470 Wiscojisin Academy of Sciences^, Arls^ and Letters. 



If in this formula "^e substitute the values already found/ and 

 put >u = .0^, v = 90°y and fcr f and f^ the values found in 

 § 12, it vnll be seen that / (c) depends on twenty sources of 

 error and that 



^(a«) =- JL sin c ^10, 76 



This value beinc: substituted in 



wF{c) = 10-6_J^ T /-^{(x*) 



it follows that 



wF{e) = 0/3033 sine 



OT w F (c) will have the values sho^\Ti in the following table: 



Thus it appears from this computation that the probable error 

 is a little less than in the formula proposed under A, but the 

 computation itself is longer on account of the auxiliaries, 

 which moreover are in this case of no further use. 



D. Lastly it is advisable to examine some equations in which 

 functions of the entire angles are used in computing triangles. 

 Let us begin with the equations 



sin c sin A = sin a sin C 



sin c cos A = cos a sin 6 — sin a cos b cos O 



cos c = cos a cos b -}- sin a sin b coe O 



and put 



sin a cos C = vi. sin 3f, 

 cos a — m. cos IT. 



