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



selected for omission under the rules of 7, may be hidden by a sheet 

 of paper when the summations are being made. 



The additions of S, M, MS may be verified by proving that the 

 grand total of all the numbers (inclusive of omitted strips in S) 

 written in each of the sets of 74 days is the same in whatever way 

 they are arranged. Thus, the sum of the 48 columns should be equal 

 to the sum of the daily sums. An incomplete verification in the other 

 arrangements, when only half the columns are summed, is found by 

 showing that the sum of all the hourly sums of each 74 days is nearly 

 equal to half the grand total of all the numbers written in that period 

 of 74 days. 



When the guide sheets become worn with many pin pricks they 

 may easily be patched with adhesive paper. There seems no reason 

 why this patching should not go on almost indefinitely.* 



* It is possible that it may be desired to evaluate the tides OO and 2N, for which na 

 guide sheets are provided. I therefore, give instructions for the preparation of guide 

 sheets for these cases. They will be understood by any one who has the set of 

 guide sheets before hhn. With the instructions given below, the computer might 

 indeed set up the strips without a guide-sheet. 



I describe the staircase as descending from left to right or from right to left, and 



1 define a short step as being one space down and one space to the left or right, as 

 the case may be, and a long step as one space down and two to the left or right, as 

 the case may be. When I say, for example, that a short follows 2, I mean that 



2 to 3 is a short step. The first mark on each sheet is specified by its incidence wi- 

 the row of hours at the top. 



OO ; descending from left to right. 



The sequence is long several times repeated and then short. 



Red ; between O h and l h ; shorts follow 2, 7, 13, 19, 24, 30, 36, 41, 47, 53, 58 y 



64, 69. 

 Yellow ; between 15 h and 16 h ; shorts follow 1, 7, 12, 18, 24, 29, 35, 41, 46, 52, 



57, 63, 69. 

 Green ; between 6 h and 7 h j shorts follow 0, 6, 12, 17, 23, 29, 34, 40, 45, 51, 57,. 



62, 68. 

 Blue; between 21 1 ' and 22 h ; shorts follow 0, 5, 11, 17, 22, 28, 33. 39, 45, 50, 



56, 62, 67. 

 Violet; between ll h and 12 h ; shorts follow 5, 10, 16 21 27 33 38 44, 50,55 V 



61, 67, 72. 



The last strip used for a year is 72. 

 2N : descending from right to left. 



The sequence is long, long, short, long, long, short, and at intervals three long* 

 and a short. 



Eed ; between 22 h and 23 h ; shorts follow 1,4,., . , 16 ; 20 23 . . , 35 39 



42,. ...,57; 61, 64, .,..,70. 

 Yellow ; between 18 h and 19 h ; shorts follow 2 ; 6, 9 . 21 25 28 40 - 



44,47 ,59; 63, 60, ....,72. 



Green ; between 13 h and 14 h ; shorts follow 1, 4 : 8, 11, . 26-30 33 45 



49, 52,.. ..,64; 68,71. 

 Blue; between 8" and9 h ; shorts follow 0, 3, 6, 9 ; 13 16 28- 32 



35,. ...,50; 54, 57, ....,69; 73. 



