MESSES. DE LA RUE, STEWART, AND LOEWY’S RESEARCHES 
2 
one of which is perpendicular to the other ; and consequently an impression of these 
wires is produced in every sun-picture which is obtained. 
The nature of the measurements made will be better understood by supposing for the 
moment that this system of wires is in exact adjustment, and that their centre is also 
the centre of the sun-picture. Then by means of the measuring-instrument the follow- 
ing elements are measured : — 
(1) The diameter of the sun in the picture taken (in inches). 
(2) The distance of a spot from the sun’s centre (in inches). 
(3) The angle which the line joining the spot and the sun’s centre makes with one of 
the wires. 
Sufficiency of Observational Data afforded by means of Measurements: 
3. It will now be necessary to show that these observational data are sufficient for 
the determination of the heliographical position of the sun-spots. As will be seen from 
the following general considerations, two elements are required for this purpose, viz. 
the angular distance of a spot from the centre of the sun, and its angle of position with 
reference to a fixed line, at the time of the observation. 
It is perhaps almost superfluous to remark that our object is to ascertain the helio- 
graphical latitude and longitude of spots — that is to say, the angular distance of a spot 
from the solar equator, and also from a certain meridian of solar longitude, the meridian 
chosen being that which passes through the vernal equinox, and the degrees being 
reckoned from west to east. 
Let PESW (fig. 1) represent the visible disk of the sun, 
of which circle T, the earth, is the pole, and let S' be the 
place of a spot ; also let W E denote the plane of the ecliptic, 
and let P and S be its poles. 
In the spherical triangle P T S' the angle T P S' is obviously the 
difference of longitude of the spot S' and the earth, while the 
arc P L S' represents the north polar distance of the spot, and 
gives consequently the latitude. But in this triangle we have 
the necessary parts given for finding P S' and T P S' ; 
for the side PT =90°, 
the angle PTS'=90°-J-ETS' is the angle of position of the spot S', 
the side T S' =the angular distance of the spot from the centre, 
which is given by the consideration, that 
. , . r. . . , , . , measured distance T S' 
the sine ot the angular distance= r T 
° sun s semidiameter 
Hence we see that the observational data required for our purpose are, as far as the 
ecliptic is concerned, the measured length of the distance of a spot from the centre, and 
its angle of position, both of which data are given with the greatest precision by our 
measuring-instrument applied to the solar photographs. 
Fig. 1. 
