How did Men Learn to Count?
Historians tell us that man was able to count long before he was able to
write. Of course, he could not count very far, but it was enough for his
needs at that time. He had no money and very few possessions of any
kind, so that he did not have much occasion to use arithmetic.
It was fairly simple for prehistoric men to distinguish one from two,
and to distinguish a few from a great number, but it was more difficult
for him to learn to think of a definite number of objects between these
extremes. Those who have studied the evolution of figures say that man
found it hard to think of a number of objects without using a mark or a
finger or something to stand for each object. That is how the first
method of counting came into use.
Because man had ten fingers and thumbs, he learned to count in tens.
When he had counted ten, he could make a mark to remind him of the fact,
and then count them over again. Some of the early races learned to
designate units from tens and tens from hundreds by working their
fingers in various ways. Other peoples also made use of their toes in
counting, so that they could count up to twenty without getting
bothered.
Cantor, the historian, tells of a South African tribe which employed an
unusual system of finger counting. Three men sat together facing a
fourth who did the counting. Each of the three held up his fingers for
the fourth man to count. The first man’s ten fingers and thumbs
represented units; the second man represented tens, and the third
hundreds. By this means, it was possible to count up to 999.
Who Invented the First Adding Machine?
Early cuneiform inscriptions, made about 2200 B. C., show that the
Babylonians had developed a fairly extensive system of figuring. This
was in the days of the patriarch Abraham. When men’s minds were
overtaxed with the strain of counting into the hundreds and thousands,
the Babylonians invented the first adding machine, a “pebble board,” a
ruled surface on which pebbles were shifted about to represent different
values.
The next adding and calculating machine was an evolution from the digits
of the human hand and is known as the abacus in China, and the soroban
in Japan.
The abacus may be defined as an arrangement of movable beads which slip
along fixed rods, indicating by their arrangement some definite
numerical quantity. Its most familiar form is in a boxlike arrangement,
divided longitudinally by a narrow ridge of two compartments, one of
which is roughly some three times larger than the other. Cylindrical
rods placed at equal intervals apart pass through the framework and are
fixed firmly into the sides. On these rods the counters are beaded. Each
counter slides along the rod easily and on each rod there are six tamas
or beads. Five of these slide on the longest segment of the rod and the
remaining one on the shorter. Addition, subtraction, multiplication,
division, and even square and cube root can be performed on the abacus,
and in the hands of a skilled operator considerable speed can be
obtained.
[Illustration: FINGER COUNTING WAS COMMON AMONG EARLIER PEOPLES, AND WAS
BROUGHT TO A FAIR DEGREE OF EFFICIENCY BY SOUTH AFRICANS
_Courtesy of the Burroughs Adding Machine Company._]
[Illustration: THE “ABACUS” WAS ONE OF THE EARLIEST AIDS TO CALCULATION
It is still used extensively in China, and occasionally will be found in
Chinese laundries in the United States.
_Courtesy of the Burroughs Adding Machine Company._]
The Oriental tradesman does not deign to perplex himself by a process of
mental arithmetic; he seizes his abacus, prepares it by a tilt, makes a
few rapid, clicking movements and his calculations are completed. We
always look with some slight contempt upon this method of calculation,
but a little experience and investigation would tend to transform this
contempt into admiration, for it may be safely asserted that even the
simplest of all arithmetical operations, the abacus, possesses
distinctive advantages over the mental or figuring process. In
competition in simple addition between a “lightning calculator” and an
ordinary Japanese small tradesman, the Japanese would easily win the
contest.
Blaise Pascal, the wonderful Frenchman, who discovered the theorem in
conic sections, or Pascal’s hexogram, was not only one of the foremost
mathematicians of his day but also excelled in mechanics; when he was
nineteen years old he produced the first machine for the carrying of
tens and the first arithmetical machine, as we know it, was invented by
him about 1641. This was the first calculating machine made with dials.
The same principle, that of using discs with figures on their
peripheries, is employed in present-day calculating machines. Among
these are numbering machines of all kinds, speedometers, cyclometers and
counters used on printing presses.
