THE LATITUDE-VARIATION TIDE. 
109 
From the weighted values of dj resulting from the treat¬ 
ment of the several terms of the ^'-tide that are sensible, a 
mean correction to the assumed speed, and hence a correc¬ 
tion to the assumed period, is obtained. 
The preceding formulae, which are worked out in accord¬ 
ance with received principles, are those employed by me in 
1892 in finding the latitude-variation tide in Penobscot ba} r , 
and they differ from those submitted to the Philosophical 
Society in my paper of May 21,1892, which I had employed 
in 1891-92 in finding the same tide in San Francisco bay, 
only in the simplifications arising from assuming the middle 
instant of the observations, instead of the initial instant, as 
the secondary time zero. In my revision of the work for 
publication in the Coast Survey annual volume, I employed 
the simplified formulae at both stations. This transference 
of the secondary time zero is especially important in connec¬ 
tion with a solution which I now proceed to develop. I early 
perceived its possibility, and had it under consideration when 
I left the Coast Survey in 1893. 
When dj is null—that is to say, when the period assumed 
in the grouping of the observations is precisely that of the 
inequality sought—the amplitudes will not suffer in the 
summations, nor will the epochs be displaced ; but when dj 
differs from zero the amplitudes will be diminished and the 
epochs advanced or retarded in the process of their deriva¬ 
tion. It is my purpose now to determine, in this latter the 
general case, the corrected values of the amplitudes and 
epochs without having recourse to the tedious operation of 
redistributing the observations according to the corrected 
period. 
In the case to be considered, namely, when dj is not null, 
there is in reality noj-tide, C pj and S vj in (3) are null, and the 
tide of speed i =j -f dj t with its harmonics, is to be found 
among the terms of C v ." and S vj ". We then have as the 
correct solution 
0 = Cp/+Cp" 
o = s v .; + v, 
