162 
THE REV. W. WHEWELL’S RESEARCHES ON THE TIDES. 
high water) on October 11 and 12, 1827, were as follows: 5 h 38 in , l h 39 m , 5 h 20 m , 
0 h 56 m ; on June 23 and 24, 1828, they were 7 h 9 m , 3 h 9 m , 7 h 21 m , 2 h 51 m ; on October 
15 and 16, 1828, they were 5 h 13 m , 2 h 0 m , 6 h 7 m , 2 h 46 m ; showing an alternate increase 
and diminution to the extent I have mentioned. The greatest alternate inequalities 
of the heights of high water during the series of observations which I have mentioned, 
were something more than a foot. 
But when we examine the observations of low water, we find the case marked by 
additional features, which render it still more curious. For, in the low waters, the 
diurnal inequality of the times appears indeed, but is neither so large nor so regular 
as the inequality of the times of high water ; it amounts at some periods to one hour , 
but not often to more. The diurnal inequality of the height of low water, on the other- 
hand, is much larger than that for high water, reaching the amount of three, or even 
four feet ; and this, in a tide of which the whole rise, from the lowest to the highest, 
rarely exceeds five feet. 
The diurnal inequality depends, as is well known, upon the moon’s declination ; 
and its maximum and its disappearance have been found, at most places hitherto ex- 
amined, to follow at a short interval (one or two days) the maximum and the vanish- 
ing of the moon’s declination. If we examine the Petropaulofsk observations with 
regard to this point, we find that the greatest and most regular of the diurnal in- 
equalities which I have noticed, the inequality of the time of high water and of the 
height of low water, correspond with the moon’s declination ; they have their maximum 
when the declination is greatest, whether north or south, and pass from positive to 
negative on the very day on which the moon crosses the equator. Using the phrases 
which have previously been employed on this subject, the epoch of the diurnal in- 
equality is zero, and the effect of the moon’s declination reaches Petropaulofsk with- 
out any delay or retardation. 
But this view of the laws of the tides at this place, which might otherwise be ac- 
cepted without difficulty, is extremely perplexed and interfered with by the other 
parts of the diurnal inequality, — the inequality of heights at high water and of times 
of low water. For though these inequalities are not so large or so regular as the 
others, still they are sufficiently marked and steady to allow their laws to be seen 
beyond doubt. And it appears, not only that the epoch of these parts of the in- 
equality does not agree with that of the others, but that these two inequalities alter- 
nate with the other two, vanishing when the other reach their maxima, and showing 
their maxima when the others vanish. 
This is a very perplexing circumstance ; for we cannot doubt that the diurnal in- 
equality depends upon the moon’s not moving in the equator ; and therefore, how this 
inequality should affect the height of high water and the time of low water most, at 
that period at which the moon is in the equator, it is difficult to conceive. As the 
series of observations upon which my inferences are founded are but short (three 
series of a few weeks each), it might be doubted perhaps whether they are sufficient 
