ARCTIC SEAS —PART V. REFUGE COVE. 
333 
Table I. (continued). 
Time. 
High Water. 
Height. 
Low Water. 
Height. 
Diurnal Tide 
at 
High Water. 
Diurnal Tide 
at 
Low Water. 
1853. h m 
ft. in. 
ft. in. 
ft. 
ft. 
Oct. 8. 4 0 a.m 
12 6 
0*031 
8. 10 0 „ 
7 2 
0-688 
8. 5 0 p.m 
12 3 
0-172 
8. 10 50 „ 
8 8 
0-755 
9. 4 15 a.m 
11 5 
0-370 
9. 10 50 „ 
7 3 
0-823 
9. 4 40 p.m 
12 2 
0-547 
10. 12 10 A.M 
9 4 
0-823 
10. 4 30 „ 
10 9 
0-651 
10. 12 30 p.m 
8 0 
0-709 
10. 6 45 
11. 2 0 A.M 
12 2 
9 6 
0-646 
11. 6 40 „ 
11 0 
A. Diurnal Tide. 
The general expression for the Diurnal Tide is 
D=M sin 2(a cos(m— 4)+S sin 2<r cos(s— i s ), (1) 
which at the Equinoxes reduces simply to the Lunar Tide, viz. 
D=M sin 2^ cos(m— i m ) (2) 
If the Tides be plotted carefully to scale, it appears that the Diurnal Tides in height 
vanish together at High Water and Low Water, when [a=0, or nearly so. 
The mean interval from the time of the Moon’s declination vanishing to the dis- 
appearance of the Diurnal Inequality is about 36 hours, which may be regarded as the 
age of the Lunar Diurnal Tide. It is evident from equation (2) that if h and l repre- 
sent the range of Tide at Lligh Water and Low Water respectively, since the phase 
changes by 90 3 from High Water to Low Water, we have the following equations to 
determine the unknown constants i m and M: — 
2M sin 2(max. value of [a)= s /Ii 2 -{-1 2 . . (4) 
The mean maximum values of h and l were found to be 
hence we find 
Ar=0'849 foot, 
Z=0-761 foot; 
cot(m— ?' m ) = 
± 
849 
76T 
m-4=4 1°52' or -138° 8' 
=2 h 53 m or — 9 h 7 m . 
2 T 
MDCCCLXXV. 
( 5 ) 
