135 



RESIDUALS 



The time in lunar hours after a lunar transit is entered in column (1) 

 and the primary current corrected by i, table X, in column (2). 

 Column (3) shows the increase in the velocity during the preceding 

 interval, the entry for hour being repeated from the twelfth hour. 

 The values of Av, column (4) are the means of the entries for the given 

 and the following half hours, and are consequently the average of the 

 increments in v during the preceding and following intervals. The 

 tidal elevations, yo, at the initial end of the section, station 180 + 30, 

 taken from the equation of the tide at this station, paragraph 240, 

 are entered in column (5), and those at station 225 in column (6). 

 The tidal elevation, y, in the section, column (7) is the average of the 

 entries in columns (5) and (6). The corresponding values of F, from 

 the diagram, are entered in column (8). 



The surface heads, hs, column (9) are the algebraic differences, 

 yi — yo, from columns (6) and (5). The entries in column (10) are the 

 products of Av, column (4) times the constant 6 = 0.0746. The slide 

 rule affords satisfactory accuracy for these and the subsequent com- 

 putations. The entries in column (11) are obtained by multiplying 

 v^, from column (2) by F, column (8) and have the algebraic sign of v. 

 The residuals, R, column (12) are then the algebraic sum of the entries 

 in columns (9), (10), and (11), with the sign reversed; the sums of the 

 entries in columns (9), (10), (11), and (12) being zero. 



The computation for hours 3.5 to 9.5 is not shown, but is carried 

 out by the same procedure. In the example chosen, the tides at 

 the ends of the section, and consequently the surface head, have in 

 fact a simple harmonic fluctuation, but the computation would be in 

 the same form if they had any other repeating fluctuation. The 

 velocity head is omitted. If computed, it would be entered in an 

 additional column and included in the derivation of R. 