[Illustration: A MODERN BOOKKEEPING MACHINE, USED FOR LEDGER POSTING AND
STATEMENT MAKING
It has seventeen “banks” or rows of keys, is electrically operated, and
automatically adds, subtracts, and computes balances.
_Courtesy of the Burroughs Adding Machine Company._]
Who Discovered the Slide Rule Principle?
It was early in the seventeenth century that Napier, a native of Naples,
invented the first actual mechanical means of calculating. He arranged
strips of bone, on which were figures, so that they could be brought
into various fixed combinations. The instrument was called “Napier’s
rod” or “Napier’s bones.” It was the beginning of the slide rule, which
has been found of invaluable aid to accountants and engineers.
One trouble with all these contrivances was that, although they aided
man to figure, they offered no means of making a record of the work. The
man who used these machines had no way of checking his work to know if
it was right unless he did it all over again.
The first machine to perform multiplication by means of successive
additions was invented by Leibnitz in the year 1671 and completed in
1694. It employed the principle of the “stepped reckoner.” This model
was kept first at Göttingen and afterward at Hanover, but it did not act
efficiently, as the gears were not cut with sufficient accuracy. This
was long before the days of accurate machine tools.
The first satisfactory calculating machine of this nature was that of
C. X. Thomas, which was brought out about 1820. It is usually called the
Thomas de Colmar Arithmometer. This Thomas type of machine, which is
commonly known as the beveled gear type, is still in use today in modern
business.
The “Difference Engine.”
In the year 1822 a very ambitious project was conceived by Charles
Babbage. He commenced to construct an automatic calculating machine,
which he called a “difference engine.” The work was continued during
the following twenty years, the English government contributing about
$85,000 to defray its cost. Babbage himself spent a further sum of about
$30,000. At the end of that time the construction of the engine, though
nearly finished, was unfortunately abandoned, owing to some
misunderstanding with the government. A portion of this engine is
exhibited in South Kensington Museum, London, along with other examples
of Babbage’s work. If the engine had been finished it would have
contained seven columns of wheels, twenty wheels in each column, and
also a contrivance for stereotyping the tables calculated by it. It was
intended to perform the most extended calculations required in astronomy
and navigation, and to stamp a record of its work into plates of copper
or other material.
[Illustration: CHARLES BABBAGE’S “ENGINE OF DIFFERENCES” WAS THE FIRST
ADDING MACHINE INVENTED WHICH WAS DESIGNED TO PRINT A RECORD OF ITS
WORK, BUT IT WAS NOT A SUCCESS
_Courtesy of the Burroughs Adding Machine Company._]
Babbage began to design his “analytical engine” in 1833 and he put
together a small portion of it shortly before his death in 1871. This
engine was to be capable of evaluating any algebraic formula. The
formula it is desired to evaluate would be communicated to the engine by
two sets of perforated cards similar to those used in the Jacquard loom.
These cards would cause the engine automatically to operate on the
numerical data placed in it, in such a way as to produce the correct
result. Notwithstanding its simple action, its structure is complicated
by a large amount of adding mechanism. A complete set of adding wheels
with carrying gear being required for the tabular number, and every
order of difference except the highest order.
After Babbage, there was much experimenting done by inventors to produce
a real adding and listing machine. Also inspired by Babbage’s work
Scheutz of Stockholm made a “difference engine,” which was exhibited in
England in 1864, and subsequently acquired for Dudley Observatory,
Albany, N. Y. Scheutz’s engine had mechanism for calculating with four
orders of differences of sixteen figures each.
As far as we know the first patent in this country issued by the patent
office for a calculating machine was to O. L. Castle of Alton, Illinois,
in 1850. It was for a ten-key adding machine which did not print and
only added in one column.
Work on Some of the Present-Day Models.
Frank S. Baldwin, a construction engineer, living in the United States,
began to work on calculating machines in 1870. In 1874 he received a
patent for a small hand adding machine. In 1875 a patent was granted
him on a calculating machine. This machine was along entirely original
lines. Mr. Baldwin did not even know of the existence of the Thomas
machine at that time. The machine had a number of important advantages
over the Thomas system. Scientists were very much interested in the
invention at the time, and the John Scott medal for meritorious
inventions was conferred upon Mr. Baldwin by the Franklin Institute. The
only other invention being honored in that year (1875) was the George
Westinghouse air brake.
