the calculating machine of blaise pascal

PHILIPS
102
TECHNICAL
British
THE
CALCULATING
VOLUME
REVIEW
MACHINE
Crown
Copyright,
OF BLAISE
Science
Museum,
24
London
PASCAL
681.14(091)
The digital electronic computer PASCAL in
Philips Computing Centre has been given this name
in honour of the French mathematician and philosopher Blaise Pascal I), who in 1642, at the age of
eighteen, designed a calculating machine at Rouen.
His obj eet with this machine, which became known
as the Pascaline, was to ease the burden on his
father who, as a tax official, had a great deal of
figure work to do. Although in the later years of his
short life (Pascal died in 1662, almost exactly three
hundred years ago) he was mainly concerned with
other matters, he nevertheless had more than 50
models made of his machine 2), each being an improvement on the preceding ones. In 1645 he presented one to Chancellor Pierre Séguier, through whose
good offices he obtained in 1649 a royal privilege
on his invention; in 1647 he showed one to Descartes; in 1652 he finally arrived at a form that
satisfied him; he sent one machine to Queen Christin a of Sweden, and another he demonstrated personally to a distinguished gathering in Paris successfully, to judge from the poetic effusion of a
contemporary 3).
1) W. Nijenhuis, The PASCAL,
2)
a fast digital electronic computer
for the Philips Computing Centre, Philips tech.
Rev. 23, 1-18, 1961/62 (No. 1). -It should be mentioned
that according to some, the name is an acronym derived
from Philips Automatic Sequence CALculator.
P. Humbert, L'oeuvre scientifique de Blaise Pascal, Albin
Michel, Paris 1947, p. 56.
One model of the Pascaline dating from 1652
has been well preserved and is to be seen at the
Conservatoire des Arts et Métiers, Paris. The title
photograph is of a replica in the Science Museum
in London. The Paris Conservatoire has three
other machines; all four bear the arms of the Pascal
family (see fis. 1).
Various mechanical aids to arithmetical work,
such as the time-honoured abacus and the graduated rods invented by Napier in 1617 (Napier's
"bones"), were already in use before Pascal's machine. But Pascal went an essential step further, in
that his machine contained a discontinuous mech-
3)
Muse historique, Loret, of 14th April,
quoted in footnote 2), page 57).
1652 (see the book
"Je me rencontrai l'autre jour
Dedans le petit Luxembourg,
Au que! beau lieu que Dieu bënie
Se trouva grande compagnie,
Tant duchesses que cordons bleus,
Pour voir les effets merveilleux
D'un ouvrage d'arithmétique,
Autrement
de mathématique,
Oil, par un talent sans égal
Un auteur qn'on nornme Pascal,
Fit voir une spéculative
Si claire et si persuasive,
Touchant Ie calcul et Ie jet,
Qu'on admira Ie grand projet.
11 fit encor sur les fontaines
Des démonstrations
si pleines
D'esprit et de subtilité,
Que Pon vit hien, en véri té,
Qu'un très beau génie il possède
Et qu'on le traita d'Archimède."
1962/63, No. 4/5
CALCULATING
MACHINE
anism - the "sautoir" - for automatically carrying over tens, etc., in adding operations (fip,. 2).
This is the basis of all digital techniques and the
logical consequence of the digital or positional
system of writing numbers.
Pascal's contemporaries were aware of the potentialities of his idea. Speaking of the "machine
arithmétique"
his sister Gilberte expressed it
thus 4): "This accomplishment has been regarded
as something new in nature, to have reduced to a
machine a science that belongs entirely to the mind,
and to have found the means of performing all operations with complete certainty, without the need
for reasoning". People felt a kind of uneasiness or
amazement about the Pascaline, such as many of
4)
Pascal, Pensées
Hachette, Paris
et Opuscules,
1945 (p. 10).
éd.
par
L. Brunschvicg,
OF BLAISE
PASCAL
103
us feel today about automation, which seems capable, through the use of electronic computers, of
taking over our whole function of logical thought.
Gilberte Pascal, incidentally,
went on to say:
"This effort tired him very much, not because of
the brainwork or of the mechanism, which he found
without any trouble, but because of the difficulty
of making the workers understand all these things".
