THE LOCATION OF THE CUBIC PARABOLA. 131 



In Table II the interval between the arguments has been 

 diminished so as to avoid additional terms ia the formula 

 of interpolation. The value of "w" must therefore be 

 reduced to the proper unit by dividing "»" by w, the interval 

 of the argument. 



If we desired to find the value of <f> corresponding to h/E 

 equals 0*0132572 then 



2n = 0*0132572 - 0*01324 = 1'72 

 n = 0*86 and (1 - n) = 0*14 



If the value of "n" exceeds 0*5 then adopt formula (9). 



The values of the derivatives are not given at the begin- 

 ning or end of Table II. To secure accurate interpolation 

 would necessitate an additional term in the formulae, and 

 the tabulation of the higher derivatives. 



When a value of h/fi comes within these limits, then <£ 

 should be determined from equation (2) if it is not equal to 

 one of the tabulated arguments. 



The following equation forms a useful control 



a — h 



Cos <t> = 1 



Hi ~ R\ 



The following typographical errors have been noted in 

 the table Vol. xxxiv, page 285. 



x/E Tabulated. Correct. 



0*40 12° 4' 20"*0 12° 4' 20"*9 



0*43 2*622733 9*622733. 



