\\.\r 1 ". LI'"*] li,li'n,l,i,'Unii 



Turning to the equation lor t', we ha 



21 8,8893 E' - 272.6286 



= 



4-498,043 + 6'895,850#' - 5-472,223 #' 



Hence fa r = p * + ' = '173,913!), and p 4 = '347v 



This value again is very different from the observed value r*5 and from the 

 most likely value /3 = '49217. 



A somewhat different method of approximation consists in equating E n to K n -\. 

 The quadratic equation is then 



Solving this for E', we take the answer to be E n and then find E n +i from 



n ~ l .................. (liv). 



We then substitute in equation (li) for e' both E n and /? n+1 ,and do not treat them 

 as equal. 



Thus, in the last illustration, taking ^ = -40 as before, we have po* = rpi = "20, 

 and find for E' the equation 



23-04 E' 2 -9'4 #'-23 = 0, 



which gives E n = E' = 1 '223,7367. 



Equation (liv) then gives E n+ i = 1*225,5025, 



whence substituting in (li) we have 



e'=- '015,1371, 



rp 2 = '20 - '015,1371 = -184,863, 

 or p 2 ='36972. 



Storting with p 2 = '18486, near enough to '184,863, our quadratic becomes 



23-179,842 E' 2 - 8-68842 E' - 23 = 0, 

 giving E n =E'= 1-201,003, 



and from (liv) E n+1 = 1 '202,760. 



Whence we deduce e' = + '008,543, 



and p 3 r = po a + e' = -176,317, 



and p 3 = '35263. 



Proceeding to a fourth approximation we take pa = '35263, po 2 -'17632, and 

 find # = 1188,549 and E n +i= l'190,300 leading to e' = -'002,462 and p 4 = '3477 . 

 which is in excellent agreement with the result p 4 = '34783 above. We have 

 confirmed our previous result, but the process is not shortened. Without further 

 approximation we may take p as nearly equal to '3480; it will be seen that (his 

 " most reasonable value" differs considerably from the ' most likely value" p = '4!'J2. 



