1919-20.] The Daily Temperature Curve. 93 
I write out the successive first to fifth differences of r, / , . . . / v , and 
calculate t and f at each full hour of t from the formulae * 
f=/u_ r2 /lv - 
The zenith distance, of the sun is computed from the formulae (I) with 
i( = 0 h , l h , . . . 23 h , and the declination of the sun at the middle of the 
month. The values t r of t at sunrise and sunset are also calculated. 
(5) The Cloud-Factors , / a 1 and /ul 2 , for each month. — Let D stand for 
half the difference and S for half the sum of the observed temperatures 
or their differential quotients at corresponding hours in the afternoon and 
forenoon when the sun has the same zenith distance. Formula (I) then 
becomes with regard to (I*) — 
(III) . . . / x 1 D 1 (f) + ^ 1 aD 1 (f) + /x 1 6D 1 (r)= -gQc 
where 
D 1 = D/(cos8 sin t). 
(IV) . . /A 2 S(f) + />c 2 aS(f) + yu, 2 &S(r) — /x. 2 5c 0 = eE +/F. 
D x and S are calculated from each two corresponding points of each curve. 
In accordance with these two formulae, which contain only functions of 
z on the right-hand side (see (7)), yoqDjr) must have the same values at 
the same zenith distance in all the twelve months, and the same holds good 
for S and the arguments r and r. Therefore I may interpolate D x (t) 
for the zenith distances of 90°, 85°, 80° . . . With this object in view I 
draw for January a curve whose ordinates are D 1 (r) and whose abscissae 
are their corresponding zenith distances, and obtain from this graph D 1 (r) 
for the zenith distances 90°, 85°, 80° . . . Similarly the other, quantities 
are found for every fifth degree of zenith distance. This graphical 
interpolation is repeated for the other months. 
I arbitrarily assume that the average value of / a 1 for the period April 
to September equals unity. 
To determine in this unit, I compile the twelve monthly values of 
D x (t) belonging to the zenith distance of 90°, take the mean of the six 
values for April to September, and compute the ratios (/x x ) of this mean 
and all the individual values. Other determinations of yoq are carried out 
for the other zenith distances, 85°, 80°, . . . 55°. For smaller zenith dis- 
tances there are obviously not six values available. Thus there are 3 
determinations of fx x for December and January, 4 for November, 5 for 
February, 6 for October, 7 for March, and 8 for each of the other six months. 
* Chauvenet, Spherical Astronomy. 
