HAEMONIC ANALYSIS AND PREDICTION OF TIDES. 73 



may be used. Because of the practical difficulties of constructing 

 stencils with openings in adjacent line spaces it is desirable that the 

 original compilation of the primary sums should be made so that each 

 alternate line in the form for stencil sums is left vacant. As with the 

 primary stencils, it will generally be found convenient to use two 

 stencils for each page of the compiled primary sums, although in some 

 cases it may be found desirable to use more than two stencils in order 

 to separate more clearly the groups to be summed. The actual 

 construction of the secondary stencils is similar to that of the primary 

 stencils. A preliminary set of forms is filled out with component B 

 hours as derived by differences from Table 33 applied to the compo- 

 nent A hours. The odd and even component B hours are then trans- 

 ferred to separate forms and the spaces indicated cut o-ut. The open- 

 ings corresponding to the same component B hour are connected with 

 ruled lines and numbered to accord with the component hour repre- 

 sented. The page numbering corresponding to the page numbering 

 on the compiled primary sums and referring to the pages of the 

 original tabulated hourly heights is to be entered in the column pro- 

 vided near the left margin of the stencil. 



In using the stencils each sheet is to be applied to the page of com- 

 piled primary sums having the same page numbering in the left-hand 

 column as is given on the stencil. The primary sums applying to the 

 same component B hour are added and the results brought together 

 in a stencil sum form, where the totals and means are obtained. A 

 table of divisors for obtaining the means may be readily derived as 

 follows : In a set of stencil sum forms corresponding to those used for 

 the compilation of component A primary sums the number of hourly 

 heights included in each primary sum is entered in the space corres- 

 ponding to that used for such primary sum. The secondary stencils. 

 tor component B are then applied and the sums of the numbers 

 obtained and compiled in the same manner as that in which the com- 

 ponent B height sums are obtained. The divisors having been once: 

 obtained are applicable for all series of the same length. 



In the analysis the means obtained by use of the secondary stencils 

 may be treated as though obtained directly by the primary summa- 

 tions except that a special augmenting factor, to be discussed later,, 

 must be applied. 



The closeness of the agreement between the hourly means obtained 

 by use of the secondary stencils and those obtained directly by use 

 of primary stencils will depend to a large extent upon the relation of 

 the speeds of components A and B. The smaller the difference in, 

 the speeds the closer will be the agreement. 



To determine the extreme difference in the time of an individual, 

 hourly height and of the component B hour to which it is assigned by 

 the secondary stencils, let an assumed case be first considered in. 

 which the tabulated heights coincide exactly with the integral compo- 

 nent A hours, and that on the middle day of the page of tabulated^ 

 hourly heights one of the integral component B hours coincides, 

 exactly with a component A hour. At the corresponding component 

 A hour, one component A day later, the component B hour will have 



increased by 24 ^~ component B hours. Rejecting a multiple of 

 24 hours, this becomes 24 ( — 1), so that at the end of one compo-- 



