menu calmeca

I disagree

Several Web sites are devoted to mechanical calculation, some of them give, in my opinion, wrong information. In spite of that, even these sites are very interesting ones and I continue to visit them. Similarly, if you find any errors in my pages, please send me an email so that I can improve their content.

The pascaline :

About the horizontal position required to the good acting of the calculator :

sautoir pascaline

Some people say that without a perfect horizontal position the pascaline does not work. This argument comes from the fact that the internal gears as well as the carry mechanism are connected to catch bars and weights subject to the gravity.

Indeed the intensity of the strength applied by these weights depends of the slope of the calculator. The maximun of this intensity is obtained when the pascaline lies in an horizontal position. The intensity of the strength changes proportionally to the cosinus of the inclination angle of the machine. A decrease of 0.5 percent is obtained at at angle of 5.7 degrees. A wedge of 10 centimeters thickness must be placed under the legs of a one meter long table to obtain this slope.

The acting of the calculator was probably not disturbed by such a little variation (just like the replica I have worked with). Moreover, with this slope, it is obvious that the table is not horizontal when observed with the naked eye (try to place a wedge of 10 centimeters thickness under the legs of a one meter long table !!!).

The movie demonstrates than the carry works well on a 6 degrees leaned pascaline replica.

armorial bearings of Blaise Pascal

To conclude : the assumption according to which the pascaline could not work properly in a non perfect horizontal position is incorrecte (however, the slope must be reasonable).

About the carry :

Sometimes the carry mechanism of the pascaline is wrongly described.

The mechanism invented by Blaise Pascal has nothing to do with a single toothed 'mutilated' gear which at every full turn advances the next wheel by one unit (system used on the mechanical mileage counters of the old cars. Some adders of the 20th century were equipped with such a rudimentary carry mechanism).

In the pascaline, the carry is prepared by a progressive rising of a weight which is released when the wheel has made a complete turn (when the display passes from 9 to 0). When this weight is released, it increases the left contiguous wheel by one unit. With such a system the carry is sequential. That is to say that, when a carry must be done on several wheels, for example when you add "1" to the number "999", after you have entered "1" on the wheel of the units, the wheel of the hundreds waits until the wheel of the tens has finished his movement. On the contrary, on the adders of the same type than the old mileage counters, the carrry is simultaneous (see the heading "little story of the mechanical calculation").

The sequential carry system theorically allows to manufacture calculators with a capacity as large as one wants. The larger capacity we know for a pascaline is of ten wheels, this machine is an accountant one who is at the Mathematisch-Physikalischer Salon de Dresde.

The Blaise Pascal type calculators :


Some sites classify the calculating machines by family types.

In these classifications, lightning type adding machines are classified in the category "Pascal type adding machine".

The only similarity is visual with regard to the input dials. The same logic infers that the sea horse and the horse belong to the same species ?

Disadvantages of the pascaline :

One of the disadvantages reported on the calculator is that only Blaise Pascal could repair it. I think the context relating to the use of the machines was not the same in the 17th century and in the 19ième/20ième centuries and that this problem was not of the same importance than today.

Some other points on which I disagree are discussed in the heading explaining how to use the pascaline.

The calculating machine of Léonard de Vinci :

I will not discuss a long time on the subject. It seems surprising to me (with the informations I could find) that a drawing presenting a train of gears in a constant ratio of ten to one in each of its 13 stages, could be thought as a draft of a calculating machine.

On the drawing, I do not see how to read the results of the calculations. The wheels turn in a continuous way (that would not facilitate the reading of the results, although Tchebitchev designed a calculating machine presenting this disadvantage). Léonard de Vinci having worked much on machines of forces (cranes, tackles...) the drawing presented seems to me probably related with this type of machines.