Relating to the FIGURE of the EARfH. 15 

 -1, and nnce it has been already fhewn that 



(a'cofV -f^fin^)' 



% 



a 



— D 



-_ fin tf>* 



t or ^ = D "' cof »* , therefore wD' b± 



cofp* ' g_ — fin/ 



TT~ ih^ 1 , ,\t - -, /* , lim^ V aild " ~ 



77ZL 



^— .fin?' 



D' 



XT r , , *»*' - ° = * , therefore 



now, 1 + gHj-j - jr-^ - ; __ D -? 



otD' cof <P 

 ^i ;T -^fin? 



17. This value of a is very convenient for logarithmical cal- 

 culations for if fin <p /§7 be computed, it will always be lefs 

 than 1, becaufe D' is greater than D, and therefore may be ta- 

 ken for the fine of an arch 4, of which arch J^- gr *« ** will 



r r x. otD ' cof * 



of courfe be the cofine, to that a = - cof+ . 



The fame method may be ufed for finding £ from the for- 

 mula in § 15. L'* r ■'■ « mi t. •■ 



In the fame manner that a has been found, we will obtain 



mT>' cof <p l 



If we examine thefe formulas in the extreme cafes, viz. 

 when <p = 90 , and when £ = o, we lhall have in the for- 

 mer cafe a = |, becaufe cof 9 = o, and alfo D' = D, fo that 



