ON THE LAWS OF RISE AND FALL OF THE SURFACE. 
259 
water. I have compared the times of ascending a given space (from M to N) both 
at Liverpool and at Plymouth, but I have not thought it necessary to give the diagram 
which exhibits the result. 
(8.) Near mean water the surface is rising or falling with the greatest velocity. 
Hence the observation of the time at which the surface passes the line M or N is far 
more precise than the observation of high and low water. The observations at Ply- 
mouth were made to seconds ; and the hypothetical time of high water, obtained by 
bisecting the interval from M rising to M falling, agreed with the time obtained by 
bisecting the interval between N rising and N falling, generally within a minute or 
two, and often within a few seconds. 
(9.) Since this is the case, it might be made a question, whether it would not be 
better to observe the time of the surface passing M, or N, or both, than to observe the 
time of high water and low water. (Of course it must be understood, that it would still 
be requisite to observe the height of high water and low water, but this is very easily 
done, either by the eye, or by self-registering machinery.) There are some circum- 
stances which appear to confirm the conjecture that this would be an improvement in 
tide observations : for instance, the diurnal inequality of the times of high water at 
Plymouth is much more distinctly seen in the bisected times than in the observed 
times ; but on examining the general run of the observations, it does not appear that 
the bisected times are more regular than the observed times. 
Since the exactness with which it is possible to determine the bisected time of high 
water has not previously been practically shown, I shall give, at the end of this me- 
moir, the comparison of the bisected times obtained from the lines M and N at Ply- 
mouth, with each other, and with the observed times of high water. 
(10.) As we have already seen, the displacement of the summit of the curves of rise 
and fall, that is, the time by which the observed time of high water differs from the 
bisected time, appears to follow different laws at different places, and therefore pro- 
bably depends upon local circumstances. In general, in the cases hitherto examined, 
the observed time is later than the bisected time ; that is, the surface descends more 
rapidly than it rose. But both at Liverpool and Plymouth this difference vanishes 
very nearly at about seven hours’ transit. Thus at neap tides the curve of rise and 
fall is nearly symmetrical. 
(11.) The laws which we have investigated have been referred to the hours of the 
moon’s transit, these hours being reckoned from 1 to 12 ; but at Plymouth, if we 
refer the observations to hours of moon’s transit from 1 to 24, thus distinguishing 
superior from inferior transits, we find a great difference in the effects belonging to 
corresponding transits, as 6 h and 18 h , 7 h and 19 h , and the like. This difference ap- 
parently arises from a diurnal inequality, and would disappear when the moon’s nodes 
came into another position. 
London , June 12, 1840. 
2 L 2 
