346 Mr. Ivory on the Figure of the Earth, as deducedfrom 



These equations are next to be reduced to two, the number of 

 the unknown quantities, by employing the method of the least 

 squares : thus 



_ il^i - 267*234 5 - 277-342* 



+ ——■ = 277-342 s - 408-673 t. 



And, by solving these equations, 



Ds = — 6; A = D+ Ds - 60856 



t = _ -00009, . = 3 l 0Q + t = -00324 = Jj. 



Returning now to the original equations (B), and substituting 

 the values of A and e, we shall obtain the errors, E (,) , E (2) , 

 E (3) , E (4) , or the quantities that must be added to the given 

 measurements on the left sides of the equations, in order to 

 make both sides exactly equal ; as follows, 



E (,) = - 20, E 2) = + 10, E (3) = - 7, E 4) = + 13. 



The greatest error is in the Peruvian arc, which appears to 

 be too great, as has generally been surmised. But the small- 

 ness of the errors proves the consistency of the different mea- 

 surements ; and shows that the four portions of the meridian, 

 although very remote from one another, belong to one and 

 the same elliptical spheroid. 



If we now substitute the data of the Swedish measurement 

 in the formula (A), we shall get, 



98870 + E (3) = A (1-622022 + 0*8378 . ft - 0'022 . s 2 ) : 



and, by substituting the values of A and s, it will appear that 

 the error E (3) = + 5. This measurement is therefore very 

 consistent with the other four ; and, as it seems liable to no 

 just objection, it adds to the evidence in favour of the ellipti- 

 cal elements that have been found. 



The degree of the meridian bisected by the parallel of 45°, is 

 111115 metres at zero of the thermometer. This result is dedu- 

 ced from the actual measurement of the meridional arc between 

 the parallels of Greenwich and Formentera, and is indepen- 

 dent of any assumption about the figure of the earth. To re- 

 duce this length to fathoms at the temperature of 62° of Fahr., 



oq. ^7070 



it must be multiplied by — — — , which gives 60758 fathoms. 



Now, if we put A = 45° -f£, X' = 45 — J, we shall have, in 

 he formula (A), n = 1°, m = 90°, and the length of the de- 

 gree having its middle point in latitude 45°, wtfl be, 



A(,-^-i-,) ; 



or, 



