73 



The times of high water and of low water are those at which ?/ is a 

 maximum or minimum respectively, and therefore at which dy/dt=0. 

 They are then given by the equation: 



dy/dt=-UfJr sin (ji^+yo+^-Ji°)-ki/Ki sin (k:t+Vo+u-Kr°) 



- ■ ■ ■ -kg/Kasin (k2^+Fo+^-K2°)+ • • • =0 (97) 



136. Tide-predicting machine. — The arithmetic evaluation of y for 

 successive values of t from equation (96) would be too laborious to 

 be practicable. The solution of equation (97) for the successive 

 values of t at high and low water could be accomplished mathematically 

 only by an even more laborious process of successive approximations. 

 An elaborate machine, called the tide-predicting machine, has been 

 devised and constructed, by which the values of y and of dy/dt in 

 these equations are mechanically summed for values of t measured 

 by the angular travel of the mechanism. The height of mean sea 

 level, Ho, the values, JH, of the amplitudes of the several components 

 for the year of prediction, and the values of the initial phases, Fo+'M—k 

 of the several components at the beginning of the year, are all set 

 on the dials of the machine. The machine is then put in motion. 

 When the pointer indicating the value of dy/dt (the sine summation) 

 crosses its zero mark, the machine is stopped, the height of the tide is 

 read off the dial which indicates the summation of y, and the time of 

 the tide is read off a dial which indicates the time corresponding to 

 the angular travel of the mechanism. These are the height and time 

 of the first high or low water of the year. The machine is again set 

 in motion, the height and time of the next low or high water read off, 

 and the process continued until the predictions for the year are 

 completed. 



137. Tide Tables published annually by the Coast and Geodetic 

 Survey give the predicted heights and times of the tides at some one 

 hundred reference stations throughout the world, with data showing 

 the corrections to be applied to give these heights and times at nu- 

 merous secondary stations. 



138. Accuracy of tide predictions.- — ^The predicted times of high and 

 low water which are published in the tide tables, obviously must be 

 those which would occur without the accidental disturbances due to 

 winds and other meteorological causes. A comparison between the 

 actual and the predicted tides at Portland, Maine, and at Seattle, 

 Wash., in May and November 1919, shows that the maximum de- 

 parture in the time of the actual from the predicted high and low 

 waters was 24 minutes; but that the times were generally in much 

 closer agreement. The height of one of the tides at Portland differed 

 by 1.9 feet from the predicted height; and it was not unusual for the 



