20 
MESSES. DE LA EUE, STEWAET, AND LOEWY’S EESEAECHES 
Distance in parts of radius. 
+ 0-153 
± 0-000 
-0-153 
-0-306 
-0-459 
-0-612 
-0-765 
-0-918 
- 1-000 
Corresponding length of central unit. 
1-00226 
1-00000 
1-00677 
1-00621 
1-02257 
1-03386 
1-04910 
1-07041 
1-08126 
19. The present state of this inquiry is not sufficiently far advanced to justify us in 
applying corrections to the calculated positions of sun-spots on account of the effect of 
distortion on the angular distances from the centre of the sun. The point will, how- 
ever, have our careful attention when finally discussing the positions ; and we hope to be 
able to give thoroughly satisfactory constants for the effect of displacement by our Pho- 
toheliograph. 
With regard to the correctness of the calculated areas, it appears from the above 
that the side of our square unit, being -01 of an inch at the centre, will in consequence 
of the elongation towards the limb be *0106082 inch at the edge, and the areas mea- 
sured there will obviously have to be diminished in the ratio of (-0106082) 2 : ('01) 2 , and 
similarly at other distances, as seen in the following Table, which shows the numerical 
effect of the elongation on the values which we have assumed in our reduction for the 
square unit at different distances from the centre. 
Distance from 
centre in terms 
of radius. 
Proportion in which 
the areas ought to 
be diminished. 
Assumed values for the 
square unit, without 
regard to elongation. 
In millionths of 
sun’s surface. 
Corrected values, 
taking into account 
elongation. 
In millionths of 
sun’s surface. 
+ 1-000 
1-1125339 : 1 
00 
QO 
00 
CO 
+ 0-918 
1-1124764 : 1 
•00001050 
10 
•00000944 
9 
+ 0-765 
1-0887879 : 1 
•00000663 
7 
•00000609 
6 
+ 0-612 
1-0677089 : 1 
•00000541 
5 
•00000507 
5 
I +0-459 
1-0454294 : 1 
•00000478 
5 
•00000457 
5 
+ 0-306 
1-0238404 : 1 
•00000448 
4 
•00000437 ’ 
4 
+ 0-153 
1-0045251 : 1 
•00000431 
4 
•00000431 
4 
+ 0-000 
1-0000000 : 1 
•00000426 
4 
•00000426 
4 
-0-153 
1-0135858 : 1 
•00000431 
4 
•00000425 
4 
-0-306 
1-0124586 : 1 
•00000448 
4 
•00000442 
4 
-0-459 
1-0454294 : 1 
•00000478 
5 
•00000457 
5 
-0-612 
1-0688665: 1 
•00000541 
5 
•00000506 
5 
-0-765 
1-1006108 : 1 
•00000663 
7 
•00000602 
6 
-0-918 
1-1457776: 1 
•00001050 
10 
•00000916 
9 
-1-000 
1-1691232:1 
QO 
CO 
OO 
OO 
It will be seen from this Table that, our fractional values of the areas being expressed 
in millionths, the corrected values differ only from those employed by us in all spots 
which are very near the limb, and also in very large spots ; in both these cases, how- 
ever, the probable error of the measurements is not inconsiderable ; and to introduce a 
correction on account of elongation was therefore considered by us a hardly necessary 
refinement in the calculations. 
