474 G. H. KNIBBS AND F. W. BARFORD. 
Elderton* in statistical and actuarial fields, and of C. Runge? 
in connection with the application of the Fourier Series in 
physics, have done much to show how this task can be 
simplified. J. W. Mellor has given many valuable sugges- 
tions in his special work for students in chemistry and 
physics,’ and elsewhere. 
By way of further illustration it may also be pointed out. 
that expressions of the type 
Y= a + De + CL? ete. ae (1) 
which have had an undue vogue in the formulae of physical 
chemistry, general physics, and engineering, are not always. 
valid. Often a result could have been better represented 
by such an expression as 
Of Ok bie eee (2)4 
where 1 is not necessarily, and generally is not, integral, 
and sometimes (2) will accurately represent a series of 
results and (1) will not.* 
In such a case equation (1) is clearly inappropriate. For, 
forming new values of y by subtracting a, viz., the distance 
of the intersection of the curve with the axis of ordinates. 
(c= 0) we have, through subtraction, a new series of values, 
viz., y, say, thus:—y’ = y - a = ba 
Hence, taking the logarithms of both sides 
log y = loge b + mlosiav ae (3) 
or, Dis 4 NE sas (4) 
the graph of which, if log y' (=7) be plotted as ordinates to 
the values of log « (=) as abscissae, is a straight line inter- 
secting the 7- axis at a point distant 6 (= log b) from the 
origin, and making an angle with the é- axis whose tangent 
1 Frequency curves and correlation. ? Zeitschrift fiir Mathematik 
and Physik, Bd.48. * Higher Mathematics for Students of Chemistry and 
Physics. Longmans, London, 1905. 
* For the solution of the constants of equations of this type see Section 
10. hereinafter. 
5 As for example, the velocities of liquids flowing in pipes under 
different rates of fall in pressure. 
