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Mechanical Arithmetic 

or the 
History of the Counting Machine 



Edited by THOMAS H. RUSSELL, A. M., LL. D. 

Mechanical Arithmetic 


The History of the 
Counting Machine 



President of 

ELT & TARRANT MFG. CO., Chicago 

Manufacturers of the Comptometer 


This lecture by the well-known inventor and manufacturer 
of the famous calculating machine known to all American 
bookkeepers and office men as the Comptometer, will be 
appreciated by all business men and students of Business 
who realize the wonderful strides made in the last quarter 
of a century in the mechanical aids to efficiency in the 
accounting departments of commercial life. 

Mr. D. E. Felt stands high on the roll of successful Amer- 
ican inventors, and, unlike so many of them, he possesses a 
well-developed business instinct that has enabled him to 
reap the due reward of his inventive genius. His standing 
as an inventor is recognized in Europe as well as in the 
United States, and during the visits to the European 
museums to which he refers in his lecture he was signally 
honored by being permitted to make close examination and 
tests of the historic calculating machines preserved in those 
institutions; so that he speaks with unusual authority on 
this interesting subject of the development of "Mechanical 
Arithmetic" from the earliest times of which records exist. 

Mr. Felt tells in his lecture his own story of the dawn and 
origin of his great idea, and how he proceeded to carry it 
into effect ; and this part of his lecture, brief as it is, indi- 
cates the magnitude of his undertaking, while leaving to the 
imagination of the reader the years of effort that were re- 
quired to give to the world of commerce and finance the 
splendid mechanical calculator with which his name will 
ever be associated in the history of American invention and 
American business. 


After his invention of the Comptometer, it is interesting 
to note, it took him almost three years to sell the first hun- 
dred machines. But these were the first key-operated add- 
ing machines to be manufactured and sold in this countrj\ 
Today they are found in every large office and accounting 
department in America, effecting large savings in time, 
effort, and money. 

In 1888 Mr. Felt tackled the problem of listing machines, 
which others had tried, without success, to solve. He finally 
perfected the Comptograph, which was the first successful 
listing machine, and an invention of no small importance. 

Thus while Mr. Felt's Comptometers were the pioneers of 
key-driven adding and calculating machines, his Compto- 
graphs were the pioneers of keyboard listing adding ma- 
chines, and both have been of immense service in "leading 
the bookkeepers out of bondage." 

But the tale oi the inventor's important contributions to 
rapid calculation is not yet fully told. In 1901 Mr. Felt, 
after infinite labor, produced the first duplex key-driven 
calculator, and thus made practicable rapid multiplication 
by machinery. Since that time public contests at Office 
Appliance and Business Shows held in Madison Square Gar- 
den, New York, and in other cities have demonstrated the 
marvelous possibilities of Mr. Felt's mechanical calculators 
and a deep debt of gratitude is due him from the business 

T. H. R. 

Mechanical Arithmetic 


The History of the 
Counting Machine 

By D. E. FELT 

President FELT & TARRANT MFG. CO., Chicago 
Manufacturers of the Comptometer 

I will endeavor to give you an idea that the adding- 
machine art is not quite as new as one might think. We 
are apt to think that adding machines are something very- 

When I say "adding machines" or "computing machines," 
I mean counting machines, because all mathematics is count- 
ing. We are quite apt to consider multiplication or division 
something different from counting. Primarily it is addition, 
nothing else ; or, to be more exact, it is counting. The reason 
that we say multiplication, or practise what we call multipli- 
cation, is that we have learned the multiplication table. We 
make a sort of short-cut counting, because we have already 
learned a few simple elements in counting, like 2X4 are 8, 
or 3 X 12 are 36. 

The first arithmetic, the first counting, was undoubtedly 
mechanical. We say "to calculate." The word "calculate" 
means to count with pebbles. Calculi is Latin for pebbles, 
therefore calculating is counting with pebbles. That is 
where the term started. 

.£ • ;:•:.*•:*•,•':•.-■:.*•*-••■ MECHANICAL ARITHMETIC OR 

We call the numeral characters which we use digits. 
"Digits" mean fingers. If men had six fingers instead of 
five, we would have had the duodecimal system of notation, 
instead of the decimal, and it would have been very much 
easier to make arithmetical calculations than it is, using as 
we do the decimal system of tens. For instance, with the 
decimal system, if we want to multiply anything by twenty- 
five, simply divide by four and add two ciphers. We can 
make a few short cuts with the decimal system like that, 
but if we used twelve numeral characters or twelve digits, — 
that is, the duodecimal system, — we could have made a great 
many short cuts. That is why astronomers use a sort of 
different mathematics. That is why they divide the circle 
into three hundred and sixty degrees instead of into one 
hundred degrees, because twelve can be divided in a great 
many ways — 3, 4, 6, and 2 are all factors of 12. In ten 
we have only 2 and 5. 

