper to be done in 

 instruments of common use, for this purpose, which generally stand in need 

 of such a method of verification. But it was not at all necessary in the instru- 

 ment used at Tornea and Mount Kittis : the very make of it was such, that no 

 alteration could easily be made in it, so as to create any perceptible error in the 

 observations. The whole apparatus of the telescope and sector is all framed 

 together ; the object-glass and cross-wires, as well as the limb, so firmly fixed 

 to the tube, as not to be dislocated without great violence. Besides, the ut- 

 most care was taken in transporting it from one place to another ; being placed 

 in a chest, that the Laplanders, to use his own words, in ilia cista idolum quod- 

 dam servari facile sibi persuaderent. He adds, the same objection may be made 

 to M. Picard's observations, who does not seem to have used this precaution, 



* This happened in consequence of certain errors committed, notwithstanding ,j11 that is here said 

 to the contrary. See the note at p. 207 of this vol. of these Abridgments. 



