95 



7. Remark. This last conclusion might have been very 

 easily deduced from equat. (6) art. 3; but the above investi- ' 

 gation has been used for the sake of deriving the formulas of 

 Simpson and Bradley. 



By equat. (4) art. 3 s = 1 — — 



Therefore, by equat. (2) art. 6,s= IfizLLx H. 

 Hence by equat. (6) art. 3. 



Q b I (p) tan. 9 __ q (m — \)ltan 9 



^ '2 a COS. ^9 ^ a cos. > 9 ' 



Hypothesis of an uniform temperature. 



8. By the equat. (6) art\ 5 we; also derive the same Cbh- 

 clusion on the hypothesis of an uniform temperature, in which 

 case, as has been stated art- 4* 



—as '•: '; { v^ , ^ as 



f = (f) c ' or /J = — f- (i) G ^ 

 Hence by equation (6) art. 5. 



/' As 



^ c - — f'''^=(froms=otos=l) 



2 COS. ^ 9 



before. 



lU)itanV-'iJ}^ _, ,. ^ _ n — fcl>iifl! as 