There isn't any way to tell just what the earliest calculat- 
ing machines were. We can only make a surmise. We know 
that from the earliest historic times people have calculated 
with pebbles; then they went a little farther, because the 
pebbles lying on the ground or on the boards would get 
mixed up, and instead of using pebbles they used beads, 
strung on rods, and by putting a number of rods in a frame 
made and used the device called "abacus." 

There were different systems of those rods. There is a 
system, used largely in China and the far East, which has 
five beads on one end of one rod, then a division in the 
frame, then two beads on the other end of the rod. There 
are two 5's in ten that make a positive count, and you can 
keep track of the carrying by means of the other two. But 
the more common form of abacus is what is known as the 
Greek abacus, which is still used almost universally in 


Russia, and in many countries of Eastern Europe. It has 
nine beads on one rod, then a division, then one bead. 

It would be rather difficult for you and me to sit down 
with a lot of pebbles and try to compute with them, but that 
is because we didn't learn to do it that way. Perhaps if we 
had spent as much time learning to compute with pebbles 
as we have learning to play whist, we could do it with sur- 
prising rapidity. Orientals do those things very rapidly; 
in fact, the Japanese have a sort of mathematics with many 
short cuts that are worth studying, because they show us 
short cuts that we never thought of. They have the same 
number of fingers and consequently the same decimal system 
that we have. Naturally we can profit by some of their 
mathematical discoveries. 

The First Counting Machine 

The first counting machine that we have in written history 
comes through a man named Gerbert. Gerbert was a shep- 
herd boy. A monk noticed that he was very ingenious, very 
bright. He made an instrument for playing music by peel- 
ing the bark off limbs of trees, and fitting it with reeds ; then 
he ran water through a pipe to force air down and vibrate 
the reeds. So the monk educated him. He knew that at 
that time, which was about 900 A. D., practically all the 
knowledga and science of the world was possessed by the 
Moors. They occupied southern Spain, as well as north 

The Moors had two great universities, one at Cordova and 
the other at Seville, but no Christian could enter them, so 
Gerbert associated for some years with Moors, lived their 
life and adopted their customs, and learned the Mohamme- 
dan religion. Then he disappeared from the monks, those 
who had known him before, and in Moorish garb applied at 


one of these universities to be taken in. As he seemed to 
be a good Mohammedan, they took him in and he went 
through that university and then he went to the other. 
After he had graduated from both, he came back into 
Christian Europe. 

When Gerbert came back he brought with him what we 
call the Arabic numerals. They are what we use. But they 
were then very different in form from the Arabic numerals 
as we write them today, because we have changed them. 
They originated in northern India. The Arabians used nine 
significant digits and the ciphers. 

Gerbert came back in the year 960, I think it was, or 
within three or four years of that. Printing was unknown. 
Consequently, the knowledge that he brought back to Europe 
did not spread, and it wasn't until several hundred years 
afterwards, until the invention of printing, that the Arabic 
numerals came into general use. When he came back he 
brought with him a plan for a calculating machine that the 
Moors had been working at, but had never succeeded in 
making work. He spent many years of his life trying to 
make it work. He thought he could, but he could not. He 
could not get accurate results at all. Otherwise he was very 
successful ; afterwards he was Pope of the Roman Catholic 
Church — Sylvester II. 

Early Calculating Machines 

But another Spaniard took up the idea and made a calcu- 
lating machine. His name was Magnus. As far as we know 
his machine worked. History says it did, but having seen 
some twenty famous old calculating machines in Europe 
made three or four hundred years ago, I have my doubts 
about its accuracy. It was formed of brass, in the shape 
of a human head, and the figures showed where the teeth 


Another man, at the same time, named Bacon, made one 
also of the same character. I say at the same time. Magnus 
made his shortly after the year 1000 A. D., and Bacon made 
his perhaps ten, fifteen, or twenty years later. It is not 
known exactly. What became of the machine of Bacon is 
not known, but the one that Magnus made was smashed with 
a club. The other priests — they were both priests of the 
Catholic Church — thought it was something superhuman. 
He tried to make out that it was, and concealed the fact that 
it was a piece of calculating mechanism. So they smashed 
that one up. 

Those were undoubtedly complicated pieces of machinery, 
but they accomplished no more than the little twenty-five- 
cent adding machines that we now see, consisting of three 
or four little discs in a row, where you insert a stylus and 
turn the wheels around. This modern simplicity is due to 
the mechanic arts having developed more fully. 

