94 REPORT—1883. 
Beginning, then, with 0" of the first day, we shall begin counting 0, 1, 
2, &c., as the T-hand comes up to its hour-marks. But as the S-hand 
gains on the Y-hand, there will come a time when the T7-hand, being 
exactly at the p hour-mark, the S-hand is nearly as far as p+}. When, 
however, the 7-hand has advanced to the p+1 hour-mark, the S-hand 
will be a little beyond p+1+4: that is to say, a little less than half an 
hour before p+2. Counting, then, in 7’-time by reference to S-time, we 
shall jump from p to »+2. The counting will go on continuously for a 
number of hours nearly equal to 2p, and then another number will be 
dropped, and so on throughout the whole year. If it had been the T-hand 
which went faster than the S-hand, it is obvious that one number would 
be repeated at two successive hours instead of one being dropped. We 
may describe each such process as a ‘ change.’ 
Now, if we have a sheet marked for entry of heights of water accord- 
ing to J-hours from results measured at S-hours, we must enter the 
S-measurements continuously up to p, and we then come to a ‘change,’ 
and dropping one of the S-series, we go on again continuously until 
another ‘ change,’ when another is dropped, and so on. 
Since a ‘change’ occurs at the time when a T-hour falls almost 
exactly half way between two S-hours, it will be more accurate at a 
‘change’ to insert the two S-entries which fall on each side of the truth. 
If this be done the whole of the S-series of measurements is entered on 
the T-sheet. Similarly, if it be the T-hand which goes faster than the 
S-hand, we may leave a gap in the T-series instead of duplicating an 
entry. For the analysis of the T-tide there is therefore prepared a sheet 
arranged in rows and columns; each row corresponds to one 7-day, and 
the columns are marked 0», 15, ... 235; the 0>’s may be called 7-noons. 
A dot is put in each space for entry, and where there is a change two 
dots are put if there is to be a double entry, and a bar if there is to be 
no entry. Black vertical lines mark the end of each S-day. These 
black lines will of course fall into slightly irregular diagonal lines across 
the page, and such lines are steeper and steeper the more nearly 7-time 
approaches to S-time. They slope downwards from right to left if the 
T-hour is longer than the S-hour, and the other way in the opposite case. 
The ‘ changes’ also run diagonally, with a slope in the opposite direction 
to that of the black lines. 
We annex a diminished sample of a part of a page drawn up for the 
entry of the M-series of tides, in which 7-time is mean lunar time. 
