VOL. LXXVII.] PHILOSOPHICAL TRANSACTIONS. 251 



the latitudes, and to which he has adapted his 2d table of degrees N° 38, p. 305. 

 The ratio of the semi-diameters of this spheroid, viz. 179.4 to 178.4 differs 

 little from that appertaining to the 1st ellipsoid; but here the curve falling con- 

 siderably within, being less prominent than the ellipsoid in middle latitudes, the 

 arcs are thus contracted in such a manner as to agree within 5 fathoms with the 

 measured length of the meridian of France, in an extent of about 8°-^, com- 

 prehended between m near Dunkirk, and Perpignan situated at the bottom of 

 the Pyrenean mountains. Also the errors in the several sections of this arc are 

 not only small, but they are sometimes plus and sometimes minus, a never fail- 

 ing proof that, as far as our present data will enable us to judge, the figure here 

 assigned to the earth, notwithstanding what has been alleged to the contrary, 

 is exceedingly near the truth. According to this hypothesis, the distance mp on 

 the meridian of Paris, which is yet to be determined by our trigonometrical ope- 

 rations, should contain 27243 fathoms, being only 35 fathoms less than what is 

 given by the mean of the 7 different ellipsoids, a space not amounting quite to 

 2" of latitude. The result of the measurement of this space, answering to an 

 arc in the heavens of 26' bO" b2"' of latitude, will be a further confirmation, or 

 otherwise, of the justness of the theory. The degree at the equator being ad- 

 hered to as the standard, the 45th is defective 37.6, while that at the polar 

 circle errs in excess 9.4 fathoms. 



Differences of longitude. — Hitherto there has been no particular reference to 

 the computed lengths of degrees of longitude on each hypothesis, in 3 different 

 latitudes, namely, the equator, and 43° 32' and 51° 28' 40^. No measure- 

 ments of degrees of longitude have ever been executed with sufficient care and 

 accuracy, except that in the south of France, as mentioned in the 105 th and 

 106th pages of M. Cassini's book, which was determined by the repeated explo- 

 sions of gunpowder in the open air, and found to contain 4l6l8 toises, equal to 

 44354.4 fathoms. Hence the error in excess of M. Bouguer's theory, on the 

 length of this degree trigonometrically measured, amounts only to 19 fathoms, 

 which is little more than -^V part of a second of time. 



In fixed Observatories, where able astronomers have been for many years em- 

 ployed in repeating their observations of the heavenly bodies, it seems surprising 

 that any doubt should remain with regard to what is called the astronomical dif- 

 ference of longitude, or, in other words, the difference of time between them ; 

 yet it has been alleged, that an uncertainty of this sort exists, even with regard 

 to the situation of Greenwich and Paris, which, reckoned by its extremes, ex- 

 tends to about 10 or 11 seconds, answering in the latitude of Greenwich to the 

 enormous difference in space of between 1600 and 1700 fathqms! But it will 

 be considered as still more wonderful, if between 2 British Observatories, Green- 

 wich and Oxford, which have been long supplied with great and costly instru- 



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