16 
MESSES. DE LA EUE, STEWAET, AND LOEWY’S EESEAECHES 
January 1*958 
May 1-904 
September 1*920 
1-963 
1-903 
1-922 
February 1-969 
June 1-900 
October 1-930 
1-959 
1-897 
1-943 
March 1-956 
July 1-900 
November 1-949 
1-947 
1-907 
1-947 
April 1-930 
August 1-904 
December 1-969 
1-927 
1-911 
1-967 
The mean of these gave us 1-9326 as the mean radius, which we adopted in the 
reduction of the areas measured. The area of each square unit being -0001 of a square 
inch, it follows that, if r be the radius of the disk in inches, the area of the visible 
hemispherical surface will be 2 wr 2 , and in our pictures 
=2 XttX (l*9326) 2 =23-46734; 
therefore, at the centre of the visual disk, one of these small squares will represent a 
proportional area of the whole hemispherical surface, viz. 
•0001 1 
~ 23-46734 — 234673 - 4 ’ 
while at an angular distance oc from the visual centre the proportion will be 
sec a 
234673 - 4 ' 
From this formula Table I. is calculated. It gives in the first column the angular 
distances, in the second the corresponding distances in terms of the radius as unity, and 
in the following nine columns the number of millionths of the sun’s hemispherical surface 
covered in each position by 100, 200 &c. measured squares. 
To obtain the required values for a number of squares between 10 and 99, and between 
1 and 9, it is, of course, only necessary to cut off from the tabular values one or two 
decimals. An example will best illustrate the use of the Table. 
Let the measurement of a group, situated at a distance from the centre of 0-483 
(radius— 1), show that the whole of it covered 963 squares ; then, since 0*483 corresponds 
to an angular distance of 29° from the centre, we should find opposite to this distance 
for the area of 900 squares 4383 millionths. 
„ „ 600 „ 2922, .-. for 60 . . 292*2 „ 
„ „ 300 „ 1461, .-. for 3 . . 14-61 
consequently for 963 squares . 4690 millionths. 
The use of a mean radius of the sun-pictures in the above formula will not sensibly 
affect the correctness of the yearly amount of spotted surface ; for in our results the daily 
amount will be somewhat too small during the time of aphelion, and again slightly too 
great about the perihelion. But if for any special purposes the amount of spotted 
surface were to be determined with the greatest precision, the actual radius of each 
