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Physics. — W. H. Kensom. “Reduction of observation equations 
containing more than one measured quantity.” (Supplement 
N°. 4 to the Communications of the Physical Laboratory at 
Leiden by Prof. H. KAMERLINGH ONNES). 
(Communicated in the meeting of May 31, 1902). 
§ 1. The most widely read text books on the theory of probabi- 
lities and the method of least squares treat of the reduction of observation- 
equations each of them containing one variable. 
In physical measurements, however, we obtain equations between 
different quantities each of which must be considered as liable to 
an accidental error. This, for instance, occurs when we have measured 
the pressure of a gas or a liquid at different volumes and temperatures, 
and we want to deduce from the observations the equation which 
represents the most probable relation between these quantities inves- 
tigated. As in the literature on this subject I have not found a general 
solution for such a case, it may be useful to give it here. *) 
1) Literature on this subject: 
Cras. H. Kummer. Reduction of observation equations which contain more than 
one observed quantity. The Analyst. July, 1879 (Vol. VI, N°. 4). 
[ have not been able to find this volume of the periodical in Holland. 
Merriman. The Determination, by the Method of Least Squares, of the relation 
between two variables, connected by the equation Y= AX-+ B, both variables 
being liable to errors of observation. U. S. Coast and Geodetic Survey, Report 
1890, p. 687. A Textbook on the Method of Least Squares, § 107. 
Here an elegant solution of the problem is given for the case in which a 
linear relation exists between the two measured quantities. 
Jures Anprape. Sur la Méthode des moindres carrés. C. R. t. 122, p. 1400, 1896. 
The author gives a solution for the case when: 
yg CR yc tera Seeman lh Vie 
in which ¢; and N; represent measured quantities, and a, b, c.... are to be 
determined. 
Ravensuear. The use of the Method of Least Squares in Physics. Nature, 
March 21, 1901, p. 489. 
The author, apparently not acquainted with the literature mentioned above, points 
out that in treating equations between several measured quantities, we must make 
allowance for the fact that each of these quantities has an error of observation, 
and he gives a graphic solution for the case in which a linear relation exists 
between two quantities, some supposition regarding the accuracy of the measure- 
ments of each of those quantities being assumed. 
K. Pearson. On Lines and Planes of Closest Fit to Systems of Points in Space. 
Phil. mag. (6) Vol. 2, p. 559, Nov. 1901. 
The author gives an elaborate essay on the lines and planes (if necessary m a 
higher-dimensional space) which are such that the sum of the squares of the 
perpendicular distances between a number of points not situated in a straight line 
or a plane, and those lines or planes becomes as small as possible. 
