AT SOUTHAMPTON AND AT IPSWICH. 
53 
Treating these numbers in the same way as those for Southampton, and still con- 
ceiving the phase to commence at high water, we obtain the following formula for 
the converted depression : — 
T055 + 0* 1 1 2 . sin phase — 0*096 . sin 2 phase -f- 0*030 . sin 3 phase + 0*0 1 2 . sin 4 phase 
— 0*85 1 . cos phase — 0*041 . cos 2 phase — 0*076 . cos 3 phase — 0*023 . cos 4 phase ; 
or 
1*055 + 0*858 . sin (phase — 82° 31') — 0*104 . sin (2 phase + 22° 59') 
+ 0*082 . sin (3 phase — 68° 23') + 0*025 . sin (4 phase — 63° 2'). 
Let phase — 82° 31' = p ; this becomes 
1*055 + 0*858 . sin/) + 0*104 . sin (2 p + 8° 1')— 0*082 . sin (3 p - 0° 50') 
- 0*025 .sin (4p + 87° 2'). 
The first three terms of this expression are extremely similar to those in the expres- 
sion for the Southampton tide : the principal difference between the two expressions is 
in the fourth term, or that depending on 3 p. It is very remarkable that the algebraical 
difference between the formulae for tides which are so strikingly different in general 
character, depends entirely on a term of the third order of the fraction expressing 
the proportion of the vertical oscillation to the depth of the water ; an order to 
which (so far as I am aware) theory has reached only in one instance, namely that of 
a wave travelling along an unlimited canal, and then only on the restricted supposi- 
tions of rectangular section and absence of friction*. It is also worthy of remark, 
that the terms of the second order do not agree with those given by the restricted 
theory to which I have alluded, and that they differ materially from those given by 
the Deptford tides-f-. From a consideration of the discordance between the observa- 
tions and the present state of theory in regard to the form of these terms, as well as 
from remarking the influence which they have upon cotidal lines and mean levels, I 
am inclined to fix upon the circumstances of waves in canals as more deserving of 
notice at the present time, both in theory and in observation, than almost any other 
branch of the theory of tides. 
I take this opportunity of correcting an error in my paper on the Deptford tides;};. 
I have there stated, on the authority of Mr. Whewell§, that the age of the tide as 
inferred from the heights is greater than its age as inferred from the times. This, 
however, is incorrect. The age inferred from the heights is, in every instance that 
has been properly examined, less than that inferred from the times ||. I trust that, in 
a subject which is at first examination very confusing, it will be regarded as a venial 
fault to have erred in such company as that of Mr. Whewell. 
In a theoretical view, this correction is very important. The cause assigned for the 
* See Philosophical Transactions, 1842, p. 6, and Encyclopaedia Metropolitana, Tides and Waves, Article 210. 
t Philosophical Transactions, 1842. J Ibid. p. 8. § Ibid. 1838, p. 236. 
|| Encyclopaedia Metropolitana, Tides and Waves, Article 543. 
