348 Prof. G. H. Darwin. On an Apparatus for [Dec. 15, 



Mean solar Mean lunar 



time. time - 



Od 12* = O d 12 h 



1 12 = 1 H 



2 12 2 10 



3 12 = 39 



4 12 = 48 



5 12 = 58 



6 12 = 67 



7 12 = 76 

 &c. &c. 



The successive 12 h of m.s. time will march retrogressively through 

 all the 24 hours of m. lunar time. 



Now, if starting from strip 0, we push strip 1 one division to the 

 left, strip 2 two divisions to the left, and so on, the entries on the 

 strips will be arranged in columns of approximately lunar time. 



The rule for this arrangement is given by marks on a sheet of 

 paper 18 in. broad ; these marks consist of parallel numbered steps 

 or zigzags showing where the ends of each strip are to be placed so 

 as to bring the hourly values into their proper places. 



At the end of a lunation mean solar time has gained a whole day 

 over mean lunar time and the 12 h solar again agrees with the 12 h 

 lunar. On the guide sheet we see that the zigzag which takes its 

 origin at the left end of strip has descended diagonally from right 

 to lef b until it has reached the left margin of the paper, and a new 

 zigzag then begins on the right margin. 



When the strips are pinned out following tlie zigzags on the sheet 

 marked M, the entries are arranged; in 4>& columns, but the number of 

 entries in each column is different. The 48 columns are to be 



regarded as appertaining to O h ,.l" v .. . . .,22 h ,.23", O h , l h , , 22 h , 23 h . 



Thus, the number of entries in the left-hand column of any hour 

 added to the number of entries, in the right-Jmnd column of the same 

 hour is, in each case, 74. The 48 incomplete columns may, in fact, 

 be regarded as 24 complete ones. 



The 24 complete columns are -then summed ; the 24 sums would, if 

 divided by the total number of strips,, give the 24 mean lunar hourly 

 heights. The harmonic analysis of these sums gives certain constants, 

 which, when divided by the, n,umber of strips, are the required tidal 

 constants. It must be remarked, however, that, as the incidence of 

 the entries is not exact in lunar time, investigation must be made of 

 the corrections arising out of this inexactness. 



The explanation of the guide sheet for lunar time will serve, mutatis 

 mutandis, for all the others. 



The zigzags have to be placed so as to bring the columns into exact 

 alignment, and winters' types provide all the accuracy requisite. 



