Volume XII 
NOVEMBER, 1918 
Nos. 1 & 2 
BIOMETRIKA 
ON THE STANDARD DEVIATIONS OF ADJUSTED AND 
INTERPOLATED VALUES OF AN OBSERVED POLY- 
NOMIAL FUNCTION AND ITS CONSTANTS AND THE 
GUIDANCE THEY GIVE TOWARDS A PROPER CHOICE 
OF THE DISTRIBUTION OF OBSERVATIONS. 
By KIRSTINE SMITH, Copenhagen. 
CONTENTS 
PAGE 
Introduction 1 
I. Adjustment of a polynomial function of one variable; general 
distribution of observations . . .... 3 
II. The " best ' ' grouping of observations with constant standard deviation 1 3 
III. Uniform continuous distribution of observations with constant 
standard deviation. General formulae . . . . .17 
IV. Uniform continuous distribution of observations with constant 
standard deviation. Special formulae ..... 28 
V. Uniform continuous distribution of observations with additional 
observations clustered at the ends of the range; constant 
standard deviation of observations. General formulae . . 31 
VI. Uniform continuous distribution of observations with additional 
clusters at the ends of the range; constant standard deviation 
of observations. Special formulae . . . . . .41 
VII. Observations with varying standard deviation .... 50 
VIII. Best distribution of observations for determining a single constant 
of the function ........ 72 
IX. Adjustment with regard to both of two variates connected by a 
linear relation .......... 82 
Introduction 
In all sorts of experiments which are not simple repetitions but have at least 
one varying essential circumstance or indefinite variate the experimentalist is 
confronted with a choice in regard to the values of that variate. If the ex- 
periments be quite simple the question may be without great importance ; but 
when their requirements as to time or expenditure come into account the problem 
arises, how the observations should be chosen in order that a limited number of 
them may give the maximum amount of knowledge. It clearly depends upon the 
relationship between the observed quantity, which we shall name the primary 
variate, and its essential circumstances, the secondary variates, and upon the 
variation of the errors of the observations. 
Biometrika xii 1 
