THE LATITUDE-VARIATION TIDE. 
113 
When m = an infinity of a higher order than p — oo 
these become 
+JL 
c » = ‘hf Jda 9 o) 
j n J 
C p = — | da (p (a) COS pj a 
i/ 7r 
+ 7 
J c J 
Sp = — f da cp (a) srn pj a 
7T 
and then Fourier's integral, 
+oo +oo 
(p (x) = ^do. ip (a) j*d ft COS ft (a — a;) 
— oo — 00 
follows in the usual way. Thus a known (*) special device 
of solution is referred to a general principle, and Fourier’s 
integral, with all its consequences, is derived from the cal¬ 
culus of probabilities. 
II. 
Results of the Application of the Formulse to the Tides of San 
Francisco and Penobscot Bays. 
At the close of the official day of December 18, 1891, Dr. 
T. C. Mendenhall, at that time superintendent of the United 
States Coast and Geodetic Survey, informed me that Pro¬ 
fessor Simon Newcomb had suggested to him that the Survey 
should endeavor to find the tide corresponding to the lati¬ 
tude-variation then under discussion by astronomers, and 
to which Dr. S. C. Chandler had then recently assigned a 
*See Byerly (Wm. E.) An elementary treatise on Fourier’s series, etc., 
8°, Boston, Ginn & Co., 1893, chapter ii, which I have consulted since 
obtaining my results. 