Indeed one may assume that the realization of Pascal's invention was seriously hampered by the fact
that the schooling and probably the equipment of
the instrument makers at that time were inadequate for making such intricate devices with the
necessary precision. No model of the Pascaline seems
to have worked for long without faults, and the
manufacture of calculating machines on a commercial
scale had to await the perfecting of the mechanism
and a general improvement in the standard of
engineering.
a
b
Photo
Fig. 1. One of the four models of Pascal's calculating machine
preserved in the Conservatoire
des Arts et Métiers, Paris.
This model, like various others, was designed for the addition
of money up to 1 million livres. For this purpose six decimal
places are available, plus a seventh place with 20 units for
the sous and an eighth with 12 units for the deniers. (The
same division, into pounds, shillings and pence, has persisted
in Great Britain up to the present day.) The divisions can
clearly be seen, on the removed cover (b), on the eight selector
discs which serve for setting the digits to an amount
to
be added.
It is worth noting that even the earliest calculating machines
demonstrate
in this way that digital compnting is not tied
to the decimal system. The binary system 1) employed in
electronic compnters is just another
variant.
Conservatoire
des A rts et Métiers,
Paris
The machine is operated by inserting a peg in each of the
eight selector dials and turning the dial through successive
stops. The number thus set, and the result of the addition
when the next number is set, appear in the sight holes in the
cover, below which rotate the figure wheels seen in (a). The
carry-over
of the tens (and the twelves and twenties) is
auurmatic,
Subtraction is done by pushing down the bar above the sight
holes which carries the eight "register" wheels, thus exposing
the top halves of the sight holes, in which there now appear
the figures in the reverse sequence (the complements respectively of 10, 12 or 20). A number is set and subtracted by turning the selector dial in the same direction as for addition. Pascal devised this method because his automatic carrying device,
the "sautoir",
worked only in one direction (see fig. 2).
104
PHILlPS
TECHNICAL
}Y./I.
Photo
Science
VOLUME
REVIEW
Museum,
London
Fig. 2. Mechanism for automatic carry-over in Pascal's calculating machine.
The drawing is reproduced from the Diderot and d'Alembert Encyclopedia,
Paris 1752-1777. We have added the letters printed in red, for denoting
components. The mechanism (the "sautoir")
works roughly as follows. The
drawing in the middle shows all components for one digit; the selector dial
is seen on the cover, at the right, and the figure wheel. or drum is on the left,
under the cover. The movement of the dial is transmitted by two pairs of gear
wheels (pin wheels) via the shaft A to the figure wheel. The middle pin wheel
B on this shaft serves for carrying over the tens. In the top drawing can be
seen the pin wheel Bl for one digit and the pin wheel B2 for the next higher
digit. Towards the end of a full revolution of BI the two pins Cl engage the
two teeth of the doubly-bent lever Dl turning about the spindle A2 and lift
the lever. When Bl has completed a full revolution (i.e. completing a ten)
the pins Cl release the teeth of DI' tbe lever drops and a pawl El on the lever
pushes the pin-wheel B2 one step further. This is made clear by the bottom
drawing, which shows the components from the other side. The arm of pawl
El hinges on the spindle FI and is lifted by the leaf spring Gp so that when
Dl drops, the pawl can engage a pin on B2 whereas during the lifting of Dl
(and also when B2 is turned independently)
the pins are free to slide off along
the arm of El' A catch H2 prevents B2 from being dragged in the wrong
direction when Dl is lifted.
24
Some stages in this further development of calculating
machines may
usefully be mentioned. In Britain, in
1666, Morland
built
a calculating
machine (two examples of which are
preserved in London) which, compared
with the Pascaline, represented a step
backwards. The machine worked on
the same principle - the adding of
figures by successive rotations of a kind
of selector dial through discrete angles but there was no automatic carrying
device. In 1672 Leibniz began work in
Hanover, and later In Paris, on a
calculating machine based on a new
idea, the "stepped gear", which could
also perform multiplication and division.
He worked on this for many years helped
by various instrument makers. It was
not until 1694.that his first machine was
completed, and even then seems never
to have been reliable in operation. This
machine is still at Hanover, and a
replica is in the Deutsches Museum in
Munich. In Padua in 1709 Poleni utilized
the same principle
as Leibniz and
a
novel,
highly effective
conceived
mechanism for the automatic carryover - virtually the same construction
is still used in mechanical counting
mechanisms today, such as mileometers,
gas and electricity meters, etc. A wooden
model of his machine so disappointed
Poleni, however, that he destroyed it.
