396 M. BES8EL ON THE ELLIPTIC SPHEROID OF REVOLUTION 



alterations of the results assumed as obsei'ved, for the purpose of 

 correcting my calculation without being obliged to repeat it 

 throughout. In order to avoid unnecessary multipUcation of 

 figures, I will assume the unknown quantities sought, instead of 

 i and k, to be 10000 i =p and \0k= q. I set out from the as- 

 sumption that 



570O8T \-\-k 



^ 1 + i ' 400 



1. Peruvian Arc. 

 Xy^-x^ = + l"-966 + \'\225p + 5-6059 . q. 



2. First East Indian Arc. 

 x^^ -x^=+ 0"-937 + 0-5697/? + 2-5835 . q. 



3. Second East Indian Arc. 



x^^-x^= +0-455 + 1-0212^+ 4-8270. g, 

 a^g^- ^3= +6-681 + 1-7428/?+ 8-1250.8', 

 x^-x.^= + 1-745 + 2-4983/> + 11-4652 . q, 

 a'g4_^3= 4- 3-878 + 3-5624 p + 15-9264 .gr, 

 iPgS- a?3= + 8-272 + 4-6585/) + 20-1840 . q, 

 x^^-x^= + 2-677 + 5-7458/) + 24-0262. q. 



4. French Arc. 



x^^ -x^=- 0-297 + 0-9709/) + 0-8601 . q, 

 x^"" — x^=- 3-641 + 0'976Sp + 0-8642 . q, 

 xi-x^= -4-259 + 1-6374/) + ri889 . q, 

 ^■44-^4= -9-S19 + 2-7037i^ + 1-2671 . q, 

 a?/ - ^4 = - 3-092 + 3-6651 J!) + 0-8659 . q, 

 x^ - ;«-4 = + 0-889 + 4-4533 p + 0-205 1 . /). 



5. English Arc. 



x^^ - .^5 = + 3-504 + 0-3095;) - 0-3178 . q, 

 x^ — ^5 = + 4-937 + 0-4405^ - 0-4658 . q, 

 a-^-' -«'5= + 3-758 + 0-5784/) - 0-6308 . q, 

 x^ -x^=- 0-892 + 1-0223/) — 1-2226 . q. 



6, Hanoverian Arc. 

 x^ - x^ = + 5"-679 + 0-7263/) - 0-9294 . q. 



7. Danish Arc. 

 xJ -x^=i- 0"-369 + 0-5513p - 0-8537 • g- 