In those days the necessity for calculating machines was 
realized much more than it is now. If you write down a 
problem, like 4,625 multiplied by 360, in what are called 
Roman numerals — the numerals that we use on the dial of 
a clock — you will see it would be very difficult to multiply. 
For that reason you will see that addition was almost as 
difficult, because there were no individual columns — units, 
tens, etc. — the digits in each falling one beneath the other. 
So there were only a very few of the people who could mul- 
tiply, or add or divide, or do anything in mathematics. 
Those that could were considered something strange, like an 
astrologer. That condition continued until the middle of the 
seventeenth century. 

They had adopted the Arabic numerals, I think, quite gen- 
erally, about the fifteenth century, but it was easily some 
hundreds of years after that before arithmetic, as we teach 


it to the children in school, became generally spread among 
the people. Even for hundreds of years afterwards the 
people did not seem to acquire that facility of mental calcu- 
lation that we practise today. Consequently, efforts to make 
mechanical calculators were very great and very long con- 
tinued. A mere list of the noted scientific men that devoted 
many years to the subject would contain hundreds of names. 

Pascars Mechanical Calculator 

But among all that number certain ones made a little step 
forward here and there; they made some progress. There 
were many ambitious efforts to make what we would now 
call a highly organized mechanical calculator. None of those 
succeeded. The most famous was by Pascal in 1642. He is 
credited with being the first to make a mechanical calcu- 
lator. But I do not think he fully deserved it. He didn't 
make one that would calculate accurately, even if you 
handled it with the greatest care and took hold of the wheels 
and cogs after taking the top off the machine, trying to help 
them along. I have tried them myself on several of his 
machines which are preserved, and making due allowance 
for age they never could have been in any sense accurate 
mechanical calculators. Furthermore, they were very large ; 
probably eighteen inches long, ten inches wide and six or 
eight inches high. They would have accomplished nothing 
more, even if they had worked, than these little things you 
stick in your vest pocket, with four dials which are operated 
with a stylus. His machine was operated exactly the same. 
But its great bulk, the largeness of the machine, was occa- 
sioned by the very complicated carrying mechanism, to 
transmit tens from one order to the next, units to tens, and 
tens to hundreds, etc. But, having been the greatest scien- 
tist of his time, and having a great many friends, and being 
a Frenc'hman — (the French recorded the efforts of the dif- 


ferent attempted inventions in calculators more perfectly 
than any other nation) — ^he is given a great deal of credit 
in that direction. 

Sir Samuel Moreland, in England in 1663, made a mechan- 
ical calculator which was practically in all respects the same 
little disk machine of today, compact and simple. He was a 
famous scientist also, but his machine didn't come into very 
general use. Probably there were a few hundred used. 
Some are still in existence. That was about two hundred 
and fifty years ago. 

Pascal was undoubtedly a great scientist in many different 
ways. He did many things for the human race, and one of 
those for which he is most celebrated is the invention of the 
omnibus, called the twenty-centimes omnibus. That would 
be about four cents fare, and his omnibus was the first thing 
of the kind known. He is very famous for that, much more 
so than for the great many books he wrote on science. The 
foundation of several branches of science is lound in his 

Pascal started at his calculating machine very young. He 
was only about eighteen. His father was what we call a 
customs officer and the boy was often made to compute. 
It was very laborious, and so he conceived the idea of making 
this machine. It is said that he had never heard of anything 
of the kind before, but there are records of many attempts 
before him. 

The Work of Leibnitz 

About that time, or a little later, there was a great 
scientist in Germany, named Leibnitz. He was probably a 
greater man than Pascal. He is said to have been the in- 
ventor of the differential calculus, on which nearly all the 
higher mathematics, as practised in engineering, is based. 


It is a question, however, whether he really was the first 
to invent the differential calculus. The English say Napier 
did it. Napier was also a great scientist and wrote books, 
so what he did was preserved. 

Leibnitz never wrote many books, but wrote a great many 
letters. Those letters are so important that you can go to 
our libraries today and find photographs of hundreds of let- 
ters written by Leibnitz. Many of the fundamental princi- 
ples of our present-day science are found for the first time in 
those letters. He is said by some recent scientists to have 
possessed the greatest brain the world has ever known. He 
was honored and decorated and received by the Czar of 
Russia and the Emperors of France and Austria, and by 
many of the German kings, but he was not satisfied. He 
was jealous of Pascal, so he went to work to make a calcu- 
lating machine, because in that day Pascal was noted more 
for his calculating machine than for other things much more 
valuable and wonderful. 

Leibnitz had some money — 250,000 francs, they say. He 
spent all he had and his calculating machines didn't work. 
He made two or three. He employed watchmakers to do the 
work, and he blames their failure to the watchmakers, the 
same as Pascal does. Both blame it to the mechanics that 
their machines were not entirely satisfactory. 

