354 Prof. A. D. Bache on Tidal Observations. 
formula is not the sum of the two greatest heights of the diurnal 
and semidiurnal tides. The hypothesis of the interference of 
the two waves makes the high water the sum of two ordinates 
(neither of which is the maximum), depending upon the laws of 
increase and decrease of the curves respectively, and of the rela- 
tive position of the two ordinates. The correction due to this 
cause is readily found. The part of it which belongs to the 
diurnal curve will be the difference between D and D. cos (¢-E); 
where E, according to the hypothesis of the interference of the 
two waves, is 9 hours; and ¢ is the value for the maximum ordin- 
ate of the compound curve, namely (Proc. Amer. Assoc. Cam- 
bridge Meeting, page 289), 
cosec ¢ — sec f= Sia th 
~~ Dis * 
This value of ¢, containing C (the maximum ordinate of the semi- 
diurnal curve), shows that the quantity will vary with the time 
of the moon’s transit, according to the half-monthly inequality of 
the height. Following the course which I have taken through- 
out this communication to give the resulting tables merely, I sub- 
join the corrections thus derived from the tables for D/4 from 
observation, the computed values of t, and of D.cos(t-E). The 
agreement of the general form of this correction with the theory 
is a new confirmation of the values of the quantities C and D, 
deduced from observation, which it contains. 
TABLE No. XI 
* 
Showing correction to height of the diurnal wave for difference of maximum ordinate, 
and of high water ordinate in compound curve. 
peariebenecite re; piste ed 
hours. feet, 
= *o3 
13 —-o5 
24 —='os 
33 —-*o4 
4s —'04 
54 —-"07 
64 un 
74 —-'O7 
83 —-06 
—-o05 
10g aia 
113 -+-of 
The correction furnished by the last two tables, and the cor 
on cone from the table, are given in Table No. 12 next 
owing. : 
ing. 
