166 



At the further end: 



y=2 cos (m2^ + 60°) 

 2;=4.67 sin (m2^-17°34') 



Since the speed of any competent, in degrees per component hour 

 (par. 84) is 360°/12=30°, and the component hour of the Mg com- 

 ponent is the mean kmar hour of 1.035 mean solar liours, the tides and 

 currents represented by these equations are most conveniently 

 plotted in terms of lunar hours, by placing m2^=0, 30°, 60°, etc. The 

 tides and currents at the entrances and at the middle of the canal, and 

 the instantaneous profiles at the successive lunar hours, designated as 

 0, 1, II, III, etc., are plotted in figure 52. 



It will be noted that the amplitudes and phases of the tides and 

 currents go through a progressive, but not uniform, variation from 

 one end of the canal to the other, and that the amplitude of the 

 current increases as that of the tide decreases. 



329. Progression of high and low waters, and of the strength and turn 

 of the current, through a connecting canal. — ^The times of high and low 

 water, of the strengths of the positive and negative currents, and ot 

 the turn of the current, at points along the canal may be determined 

 immediately from the phases of the tides and currents at these points. 

 Thus in the example set forth in paragraph 328, in which the origin of 

 time was taken at a high water at the initial entrance to the canal, 

 the current at this entrance turns when ^' = and m2f— 49°.6 = 0. As 

 the speed of the component is 28°. 98 per solar hour, the turn of the 

 current occurs 49°. 6/28°. 98 = 1.71 solar hours after high water; and 

 the strength of the positive current 90°/28°.98 = 3.11 hours after the 

 turn, or 4.82 hours after high water. Similarly, at the first quarter 

 23oint the phase of the tide is 8°.l, and high water occurs when 

 ^=—8°. 1/28°. 98, or 17 minutes before high water at the entrance; so 

 that if high water at the entrance is at noon, high water at the quarter 

 point is at 11 .43 a. m. A plot of these times at successive points along 

 the canal (fig. 53, page 168) show^s how high and low water and the 

 strength of and turn of the current, progress through it. 



Obviously, high water and low water must travel through a connect- 

 ing canal at such rates as to reach the far end at the time of high and 

 low waters at that entrance, the total time of travel being fixed by the 

 difl'erence in the timing of the tides at the two entrances; but the rate 

 of travel is not in general uniform. The progress of the strength and 

 turn of the current through the canal is determined, on the other 

 hand, by the rate of storage and release of water in the successive 

 sections of the canal, and is dependent on the depth of the canal. No 

 fixed relation exists therefore in the general case betweeu the progress 

 of high water and of the strength of the current through a connecting 

 canal. 