A machine built in 1727 by Antonius
Braun fared better. Embodying a device
similar to that used by Leibniz and
Poleni 5), this machine (jig. 3) was put
together with great care and precision
- Braun was apparently both inventor
and craftsman and gives the impression of having worked well although
it does not appear to have been easy to
operate. After numerous other intermediate stages the first calculating
machine to be manufactured on a commercial scale appeared in 1820; this
machine was designed by Charles Xavier
Thomas of Colmar and remained on the
market, with few modifications, for
almost 100 years.
5)
J. Nagler, Beschreibung
des Antonius Braun,
geschichte,
No. 22,
Vienna 1960.
der Rechenmaschine
Blätter
für Technikpp. 81-87, Springer,
1962/63, No. 4/5
CALCULATING
MACHINE
OF BLAISE
PASCAL
105
Fig. 3. Calculating machine made
by Antonius
Braun in 1727. It
was intended as an aid to surveying
work, and could add, subtract,
multiply
and divide. Whether it
worked satisfactorily is not known.
The photo shows the machine without the cylindrical side panel that
protects
the
mechanism
from
dust. The top plate, with the setting levers and figure dials, bears
a Latin inscription
in which the
maker ("Opticus
Et Mathematicus") humbly dedicates the instrument to the Emperor Charles VI.
The instrument
can be seen in
the Technisches
Museum für Industrie und Gewerbe at Vienna 5).
Photo
Fig. 4. Sketch of W. Schickard's calculating machine, taken
from his letter to Kepler of 25.2.1624. The text referring to
the machine reads (translated from the Latin): "I shall outline the arithmetic
apparatns
in more detail another time;
being in haste the following must suffice: aaa are the top ends
of vertical cylinders, on which are written the multiplications
of the figures, and those [multiplications]
which are necessary
can be seen through the sliding windows bbb. Fixed on the
inside to ddd are gear wheels with 10 teeth, that mesh with
one another such that if any wheel on the right turns round
ten times, the wheel to the left of it turns round once; or if
the first-mentioned
wheel makes a hundred turns, the third
wheel turns once, etc. To wit, [they all do this]
in the same direction, for which purpose
an
~
~
identical intermediate
wheel It was necessary.
??i:
Any gi.ve~ inte~med~ate wheel. s.ets all to .the
\V
left of It 111 motion, In the requisrte proportion;
but none to the right of it, which called for
special measures.
The number on these wheels is visible
through the holes eee in the centre ledge. Finally, the letters
e on the bottom ledge denote rotary knobs and the letters f
are again holes through which figures used when working
can he seen."
~ D
Teelmisehes
Museum,
Vicnna
This account of the earliest history of the calculating machine cannot be closed without mentioning that a few years ago Hammer and v.
Freytag-Löringhoff 6) discovered a predecessor of
the Pascaline: the hebraist, astronomer and mathematician Wilhelm Schickard at Tübingen had already constructed in 1623, i.e. 20 years before Pascal,
a calculating machine with automatic carry-over
of tens which could apparently add and subtract
(even alternately, which was not possible with the
Pascaline) and which, moreover, had a device that
facilitated
multiplication
and division. In two
letters to Kepler, dated 20.9.1623 and 25.2.1624,
Schickard reports and describes his invention
(fig. 4), and on the basis of this description and a
sketch found in the papers Schickard left behind,
a reconstruction has been made of the machine.
Unlike Pascal however, Schickard evidently did
not arouse the interest of his contemporaries in his
machine. A second, improved model which he had
designed was destroyed by fire before completion,
and probably also because of the war at the time
and his death soon after (he and his whole family
died of the plague in 1635), his invention was immediately forgotten.
S. GRADSTEIN
6) B. v. Freytag-Löringhoff,
*).
Wiederentdeckung
und Rekonstruktion der ältesten neuzeitlichen Rechenmaschine,
VDINachrichten 14, No. 39, 21st December 1960 (p. 4).
*) Philips Research Laboratories,
Eindhoven.