Observations zvitJi Kater's Peiidiiliuns. 



11 



Hence we obtain, if V-^ and V., are the vibration numbers in 

 latitudes A^^ and A^ 



■ ~' (2). 



l\-' 



D \ sin-Ai — sin-Ao 



- w -e] — ^ ^ 



1 4- ('- w - ejsin'-Ai 



;// is known to be very accui'ately expressed by 0'0034674 ; tlie 



mean value for e obtained by Colonel Clarke from a comparison of 



5 

 all previous observations is 0"0034223 : whence -;;/ — <? = 0"00o25 



2 



with sufficient accuracy for our purpose. Owing to the sraallness 

 of this quantity we may omit the term depending on it in the 

 denominator of the right-hand member of equation (2); further- 

 more, as J^-^ - v., is small compared with [/\ or Fo we may 

 write the equation thus 



2 ^\^'' = (| ^n - e){^\n- A, - sin"-^ A,) - - - (3). 



For Fi in the denominator of the left-hand member of equation 

 (3) we may substitute 86000 without sensible eri-or ; and we 

 obtain 



Vi- V.,= 43000 X 0-00525 x (sin-A^ - sin-A..,) 



= 225'75(sin-Ai -sin-Ao) - - - (4). 



the formula used in the computation. 

 The latitudes are as follows : — 



Greenwich: Ai=51° 28' 31". 

 Melbourne : A._, = - 37° 49' 53". 

 Sydney : Ag = -33° 51' 41". 



The experimental values for (rreenwich, Melbourne, and 

 Sydney are summarised in Table lY. 



Table IY. 



From this table we obtain the following differences : — 



