CALCULATING MACHINES. Machines of this kind are designed
to produce arithmetical and other tables which shall be rigorously
correct. In navigation and the higher branches of astronomy the
use of tables is very great, and, being constructed by human heads
and hands, they all contain errors of greater or less magnitude.
The principle upon which these machines are constructed may be
described as follows: In the manner in which quantities are combined
in the common system of numeration, the value of each figure is
ten times greater than it would be if it occupied a position one
place to the right. Thus, in the number 1879, although 9 is greater
than 7, yet the 1 in this position represents a larger sum than
the 9, because it occupies a place to the left of the 9. The quantities
really expressed by the figures 1819 are 1,000, 800, 70, 9 ; but
in practice we omit the ciphers, and place the significant figures
side by side, preserving their proper position from the right
hand. If a wheel be constructed on whose axis is a pinion with
leaves or teeth, if these teeth work into another set of teeth
or cogs on the periphery of another wheel, and if the teeth on
the latter wheel are just ten times as numerous. as those on the
pinion, this system being made to revolve, the pinioned wheel
will revolve just ten times as fast as the other. This produces
a kind of analogy between the decimal notation and the working
of the wheels; for it takes 10 units to make up one figure or
unit in the second place in common numeration, and it requires
10 revolutions of the pinioned wheel to impart one revolution
to the larger wheel. This is the fundamental principle in calculating
machines. In such machines there are a number of dial-faces,
each marked with figures from 1 to 10; these dial-faces are fixed
upon wheels, the teeth of which work into the pinions of other
wheels, on which are similarly divided faces or disks, so that,
while one face indicates units, another indicates tens, a third
hundreds, and so on. These wheels and dial-faces may be differently
arranged in different machines, but the principle is the same
in all.
A calculating machine, called the difference engine, was constructed
by Mr. Babbage for the English government at an expense of £20,000,
to be used in preparing logarithmical and trigonometrical tables.
A valuable feature introduced into this machine is the power
of printing the tables as fast as it calculates them. Another
machine, called the analytical engine, was invented by the same
gentleman, of greater power than the first. This contains a hundred
variables, or numbers susceptible of changing, and each of these
numbers may consist of twenty-five figures. The distinctive characteristic
of this machine is the introduction into it of the principle which
Jacquard devised for regulating by means of punched cards, the
complicated patterns of brocaded stuff.
The machine in the Dudley Observatory, Albany, was invented
by G. and E. Scheutz, of Stockholm, Sweden, who sought to attain
the same ends that Mr. Babbage had attained, but with simpler
means. Their engine proceeds by the method of differences, calculating
to the 15th place of decimals, and stamping the eight left-hand
places in lead, so as to make a stereotype mould, from which plates
can be taken by either a stereotype or electrotype process, ready
for the printing-press. It can express numbers either decimally
or sexagesimally, and prints by the side of the table the corresponding
series of numbers or elements for which the table is calculated.
Fig. 600 represents a simple form of calculating machine
devised by Mr. George B. Grant. There is an upper cylinder, which
is turned by the crank, and which itself drives a smaller shaft
underneath. A slide, that can be set in eight different positions
on the cylinder, carries eight figured rings that can be set to
represent eight or any smaller number of decimal places. Each
turn of the crank adds the number set up on the rings to the number
represented on the ten recording wheels carried by the lower shaft.
The multiplication process will best be understood by an example.
To multiply 347 by 492, the three upper rings are set at 3, 4,
and 7, respectively. The cylinder is then turned twice to multiply
by the units figure of the multiplier. If now the slide is carried
along one notch, where each ring will act on the next higher recording
wheel, and turned 9 times, 347 will be multiplied by 90, and the
product at the same time will be added to the product already
scored. Another shift of the slide and four turns will complete
the operation, and show the result, 170724 = (347 x 2) + (347
x 90) + (347 x 400), upon the recording wheels. A half-turn of
the crank backward erases this result, bringing all the wheels
to 0, ready for the next operation.
Division is the reverse of multiplication. The dividend is
set up on the wheels, the divisor on the rings, and the quotient
records itself on the upper recording wheels. The machine of
the size illustrated will use numbers of eight or less figures,
and show the result in fall, if not over ten figures,
Your Comments Welcomed! Copyright
© 1995 Roger Corrie