It is said that Leibnitz worked twelve years on his ma- 
chine. He wasted all the money he had, and dropped out of 
sight. There was only one man that went to the grave with 
his remains when he was buried, in absolute poverty. A few 
years before he had been noted as the greatest scientist in 

It was claimed by some that another man in France, 
Grillet by name, who knew of Pascal's efforts, tried to make 
a calculating machine, and that he came much nearer to 


success in making an accurate machine than did Pascal. 
The machine was not used, but was exhibited for a fee, and 
then all of a sudden it dropped out of sight and nobody knew 
what became of it. So some claim that Leibnitz didn't gen- 
erate any machine, or rather any mechanism for his ma- 
chine, out of his own head, but that he procured this machine 
in France and took the inside out of it and put it in another 

When I was in Paris a few years ago, I saw the case Leib- 
nitz is supposed to have taken the mechanism out of. I 
examined it very carefully, and I also examined another 
machine very much like it, that has the insides still in it. 
When I was at the Royal Library, Hanover, Germany, I 
had Leibnitz's machine open and examined that very care- 
fully, and I am sure that there is no possibility that Leibnitz 
could have used any of the mechanism out of the machine 
made in France. The two machines are entirely different in 
organization, starting from different conceptions, and, I was 
going to say, arriving at different results ; but they all ended 
in failures, which is true of all attempted highly-organized 
calculating machines up to the year of 1820. 

The First Successful Machine 

Charles Xavier Thomas, a director of an insurance com- 
pany in France, made a calculating machine in 1820 and it 
worked. Without question it was the first one that ever did 
work practically and usefully. When I say a calculating 
machine I mean a highly-organized machine, because there 
had been devices for calculating, like the abacus, before that, 
which worked ; simple devices that were practical and useful, 
some of them used to a very large extent, but they were not 
devices that we would use. They were less automatic. 

One of these simple devices, which is quite as famous as 


the machine of Pascal, was invented by Napier, of Scotland, 
the inventor of the differential calculus. Napier wrote the 
multiplication table on some little rods. He didn't write it 
as we find it in our textbooks in school, but he wrote it on 
square rods, in such a manner that the tens figure of each 
product in the multiplication would fall in a triangle, oppos- 
ing another triangle in the same square containing the units 
figure of the product corresponding. He used rods about 
the size of a pencil, with parts of the multiplication table 
written on them, only there were four sides. For instance, 
the products of 6 written on one side, those of 7 on another 
side, and so on. He would select rods corresponding to the 
multiplication and Jay them alongside of one another, ascer- 
tain the first sub-product by a simple addition, write it down, 
then get the next sub-product by the same means, and so on, 
finally adding all the sub-products together. If he had to 
multiply 243 by 46 he would do it by three mental additions. 

Those rods (Napier's rods) were used very largely, not 
only in England, but all over the Continent. They were 
considered a great thing, and people not understanding that 
it was simply the multiplication table written on strips, 
thought there was something mystic about it, and he was 
very much honored for the invention. No doubt he orig- 
inated it out of his own mind, but the same thing was known 
to the Arabs many years before that ; in fact, they practise 
something like that today, but have it arranged a little 

In the meantime, between Leibnitz and Thomas, there 
were several men who made machines which are still in 
existence. There was a man named Poleni in Venice, who 
made a machine in 1709, but that machine is not in exist- 
ence. It was a very near approach to an accurate calculator, 
but not reliable enough to be used to any extent. There are 


two machines in the museum at Munich, Germany, which 
are said to be copies of it, made at the same time, and they 
are wonderful pieces of mechanism. They are beautiful to 
look at, very far superior to most of the calculating machines 
of early times. 

The Odhner Type of Machine 

In 1775 Earl Stanhope, in England, made two machines. 
Some say he copied Pascal, but he didn't. His are very dif- 
ferent. One of them, if it had worked accurately, would 
have been the prototype of that class of machine known as 
the Odhner type. Odhner lived in Russia. Some say he was 
a Pole, but I believe he was a Scandinavian. He made a 
successful machine about 1876. There is a great family of 
machines made in Europe at present, known as the Odhner 
type ; probably twenty factories making such machines. The 
Brunsviga is one of them. Odhner manufactures them him- 
self in Russia, but he is not so successful commercially as 
are the French and German manufacturers of that type of 

But a hundred years earlier — 1775 — Lord Stanhope had 
in his machine the heart of the Odhner machine. Each kind 
of machine — I do not care whether it be an automobile or a 
calculating machine — has some fundamental feature, some 
heart, some key to it, which represents the invention, which 
once thought of and produced successfully, the rest is easy. 
That feature of the Odhner machine is found in the machine 
of Earl Stanhope for the first time. But it is not accurate 
and never was. It is very fragile. They wouldn't let me 
operate it in the museum where it is preserved in London, 
but I examined it very closely. No doubt it could be operated 
if handled very delicately and would get results. 


