an4 Printing Mathematical Tables. ^75 
cliinery, which, at the same time, made the calculations and 
composed, with a proper type, the tables when computed. At 
the commencement, of course, of these operations, certain preli- 
minary calculations must be made ; and, at intervals, the machi- 
nery must be set to these numbers ; but, in some cases, when 
once set, the machine will continue working to the end of the 
tables. 
In these contrivances, there are two distinct parts, viz. mie^ by 
which the tables are computed^ and the other j by which they are 
composed ; but, as the actual execution of such machinery re- 
quires a great expence, both of time and money, Mr Babbage 
has contented himself with sketches on paper, accompanied by 
short memoranda, by which his contrivances may be at any time 
more fully developed ; and, when any new principles have been 
introduced, he has examined their actions by models executed 
on purpose. In order, however, to prove the practicability of 
these views, he has finished a small engine, by which the calcu- 
lations are accomplished, and which has actually computed the 
following table, in which the second differences are constant. 
Table computed by Mr Babbage^ s Arithmetical Engine^ from 
the Formula a? -f 41. 
41 
131 
383 
797 
1373 
43 
151 
421 
853 
1447 
4T 
173 
461 
911 
1523 
53 
197 
583 
971 
1601 
61 
2f3 
547 
1033 
1681 
71 
251 
593 
1097 
1763 
83 
281 
641 
1163 
1847 
91^ 
313 
691 
1231 
1933 
113 
347 
743 
1301 
2021 
The figures, as they are calculated by the machine, are not 
exhibited to the eye, as in sliding-rules, and similar methods, but 
are actually presented to the eye on two opposite sides of the 
machine ; the number 593, for example, appearing in figures be- 
fore the person employed in copying. When the machine was 
engaged in calculating the preceding table, a friend of the in- 
ventor undertook to write down the numbers as they appeared. 
In the earlier numbers, the copyist, in- consequence of writing 
quickly, rather more than kept pace with the engine, but as 
soon as four figures vrere required, the machine was at least 
