228 THE REV. w'. WHEWELL ON THE RESULTS OF CONTINUED TIDE 
transit ; a constant quantity being, as before stated, added or subtracted in order to 
refer the height to the proper zero. 
According to the theory, the 0^ or 12*^ hour-points would be at A; the ratio of DC 
to AC would be that of the lunar to the solar tide ; and the distances of the hour- 
points from D would be the heights of high water above mean water. But all these 
properties are, in the actual cases, modified in a manner which must be noticed. 
The tides in these discussions are not referred to the transit of the moon immediately 
preceding, but to some earlier transit, namely, the second, third, fourth or fifth pre- 
ceding transit ; it being found that in this way the accordance with the theory be- 
comes more exact. Thus in the British Channel the tides are referred to the third 
preceding transit ; and this extends also to Ireland and to the west coast of England 
and Scotland. On the east coast of England, in the northern parts, as at Shields, 
Sunderland, Scarborough and Hull, the fourth preceding transit is used ; at Harwich, 
Sheerness and London, the fifth (see Table B). But this reference to an earlier transit 
does not make the highest tide correspond exactly with the hour of transit 0*^ or 12^: 
and it is found, in the cases which have been included in the present examination, 
that a displacement of the 0*^ point about fifteen minutes from A will best make the 
theoretical and the observed curves agree with each other. 
The ratio of DC to AC is, as has been said, 12 to 5 ; and this, according to the 
theory, would be the ratio of the lunar to the solar tide. If this were the case, the 
spring tide measured above mean water would be 17, and the total spring tide above 
spring tide low water would be 34. The neap tide in this case would be 7 above 
mean water, and therefore 24 above spring tide low water. Hence the difference of 
springs and neaps would be to the height of neaps above low water springs as 10 to 
24, a ratio constant for all places. 
But in fact, this ratio of the excess of springs to the total height of neaps above 
low water springs is different at different places : and the observations now under 
consideration show in some measure the law of this difference. The ratio is smaller 
when the tide is smaller. This appears from the observations at different places, as 
arranged by Mr. Ross in the annexed Table A. We have there the following results, 
taking the means of groups of places according to the amount of tide. 
Number of 
places. 
Mean neap 
tide above 
spring low 
water. 
Mean 
excess of 
spring high 
water above 
neap. 
Ratio. 
37 
ft. in. 
9 3 
ft. in. 
2 5 
38 : 10 
40 
12 
0 
3 8 
33 : 10 
39 
17 10 
5 
9 
31 : 10 
4 
27 
0 
9 
8 
28 : 10 
Where it appears that the actual ratio approaches to the theoretical ratio in propor- 
tion as the amount of tide increases. 
If the ratio just spoken of were constant, we should be able to find the [jeight of 
