104 REPORT—1883. 
deal of unnecessary labour has been incurred, and ‘when a simpler plan is 
followed it may perhaps be worth while to include more of the short- 
period tides in the clearances. 
Professor J. C. Adams suggests the use of the tide-predicting machine 
for the evaluation of the sum of the clearances, and if this plan is not 
found to inconveniently delay operations in India, it may perhaps be 
tried.} 
In explaining the process we will suppose that method (i) has been 
followed ; if either of the other plans be adopted it will be easy to change 
the formule accordingly. 
It is clear that R cos (a+114n) is the height of the tide at 11 30™; 
and the same is true for each such tide. Hence if we use the tide- 
predicter to run off a year of fictitious tides with the semi-range of each 
tide equal to s'; sin 12n/sin }n of its true semi-range, and with all the 
solar series and the annual and semi-annual tides put at zero, the height 
given at each 11" 30™ in the year is the sum for each day of all the clear- 
ances to be subtracted. The scale to which the ranges are set may of 
course be chosen so as to give the clearances to a high degree of accuracy. 
In the other process of clearance, which will be explained below, a 
single correction for each short-period tide is applied to each of the final 
equations, instead of to each daily mean. 
We next take-the 365 daily means, and find their mean value. This 
gives the mean height of water for the year. If the daily means be un- 
cleared, the result cannot be sensibly vitiated. 
We next subtract the mean height from each of the 865 values, and 
find 365 quantities 5h giving the daily height of water above the mean 
height. 
“These quantities are to be the subject of the harmonic analysis ; and 
the tides chosen for evaluation are those which have been denoted above 
as Mm, Mf, MSf, Sa, Ssa. 
Let 
dh= Acos(co—ax)t +B sin (s—a)t 
+C cos 2ct +D sin 2ct 
+C’ cos 2(¢—n)t+D’ sin 2(c—n)t }. . . (66) 
+E cos nt +F sin nt 
+G cos 2nt +H sin 2nt 
where ¢ is time measured from the first 115 30™, 
Now suppose /,, J, are the increments in 24 m. s. hours of any two of 
the five arguments (—a)t, 2ot, 2(o—n)t, nt, 2nt, and that Aj, B,; 
A», B,, are the corresponding coefticients of the cosine and sine in the 
expression for ¢ h. 
Then if 6h; be the value of ch at the (¢+1)th 11> 30™ in the year, 
we may write 
oh=A, cos 17+ B, sin l,i+ A, cos li+B, sinlyit+t ... (67) 
paper was presented in 1882 to the British Association by the writer of this Report 
upon the supposed mistake and its consequences. On his return to India, however, 
Major Baird found that the correct procedure had always been followed. 
1 Major Baird has sent three years of results to England in order that the methed 
may be tested in competition with the numerical process. 
