TIDE-PKEDICTING MACHINE NO. 2. 13 



the British machines, of another set of cranks, pulleys, and chain for 

 summing simultaneously the first derivative of the former, namely, 

 Aa sin (at + a)+Bh sin (bt + p) + Cc sin {ct + y) + . . . ., which, by 

 an ingenious device, points out upon the dial the time when the value 

 of the derived series is equal to zero, and, consequently, that of the 

 cosine series a maximum or a minimum. Theoretically considered the 

 machine requires separate settings for the times and heights, though 

 practically, for the simpler tides, such as those of the eastern coast 

 of the United States and the western coast of Europe, a single setting 

 is made to suffice. 



As this machine was designed to be set upon a table or desk, its 

 dimensions as a whole (18 by 14 by 24 inches) necessitated those of 

 its parts, as pitch and diameter of gear wheels, diameters of shafts, 

 etc., to be such as failed to provide sufhcient rigidity when set up 

 with ampUtudes for tides of the larger ranges. Also, in predicting 

 the more comphcated tides, the device for pointing out upon the dial 

 the times of the maxima and minima failed mechanically in certain 

 positions and required the operator's attention and assistance. 

 Besides, almost constant use during 12 years had developed consider- 

 able wear, and it was necessary to make frequent repairs. For these 

 reasons it was deemed advisable to replace it by a new machine. 



Sir William Thomson, engaged for a number of years with the 

 problem' of mechanically analyzing 'observed tide curves, saw in the 

 reversal of this process and the production of a tide curve from its 

 component elements the complete solution of the problem of predict- 

 ing tides. It would seem that for this reason the British machines, 

 including those made for the French and Brazilian Governments and 

 the Roberts 33-component machine, are merely 'Hide curve pre- 

 dictors." Prof. Ferrel conceived the idea of making the machine also 

 bridge over the gap which lies between the predicted tide curve and 

 the numerical data required for the tide table, by introducing an 

 additional mechanism for summing the sine terms of the derived 

 series, a system of time dials and a height scale, thus producing what 

 may justly be called the first real tide predictor. 



This machine fell short of filling all requirements, because it gave 

 the times of the maxima and minima oidy and, as stated before, 

 required resetting and a separate operation for heights of the com- 

 plicated tides. 



UNITED STATES COAST AND GEODETIC SURVEY TIDE-PREDICTING 



MACHINE NO. 2. 



A ^udy of these two types could not fail to reveal that slight 

 changes and simplification of the principles underlying them could be 

 made the basis of a new machine, capable of satisfying all demands. 



The conversion of the motion of the curve-tracing pen in the 

 Thomson type into that of a pointer indicating numerically the 



