312 Prof. G. H. Darwin. [June 19, 



(b.) Times and Angles. 



The times of H.W., numbered consecutively, are entered in a table, 

 as shown on p. 313. Since O h astronomical time is the epoch, the P.M. 

 tides will come in the half days which are numbered with integrals, 

 and the A.M. tides in the half days which fall between the integral 

 numbers. 



From time to time there will be a half day with no H.W. ; this row 

 in the table should be left blank, but there happens to be no such row 

 in the sample shown. A computation form for times and angles might 

 be printed, for, although the exigencies of the printer have not allowed 

 the entries to be equally spaced in the sample below, yet the computa- 

 tion form might be printed with equal spaces, and the dividing lines 

 are to be filled in by hand. 



The L.W. table is similar. 



Both H. and L.W. are to be divided into quarter-lunar-anomalistic 

 and quarter-lunar periods, and semi-lunations, according to the rules 

 given in E. These partitions and the numbering of the entries could 

 not be printed, because of the occasional blank rows. 



The formation of -| V m and of V f , by means of Table A and the rule 

 following it, is obvious. In the subtractions and additions under the 

 headings \V m F, and i^F OT + I 7 *, 360 is added or subtracted where 

 necessary. V m is found by doubling \V m . 



(c.) The Heights. 



The H.W. heights are written in columns (with the same blanks as 

 in the table of times and angles), and are so arranged, either on 

 strips of paper, or by folding the paper, that the heights may be 

 pinned to the times, bringing each height opposite to an angle on the 

 same row with the time corresponding to that height. The heights 

 will on one occasion have to be pinned opposite the V m column, on a 

 second occasion opposite the V s column, and on a third occasion opposite 

 the \V m column. 



The L.W. heights are written in similar columns, but the minus 

 signs should be omitted. 



It is well to divide the columns, or to put fiducial marks in the 

 table for easy verification of the proper allocation of the heights with 

 the times. Any marks suffice, but the division into quarter-anoma- 

 listic periods, as shown below, seems to be as good as any other. 



If it is proposed to evaluate the annual and semi-annual tides, it is 

 necessary to carry on the heights beyond the times by 3 (or 5) H.W. 

 and 3 (or 5) L.W., and to partition them into months. The mean 

 for each month is evaluated, and if the successive quarters of the 

 year are referred to different data, the mean monthly heights must 

 all be referred to a common datum. This process is not carried out 



