Iti 



INVESTIGAtlON OF CERTAIN THEOREMS 



To find the axes ^^' To find a and b themfelve!?, if m = 57.2957, &c. or 



of a fpheioid the number of deo;iees in the radius, fo that wD' = FR = 

 fftim comparing 



A^Td. with'one 77 ,^, , ,, ,, ,,-!• ^"^ ^"^^*^ '^ l^^^' ^een already 

 of the perpend. («*cpf<?« +6Min^2)^ 



fl2 YT ~ fin <p* a^ col (?* 

 (hewn that rj Z= t! , ori^^ — fv , there- 



folre^^D^ZZ 



/a^ cof ^^ +^^lf!!!il. X fin (?« Y 



cof ^ 





r and a zz 



niD' cof ^ "/i -j li!if!_. 



v^ ^ _ fin <f 2 



Now, 1 + — 



— — fin?» -—fin ^2 l-._.iin$« 



wD' cof (^ 

 therefore a T~ 



17. This value of a is very convenfent Tor logarithm ical cal* 

 CLilation ; for if fin ^ y^_- be computed, it will always be 

 lefs thair i, 'becaafe D' is greater thartJ), and therefore may be 

 taken for the fine of an arch xj., of which arch ^ 1 — -- fin ?' 



n r r , . ^ rwD'cof® 



Will of coiirfe be the cofine, to that a ZZ —, • 



col ^ 



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

 mula in §15. 



In 



