( 210°) 
19. The reduced daily rates I of this table show at once and 
with evidence the. presence of the supplementary term; for the rest 
the rate of the clock in the present period appears to be a very 
regular one. If, first of all, we combine the monthly means into 3 
yearly means, from May to April, we find: 
1899 — 0.5158 
1900 . 156 
1901 „157 
There is no trace of a progressive change in the rate and for the 
further investigation of the influenee of the temperature we may 
simply use the deviations from the general mean = — 0.*157 
If in the first place we assume that the influence of the temperature 
is a linear one, we find 
1st from the monthly means, 
2nd from the means for two months sorahined in such a way that 
the supplementary term is nearly completely eliminated, respectively : 
¢ = — 0.50224 
and — — 0. 0220 
which values are practically identical with that used for the deter- 
mination of the reduced daily rates I. 
In the second place let us assume the existence of a term varying 
as the square of the temperature. In this assumption we find, 
proceeding in the same way as before, for the total influence of the 
temperature: *) 
— 0.°0253 (t—10°) + 000074 (t—10°)? 
and — 0. 0247 (10°) + 0. 00069 (#—10°)? 
respectively. We thus find for this period a quadratic term of appre- 
ciable value. The difference between the two formulae is small; 
I will definitively adopt the former. 
20. It thus becomes necessary to use a quadratic formula in order 
to clear the rates completely from the direct influence of the tem- 
perature, as is required for the determination of the supplementary 
inequality. We may, however, as well take the influence of the tem- 
perature to be proportional to its first power and then consider the 
remaining periodic part of the rate as “supplementary inequality”. 
I have followed both ways. In the following table I have inserted, 
first, the values found for the supplementary term in the first way, 
giving the results of the three years separately, as well as in the 
mean. These mean values are pretty well represented by the following 
simple sine-formula: 
1) The mean temperature of the 3 years was + 11°.6 C. 
