(364 ) 
We consider an arbitrary S, which intersects the planes of 2 mn 
the axes of rotation of the section; the determination of the ratios 
of the intensities belonging to them is a well known problem. 
If, finally, we notice that between the intensities w and w' of a rotation 
in S, and its intersection with a space <A the relation w' = w sin (Ao) 
exists, then in this way the intensities of the rotations about the 
five associated planes have become known quantities. 
Mathematics. — “On interpolation based on a supposed condition 
of minimum.” By J. Werper. (Communicated by Prof. H. G. 
VAN DE SANDE BAKHUYZEN.) 
For the reduction of the daily rates of the standard clock in the 
Leyden Observatory I have developed a method of interpolation, 
which may perhaps also be profitably used for other investigations. 
The following is the problem we have to deal with: a variable 
quantity, here the correction of the clock, is given for a series of 
instants, during a long period, with unequal intervals; how can we 
find an intermediate value of that correction at any moment. 
First I tried to solve this problem with the limiting condition 
that for all the intervals of time which enter into the caleulation 
there is a smallest common divisor, which we take as unit of time. 
1. Let S (clock correction) be the variable quantity, and g (rate) the 
amount by which it increases during a unit of time. Let Sand ia, 
be two successively determined values of S separated by m units 
SES 
: PUL DE : - ° . 
of time, then — — is the average increase per unit; that increase 
m 
is represented by Q,. Hence the m quantities g, 9,.--.9Ji---9Jm Of the 
i—=m 
interval considered depend on the relation + g;= Sq — fee = m Qn 
== 
and a similar relation exists for each interval between two con- 
secutive determinations of S. 
In order to determine the quantities g, 1 put the condition that 
the sum of the squares of the differences of the first order for the 
whole period of observation should be a minimum. ‘This condition 
of minimum was selected with a view to the special case where 
we have to interpolate between the clock corrections, but I doubt 
whether in all cases these interpolated values will be the most 
probable ones. Leaving aside for the moment these considerations, I 
go on developing the problem in hand. The quantities which cor- 
respond to an interval of m units occur only in the following terms 
int de ie 
