ey oe 
On the Prediction Tables for the Tides of the U.S. Coast. 18 
which I had in view was the application of the wave theory to 
the discussion of our observations. I thought that the mind of 
an expert mathematician, directed entirely to the theoretical por- 
tions of this work, with directions by a physicist, and full oppor- 
tunities of verifying results by extended series of observations, 
the computations of which should be made by others in any 
desired form, would give, probably, the best results in this com- 
bined physical and mathematical investigation. 
The general form of the different functions expressing the 
tidal inequalities is the same in the different theories, and may 
be said on the average to be satisfactory as to the laws of change 
which these inequalities present. Whether we adopt, with La 
Place, the idea that periodical forces produce periodical effects, 
or with Airy that the tidal wave arrives by two or more canals: 
or with Bernouilli and Lubbock, the results of an equilibrium 
spheroid, or with Whewell, make a series of inequalities, semi- 
hed 
general consideration of the co-ordinates in space of the 
moon and sun, without any special theory, would lead to the 
Same results, representing the lunitidal intervals by series of 
Sines and co-sines, with indeterminate co-efficients. ; 
Calling J the luni-tidal interval from observation, 2 the mean 
luni-tidal interval, H the clock time of observation, /’¢ the moon’s 
longitude, P’ the moon's parallax, 0 P’ the hourly variation of 
the moon’s parallax, we have for the formula representing the 
correction for half monthly inequality, s sin 2H+s, cos 2H; for 
the moon's parallax correction, p (P’—57') +p, (P’—57’) sin 2H 
+P, (P'—57') cos 2H ; for the correction for hourly difference 
of the moon’s parallax, 7, (0@P) +p, (OP) sn2H+p, (8 
cos 2H, and for the moon’s declination corrections including the 
rate of change d sin 2lt+d, cos 2U't+q, sin 21t sin2 H+¢q, sin 
2 l'tcos2 H+q, cos 20't sin 2H+q, cos 2Utcos2H. There are 
corresponding terms for the inequalities produced by the sun’s 
action. The whole formula takes the form: 
I=1+5 sin 2H+s, cos 2H (ofaoqualicy conection, 
P(P'-57') +p, (P’—51')sin 2 +p, (P'—57') cos 2 Ht Moors meri 
P, OP)+ p, (0 P’) sin 2A+P, (8 P’) 008 2 eee rection 
Tsin2Vt4+9. singl’tsin2 H+q, sin 2 l’t cos 2H. Moon’s declination 
oa ; 1 2 : ao aga 
— dy cos2 Ut+q, cos 21't sin 2H+9, 00s 2 U't cos 2 Hf. Tr 
