#### English Title

New Principles of Gunnery

#### Enestrom Number

77

#### Fuss Index

602

#### Original Language

German

#### Published as

Octavo book

#### Published Date

1745

#### Written Date

1745

#### Archive Notes

The text included here comes from the Opera Omnia's 1922 printing.

#### Content Summary

This is a treatise on the ballistics annotations that Euler added to his translation of Benjamin Robins's "little budget of rules, experiments, and guesses," thus changing it into the first scientific work on artillery. However, Euler also advances the theory of fluids in this work. He investigates the physical nature of air and fire and shows that the relationship between elasticity and density depends on the temperature. He also looks at air resistance and the motion of bodies that are projected in the air. In addition, Euler clearly and precisely states the problem of resistance, and gives a "clear and explicit corpuscular derivation" of the Newtonian law of resistance that is proportional to *v*^{2}∙sin^{2}(*a*). He also shows that the constant of proportionality is half as great for elastic molecules as it is for inelastic molecules. Euler derives a law that connects resistance with the difference in speed between the fluid and the body, expressing the resultant force as an integral over the profile of the body. It is in this work, too, that for the first time, a fluid mass is divided into fillets, each of which can be treated as a tube, representing the next great step in analytical fluid dynamics. Throughout, Euler uses intrinsic rather than fixed coordinates. It is in this book also that Euler gives the first proof of the d'Alembert paradox. (Based on Clifford Truesdell's introduction to *Opera Omnia* Series II, Volume 12.)

#### Original Source Citation

Berlin: Ambrosius Haude

#### Opera Omnia Citation

Series 2, Volume 14, pp.1-412.

#### Record Created

2018-09-25

## Notes

This work is a translation, with extensive commentary by Euler, of Benjamin Robins' New principles of gunnery. The text included here comes from the Opera Omnia's 1922 printing.