Prof. A. D. Bache on Tidal Observations. 347 
TABLE No. L 
Showing the comparison of diurnal and semidiurnal deduced fi bservations, 
with curves of sines. Diagram No. 1. 
No. 1. No. 1. s No. 2. 
x FROM OBSERVATION. | FROM CALCULATION. bs FROM CALCULATION, | ¢ | 
2 a. ie 4 I on 
Er | F 8 ieogz| 2 | gs |e 
sere Le Vache ay |g | te eel a || ET ee 
3 FI ; Bs " 2s 
goi2} So h8e) 2) Fs Sa) Fe lee 28] Bs | 221 Fe 
Bele) SE 1 ot | 8 | SE ok S \Eoko| BE} se | 548 
om = —5 an =) a3 as qoBC e¢ a} S 
é = Bs oo | 2 eo oo “e aeoo| 55 23 2 
= a mn = a mn = ¢ = m | ee) 
ft. ft. ft. ft. ft. ft. ft. ft fi. ie Baz 
© |0'°00} 0:00} 0-00 jo°00} 0-00} 0°00 | O'00 | 0°00 0°00 | 0-00 
t | 17 |— 03 | +14 | +15)]— -04| “81 03 “15 “iI “02 
av }dr}= -06| -25 | -28|— -07] «21 |. *03 +29 a 9951 88 
3 | -44|— -08| -36 |} -4o/— - 32 | ‘03 “42 £ 02 
™ A) -511— -06| -45°| “50 “07 | “43 02 “St pe “44 ‘00 
Br Odi 309 | °53 F705 -04| -51 02 57 2 53 “00 
Mico Oo 75% ;4 46 ‘00 | +57 00 59 | & 5g |—-02 
7 | -56\+ -03| 59 | -55/+ -04| °59 00 oh 4 ‘61 | -"02 
Hi ee ‘06 | -57 | -50 -o7| °57 00 51 © 58 |--o1 
9 | 44 08 | -52 } -40 08| -48 | ‘03 42 I -5o 02 
10 | *31 06 | -37 | :28 07}. °35 or 2 D 56 biséo 
BS 17 °03-| +20 | +19 *04| +19 | .O1 | a "19 00 
12 | -00 00} -0o | -0o “00 | -00 00 “00 “00 ‘00 
i Nothing would be gained in closeness of representation of the 
result by displacing relatively the two tidal waves. It is only re- 
markable that in averages including the whole of the tides, even 
when most irregular, the results are so satisfactory. I have accord- 
‘ingly used the hypothesis of the representation of each wave by 
acurve of sines, deducing the maximum ordinate of computation 
from each observed ordinate. ‘These laborious computations were 
made by Alexander S. Wadsworth, Jr., sub-assistant of the Coast 
Survey, and by Mr. P. B. Hooe. They give tables of heights of 
diurnal and semidiurnal curve for each day of observation, 
which form the basis of the discussion of the heights. The next 
step after decomposing the curves of observation into diurnal and 
semidiurnal curves, is to discuss each separately to ascertain if 
they follow the laws deduced from them in regard to heights and 
times. 
1. Diurnal wave. Heights and times. 
If the diurnal curve is a curve of sines, then the ordinates found 
for each hour enable us to determine the value of the maximum 
or six-hour ordinate. Setting out from the mean line, then, we 
have for each day six determinations of the rise and fall above or 
below that line. Tables were computed from these, in which 
the daily curves were decomposed into their diurnal and semi- 
diurnal components. In making these tables, the very irregular 
tides have been in general omitted. These tables were arranged 
according to the moon’s declination, beginning and ending with 
the days on which the declination was zero, determining the 
maximum ordinate of each day from zero of declination. As the 
