Feb. IS, I9IS Fitting Logarithmic Curves 413 



Putting w = o, I, 2, successively, we obtain the three equations which 

 being solved give us the constants of the curve: 



(iv) 



r I I I 1 ^") 



+ clog,„e|^(/+?) log, (/ + <?)-- log, - + --(/ + 9)J 



'".=f[<'+')'-i]+j[<'+')"-|] 



c V I I I I 1 ('") 



+ - log,„ eyil + qf log, (/ + ?)-- log,- + g-^(/ + ?)^J 



+ ^log.„e[(/ + 9)Mog,(/ + g)-ilog,i + ^-i(/+9r] 



Multiplying equation ii by - ( / + g + - 1 and by - (/ + ?)- + -(/+</) + - I 

 and subtracting from equation iii and iv, respectively: 



+ \log,,e^{l + q)\\og,\-\og, (/ + ?)|+(/+?)=-^] 



+Jlog,„c[(/+'7)(/+9 + ^)jlog,^-log,(/+9)| + ^(/+<7)'-i] 

 Multiplying equation v by - ( / -f 7 + -j and subtracting from equation vi : 



^[(/+?)(/ + <7 + 0[log,„ J-log,« (l + q)\+'-{l + q-'^\{l+qy 



4J 



log.o f 



] 



