ON SOLAK PHYSICS. 
To transform the ecliptical coordinates thus found into the 
heliographical, let P (fig. 2) be the true pole of the sun, A that 
of the ecliptic, which is represented by W E, while Q Q' is the 
sun’s equator, and N the node. Then, if S' be a spot, the pre- 
ceding considerations make known to us the sides S' B and B N 
in the triangle S'NB, while we really require S'L and NL, 
which are the true heliographical coordinates. These, however, 
are easily deduced when we consider that in the triangle S' N B 
cos NS' = cos S' B cos B N, 
cos S' NB = cot NS' tan BN, 
and that in the triangle S'NL the angle S'NL=S'NB + I, I being the inclination of 
the sun’s equator and the plane of the ecliptic ; therefore 
sin S'L =sinNS' sin S'NL, 
sin N L = tan S' L cot S' N L, 
which gives the required coordinates. 
4. The principles of reduction here explained, however, have been considerably modi- 
fied, and we have throughout followed the elegant and convenient method given by 
Mr. Carrington in his volume of Sun-Observations. The method being now adapted 
to sun-observations by means of photography, we have thought it necessary to give in 
the following pages a detailed account of it, and here take the opportunity to express 
our gratitude to Mr. Carrington for the advice and instruction which he has kindly 
given to M. von Bose, to whom the first part of the reductions, extending over the year 
1862, was entrusted. 
We have also adopted for our calculations the values proposed by Mr. Carrington 
for the longitude of the sun’s ascending node, and for the angle of inclination of the 
plane of the solar equator and that of the ecliptic (vide Mr. Carrington’s Observa- 
tions, page 244), viz. 
1=7° 15', N=73° 40' for 1850-0. 
The auxiliary Tables necessary for the reductions, which are given in Mr. Carrington’s 
volume, pages 20 to 26, were consequently recalculated ; but as they can easily be deduced 
from those published by Mr. Carrington, by those who choose to adopt his elements 
for the calculation of the position of sun-spots, they are not given here. 
Various Steps of the Process of Reduction. 
5. We thus see that the measurements made are sufficient to determine, in the first 
place, the ecliptical latitude and longitude of a spot, and, in the second place, by knowing 
the longitude of the ascending node of the solar equator as well as the inclination of 
this to the plane of the ecliptic, to transform these ecliptical elements into others having- 
reference to the solar equator instead of the ecliptic. 
The first step in all this is to be able to trace on each solar photogram a line which 
b 2 
Pig. 2. 
A. 
