( 20 ) 



observiitiüiis do, it will be possible to draw a line tliroufih O in such 

 a manner, that on the one side all the vectors are greater tiian the 

 corresponding opposite vectors on the other side of the line. 



If, therefore, we arrange in this way a great number of cpiantities 

 which show a slight tendency to asymmetry, the radial momentum 

 will steadily increase, as the mass concentrated in the centre of 

 parallel forces is equal to the total number of observations, whilst 

 the distribution of accidental cpiantities will tend to a symmetrical 

 distribution. 



Assuming two i-eclangular axes going through (J, we tijid for I he 

 coordinates, by which the centre of gravity is determined, A^ l)eing 

 the number of observaticms : 



,/;, ::= - ^ o cw & >/. z^ ~ ^ Q dn 6» .... (1) 



N N 



The calculation, therefore, comes to the same as the determination 

 of the first couple of Foihikh coefllicients: 



a, = - ::£ o CUV & h^ = ^ 2l o sin ^ .... (2) 



X ^ N 



and, if the periodical movement is represented by the expression: 



.1 cos {fit — ('). 



.P = a;^4-^-^ tan,,(':=z^ '* = V • • • (3) 



a, 1 



This way of representing the arrangement seems preferable to the 

 development in a Foukier series: firstly because the development of 

 a function in a sei-ies, as a re|)resentati()n of the function, derives 

 its value from the composition of a great lunuber of terms, so that, 

 in calculating one term oidy, we are hardly justified in speaking of 

 a Fourierisation of the function. 



In the second place, l)ecause by this way it becomes at once 

 evident that the i)roblem is fully equivalent to that of the determin- 

 ation of a point in a plane by means of a great many inaccurate 

 observations. 



This problem has been treated by several mathematicians, but 

 certainly in the most conqilete manner by the late Prof. Schols ^), 

 whose origiiuil conception of the question leads to the detection of 

 some laws, which are independent of the assumption of any law 



1) Over de theorie der lonten in de rnimle en in liet platte vlak, Amsterdam, 

 Verb. K. Akad. v. Wet l«Sect. XV, 1875, and: Theorie des erreurs dans le plan 

 et dans I'espace, Delft, Ann. II, 188(5. 



