48 
MR. AIRY ON THE LAWS OF INDIVIDUAL TIDES 
High Water. 
Low Water. 
Range. 
ft. in. 
ft. in. 
ft. 
in. 
2 1* 
15 
oi 
4 . 
17 3f 
. 
12 
H 
4 6J 
13 
21 
17 H 
15 
9 
1 11| 
15 
61 
17 6 
15 
4 
2 2 
16 
5 
18 7 
. , 
16 
3 
The irregularities here are considerable, and, taken in conjunction with those of 
the times of low water, they seem to show that some powerful disturbing cause has 
affected the low water at February 25, 17 h 50 m . Nevertheless, the tidal curves for 
the tides on both sides of that low water are undistinguishable, as viewed by the eye, 
from the rest ; and in the grouping for the reductions, to be shortly explained, the 
numbers furnished by them do not differ sensibly from those given by the others. 
Considering it then as established that the peculiarities in these tidal curves are 
the representatives of real peculiarities in the tides at Southampton (such as may 
always be expected in every individual tide of nearly the same magnitude as those 
observed on this occasion), and in no degree due to the accidental circumstances of 
weather ; and considering also that these tides exhibit no certain trace of diurnal 
tide ; I shall proceed to explain the method by which they have been reduced into 
mathematical form. 
The method is, in many respects, similar to that which I used for the Deptford 
tides, in a paper published in the Philosophical Transactions for 1842. The first step 
was, to divide the whole series of observations into groups, each group representing 
one tide. This was done by taking the interval from low water to low water as one 
tide, and supposing it to correspond to 360° of phase , and converting the interval 
between every observation in that tide and its commencement into phase, by that 
proportion. The next step was to reduce the different observations of height to one 
uniform scale. This was done by assuming every range of tide, from high water to 
low water or from low water to high water, to be represented by 2, and converting 
the depression of the water at every observation below the high water of that tide into 
abstract number, by that proportion. In this manner every observation gave a phase 
expressed in degrees, and a converted depression expressed in abstract number. The 
next step was to collect from all the tides the phases between 0° and 5° and their 
