STUDIES IN STATISTICAL REPRESENTATION. 473 
STUDIES IN STATISTICAL REPRESENTATION, III. 
CURVES, THEIR LOGARITHMIC HOMOLOGUES, AND ANTI- 
ae a Net aM te 
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LOGARITHMIC GENERATRICES; AS APPLIED TO 
STATISTICAL DATA. 
By G. H. KNIBBS, C.M.G., F.S.S., etc. and 
F. W. BARFORD, M.A., A.I.A. 
[ Read before the Royal Society of N. S. Wales, December 2, 1914. } 
SYNOPSIS. 
Introduction. 
Character of data. 
Graphical Representation. 
Principles governing adoption of particular curves. 
Necessity for the adoption of equation with fractional indices. 
The logarithmic homologue. 
The antilogarithmic generatrix. 
. Logarithms of negative numbers. 
Geometrical conventions for representing the logarithms of 
negative numbers. 
Sine curves. 
11, Parabolas and hyperbolas. 
Exponential Curves. 
. Curves which are the product of parabolic or hyperbolic and 
exponential curves. 
. On a curve which is the sum of a series of parabolas, or of a 
series of hyperbolas, or both. 
Graphs of Curves. 
1. Introduction.—Physicists, engineers, actuaries and 
statisticians, frequently require to discover formulas which 
will represent, in the most simple and accurate way, groups 
of related facts. The work of Karl Pearson,* and W. Palin 
1 Phil. Trans. Biometrika and elsewhere. 
