TIDE-PREDICTING MACHINE NO. 2. 7 



height above mean sea level, is called the " amplitude" of the compo- 

 nent and is a constant for that station. 



Were the effects of the tidal forces upon the sea instantaneous, the 

 time of high water would always coincide with that of the meridian 

 passage of the tide-producing body. Inertia, friction, bodies of 

 land, etc., however, retard the motion of the tidal wave, and un- 

 equally so, at different stations. The lagging of an observed high 

 water behind the time when the tide-producing cause is in the me- 

 ridian may also be considered as the effect of the combined laggings 

 of all the individual components behind their respective meridian 

 passages. To find the lag of a component, therefore, it is only neces- 

 sary to determine the time from the highest point on the curve, ex- 

 pressed by the 24-hourly means, to the instant of the meridian pas- 

 sage of the component. This time, expressed in degrees of arc, is 

 called the ''epoch," and is, like the amplitude, a constant for the 

 component at the station. 



The amplitudes and epochs of the components entering into the 

 tides have been determined by this analysis for practically all the 

 important stations in the world, and have become, like astronomical 

 data, through courtesy, exchange, and publication, common prop* 

 erty. With their aid the tides can now be computed in advance by 

 the summation of the formula — 



Ji = Ho + A cos {at + a) + B cos (bt + ^) + C cos (ct + y)+.,. , 



in which Ti is the height sought, ^o is a constant expressing the height 

 of mean sea level above the datum line, which usually represents the 

 plane to which the soundings given on sailing charts are referred: 

 A, B, C . . . . are the amplitudes of the successive components, ex- 

 pressed in feet and fractions, and a,h,c.... the hourly speeds of the 

 same components, expressed in degrees of arc; t is the time in mean 

 solar hours from the beginning of the prediction, usually January 1, 

 midnight, to the instant for which the height is required, a is the 

 interval from the beginning of the prediction back to the preceding 

 high water of the component ^, expressed in degrees; ft 7 ... . being 

 like intervals for the components B, C . . . . 



Such computation of the tides, however, involves a very great 

 amount of labor of a kind particularly wearing and subject to errors 

 to an extent requiring additional labor in checking. The idea of 

 carrying out these computations mechanically, therefore, soon sug- 

 gested itself, both for reasons of economy as well as accuracy, and 

 was materialized by the construction of various machines, the latest 

 of which is here described. 



The new United States Coast and Geodetic Survey tide-predicting 

 machine which takes the place of the old Ferrel machine, formerly 

 used for the prediction of the tides, was designed and constructed by 



