167 
Singapore and St. Helena, hourly observations during a few 
months lead to a fair evaluation of the general character and 
the amplitude of the phenomenon, and the period of one year 
is sufficient to fix also the epoch of the periodical variation 
with great accuracy. 
From the twenty-two-yearly series of Batavia therefore 
conclusions may be drawn which it would be impossible to 
derive even from a thousand-yearly series in Europe. It has 
been deemed therefore of some importance to investigate 
the question of the determination of the sun’s rotatory time by 
means of the available meteorological observations; the more 
so because it seems probable that this way of attacking the 
question of the gradual decrease of the sun’s diameter, which is 
а postulate of Hetmuoutz’s hypothesis about the conservation 
of the sun’s energy will, in future, lead to a satisfactory 
answer before an experimental test of this hypothesis is af- 
forded either by direct measurement, by observation of sun- 
Spots, or spectroscopical inquiries. 
It was shown, however, in Appendix Ш of Volume IX 
by the application of Horsstein’s method, that the amplitude 
of the variation, which we may expect to find, is very small 
and that it is therefore indispensable, that the whole series 
ће taken into account and not the single years as is usual 
and necessary in Hornsrei’s method. 
The principal objection to this method is that it is impossible 
to extend the operations to a large period, because, by carrying 
on the arrangement according to an arbitrary number, the 
advantage of the elimination of disturbing influences is counter- 
balanced by the disadvantage of the gradual vanishing of the 
amplitude. x 
The periodical variation to which a quantity y is subjected 
шау be represented bij the expression: 
у = A sin (nz + С) U 
in which » denotes the number of units of time passed since 
the commencement of the arrangement, C the argument at 
