ON SOLAE PHYSICS. 
17 
picture would, of course, have to be employed in the reductions. The variation with 
the radius is as follows: — 
With the smallest radius= 1-897 in., the value of one square at the centre is 0-00000442, 
„ mean „ =1*933 „ „ „ 0-00000426, 
„ greatest „ =1-969 ,, „ „ 0-00000411. 
Distortion arising from optical deficiencies of the Photoheliograph. 
15. The question how far the trustworthiness of solar photograms is limited by the 
effects of distortion, has caused us considerable anxiety. We have for several years past 
made various attempts to arrive at a satisfactory solution of this problem, and we have 
decided that our final discussion of the positional elements of sun-spots for the deduc- 
tion of the sun’s elements shall be preceded by an exhaustive investigation of the matter. 
At present we regard our researches and their results as only preliminary ; but, on ac- 
count of the importance of the subject for Celestial Photography generally, and in order 
to convince our readers that the subject is engaging our most earnest attention, we give 
in the following a short account of our latest steps in the matter. 
16. It is obvious that if an image of some distant terrestrial object, which may be 
supposed to be of constant dimensions, is received through our photoheliograph on a 
prepared plate, we shall obtain a negative imprint of the object on a well-defined cir- 
cular disk, which has been produced on the plate by the action of the whole diffused 
light which enters the object-glass. If the distant object be small, and placed in the 
axis of the instrument, it will also appear in the centre of the disk which has been 
produced, while if placed more or less out of the axis, it will also occupy a corresponding 
position on the photogram. Now in all positions its dimensions ought to be the same, 
for we supposed these dimensions to remain constant ; hence it follows that if a relative 
change takes place in these dimensions, as determined by careful measurements of the 
same object in different positions, a distortion takes place in that part of the field where 
a change is observed. 
This principle has been made use of in the following manner. The ornamental pin- 
nacle of the Pagoda erected in the Kew Gardens, which is constructed of a number of 
rings of metal suspended in a horizontal position by vertical chains fastened to the top 
piece, was photographed by means of the photoheliograph in a series of twenty-five pic- 
tures, taken so as to bring its several parts into varying distances from the centre. The 
pictures were all taken within a few days, in which no considerable changes could possibly 
take place in the object itself, and any effect of expansion by changes in the tempera- 
ture of the air would not sensibly affect the measurements. The distance of the Pagoda 
from the Observatory is 4398-24 feet*. The figure of the pinnacle, as it appears on 
the pictures, allows us to measure certain lines, produced photographically by its different 
* We take this opportunity to express our great obligation to Colonel Sir Henry James of the Survey Office, 
who kindly presented ‘us with a sketch of the relative positions of the Observatory and the Pagoda, from which 
the above numbers are taken. 
MDCCCLXIX. 
D 