[Illustration: THE MODERN ADDING MACHINE
_Courtesy of the Monroe Calculating Machine Company._]
This calculating machine, however, seemed to be too much in advance of
the times, and Mr. Baldwin was unable to interest capital in it. He was
very successful in his business as construction engineer and continued
to spend all his spare time and money in experimental work. He brought
out a number of models at later dates with important improvements.
In the early eighties one of Mr. Baldwin’s 1875 models found its way to
Europe into the hands of one Ohdner, a Swede. He took out patents in all
European countries on a machine that did not vary in any important
particular from Mr. Baldwin’s machine, and several large manufacturing
companies in Europe took it up. It is now appearing under ten to fifteen
different names in Europe, the most important being “Brunsviga” and
Triumphator in Germany. There is no essential difference between the
machines they are turning out today and Mr. Baldwin’s original machine.
More than 50,000 machines of this type have been sold throughout the
world.
[Illustration: ONE OF THE FIRST SUCCESSFUL ADDING AND LISTING MACHINES
_Courtesy of the Burroughs Adding Machine Company._]
In 1883 a young man who started to work in a bank in Auburn, N. Y.,
discovered that nine-tenths of his work was mechanical addition. He also
found that the human brain is but an imperfect tool, incapable of
sustained effort without accident. His health gave way under the strain,
and he quit the bank to begin work in a machine shop in St. Louis.
This was William S. Burroughs. He was of mechanical turn of mind, with
an intense hobby for painful accuracy. By lamplight at home he worked
out pencil outlines of a machine which would write figures and at the
same time add them. It required the most painstaking work for him to
make a machine to do what he had in mind. His early associates say of
Burroughs that no ordinary materials were good enough for his creation.
His drawings were on metal plates that would not stretch nor shrink by
the fraction of a hair. He worked with hardened tools ground to a point,
and when he struck a center or drew a line, he did it under a
microscope.
In 1884 Burroughs took his plans to a St. Louis dry goods merchant, who
thought so well of the idea that he raised $700 toward forming a
company. The young man took up his work in the machine shop conducted by
Joseph Boyer.
It was in January, 1885, that he applied for his patent, which was not
issued until 1887.
His mechanism throughout operated on the pivotal principle. This means a
minimum of friction, therefore the least wear on the machine and the
least exertion on the part of the operator. The principle elements in
the machine remain practically unchanged today, a fact which testifies
to the excellence of the inventor’s work.
Experimenting on the machine swallowed a great deal of capital, and the
stockholders of the company he had formed became impatient. Burroughs
objected strenuously, for he did not wish to market the machine until he
was convinced that it was perfect, but he finally agreed to manufacture
fifty machines.
[Illustration: THE BOYER MACHINE SHOP, ST. LOUIS, WHERE ONE OF THE FIRST
SUCCESSFUL ADDING AND LISTING MACHINES WAS BORN
_Courtesy of the Burroughs Adding Machine Company._]
In his public demonstrations, he could do wonders with the machine. The
public was skeptical, however, and some averred that he was a “lightning
calculator” who did sums in his head and printed them on the machine.
The first machines worked all right for the inventor, but inexperienced
operators obtained surprising results through punching the keys and
jerking the crank.
To meet this trouble and make the machines “fool proof,” he invented the
“automatic control” in 1890. This was a governor, called the “dash
pot”--a small cylinder partially filled with oil, and in which was a
plunger. This, in connection with an ingenious management of springs,
absorbed the shocks and governed the machine so that no matter what was
done to it, it would operate only at a certain speed. It is this same
shock-absorbing device which is used to catch the recoil on the immense
siege guns used in modern warfare.
Other improvements were made, and in 1891 the first hundred machines
that were really marketable were manufactured. While still flushed with
his success, Burroughs thought of the first fifty machines which had
proved such a disappointment. These machines still remained in a dusty
storeroom to mock him. Determined to get them out of his sight and
memory, he seized them and threw them one by one from a window to the
pavement below.
