418 rEPorRT-— 1883. 
It will be seen that in the above table we have results during two sun-spot 
cycles nearly. If we divide (as has been done for the heights of rivers) the 
interval between each solar maximum, without regard of its exact length, into 
twelve equal parts, our data will give us values corresponding to two such sets 
of twelve. If we further smooth our values by taking means of three, and if we 
take the means of the two sets of twelve, we obtain finally one set of twelve values, 
which will, perhaps, afford us a rough indication whether there is really a connection 
between heat of sunshine, as herein determined, and sun-spot frequency, and 
whether, as in the case of rivers, there are traces of a double terrestrial period for 
one of sun-spots. 
We thus obtain— 
TasLE V1.—SHow1ne THE Sun’s Heatine PoweER, CORRESPONDING TO THE 
Various Puasss or Sun-spot Frequency. (0) Denotes Maximum Sun-spots. 
CO) @) 2) OGD) (8) A), OD 
38°57 30°28 24°91 29°16 31:58 31:39 28:92 28-78 2887 26°47 29-90 31:88 
It would thus appear that, as far as we can judge from such limited data, there 
are, as in the case of rivers, and probably rainfall, traces of a double maximum for 
one of sun-spots. This, however, isa conclusion that cannot at present be regarded 
as established, but only as more or less probable. 
5. On apparent Sun-spot Inequalities of Short Period. By Professor 
Batrour Srewart, /.R.S., and W. Lant Carpenter, B.A., B.Sc. 
By means of a method for detecting inequalities of unknown period in a mass 
of observations, which has already been described to this Association, we have 
made some way in analysing sun-spot records, and have detected several apparent 
inequalities of short period, while we are in hopes that we shall be able to show 
that there is a definite relation between these and corresponding inequalities in 
meteorology and magnetism, 
We do not intend at present to raise the question as to the true or merely 
apparent periodicity of these inequalities. We simply take them as we find them, 
and see whether there are corresponding apparent inequalities in meteorology and 
magnetism, for it is obyious that there may be a true relation between celestial and 
terrestrial inequalities quite apart from the question of their true periodicity. 
Meanwhile it may be of interest to the Association to exhibit the most striking 
evidence of repetition which we have obtained in the progress of our sun-spot 
analysis. The observations analysed have been those of Schwabe, Carrington, and 
De la Rue, extending over a period of thirty-six years, and these have been divided 
into three periods of twelve years each. The inequalities for each year are 
proportionally represented, so that each carries equal weight whether it be a year 
of maximum or minimum sun-spots. In doing this the average of spots for each 
year is reckoned =] ,000, the departures of each term of the year’s inequality from 
this average number being noted—in red when deficient, and in black when in 
excess. 
As the departures for each year are added algebraically together, it will be 
necessary for the twelve years series to divide the sums red or black by twelve, in 
order to estimate the true extent of the inequality, and in like manner it will be 
necessary to divide the sums for thirty-six years by thirty-six. When this is done 
we shall have the true measure of the positive (black) and negative (red) departures 
from the mean (1,000). In the following table, the numbers of which have not 
been submitted to any smoothing process, we have represented the two most 
prominent sun-spot inequalities which we have hitherto detected. It will be seen 
from these that there is in each very marked evidence of repetition, the results 
for the twelve years being very lilxe each other. 
Dividing the gross results by thirty-six, we have in the first of these inequalities 
