1822.] 
of computing any table by the aid of dif- 
ferences, whetlier they are positive or ne- 
gative, or of both kinds. With respect to 
the number of the order of the differences, 
the nature of the machinery did not in my 
own opinion, nor in that of a. skilful me- 
chanic whom I consulted, appear to be re- 
stricted to any very limited number; and 
I should venture to construct one with ten 
or a dozen orders with perfect.confidence. 
One remarkable property of this machine 
is, that the greater the number of differ- 
ences, the more the engine. will outstrip 
the most rapid ealculator.—By the appli- 
cation of certain parts of no. great degree 
of complexity, this may be converted into 
a machine for extracting the roots of equa- 
tions, and consequentiy the roots of num- 
bers ; and the extent of the approximation 
depends on the magnitude of the machine. 
—-Of a machine for multiplying any 
number of figures by avy number, I 
have several sketches; but it is not yet 
brought to that degree of perfection 
which I should wish to give it before it is 
to be executed. I have also certain prin- 
ciples by which, if it should be.desirable, a 
table of prime numbers might. be made, 
extending from 0 to 10 millions. Another 
machine, whose plans are much more ad- 
vanced than several of those just named, 
is one for constructing tables.which have 
no order of differences constant.—A vast 
variety of equations of finite differences 
may by its means be solved, and a variety 
of tables, which could be produced in suc- 
eessive parts by the first machine I have 
mentioned, could be calculated by the lat- 
ter one with a still less exertion of hnman 
thought. Another and very remarkable 
oint in the structure of this machine is, 
that it will calculate tables governed by 
laws which have not been hitherto shown 
to be explicitly determinable, or that it 
will solve equations for which analytical 
methods of solution have not yet been con- 
trived, Supposing these engines executed, 
there would yet be wanting other means 
to ensure the accuracy of the printed ta- 
bles to be produced by them. ‘the errors 
of the persons employed to copy the 
figures presented by the engines would 
first interfere with their correctness. ‘To 
remedy this evil, I have contrived means 
by which the machines themselves shall 
take from several boxes containing type, 
the numbers which they calculate, and 
place them side by side ; thus becoming at 
the same time a substitute for the compo- 
sitor and the computer: by which means 
all error in copying, as well as in printing, 
is removed.—There are, however, two 
sources of error which have not yet been 
guarded against. The ten boxes with- 
which the engine is provided contain each 
about three thousand types; any box hay- 
Moxruicy Mac. No $73. 
Report of Chemistry and Experimental Philosophy. 
205 
ing of course only those of one number in 
it. It may happen that the person em- 
ployed in filling these boxes shall acciden- 
tally place a wrong type in some of them ; 
as, for instance, the number 2 in the boxes 
which ought only to contain 7s. When 
these boxes are delivered to the superin- 
tendant of the engine, I have provided a 
simple and effectual means by which he 
shall in less than half an hour ascertain 
whether, amongst these 30,000 types, there 
be any individual misplaced or even in-* 
verted. The other cause of error to 
which I have alluded arises from the type 
falling out when the page has been set up : 
this I have rendered impossible, by means 
of asimilar kind.—To bring to perfection 
the various machinery which I have con- 
trived would require an expense, both of 
time and money, which can be known 
only to those who have themselves attempt- 
ed to execute mechanical inventions, Of 
the greater part of that which has been. 
mentioned, I have at present contented 
myself with sketches on paper, accompa- 
nied by short memorandums, by which I 
might at any time more fully develop the 
contrivances; and, where any new princi- 
ples are introduced, I have had models 
executed, in order to examine their ac- 
tions. For the purpose of demonstrating 
the practicability of these views, I have 
chosen the engine for differences, and have 
constructed one of them, which will pro- 
duce any tables whose second differences 
are constant. Its size is the same as that 
which I should propose for any more ex- 
tensive one of the same kind: the chief 
difference would be, that in one intendid 
for use there would be a greater repeti- 
tion of the same parts, in order to adapt it, 
to the calculation of a larger number of 
figures. Of the action of this engine, you 
have yourself had opportunities of judging, 
and I will only at present mention a few 
trials which have since been made by some 
scientific gentlemen, to whom it has been 
shown, in order to determine the rapidity 
with which it cateulates, The computed 
table is preseuted to the eye at two oppo- 
site sides of the machine ; and, a friend 
having undertaken to write down the num- 
bers as ‘they appeared, it proceeded to 
make a table from the formula »*+.24 41. 
In the earlier numbers my friend, in -wri- 
ting quickly, rather more than kept pace 
_With the engine; bat, as soon as four 
figures were required, the machine was at, 
least equal in speed to the writer. In ane- 
ther trial it was found that thirty numbers 
of the same table were calculated in two 
Minufes and thirty seconds; as these con- 
tained eighty two figures, the engine pro-. 
duced thirty-three every minute. In 
another trial it produced figures at the 
rate of forty-four im a minute. As the 
Mm machine 
