The Midget Calculator is a calculating device for multiplying and dividing, created by LeRoy James Leishman in the early 20th century. The word "Midget" is offensive, so I call it "The Marmite Calculator".
The thing is just a ruler with a strange scale, and is very easy to use. Print one out and try it for yourself!
These images are my own creation. I have tried very hard to make this image look exactly like the original Midget Calculator, but this is not a scan- it is a recreation. The fonts do not match exactly to the original, but it's pretty close.
Here is a PNG with a high-quality image of the Midget Calculator. If you want to play around with it, you can get the SVG of it too.
The fonts used in the SVG are standard on Mac OS. It may look weird on another operating system, especially the script logo text.
I explain how it works in this short video I made:
This is part of my series of videos about antique computational devices. Here is the full series playlist
Here is the original text instructions from the back of the machine, written (apparently) by the inventor LeRoy James Leishman:
Multiplication:-The value of the numbers upon the scale is relative: that is, the position of the decimal point may be disregarded. For instance, 10 may mean 1, 10, 100, etc. To multiply, one of two slightly different methods must be used, only one or two experiments being necessary, however, to teach the operator to tell at a glance which method to apply. The methods are as follows:-
a. Place the calculator on a sheet of paper and with a sharp pencil mark on the paper as accurately as possible the position of 10 on the scale. Then, holding the instrument in the same place, mark the position of your multiplicand as you find it on the scale. Now move the calculator, placing the multiplier at the mark made for 10; and where the other mark appears (the mark indicating the position of the multiplicand) the product of the two numbers is found on the scale. When this method is used, we place the decimal point so that there will be one figure less to the left of the point in the product than the sum of the figures to the left of the points in the factors. For example, in multiplying 13 by 12, we mark the position of 10 and 13, and moving the calculator till 12 appears at the 10 mark, we find a certain number where the other mark appears, the real answer having three figures to the left of the decimal, since four is the sum of the figures in the two factors; and placing the decimal accordingly, we find the answer to be 156.
b. Mark as accurately as possible the position of 100 on the scale; and then, without moving the instrument, mark the position of the multiplicant. Now move the Calculator, placing the multiplier at the mark made for 100; and where the other mark touches the instrument, the product may be read. When this method is used, the number of figures to the left of the decimal in the product equals the sum of figures to the left of the points in the factors. For example, in multiplying 12 by 9, we mark on the paper the positions of 100 and 12; and then moving the instrument so that the multiplier appears at the 100 mark, we find the product where the other mark appears. To the left of the decimal points in these two factors we have three figures in all; and the answer therefore has three figures to the left of the point, and is found to be 108.
Division:-Place the calculator on a sheet of paper, and with a sharp pencil mark the position of both the divident and divisor without moving the instrument. If the dividend appears to the right of the divisor, place 10 at the divisor mark: if the dividend comes at the left of the divisor, place 100 at the divisor mark. Where the other mark appears the quotient is found. If 100 is placed at the divisor mark, the quotient has as many places to the left of the decimal point as there are to the left of the point in the divident, minus the number to the left of the divisor. For example in dividing 112.5 by 45, we find that the quotient must contain, to the left of the decimal, three figures less two, which would be one; and, following this out, we obtain 2.5 for the answer. If, on the other hand, 10 is placed at the divisor mark, this difference must be increased by one- that is, one place must be added. For example, in dividing 144 by 12, we find that the quotient must contain three figures less two, plus one, which would be two; and following this out, we obtain 12 as the answer.
Proportion and Percentage:-Find the first and second term of the proportional on the scale and mark their location with a sharp pencil. Then move the Calculator, placing the third term at the first term mark; and where the other mark appears the answer is found. For example, mark 10 and 20, and moving the instrument so that 40 comes at the 10 mark, we find 80 to be the four term.
In percentage, the lesser number is to the greater as the unknown is to 100.