( 196 ) 
Partly neglecting the variations of the monthly tide-ranges in 
different years, which are at a maximum 120 mm. and give 
only a maximum error of 3 mm. in the value of A, we can put 
275 X 2750 + az cos (p—yz) instead of 2%, V — 2%/,, E mm. 
The formula then becomes : 
A = 78 — 0,08 E + az cos (p — y3) + Y. 
The errors calculeted from this formula do not differ much from 
the above-mentioned, for now the mean error is 6,4 mm. and the 
formula is therefore as exact, while the computation is much more 
easily carried out. 
In conclusion [ will add the following remarks. 
First I should mention that I found some errors in the tables 
containing the observed height of the sea-level at Delfzyl during the 
months in which the greatest differences occurred and in those of 
two other tide-gauges during five months. For instance at Delfzyl I 
found a month in which one height had been read from the half 
hour-mark instead of the hour-mark, and also one reading with a 
wrong sign. After making the correction the great divergence was 
very much reduced. Although this is no proof, we.may suppose that 
the greatest differences very nearly give the limit of precision. 
Further I notice that the second correction mentioned above does 
not agree with the principle on which the method of harmonic 
analysis is founded, so that this method cannot give exact results 
in the reduction of the observations at Delfzyl. Still, I do not affirm 
that any other is better. 
This want of agreement is demonstrated by the term 0,08 Z in the 
preceding formula. For the same month in two different years 
(February 1889 and 1890) the difference of the two values of Z is 
983 mm., so that 0,08 # = 47 mm., and although this difference 
would not be of much importance for a single observation, it is far 
too great for an error of the monthly mean. 
\ 
Mathematics. — Prof. Jan De Vries reads for Prof. L. GEGEN- 
BAUER at Vienna a paper entitled: “New theorems on the 
v 
roots of the functions C Came 
Up to this moment we know of the roots of the coefficients 
Ee (x) of the development of (1 —2a - @?)—’ aceurding to ascending 
powers of @ only this, that they are all real and unequal, are situated 
