21. Finally IT have reduced the monthly means of the rates both, 
by the linear temperatureformula with the curve of fig. 7, and by 
the quadratic formula with the sinusoid of fig. 6. The rates, thus 
reduced, have been inserted in the columns Red. D. R. II and Red. 
D. R. III of the general table. 
These columns do not contain the reduced rates themselves, but 
their mean values, together with the deviations from the latter. 
These deviations lead to a mean error of a monthly mean 
Mo ae O20 21a 
if we adopt the linear formula (Red. D. R. ID), and 
ME 200218. 
if we adopt the quadratic formula (Red. D. R. III). 
The two methods of reduction thus lead to nearly the same degree 
of agreement and a decision about the preference to be given to one 
of the two Gannot, therefore, be derived from the monthly rates. 
If no reduction for the supplementary inequality had been applied, 
we should have found in the two cases : 
ME = == 00422 
+ (0 .0398. 
The increase of the M. H. is still considerably greater than it is 
for the other periods. The quadratic formula now leads to slightly 
better results than the linear one; the difference is small, however. 
| 
Il 
V. Amplitude of the oscillations of the pendulum in the 
period 1878—1888. 
22. As has been mentioned before, H. G. vAN DE SANDE BAKHUYZEN 
caused a small mirror to be attached to the pendulum in 1877 5), 
for the purpose of determining accurately the amplitude of the oscil- 
lation by the aid ot the reflected image of a metallic wire placed 
before a flame of petroleum. The image was projected on a divided 
scale by means of a lens. 1 Mm. in the scale nearly corresponds to 
0.'5 in the total amplitude; the reading could be made accurate to 
tenths of the millimeter. In this way a determination of the amplitude 
was made, generally 4 times a day, from 1878 April to 1899. 
The determinations of the years 1878, 79 and 80 were elaborately 
studied by H. G. vaN Dr SANDE BAKHUYZEN. The influence of the 
temperature, of the atmospheric pressure and also that of the position 
of the driving weight were thoroughly investigated. Having the inten- 
1) See: Verslag van den staat der sterrenwacht te Leiden 1876—77 pag. 12, 