Another machine made by Earl Stanhope about the year 
1777, contained the heart of what is known as the Thomas 
type of machine. That machine contained a series of toothed 
wheels, having wide faces bearing ten very long teeth ; the 
first one, reaching clear across the face, representing 9, the 
next tooth being one-ninth shorter, the next one-eighth 
shorter, and so on. If you want to add 9, you shove the 
toothed wheel along so that nine teeth will engage; if 8, 
you shove it along so that eight will engage. That is in the 
second Stanhope machine, and it is the general principle of 
the Thomas machine. In the Odhner type they get the 
variable number of engaging teeth by having a wheel with 
movable teeth in it so they can slide in and out. As they 
turn a lever more or fewer teeth slide out. 

Those two Stanhope machines are probably, barring Leib- 
nitz's, the first attempts to make any machine on either the 
Thomas or Odhner principle, although there are some very 
old machines in Germany that contain the Odhner principle, 
and I am trying to find out about them. 

Perhaps, however, I am not quite fair to Leibnitz. Leib- 
nitz anticipated the Thomas type of machine in so far as 
he had the cylinders with longer and shorter teeth, etc., but 
his organization was so entirely different from the Thomas 
organization or anything that has ever been brought to a 
successful conclusion that I could hardly say that he antici- 
pated Thomas in the same sense that Earl Stanhope did. 

"The Fault of the Mechanic" 

Earl Stanhope was another fellow who had his machines 
made by watchmakers, and he also blames the lack of suc- 
cess to the men who made the machines. I guess he is 
right. There is no doubt it was the fault of the mechanic. 
The whole thing rests with the mechanic. He deserves all 


credit and all blame. Anybody, with a little bit of study, 
can think up a calculating machine; it is no trouble at all. 
There are any number of ways to go about it, and devise 
something in the air or on paper; but it is a very difficult 
proposition to make one that will be simple and produce 
accurate results in use. There is hardly a week that I don't 
get a letter from some man who has invented a calculating 
machine far superior to anything now on the market, and 
he wants me to give him the money to patent it, and if I 
don't, he says he will take all the calculating-machine busi- 
ness away from all the rest of us. 

It looks simple. When I first thought of making a calcu- 
lating machine, I was working in a machine shop. I was 
running a planer. A planer has a tool that runs back and 
forth across one or more notches according to how you 
adjust it. I said, "Why can't that be used for counting?" 

I thought about it all night, and pretty soon I said, "I 
will make such a machine." 

I had a friend who was an electrical engineer, and I told 
him what I was going to do, and said : "In ninety days every 
office in the United States will be doing its calculating by 

So I went to the grocery and bought a macaroni box to 
make the frame of. I went to the butcher and bought 
skewers to make the keys of, and to the hardware store and 
bought staples, and to the bookstore and bought rubber 
bands to use for springs. I went to work to make a calcu- 
lating machine, expecting to have thousands in use in ninety 
days. I began on Thanksgiving Day, because that was a 
holiday, and worked that day, and Christmas and New 
Year's, but I didn't get it done in three days. It was a long 
time before I got it done. 


Modern European Machines 

To go back to the history of calculating machines : 

Another mar made a wonderful machine in 1777, contain- 
ing the Odhner principle which I saw in Germany. He made 
another in 1809 which did not contain the Odhner principle. 

The Thomas machine is still being manufactured in the 
same place, in Colmar, France, in which the first one was 
made, three generations ago. It worked. It was useful and 
a great many were used. It didn't get out of France until 
about forty years ago, when the insurance people took up 
the subject, and particularly through the efforts of a college 
for actuaries in Scotland, the science of using the Thomas 
machine was written up and advanced. There is a lot to 
know about mechanical arithmetic. 

Then a man in England began manufacturing a copy of 
the Thomas machine, a man named Tait, and he is still 
manufacturing it in London. He made a splendid machine. 
It is the best constructed machine made in Europe. He sold 
it for $450, and a good many were used in this country 
twenty-five years ago. It is the most accurate calculating 
machine and the only durable calculating machine ever made 
in Europe. 

