Prof. A. D. Bache on Tidal Observations. 347 



The interference in this case would be between the diurnal tide- 

 wave, which represents the diurnal -inequality and the ordinary 

 semi-diurnal wave, whether this wave has a regular progress 

 along the coast independently of the semi-diurnal^ wave, as was 

 at first supposed by Mr. Whewell, or whether its phenomena 

 are local, as he has since been led from his investigations to be- 

 lieve- If the observed wave is produced by its interference with 

 a semi-diurnal wave, we can only study the phenomena to ad- 

 vantage after the observed wave has been separated into its com- 

 ponents. 



5. As a first approximation, I assumed the two waves to be 

 governed by the law of sines, and then determined the curve 

 which would result from the superposition of two such waves, 

 having the same or different origins. The mean of the regular, 

 double tides about the zero of declination would present a first 

 approximate value of the rise and fall of the semi-dinrnal tides, 

 and the mean of double and single tides at the maximum of de- 

 cimation would, especially when near the quadratures, give a 

 first approximation to the height of the diurnal tide. The com- 

 parisons with the forms of curves already traced, addressing the 

 eye, are easily made. 



I present herewith diagrams (PL 6, or No. 4) for the case, in 

 which the maximum of the diurnal tide coincides with that of the 

 semi-diurnal, is three hours in advance, (or coincides with mean 

 water falling,) six hours, (or coincides with low water,) and nine 

 hours, (or coincides with the second mean, or mean water rising;) 

 nsiug the approximate quantities referred to above for the greatest 

 height of two component curves. It requires little examination to 

 see that neither of the first three forms represents the case, and that 

 the fourth does so remarkably, even in what appear to be small 

 inegnjarities \n the daily curves. This will be seen in the re- 

 sults for October, of which a diagram on a large scale is presented, 

 g*^ing the tidal curves near the zero, and thence up to the maxi- 

 ^"m of declination for the first half of the month. In the sin- 

 gle day tides there was the same slow rise compared with fall, 

 sharp rise and fall near high and low water, with the tendency to 

 a stand during the risej the same excess in the interval o( time 

 trom low to high water, over that from high to low water. This 

 hypothesis as to the position of the two waves may perhaps be 

 slightly improved by further discussion. It is obvious from the 

 ^quatiou of the curve (which I have already referred to as given 

 by Mr. VVhewell), that the form and position of remarkable 

 points will vary with the constants in the component curves, as 

 ^ell as with the position of the origin of each in reference to 

 that of the other. 



To carry out the representation graphically, I have drawn the 

 curves for four values of the constants of the diurnal and semi- 



