272 Trans. Acad. Sci. of St. Louis. 



Differentiating (5), regarding o, t and a as variable, we 

 have, 



— sin^ cos^ do — cosJ sin^ dt = — sine sin^ sina da. 



By (10) and (6), 



coso dt = sin' cos^' da, 

 or, 



coad da = — sin^ cos^- da. (H) 



We then have from (8), (10), (9) and (11), 



jd = sin^ sine fZa — cosqd^ ) (^9\ 



cosd Ja = — cos^sinCcZa — sin^-tZ' )' ^ * 



in which Jo and Aa are the sum of the differentials in o and a 

 respectively which depend upon the differentials in a and 

 in c. 



If h^ and /«., represent the vertical and horizontal flexures 

 respectively, in arc, of a great circle we may, since they are 

 small quantities, substitute them in eqs. (12) for tZC and 

 sin^da respectively. 



We then have to second powers of h^ and A, 



Ad = h.^s'mq — AjCOsg 

 coso Ja = — h.fiosq — /iji^inq. 



Issued November 21, 1896. 