But Tait had no commercial ability whatever. The chief 
accountant of the Great Western Railway in England called 
at my hotel in London one day, a few years ago, and I asked 
him about Tait. He said Tait had then two or three mechan- 
ics working in London; yet he was then making, and has 
made for twenty-five years, the only nearly accurate and 
durable calculating machine made in Europe, in the sense 
that we Americans consider a calculating machine accurate 
and durable. I don't mean like the old machines that 
wouldn't be accurate no matter how delicately you use them ; 


but the Tait is a very accurate machine. Yet I have in my 
possession a pamphlet issued about twenty years ago, when 
Tait was doing considerable business, in which he starts out 
by telling that you must, every time before you start to use 
your machine, test it and then adjust the springs with some 
little screws until it computes accurately; and then he goes 
on and cautions three or four times, "Don't run it too fast." 
Nevertheless, the Tait machine was far and away above any 
European machine made today or heretofore, regardless of 
the fact that many calculating machines are being used in 

The Brunsviga Machine 

Nearly every large office in Europe uses a number of the 
Brunsviga machines, but every one of them will overthrow 
the numeral wheels and give a wrong answer if operated 
rapidly. The recent catalogues of the Brunsviga machine 
say they have overcome that difficulty. We have seen that 
claim time and again for — I guess — fifteen years, and we 
will see it until they start from a different standpoint to 
build a machine on a different principle. 

The Brunsviga people are very energetic. They put 
money into pushing their business, and they sell a great 
many machines all over Europe. Even the French, before 
the Great War, bought this German machine. If you were 
a German on the streets of Paris before the war, and called 
a cabman, most likely he wouldn't take you, although it was 
against the law to refuse. Yet they bought the machines 
made in Germany, despite their having eight or ten calcu- 
lating-machine factories in France. 

There is no question but what the first machine that was 
accurate enough to be of any practical value was the Thomas 
machine of 1820. The Odhner machine was the next. And 


the Brunsviga machine was originally made under patents 
granted in Germany, which, of course, have expired. 

The Babbage Calculator 

Perhaps the most famous machine in English literature 
is the Babbage machine, and it is always spoken of as a 
calculator. It was a calculating machine in one sense. But 
it was not a machine that would do multiplication, or divi- 
sion, or addition. The theory was to make tables by use of 
the Babbage machine and then use the tables. To compute 
mentally and print accurate tables is very difficult. Babbage 
was a noted English scientist. You can find his books in all 
the large city libraries, many large volumes pertaining to 
different scientific topics. 

In the case of the Babbage machine the idea was to con- 
struct a machine to grind out a single table, and then after 
making and putting into the machine many new pieces of 
mechanism, grind out another table, and so on ; — practically 
making a new machine for each table. It was quite a large 
machine. Babbage never finished it, but about 1833 he 
made part of it. The part he made was about three feet 
high. It was beautifully made, but it was not wholly relia- 
ble. He ran out of money, and the Parliament of England 
appropriated for his use seventeen thousand pounds sterling. 
He used that up and then for some time did not do anything 
more to the machine until Queen Victoria offered to assist 
him ; but then, instead of completing the first one, he started 
in to make quite a different machine, called an "analytical 
engine." It was for a different purpose altogether. It was 
intended to develop algebraic expressions. Then he died. 
So he never completed either one, but the one which he 
partly made, called a "difference engine," is now on exhibi- 
tion in England, and is very famous. 


One British encyclopedia devotes many pages to that 
machine, and Babbage wrote about it as though he had 
actually made a machine. He never made it, and could not 
if he had lived a thousand years. The object he was trying 
to attain was all right. He was aiming at the right thing, 
but he could not produce it. 

A Successful Swedish Machine 

Just about that time a man named Scheutz, in Stockholm, 
conceived the idea of making a machine for the same pur- 
pose. He was publishing a technical journal for civil and 
mechanical engineers, but he did not produce the machine 
alone. His son, before he was twenty, while in school, or 
just about the time he came out of school, took it up and 
between the father and son they constructed a machine. 
They were assisted by one appropriation of $2,700 by the 
Swedish Government. That machine worked. It was begun 
in 1837 or before. Just when it was completed is not certain. 
But it was exhibited in England in 1855. It was being used 
in one of the Government offices in London in 1862. It was 
employed to compute a mortuary table — a table of the prob- 
abilities of the length of human life. They had very few 
data to work on, but they had the life statistics of several 
cities in England, and from them they made the table, which 
was published in book form and used by insurance companies 
for many years. It was the first mortuary table ever made. 
It was accurate. 

One thing that both Babbage and Scheutz appreciated was 
that all tables computed mentally are more or less inac- 
curate, due to errors in transcribing and typesetting the 
figures. So they were going to overcome that difficulty by 
having a machine make the type forms they printed the 
tables from. Babbage never completed this machine, but 


Scheutz made his successfully. To make the type to print 
them from, he had a strip of lead about three inches wide, 
into which the answers were impressed as fast as computed, 
something like a listing machine prints its answers on paper. 
The answer mechanism used by Scheutz was the same 
stepped device used by Hiett. The machine was turned with 
a crank, as we turn a cider mill, and as the machinery ran 
along it computed and pressed the figures into lead. Then 
they made stereotjrpes from the lead plates to print from, 
so that they got right onto the paper the very figures made 
by the machine. There was no chance for a mistake in 

They found it was very difficult to keep the Scheutz ma- 
chine in running order. The British Government appro- 
priated some money to build another on the same plan, only 
larger, — that is, to take in more columns, — and was going 
to have it built in a British shop, and then, of course, accord- 
ing to British ideas, it would work accurately. The people 
in those Islands think it must be perfect if made in Britain, 
and if it isn't made there it isn't perfect. 

