VOL. LVIII.J 



PHILOSOPHICAL TRANSACTIONS. 



577 



standarxl, for the length of the degree. But to this it seems proper to add 21 feet, to correct the 

 position of the point c, determined by the sector, which cannot be so certain as that inferred from 

 the azimuth of the line Ps. Therefore the true length of the degree, according to the r. s.'s brass 

 standard, in the temperature of 62"* of Fahrenheit's thermometer, is 36.3771 feet, or 68,8;}60 

 English statute miles. To reduce this to the measure of the Paris toise, by the proportion above 

 established, say as 76,734 is to 72, so is 363771 to 34132S French feet, or ad'SiiS Paris toises, of 

 the standard of that used in the measure of the degrees of the meridian at Peru. 



The method used by Mr. Bird, in finding the length of the toises by his scale, was as follow.s, 

 which may serve as a direction for the like purpose on any future occasion. Two brass pins were 

 driven into a strong deal board 4 inches thick, and longer than the toise ; and two brass cheeks were 

 made very square, and the ends brought upon the pins. The toise was then put in between the 

 cheeks, one of which was made to slide so as to be easily brought into contact with the end of the 

 toise, and the other end at the same time touching the other cheek, the moveable cheek was screwed 

 fast ; and thus the toise was exactly contained between the cheeks without any shake, and it is evi- 

 dent that the interval between the cheeks was exactly equal to the length of the toise. Jn order to 

 measure this interval, the toise being taken away, very fine lines were drawn with a fine point, at 

 the end of each cheek, upon the brass pins which were in the same plain with the board : then the 

 cheeks were removed, and fine points made at the outer extremity of each line, and this distance 

 being taken between the fine points of a beam compass, was transferred to the scale, and thus the 

 length of the toise was found in measures of the scale, which is divided by a vernier to thousandths 

 of an inch. The toises and brass scale had been left together in the same room, and near one 

 another all the night before, and till the very time of making the comparison of the toises with the 

 scale, in order to be sure that they were all affected with the same degree of heat. 



As it may be agreeable to the reader to see the result of the principal measures of degrees of lati. 

 tude, that have been taken with later instruments and proper accuracy, brought together into one 

 view, the following table is here added. 



Length of a 



degree in 



Paris toises. 



57422 

 .57074 

 570.91 

 57028 

 57069 

 ^6979 

 56888 

 56750 

 57037 



Names of the observers. 



M. de Maupertuis, &c 



M. de Maupertuis, &c. and M. Cassini 



P. Liesganig 



M. Cassini 



P. Beccaria 



Le Pere Boscowich and le Maire .... 



Mess. Mason and Dixon 



M. Bouguer and M. de la Condamine 

 Abbe de La Caille 



Years in which the 



degrees were 



measured. 



1736 and 1737 



1739 and 1740 



1768 



1739 and 1740 



1768 



175'2 



1764 to 1768 



1736 to 1743 



17.52 



If this degree be compared with the degree measured at the equator = 56/50 toises, in the hypo- 

 thesis of the earth's being an oblate spheroid, the ratio of the equatorial to the polar diameter will 

 come out as 49 V to 493. But, if it be compared with the degree measured in Lapland, in the lati- 

 tude 66"^ 20', = 57419 toises (having subtracted 3 toises, because the toise used in Lapland was 

 ■jVtli <"■ Vt''^ "f ^ ''"^ '^** '''^" '^he toise used in' Peru, see M. De la Lande's Astronomy, Article 

 2107), the ratio of the diameters will be as 142 to 141 . The great difference of these results is a 

 fresh proof of what has appeared from the comparison of the measures of the several degrees taken 

 before, either that the figures of the meridians are not accurately elliptical, or that the inequalities 

 of the earth's surface have a considerable effect in deflecting the plumb-line from its true situation, 

 or both. Mr. M. had indeed supposed that any deflections of the plumb-line were not to be teared 



VOL. XII. 4 E 



