1890.] Harmonic Analysis of Tidal Observations. 303 



It would be advantageous to extend the table up to 90 days, but it 

 can be used as it is for periods greater than 30 days by the division of 

 the time into sets of 30 days. In the second period of 30 days 5'7 

 must be subtracted from the tabular entry, for the third period 11'4, 

 and so on.* 



For example: Find $V m for 78 d ll h 23 m . The day is 18| of 

 the third 30, and the tabular entry for 18| d ll h is 113'9, and sub- 

 tracting 11'4 we have 102'5; 23 m gives 5'6, so that V m = 108'l. 

 The correct result is 107'99, and it is obvious that an error of 0'l 

 may easily be incurred by the use of the table. 



The row for day ^ is given because it may be necessary to use 

 one tide before epoch ; this row is used in the example below. 



* Observe that the decimals run thus, '0, '5, '0, &c., then '4, '9, '4, &c., then 

 '8, "3, '8, &c., and so on. The first entry in which the sequence alters I call a 

 " change." The incidence of " changes " may be found thus : y a is 14| '00795 ; 

 take Crelle's multiplication table for 795, and note where the last digit but three, 

 having been 4, becomes 5 ; I say that this is a " change." For example, 559 x 795 

 = 444405, and 560 x 795 = 445200 ; then a change occurs at the 560 th hour, or at 

 the (12 x 46 + 8) tt hour, or at 23 d 8 h . If the table be continued to 60 and 90 days, 

 &c., by subtracting 5'7, 11'4, &c., the changes will fall a little wrong, but they may 

 easily be corrected by means of Crelle's table, as here shown. (Added Aug. 2, 1890.) 