They built this machine in the great engineering works 
of Bryan, Donkin & Co., in England, and it is supposed to 
have been very much better than the one built by Scheutz, 
but I have not seen it. It was said to have been in the South 
Kensington Museum at one time, but I could not find it or 
any record of anybody having seen it for years. 

The first Scheutz machine is now at the Dudley Observ- 
atory, Albany, New York, and while the workmanship is 
not that finely finished instrument-maker's work seen in the 
portion of the Babbage machine that was constructed, it is 
"all business." You can see it is a machine in which the 
man kept the object he wanted to accomplish in mind, and 
didn't want to make any mirrors for the ladies to look into. 


so his money held out till he produced a thing that could be 
used. It was bought by Mr. Rathbone, an American, and 
presented to the Dudley Observatory some years ago. They 
tried to use it, and I believe did use it somewhat in the 
Dudley Observatory, but they are not using it any more, 
and when I saw it, they kept it in a room full of old rubbish. 
If that machine was in Europe, they would build a special 
building to keep it in. France would, anyi;vay, and so would 

Historic Machines in France 

In Paris they invited me to come to the National Conserv- 
atory of Arts and Meters, on a day when it was closed to 
the public, and gave me a man with a screw-driver to open 
machines for me to examine. I spent several hours there. 
They have many historic old calculating machines there, 
and I brought away the catalogue and a volume on calculat- 
ing machines, WTitten by Professor Maurice d'Ocagne. Nat- 
urally, I paid most attention to the machines the histoiy of 
which I was already familiar with. But I hope to be able 
to determine whether there is any older machine than the 
Pascal. In the literature the Pascal is the oldest — but I 
think there are some machines that date back nearly to the 
year 1000. 

There is one interesting Chinese machine there. We have 
always thought of Chinese calculators as being the abacus 
and nothing else, because that is what they usually use. 
But in Paris there is a Chinese machine that has wheels and 
springs and is operated with a stylus. This machine is 
about four inches deep and six inches wide, and it has a lot 
of slots in the top of it, shaped like a shepherd's crook. It 
is operated something like the Goldman machine, which is 
v\'ell known in America, only instead of having carrying 
mechanism inside, the slot for the stylus ends in a turn so 


as to carry the stylus around and back. It has a series of 
black and a series of white numerals showing through each 
slot. If the number to be added is found among the black 
numerals, you go in one direction ; if found among the white, 
go in another direction. There was a very simple machine 
on something like that principle — really a very wonderful 
principle — advertised from Iowa by Locke up to quite 

Thomas was French and Stanhope was English. Leibnitz 
was German. Moreland was English and Pascal was French. 
There are a great many French inventors in the books, hun- 
dreds of them, but no one until Thomas ever made any 
highly-organized machines that would work accurately until 
very recent years, and none, except those who directly copied 
Thomas and Odhner and maybe Grant, made anything that 
would be considered useful in our day, until key-operated 
machines came in. 

BoUee's Machine a New Type 

In the year 1889 a Frenchman named Bollee made a ma- 
chine of an entirely new type on entirely new principles. 
He made it when he was eighteen years old, and they say 
he never had heard of a calculating machine before. That 
was another case where the boy's father was a customs 
officer and he had to do computing. (By the way, Pascal 
was only twenty when he made his first machine; and 
Scheutz, the real inventor, Scheutz the son, was only about 
twenty when he made his machine. Several of the early 
inventors of calculating machines were under twenty-two 
or twenty-three.) This machine made by Bollee was for mul- 
tiplication and division. It would be entirely impracticable 
for addition, and it wasn't as useful for dividing as the 
Thomas or the Odhner. For multiplication and division it 


was very good, but for division you had to estimate what 
your quotient figure was every time before operating the 
machine, which you don't have to do with the Thomas or 
Odhner. Nevertheless it is often used for division, and is 
very good for multiplication. You probably sometimes see 
that machine now, or one containing the same principle, in 
what is called the Millionaire. The Millionaire is manufac- 
tured under the patents of E. Steiger of Germany. It is 
manufactured in Switzerland. The principle of the Bollee 
machine was another case of the multiplication table put 
into material form. 

