K. Pkarson 21 



] st parabola : 



y = 10-7.S(>7 \\ - 1-0455 f j]! . 



2n(l parabola : 



y= lOwMdT |l-lL>.-,,lG3.5- 10455 ^^j - -375,4905 f^Vl . 



3rtl panibola : 



y = 10-7867 |l-125,1635 - 1-332,7459 {^^ - -375,4905 (^^y+ •478,7431 (''^'j 



4th paiabola : 



y = 10-78G7 |l-159,1392 - 1-332,7459 (1) --715,2475 (^ 



xy „„.. , fx 



+ -478,7431 (^1 +-396,3832, 



öth parabola : 



y = 10-7867 ] 1159,1392 - 1-428,4973 (j) - -715,2475 (j 



+ •925,5752(1)' + -396,3832 (^V- -402,1555(^1 



6th parabola: 



y = 10-7867 1-108,0239 - 1-428,4973 (|j + -358,1736 (j\ + -925,5752 (j 

 - 2-823,8816 f-"")'- -402,1555 fljV 2-361,5275 ['*' 



The (inlinates of these six curves were then calculated for thc 31 values of x, 

 and the curves theinselves with the observations plotted in Fig. 10. We have 

 again an instructive graphical representation of the closer and closer approach of 

 a series of parabolas to a fairly smooth System of observations. It will be seen 

 that the parabola of the 4th order gives quite an excellent representation of the 

 observations, better indeed tlian the 6th parabola which has tuo niany points of 

 infle.xion to dispose of 



(15) With this illustration I elose my discussion for the present of curve- 

 fitting. I have emleavoured to shovv : 



(1) that the niethod of nioiiients inust theoretieally give good fits ; 



(2) that it provides a systcmatic inuthod ol litting a great variety of 

 curves ; 



(3) that it is over and over again available when the method of least 

 Squares fails, or can only be applied with excessive labour; 



