350 
EEY. S. HATTG-HTON ON THE TIDES OE THE 
^=0 
Ase= 
d h m 
5 5 11 
1 4 14 
d h m 
19 17 14 
1 4 14 
6 9 '25 20 21 28 
If we take the values of A nearest to these times, from Table V. we find 
ft. in. d h m 
A=S"==1 5 at 6 9 25, 
A=S"=1 3 at 20 21 28, 
and using the Sun’s declination at noon of the day before, we find 
S" 
S'=— 
sin z <y ’ 
and 
S'= 
S'= 
17 
sin (45 40') 
15 
t^= 23*8 inches, 
= 22-6 inches. 
'sin (41° 40'; 
The mean of these values is 
S , =23 , 4 inches • (8) 
We can obtain the ratio of M' to S' from Tables III. and IV., and thus calculate M' 
as follows. Differentiating (7) so as to make B a Maximum or Minimum, we find the 
equation of condition 
M"+S"cos (s—m—i s — 0=0 (®) 
Substituting in (7), we find at the Maximum and Minimum 
tan B : 
VS" 2 — M " 2 sin i s + M" cos i s . 
( 10 ) 
V S" 2 — M " 2 cos i s — M" sin i s 
when ^=0, M"=0, and the equation reduces to 
tanB— tan£ s , or B=4, 
as we assumed in determining the value of the true Diurnal Solitidal Interval from 
Table III. 
If we write 
M" 
S"’ 
w T e can reduce (10) to the following form, 
tan B = tan (i s -f 6), 
or 
B=?,+4. . 
( 11 ) 
( 1 - 
The Maximum and Minimum values of B are found from Tables III. and IV. 
h. m s 
B = Maximum = 5 12 7£, 
B= Minimum = 0 29 30 ; 
when B is a Maximum, M"=0 and 4=0 ; therefore (12) reduces to 
h m s 
B=i s = 5 12 7£; 
