34 MR. AIRY ON THE LAWS OF THE TIDES 



^= +45°, and divide by |' we obtain the expression for the mean of large tides. If we 



integrate from ^ = 45° to 0= 135°. and divide by ^ » we obtain the expression for the 



4 2 S^ 

 mean of small tides. The difference between these, which will be found to be S—^-rr^' 



is the same as the difference between the second and fifth columns in the table of p. 30, 

 if high water is under consideration, or as the difference between the third and sixth 

 columns, if low water is under consideration, or as the difference between the 2nd co- 

 lumn — 3rd, and 5th column —6th, if the range is considered. The second term of the 



4 TT 



formula may sometimes be omitted : and then we have -S= difference, and S = ^x 



difference, S being the solar effect in the elevation or range under consideration. If 

 we add this to the mean elevation, which is represented by A-j-M nearly, we shall 

 have A+M+S which is the absolute maximum ; and if we subtract it, we have 

 A+M— S, which is the absolute minimum. The same applies to range, with this 

 difference only, that the constant A will be eliminated in subtracting the heights at 

 low water from those at high water. 



S 

 In order to obtain the value of jttj we may remark that the difference of the two 



_S 2_S3 



M 3 M^ 

 means divided by half the sum is — f-o2\ » ^^^ ^^ ^® ^^^ ^^^^^ ^^ ^^^ easily find 



=-j=-§j ^-\-To\^) ( ' in which the last term is small. 



Neither of these expressions is perfectly correct, because they assume that the tidal 

 day is always of the same length. 



By means of these formulae, and the numbers on page 30, the following Table is 

 formed. 



