The ballistic pendulum and air resistance
New Principles of Gunnery, published by Benjamin Robins in London in 1742, was an answer to the gap between Galileo's calculation (a parabola in vacuum) and observed practice (the shot flies quite unlike a parabola). Robins built a ballistic pendulum: a heavy target on a suspension. The ball, passing through the pendulum, transfers to it a momentum that is read off from the amplitude of the swing. From this reliable velocities of cannon balls and, indirectly, the force of air resistance as a function of velocity were obtained.
Robins' work showed that air resistance rises by a jump above the speed of sound, not by the square of velocity as had been commonly assumed. Practical ballistics ceased to be a frictionless geometry; it became an experimental branch of mechanics. Euler thought Robins' book so important that he translated it into German with a commentary (Berlin, 1745).
Why this date
exact: London, 1742.
What grew out of it
-
The German edition of Robins with Euler's mathematics
improved · Confidence: high
Euler put his own mathematical apparatus and appendices into the translation of Robins; the Neue Grundsätze der Artillerie of 1745 stands directly on the New Principles of Gunnery of 1742.
Link sources
- MacTutor History of Mathematics, «Benjamin Robins» Verified 5 Oct 2026
The New Principles of Gunnery was rated highly by Euler who translated it into German, adding his own commentary, and the translation was published in Berlin in 1745.
"Verified" means that on that day the quotation was found at the address given, word for word. No date means we have not been able to open the source yet, not that the quotation is wrong.
- MacTutor History of Mathematics, «Benjamin Robins» Verified 5 Oct 2026
Node sources
- MacTutor History of Mathematics, «Benjamin Robins» Verified 5 Oct 2026
The work Robins published in 1742 was New Principles of Gunnery.
"Verified" means that on that day the quotation was found at the address given, word for word. No date means we have not been able to open the source yet, not that the quotation is wrong.