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CHAPTER I.

Planimeters in General.

History.

To whom the credit belongs for the invention of the Planimeter seems to be a disputed question.

While claims to that distinction have been made by and for several well-known and distinguished mathematicians who have devoted their time and attention to the subject, the best evidence goes to prove that the Planimeter, instead of being the product of the inventive skill of any one mind, is rather the combined results of the investigations of several, each working independently and often entirely unknown to othersó a fact which has characterized the production and perfection of many of the most important of modern inventions.

The employment of a wheel of known circumference rolling along a curved or broken line to determine its length is very oldó mention being made as having been thus used by the earliest of Egyptian mathematiciansó and the principle is still in use in the present so-called Opisometer and other instruments of similar nature.

Its application as a factor in an instrument for the measurement of the areas of plane figures seems, according to Prof. Shaw, to have been first adopted by Hermann of Munich about the year 1814.

The first complete Planimeter of which we have definite record appears to have been invented by Oppikofer and to have been exhibited by him in Paris in 1836.

A patent on a Planimeter was granted in 1849 to Wettli and Starke, who invented the instrument which still bears their names.

Other investigators who have devoted time and labor to the design and perfection of the instrument are Profs. Miller and Lorber of Loeben, Lämmle of Munich, and Bouniakovsky of St. Petersburg.

Since then the subject has received the attention of a large number of scientists and mathematicians, among the most prominent of whom are Mr. Coradi of Zurich and Prof. Amsler Laffon of Schaffhausen, who have both added improvements and extended the field of usefulness of the instrument until the Polar Planimeter of to-day is a marvel of mechanical skill and mathematical accuracy, performing the operations for which it was designed in a manner which leaves little to be desired.

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