ON SOLAE PHYSICS. 
15 
Measurement of the Areas of Sun-spots. 
13. The second part of the results of our researches published in this paper, exhibits 
the amount of spotted surface for every day on which a solar photogram was taken, 
expressed as a fraction of the visible hemisphere. The information is given under two 
heads, viz. the area covered by the penumbra , umbra , and whole of the spots forming 
one group, and also the same values for all groups, taken together, which were visible 
on each day, thus enabling us to trace not only the behaviour, as regards increase or 
decrease, of every group, but also to express numerically the variations in the energy 
manifested by the sun’s surface from time to time. 
We had previously published the area-measurements of the whole of Mr. Carrington’s 
observations, and were induced to devote to his sketches the considerable labour which 
these measurements require, on account of the excellence and care with which they 
were executed. But if, as every one will probably admit, these area-measurements are 
a more scientific representation of the sun’s activity than the mere numbering of the 
groups, it must also be conceded that solar photograms are a more trustworthy basis for 
such measurements than drawings, however carefully the sun’s surface may be delineated. 
We shall therefore continue these measurements from year to year, convinced that 
they will afford materials of very great scientific value. 
14. The method adopted for measuring the areas is to place a plate of glass engraved 
with a series of small squares in contact with the spot to be measured, and to note inde- 
pendently how many squares and fractional parts of a square were occupied by the 
umbra, the penumbra, and the whole spot ; if the number of squares occupied by the 
whole spot is equal to the sum of those occupied by the umbra and penumbra separately, 
then the observation is supposed to have been correctly made. If, in addition to the 
measurement, we know the angular distance of the spot from the visual centre, we have 
the elements for ascertaining the area occupied by the spot. This area we have expressed 
in millionths of the sun’s hemispherical surface. 
It ought perhaps to be noted that we could not place the engraved square absolutely 
in contact with the collodion side of the picture, for fear of destroying it ; and it was 
therefore necessary to interpose the thickness of the glass plate betwixt the measuring- 
squares and the picture. To obviate an objection to the process which might arise from 
considering that the engraved lines were not precisely in contact with the object mea- 
sured, an experiment was made which showed that this difference of distance did not 
occasion a perceptible error in the determination. The area of the square which forms 
the unit of measurement is 1 0 * 0 0 ^ of a square inch, the side of each square being 
Too inc h. 
To find the mean radius of the sun-pictures, we took for each month of the year two 
photograms distant from each other by about a fortnight, and found their respective 
radii to be of the following lengths, expressed in inches : — 
