120 RELATIONS BETWEEN SEVERAL [BOOK I. 



moderate values of g ; thus, for example, for E - -E=~LQ, or y=5, when 

 x = 0.00195, is = 0.0000002. It would be superfluous to continue the table fur 

 ther, since to the last term z=Q3 corresponds g = 66 25 , or E E= 132 50 . 

 The third column of the table, which contains values of | corresponding to nega 

 tive values of x, will be explained further on in its proper place. 



91. 



* 



Equation 12, in which, in the case we are treating, the upper sign must evi 

 dently be adopted, obtains by the introduction of the quantity \ the form 



Putting, therefore, 

 and 



fnm 



H- + *~ 

 the proper reductions being made, we have 



[15] h = 



If, accordingly, h may properly be regarded as a known quantity, y can be de 

 termined from it by means of a cubic equation, and then we shall have 



n o~\ &quot;* &quot; 7 

 [16] X= I. 



L J yy 



Now, although h involves the quantity |, still unknown, it will be allowable to 

 neglect it in the first approximation, and for h to take 



t+l f 



since is undoubtedly a very small quantity in the case we are discussing. 

 Hence y and x will be deduced by means of equations 15, 16 ; will be got 

 from x by table III., and with its aid the corrected value of h will be obtained by 

 formula 14, with which the same calculation repeated will give corrected values 

 of y and x: for the most part these will differ so little from the preceding, that 



