of Edinburgh, Session 1880-81. 
3 
Thus, let it be proposed to construct a table of the Sun’s mean 
daily motion in longitude, true to the nearest hundredth part of a 
second of the modern division. Taking the length of the equinoctial 
year as 365*242217 mean solar days, the motion in one day is 
r 09' 51" 63"' 6513585 or, as is far within the accuracy of our 
knowledge, 
1‘ 09' 51" 63"' 65136. 
We should then write this number on the lower edge of a card, 
and make the successive additions as under : — 
1 
1 
09 
51 
63 
65136 
2 
2 
19 
03 
27 
30272 
3 
3 
28 
54 
90 
95408 
4 
4 
38 
06 
54 
60544 
5 
5 
47 
58 
18 
25680 
6 
6 
57 
09 
81 
90816 
7 
7 
66 
61 
45 
55952 
8 
8 
76 
13 
09 
21088 
9 
9 
85 
64 
72 
86224 
10 
10 
95 
16 
36 
51360 
separating the redundant figures by a line, and afterwards making 
the requisite augmentations. 
In order to lessen the labour of such work, I have for many 
years used two simple artifices, and find among my papers that 
these were applied in 1845 to the formation of tables of the 
equivalent values of solar and sidereal time. 
The first of these artifices is to augment the initial value by 
*50000 ; by this means the requisite augmentations are made 
throughout, and we have only to reject the surplus figures; or, if 
these have been written on a slip of paper placed alongside, to 
remove that slip : — thus 
days. 
0 
c 
0 
00 
// 
00 
/// 
00 
50000 
1 
1 
09 
51 
64 
15136 
2 
2 
19 
03 
27 
80272 
3 
3 
28 
54 
91 
45408 
4 
4 
38 
06 
55 
10544 
5 
5 
47 
58 
18 
75680 
6 
6 
57 
09 
82 
40816 
7 
7 
66 
61 
46 
05952 
8 
8 
76 
13 
09 
71088 
9 
9 
85 
64 
73 
36224 
10 
10 
95 
16 
37 
01360 