Napier put the multiplication table on bone rods by en- 
graving on them the figures representing the multiplication 
table. Bollee didn't do that. Bollee took a plate of metal 
and stood on it a series of pins of graduated lengths. One 
pin would be 1 unit high, the next 2 units high, the last pin 
of the series 9 units high. This represented the first nine 
steps of the multiplication table, once one, once two, once 
three, etc. The next series of pins was first 2 units high, 
the next 4 units high, and so on, and stood for 2X1, 2X2, 
and so on. 

He arranged these plates to slide back and forth in the 
machine in such manner that when the operator moved the 
knobs attached to the plates carrying the graduated pins so 
as to set up on the machine any certain number, — ^for in- 
stance, as one would set the multiplicand on the Thomas or 
Brunsviga, — and then moved a crank along an index, leav- 
ing it at any particular figure, — ^for instance, 7, — then by 
moving a second crank the machine would instantly indicate 
seven times the multiplicand originally set up. By an opera- 
tion of this kind for each figure of the multiplier any prob- 
lem in multiplication could be performed. 

A small number of the Bollee machines were made and 


used, but in recent years he has gone into the automobile 
business and I guess he will not make another, because 
money is easier made in automobiles than in calculators. It 
was a fine machine, with much mechanism in it. It was 
used for making tables as well. 

The Steiger machine, usually known as the Millionaire, 
instead of using pins, employs notches in disks, the disks 
turning around. It is the same principle, except that disks 
with notches supplant the rows of pins. 

A man named Saunders in New Jersey about ten years 
ago carried the Bollee principle still farther, using the 
Steiger form. On the Millionaire and Bollee you have to set 
two or three things and move a crank for each figure of one 
factor, but Saunders made a machine in which you simply 
set up on one series of indices for the multiplicand, and 
another for all the digits of the multiplier, and then by 
moving the second crank once the answer is at once dis- 
played, instead of having to move both cranks for each digit 
of the multiplier. 

Machines of Recent Invention 

Now, to come down to more immediate times, Pottin — I 
believe he was a Frenchman — made the first attempt to 
construct a key-operated machine to add and print. A man 
named Baldwin in St. Louis, in 1872, made a calculating 
machine that added and printed, but it was not key-oi)er- 
ated. He used the Odhner principle in his calculating 
mechanism. He made a number of machines. In the litera- 
ture of the subject he is quite famous as a maker of calcu- 
lators, although he never made but four or five. One of his 
models is in the Patent Office at Washington. It is a beau- 
tiful piece of mechanism; but it would last about thirty 
minutes if you tried to use it in the rapid and rough way 


calculating machines are used in this country. It worked 
if you handled it with great care. That machine would 
add and print a list of numbers on a tape of paper. 

There was a machine made about the same time by a 
man in Germany named Sellings, which did the same thing. 
It is in the museum in Munich. Also a later machine by 
him, which does not print. I believe it was all right as a 
multiplying machine, but as a listing machine I don't think 
it amounted to much. The underlying principle of the 
Sellings machine was quite original. There are two Sellings 
machines in the museum at Munich, each very different from 
the other. The first was somewhat crude and fragile. The 
second one was more substantial and looks as though it 
would stand some practical use. 

Of course, it could be said that the Scheutz machine added 
and printed, because you could read the type that it made 
to Drint by. It could be said that that was a listing machine, 
but it was a mighty slow one. Some of those early machines 
were operated by power. I believe the second Scheutz 
machine was. Prof. d'Ocagne in his book on mechanical 
calculators mentions several early machines operated by 
power, one by an electric motor. 

Pottin in 1883 took out a patent in France, and a patent 
in England. He registered in each case from Paris, France. 
He has taken out four patents in this country, but I have 
never been able to find out for sure what Pottin's native 
country was, and I wouldn't be surprised to find that it was 
America, because his first patent was taken out from Phila- 

Pottin actually made a machine, but I cannot find what 
became of it. Prof. d'Ocagne, who has written several vol- 
umes on the history of mechanical calculators, never heard 
of Pottin until I told him about him. Once I met a patent 


^awyer who claimed to have gone to Europe and investigated 
Pottin's machine, and said he found that one was made and 
that it worked; but it seems strange to me that, if it did 
work, they would not know something about it in France, 
where they get so excited over our Comptograph or Compt- 

[Editor's Note. — With the modesty of a successful in- 
ventor, Mr. Felt concludes his lecture without mentioning 
the marvelous results of his own efforts to give the business 
world a practical counting-machine of convenient size, abso- 
lute accuracy, great durability, and moderate cost. But his 
machines speak for themselves in thousands of busy offices, 
not only in the United States, but throughout the civilized 


TO— #^ 202 Main Library 


2 : 



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itecCJJt SEP20^ 


FORM NO. DD6, 60m, 1 / 83 BERKELEY, CA 94720 

Gaylord Bros., Inc. 


Stockton, Calif. 

PAT. m. 21, 1908 

UX. BERKELEY UH^^^^^^^^