DE. T. E. EOBINSON ON THE EEDUCTION OE ANEMOGKRAMS. 
429 
work in computing, has this advantage, that it permits the combining the constants 
obtained at different periods by simple meaning, which the sine formula does not. It 
also lends itself more easily to an examination of any influence which may be supposed 
to change the coordinates periodically. Any such may be developed in a similar series, 
and the sum or difference of the two will give the residual part which is to be accounted 
for by other causes. If this residue be larger than the original periodic part, the 
hypothesis must be rejected; and even though it be diminished, this is not sufficient 
unless there be a priori evidence of a vera causa. As an example of this may be 
mentioned one of the elements of the sun’s action. Its heating-power on a given day 
depends, among other things, on the sum of the sines of its altitude during that day. 
This sum 
=2$™- e 'dQ{sm lat. sin declin. — cos lat. cos decl. sin 6} 
=2 sin lat. sin decl. X +2 cos lat. cos deck sin &, 
6' being the value of Q at sunrise. If the value of this integral be computed for 12 
values of <p, it can be developed in a series y=k-\-a cos <p+o sin <p-\-b cos 2 p+ &c. This 
belongs to the midday of each month, and ought in strictness to be summed for the 
entire month by means of the expression of deck in terms of <p ; but it is sufficient for 
illustration, u is evidently diminished by y, and we have what would be found if the 
altitude had no effect, 
x=u-\-qyz=¥L-{-kq J rC,os <p(A+a#)-|-sin <p(0+ og'j + cos 2<p(B-J-#2')-J-&c. 
If q, the measure of the altitude’s effect on the coordinates, were known, no more would 
be required ; but a probable value of it is that which would make the sum of the squares 
of the periodic parts of the residues or K — Jc) a minimum. This gives 
<p <p 
q(Sy 2 - 1U 2 ) = - S uy + 12K& 
For K^=2 - 422 ; for lsJu= 4-723. With these I computed the series for x and x\ 
which need not be given, remarking merely that the coefficients of the first order are the 
only ones much altered. It may suffice to give the variable parts of u, x ; u', x'. 
January. 
February. 
March. 
April. 
May. 
June. 
July. 
Aug. 
Sept. 
October. 
Nov. 
Dec. 
2-109 
1-016 
0-778 
0-032 
2-758 
2-630 
-1-931 
-1-258 
-1-715 
— 0*575 
— 1-576 
-0-299 
0-438 
0-680 
0-217 
0-886 
-0-180 
-0-150 
-0-361 
-0-929 
-0-386 
-1-397 
1-658 
0-467 
3-170 
1-030 
2-190 
0-778 
-0-541 
-1-092 
-1-345 
-0-137 
-1-596 
0-398 
-2-068 
0-420 
-2-278 
-0-100 
-1-196 
0-117 
-0-102 
-0-045 
0-017 
-1-092 
0-173 
-1-800 
3-879 
1-655 
It seems from these numbers that the sun’s altitude may account for 0-27 of the 
variation of W, and for 0-53 of that of S. 
This discussion suggests the notion that the equatorial current which produces the 
positive W and S coordinates may possibly be more constant than appears at first sight, 
and that a part of these variations may be due to a current in the opposite direction 
