S80 Mr Babbage Machinery for calculating Tables. 
be reduced to twelve. This number might, however, be consi- 
derably diminished ; because when an engine is used, the inter- 
vals between the differences calculated by the second section may 
be greatly enlarged. In the tables of logarithms, M. Prony 
caused the differences to be calculated at intervals of SOO, in or- 
der to save the labour of the third section ; but as that would 
now devolve on machinery, which would scarcely move the slow- 
er for its additional burthen, the intervals might properly be en- 
larged to three or four times that quantity. This would cause 
a considerable diminution in the labour of the second section. 
If, to this diminution of mental labour we add that which arises 
from the whole work of the compositor being executed by the 
machine, and the total suppression of that most annoying of all 
literary labour, the correction of the errors of the press, I think 
I am justified in presuming, that if engines were made purposely 
for this object, and were afterwards useless, the tables could be 
produced at a much cheaper rate : and of their superior accura- 
cy there could be no doubt. Such engines would, however, be 
far from useless : containing within themselves the power of gene- 
rating to an almost unlimited extent, tables whose accuracy would 
be unrivalled, at an expence comparatively moderate, they would 
become active agents in reducing the abstract inquiries of geo- 
metry to a form and an arrangement adapted to the ordinary 
purposes of human society, 
r should be unwilling to terminate this letter, without noticing 
another class of tables of the greatest importance, almost the 
whole of which are capable of being calculated by the method of 
differences. I refer to all astronomical tables for determining 
the positions of the sun or planets. It is scarcely necessary to ob- 
serve, that the constituent parts of these are of the form a sin 
where « is a constant quantity, and 0 is what is usually called 
the argument. Viewed in this light, they differ but little from a 
table of sines, and like it may be computed by the method of 
differences.” 
Having thus given our readers a succinct description of the 
nature and objects of Mr Babbage’s arithmetical machinery, we 
have only to express our hope that the British government, or 
some of those Institutions which it so liberally supports, will af- 
ford Mr Babbage the means of constructing a large engine, and 
