ON THE MERIDIAN. 115 



brought out by the general mean. However as I am not at prefent in 

 pofTeffion of the account of the Swedifh meafurement, nor of that of 

 the Englilh fince the operations have been extended to the northward 

 of Chfton, I fliall not depend on this fmgle comparifon but abide by 



the compreflfion — — which for reafons already given, cannot be far 



304 



from the truth. 



1 

 19. Since then it is determined to adopt — —as the comprefiion, 



304 



and 60491.4 fathoms for the meafure of the degree due to latitude 



5:3 34 44, we fliall have m= 60491.4; / = I3 34 44; and ihe fraC" 



1 



tion — • will give i ^ e = 1.0033896. Then let A: 57° 2957795, 



304. 



the arc equal radius, and fi= et^uatoriat diameter; we have j; a = 



1 i t 



mJ (Cos.* / . (1+e)* + (SiD.» 01 



' = 3486852.4 fathoms for the radius of 



1 + « 



the equatorial circle, which divided by 57** Sec, gives 60857.05 fathoms 

 for the degree on the equator which will be of ufe for computing 

 both the degrees perpendicular to the meridian, and the degrees 

 of longitude.. Then becaufe the ratio of the two diameters 



la 



is- as 1 :: 1.003x896; we fliall have the femi > polar axis = —— ==. 



3486862.4 1 



- = 34754i9'66 fathoms^ Since m is the degree for lati.» 



1.00328C6 



tilde /, kt m be the degree for any other latitude /. Then by the for- 

 mula in art. 2 (Afiatick Res. vol. 12th, page 93,) we have 7n =-- 



« X. a 



w (Cos.* / . (1 + e) + Sin.* 01 



— and if m be at the equator where Cos. / 



Cos.* / . (1. + 0' + Si".* 01 



m {Coi.» / . (1 + ey- + Sin.* l)\ 



r= I, and. Sin. / = 0, Then m :=zz * . , , Now if 



1 + ey 



Soi.91.^ be fubflitutcd for m and is 34 44 for /, wc have m =;- 



