Feb. IS. I9IS Fitting Logarithmic Curves 415 



-~[ (^ + ?)(' + ?+2)(log,o/ + ^-logx„ (xii) 



- i (/+^^ + f / + 9- I /T7/ - log,„ c j] 



+ 9) (logic ; - log.o / + ?) + (Thi' - i) log.o e | J 



(xiii) 



"■(/ 



l+q 



i[".-si('-y--i-'3i(-')'-i 



-(/|(/ + 9)log,o(Z + 9)-ilog,„i-(/+7-01og,„e|J 



(xiv) 



For the cun'e 



(XV) 



the equations for determining the constants are : 



6[(/ + ?+0M,-A/,]-[(/+# + 2(/ + 9)+i]M„ 

 («+i)(/ + 9+«)(/+g+2«+ij|^log,„(«+ij-log,„(/+?+«) 

 + (/ + '/-0[6[('+#+5(/+'?)+^j+2«(/+9+0+2«^]log.„e 



- log.„/ + <?+«) + i(/ + 7 - ;) (/ + <7 + 2 «' + ^logio^-l] 



s'- " (xvii) 



-(« + 01og,„(«+i)-(/ + 9-01og,„,|] 



By the use of the third moment an equation might also be derived for 

 determining n. As this, however, is a somewhat complex logarithmic 

 expression, from which n can be obtained only after much labor, it has 

 seemed best to determine "^ empirically, as in working by the method of 

 least squares. 



