harmojStic analysis and prediction of tides. 65 



If the summations for the short-period components were made 

 strictly in accord with the principles outlined above, it would be nec- 

 essary to have a separate tabulation for each component sought, in 

 which the heights would strictly apply to the beginning of each com- 

 ponent hour. The labor involved in such separate tabulations would 

 be too great to be considered. Instead of making independent tabu- 

 lations for each component a single tabulation with the heights of the 

 tide taken to correspond to each solar hour of the series is used. 

 These solar hourly heights are then assigned to the component hours 

 with which they most nearly coincide and the summations made as 

 though the heights applied exactly to those component hours. Cor- 

 rections are later applied to take account of any systematic error in 

 this approximation. 



Two systems of distribution of the solar hourly heights differing 

 only slightly in detail will be considered: In the system ordinarily 

 adopted each solar hourly height is assigned to the nearest component 

 hour. In the second system there is selected for each component 

 hour the nearest solar hourly height. By the first system each solar 

 hourly height is used once, and once only, in the summation for each 

 component, but each component hour may not be equally represented 

 by the solar hourly heights. If the component day is shorter than the 

 solar day, some of the individual component hours will be unrepre- 

 sented; but if the component day is the longer, some of the individual 

 component hours may have two solar hourly heights assigned to them. 

 By the second system the component hours are equally represented, 

 but it will be necessary to reject some solar hourly heights or to use 

 some of them tmce in order to accomplish this purpose. The differ- 

 ence in the final results obtained by using the two systems will be 

 practically negligible, and as the first system affords a quicker method 

 of checking the summations it is the one generally adopted. 



The distribution of the solar hourly heights was at first accom- 

 plished by making separate copies of the heights for each component, 

 using tables that had been prepared to show the assignment of each 

 hour. The making of these separate copies involves muchlabor which 

 has since been eliminated by various devices. The U. S. Coast and 

 Geodetic Survey has adopted a system of stencils devised by L. P. 

 Shidy, which will be described in the next section. 



The British have been using a set of movable strips devised by Sir 

 George Darwin. These are made of xylonite, an artificial ivory, and 

 each strip is 9 inches long and one-fifth of an inch wide and is divided by 

 black lines into 24 equal spaces to provide for the 24 hourly heights of 

 the day. The set used by Darwin consists of 74 strips on which are to 

 be written the hourly heights for 74 consecutive days. By the aid of 

 printed forms these i ;trips are arranged so that the heights correspond- 

 ing to any parti cuIj r component hour which are to be summed to- 

 gether will be found in a vertical column. By rearranging the strips 

 summations can be made successively for the different components. 

 After the summation of the first 74 days of the series for all of the com- 

 ponents has been completed the strips are cleaned off with a damp 

 cloth and entries made for the next 74 days of the series, and these are 

 then summed for all the components. These operations are repeated 

 until the entire series has been summed. A more detailed descrip- 

 tion of this apparatus will be found in Scientific Papers by Sir George 

 Darwin, volume 1, pages 216 to 220. 



