PEOFESSOE BIJNSEN AM) DE. H. E. EOSCOE’S PHOTO-CHEMICAL EESEAECHES. 895 
sky would produce on the same point is obtained by the equation 
, Q . . 
The relation -q* is easily found by help of the following considerations. If r be the 
radius of the hemispherical cap, we have = and if i is the diameter of the hole, 
its area is 4:^7^ bvd?-, when sin^=:^; and if there are n holes. 
Q = w . sin^ or ^’ = 
2ra.sin®- 
2 
In the apparatus above described the values of these constants were as follows : — ^ 
w— 184; ^? = 0-775 millim.; r=77-5 millims.; hence we obtain = 436. The value of 
q is determined in the following manner :~Let be the diameter of the circle through 
the open sector of which the light falls on the diaphragm ; let be the distance from 
any point in the circumference of this circle to the centre of the paper diaphragm ; and 
lastly, let be the number of degrees to which the sector was opened; we have then 
•d/ j . 
^=sin and the area of the whole visible sky 
=2t. If we suppose that q^ 
has an arbitrary value of the of Ike hemisphere, that is, if we have 
, 1000 
^50 $ 
^~~9 '^•sin®^- The values of these constants in our instrument are, c^i = 45-5 millims. ; 
ri = 190'6 millims. ; hence ^ = 0-0197 %//. The amount of light (I) which a point on the 
earth’s surface receives from the whole sky, expressed in units of the amount which is 
reflected from a portion of sky at the zenith equal in area to xwo^k part of the whole, 
is found from the equation 
Q q,'*' ^ 
In order to obtain the exact value of I certain precautions must be taken, which if 
neglected would give rise to very considerable errors. It is of primary importance to 
notice, when two observations have to be compared together, that the amount of light 
which the white surface of the inside of the photometer receives, and which is reflected 
on to the lower side of the diaphragm, remains perfectly constant. If the inside of the 
photometer is illuminated by the reflected light from houses, hills, or other neighbouring 
objects, a passing shadow may render the observations useless. Even when a portion of 
the light which should fall into the photometer is by chance obstructed by the hand 
whilst altering the opening of the divided circle, an error of considerable magnitude is 
introduced. In order to avoid irregularities of this kind, it was found most convenient 
to expose the white sides of the photometer to the diffuse light of the cloudless sky, 
avoiding altogether other reflected or direct sunlight. It is self-evident that no direct 
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