STUDIES IN STATISTICAL REPRESENTATION. 475- 
is n, whereas the graph of 
foe ty a) los (bu y+ yen? GE ete.) Win5! oc aie). (5) 
is clearly not a straight line.* 
For brevity \ may be used for log. 
The data furnished by any series of observations whatso- 
ever, susceptible of numerical expression, consist essenti- 
ally of a series of quantities, the members of which stand in 
immediate relation to those of a series of other quantities. 
This relation may be expressed by 
Gy ao Ae aN OWCS)) Na IN eal (6) 
The problems which arise will be (i) to ascertain the 
precise nature of the function through which y may be 
related to x, and (ii) the values of the associated constants 
a,b,etce. The independent variable is the argument of the 
function, the related dependent variable, the value of the 
function for that particular argument. 
It will sometimes suffice to note merely that the points. 
lie on some particular curve, e.g., a straight line, circle, 
ellipse, parabola, a sine curve, a damped harmonic, etc. 
2. Character of Data —The data for examination may be 
either continuous, as in the record of a self-registering gauge 
or apparatus (tide, barometric pressure, wind-velocity,. 
automatic stress-strain, and indicator diagrams, may be 
cited as examples) in which case there is an infinite number 
of related values, or may be discontinuous viz., for a finite 
number of points only, as, where the values of y are observed 
for a finite number of values of theargument «. Or again, 
as frequently occurs in the field of statistic, the data may 
* This was pointed out in an incidental way by St. Venant in 1850. 
Vide Comptes rendus, t. 31, pp. 283-286, 581, 583. He says:—On en 
acquiert facilement la conviction en prenant les logarithmes, ce qui donne 
(RI) = loge + m log U et en construisant deux suites des points. . - 
on voit que chacun de ces deux ensembles affecte une direction rectiligne 
See also Prof. Karl Pearson, Biometrika, Vol. 1, p. 266. 
