and negative terms neutralize each other for the greater part. Hence 
the difference /s — Jz, does not exceed 6 &, (7, — fr), the value - 
of which depends only on the errors and the lengths of the intervals; 
the mean value of this expression for every possible distribution of 
the errors of the observations may be derived from the mean error 
of those observations. 
This is the utmost limit to which by means of corrections to the 
observed quantities S we can diminish /s, lest the interpolation 
curve found should assume a less sinuous form than would be 
probable with regard to the results of the observations and their 
precision. 
Here follows an example of the computation. 
The annexed table contains the interpolation coefficients of a part 
(period 1882 June 8 to August 30), taken from a longer series of 
observed rates of the clock Hohwii 17. Therefore the coefficients 
at the limits of this period are not in accordance with the boundary- 
conditions supplying the formula (C). 
We compute the interpolated clock corrections by means of the 
formula: 
2 
S= 8, +t (v + % Cy xs + u? e, i ) 
7 VL 
Sy is the clock correction of the last preceding observation and 
the coefficients gy, nej, n'en are given in the columns 5, 6 and 7; 
they are expressed in the unit 0001. The values g, and nec, to 
be used are placed a little above the horizontal line corresponding 
to the length of the interval expressed in days, which interval 
contains the moment ¢ for which we interpolate. Because of its 
connection with the constant derivative of the third order of the 
interpolation curve within each interval, the coefficient 17e, for each 
interval has been placed on the horizontal line of that interval. 
The 8 column contains the coefficients e and the 9% their differ- 
ences 6 by passing from one interval to the other. For each of 
these differences I have calculated the variation 46, of a given 
6,, as the corresponding correction of the clock ‘S, increases by 
+ 08.100 while the other corrections remain unmodified; they are 
Og 
given in the 10% column. By the increase AS, = — > 08.100 
6; 
the difference 6, becomes zero, so that by means of this Hees, we 
obtain the same result as if in the determination of the interpolation 
curve we had omitted the observation S,. Hence the correction of 
the clock S, derived from this interpolation is equal to the observed 