[Illustration: “THERE’S AN END TO MY TROUBLES,” SAID WILLIAM SEWARD
BURROUGHS AS HE THREW INTO THE STREET THE FIRST FIFTY ADDING MACHINES HE
HAD MADE
He wished nothing to remain to remind him of this early failure.
_Courtesy of the Burroughs Adding Machine Company._]
When he had disposed of the last one, he called Mr. Boyer to see the
ruin. “There,” he exclaimed, “I have ended the last of my troubles.”
The first machines were called “Registering Accountants,” and
“Arithmometers.” Burroughs lived to see the fulfilment of his dreams and
the machine a commercial success. He died September 14, 1898, at his
country home in Citronelle, Alabama, a victim of tuberculosis.
There were at that time 8,000 banks in the country, and it was
Burroughs’ idea that as soon as these were supplied the market for
adding machines would be exhausted. Today, there are more than 200,000
adding machines of that one make in use.
The need for an all-around office assistant that could multiply, divide,
subtract as easily as it could add, was an idea nourished in the mind
and thought of a young student of the University of Michigan.
After graduation, Jay R. Monroe turned his attention to clerical and
commercial lines. He became acquainted with all the different types of
adding and so-called calculating machines. He saw their limitations and
restrictions. He saw the need for versatility--for more simplicity in
operation--for getting away from arbitrary rules--for release from the
sapping mental tax.
[Illustration: THE LATEST MODEL CALCULATING MACHINE
_Courtesy of the Monroe Calculating Machine Company._]
So in 1911 Monroe met Mr. Baldwin. Mr. Monroe realized the possibilities
of Mr. Baldwin’s idea. Together they set about designing the machine to
make it as nearly perfect as possible in adaptation to the needs of
modern business.
They produced a machine in which the best of the European features are
said to be combined with the operating ease and simplicity of
American-made machines. Provision is made for the correction of errors,
and operation is in two directions, forward for addition and
multiplication, and backward for subtraction and division. The latest
model is a desk machine, occupying less than one square foot of space
and weighing about twenty-six pounds.
One of the latest developments of the adding machine is a type that will
post ledgers and statements. This machine is said to be the final step
in relieving bookkeeping of its drudgery.
[Illustration: THE “DUODECILLION”--THE LARGEST CAPACITY ADDING MACHINE
IN THE WORLD--HAS FORTY ROWS OF KEYS AND WILL ADD TO WITHIN A UNIT OF
TEN DUODECILLIONS
To appreciate this prodigious figure, imagine that a marvelous
high-speed flying machine were invented that would go to the sun and
back in a day. If you made this 186,000,000-mile trip every day, it
would take you just 14,729,700,000,000,000,000,000,000,000 years to
travel a duodecillion miles.
_Courtesy of the Burroughs Adding Machine Company._]
How Big is the Largest Adding Machine in the World?
The largest adding machine ever made was produced in 1915 and has a
capacity of forty columns, or within one unit of ten duodecillions. This
is a number too prodigious for the mind of man to grasp. This machine
was exhibited at the Panama Expositions in 1915.
To get an idea of the capacity of this machine, suppose that your
income is $1,000,000 a second. At this rate for twenty-four hours a
day, with no stops for eating or sleeping, it would take you
352,331,022,041,828,731,333,333,333 years to accumulate a duodecillion
dollars. All the hairs on the heads of all human beings, which are
supposed to be numberless, are only a small fraction of a duodecillion.
This machine has a practical use in adding several sums simultaneously,
and takes the place of from ten to a dozen smaller machines.
Adding machines are made that figure in English pence, shillings and
pounds; in Japanese yen, and in the monetary system of most civilized
countries. They will change inches into feet, pounds into bushels, and
do other “stunts” that would make the average schoolboy envious when it
comes to arithmetic.
The most complicated problems of multiplication, division and fractions
may be handled with ease on these machines. They have taken a great part
in the day’s work of modern business, and it would be hard to imagine
how the world’s finance and industry could be handled without them.
Adding and calculating machines have become almost as necessary in
modern business as the telephone and the typewriter.
How are Adding Machines Used?
Adding machines may be found at work in all kinds of business places
from corner groceries to department stores and manufacturing plants. In
the various offices and plants of the Western Electric Company, which
are scattered through the country, more than 1,600 machines are in use.
Other big users are railroads, banks, mail-order houses, and city, state
and government offices.
The Bank of France, the Bank of England, and other of the world’s
largest financial institutions do the burden of their figure work on
adding machines made in the United States. The German post-office uses
more than 1,200 machines. There are individual American banks, like the
Corn Exchange National Bank of New York, that employ as many as 150
adding machines in their work.
[Illustration: ONE OF THE SMALLEST ADDING MACHINES IS ADAPTED FOR USE BY
RETAIL MERCHANTS AND OTHERS WHO DO NOT ADD FIGURES OF MORE THAN FIVE
DIGITS
_Courtesy of the Burroughs Adding Machine Company._]
Some surprising uses are found for adding machines. One is used in a
Japanese boarding house in California; another is used by a retired
Dayton millionaire to count the coupons he clips; the Rockefeller
Sanitary Commission uses a machine in fighting the hook-worm; the United
States government uses thousands in making census tabulations and in
other ways. Others are used by newsboys, egg farmers, housewives,
undertakers, dentists, judges in automobile races, and by persons in a
thousand different lines of business. Without adding machines the public
would be obliged to wait for days for the results of most elections.
In this way, the idea of a tired bank clerk came to change the figuring
methods of the world.
* * * * *
The words “Almighty Dollar” have been generally adopted since Irving
first used them in his “Creole Village,” and the use of “lynching” to
represent mob law and the action of mobs has become common since a
Virginia farmer by that name instituted the first vigilance committee in
America.
Where does Ermine Come From?
The ermine fur, with which we are all familiar, is furnished by the
stoat, a small animal of the weasel tribe. It is found over both
temperate Europe and North America, but is common only in the north.
Because of that change which occurs in the color of its fur at different
seasons--by far most marked in the Arctic regions--it is not generally
known that the ermine and stoat are the same. In winter, in cold
countries or severe seasons, the fur changes from a reddish-brown to a
yellowish-white, or almost pure white, under which shade the animal is
recognized as the ermine. In both states the tip of the tail is black.
[Illustration: ERMINE (_Mustela Erminea_)]
Like many other species of this genus, the ermine has the faculty of
ejecting a fluid of a musky odor.
Its fur is short, soft and silky; the best skins being brought from
Russia, Sweden and Norway and Hudson Bay territories. Its fur was
formerly one of the insignia of royalty, and is still used by judges.
When used as linings of cloaks the black tuft from the tail is sewed to
the skin at irregular distances.
What is the Principle of “Foreign Exchange”?
Exchange, in commerce, is a transaction by which the debts of people
residing at a distance are canceled by a draft or bill of exchange,
without transfer of any actual money.
A merchant in New York who owes $1,000 worth of goods in London, gives a
bill or order for that amount which can be negotiated through banking
agencies or otherwise against similar debts owing by other parties in
London who have payments to make in New York. This obviates the expense
and risk of transmitting money.
The process of liquidating obligations between different nations is
carried on in the same way by an exchange of foreign bills. When all the
accounts of one country correspond in value with those of another, the
exchange between the countries will be at par, that is, the sum for
which the bill is drawn in the one country will be the exact value of it
in the other.
Exchange is said to be at par when, for instance, a bill drawn in New
York for the payment of $1,000 in London can be purchased there for
$1,000. If it can be purchased for less, exchange is under par and is
against London. If the purchaser is obliged to give more, exchange is
above par and in favor of London.
Although the thousand circumstances which incessantly affect the state
of debt and credit prevent the ordinary course of exchange from being
almost ever precisely at par, its fluctuations are confined within
narrow limits, and if direct exchange is unfavorable between two
countries this can often be obviated by the interposition of bills drawn
on other countries where an opposite state of matters prevails.
What do We Mean by “The Old Moon in the New Moon’s Arms”?
“Earth-shine,” in astronomy, is the name given to the faint light
visible on the part of the moon not illuminated by the sun, due to the
illumination of that portion by the light which the earth reflects on
her. It is most conspicuous when the illuminated part of the disc is at
its smallest, as soon after new moon. This phenomenon is popularly
described as “the old moon in the new moon’s arms.”