His 1892 textbook on applications of elliptic functions is of acknowledged excellence. He was one of the world's leading experts on applications of elliptic integrals in electromagnetic theory.[3]
He was a Plenary Speaker of the ICM in 1904 at Heidelberg[4] (where he also gave a section talk)[5] and an Invited Speaker of the ICM in 1908 at Rome, in 1920 at Strasbourg,[6] and in 1924 at Toronto.
Greenhill formulaedit
In 1879, Greenhill developed a rule of thumb for calculating the optimal twist rate for lead-core bullets. This shortcut uses the bullet's length, needing no allowances for weight or nose shape.[7] Greenhill applied this theory to account for the steadiness of flight conferred upon an elongated projectile by rifling. The eponymous Greenhill formula, still used today, is:
where:
C = 150 (use 180 for muzzle velocities higher than 2,800 ft/s)
D = bullet's diameter in inches
L = bullet's length in inches
SG = bullet's specific gravity (10.9 for lead-core bullets, which cancels out the second half of the equation)
The original value of C was 150, which yields a twist rate in inches per turn, when given the diameter D and the length L of the bullet in inches. This works to velocities of about 840 m/s (2800 ft/s); above those velocities, a C of 180 should be used. For instance, with a velocity of 600 m/s (2000 ft/s), a diameter of 0.5 inches (13 mm) and a length of 1.5 inches (38 mm), the Greenhill formula would give a value of 25, which means 1 turn in 25 inches (640 mm).
Recently, Greenhill formula has been supplemented with Miller twist rule.
Textbooksedit
A. G. Greenhill Differential and integral calculus, with applications ( London, MacMillan, 1886) archive.org
A. G. Greenhill, The applications of elliptic functions (MacMillan & Co, New York, 1892)[8] University of Michigan Historical Mathematical Collection
A. G. Greenhill, A treatise on hydrostatics (MacMillan, London, 1894) archive.org
A. G. Greenhill, The dynamics of mechanical flight (Constable, London, 1912) archive.org
A. G. Greenhill, Report on gyroscopic theory (Darling & Son, 1914)[9]
Referencesedit
^"Greenhill, George Alfred (GRNL866GA)". A Cambridge Alumni Database. University of Cambridge.
^Greenhill, Alfred George (1907). "The elliptic integral in electromagnetic theory". Bull. Amer. Math. Soc. 8 (4): 447–534. doi:10.1090/s0002-9947-1907-1500798-2. MR 1500798.
^"The Mathematical Theory of the Top considered historically by A. G. Greenhill". Verhandlungen des dritten internationalen Mathematiker-Kongresses in Heidelberg von 8. bis 13. August 1904. ICM proceedings. Leipzig: B. G. Teubner. 1905. pp. 100–108.
^"Teaching of mechanics by familiar applications on a large scale by A. G. Greenhill". Verhandlungen des dritten internationalen Mathematiker-Kongresses in Heidelberg von 8. bis 13. August 1904. ICM proceedings. Leipzig: B. G. Teubner. 1905. pp. 582–585.
^"The Fourier and Bessel Functions contrasted by G. Greenhill" (PDF). Compte rendu du Congrès international des mathématiciens tenu à Strasbourg du 22 au 30 Septembre 1920. 1921. pp. 636–655.
^Mosdell, Matthew. The Greenhill Formula. "Archived copy". Archived from the original on 18 July 2011. Retrieved 19 August 2009.{{cite web}}: CS1 maint: archived copy as title (link) (Accessed 2009 AUG 19)
^Harkness, J. (1893). "Review: The Applications of Elliptic Functions by Alfred George Greenhill" (PDF). Bull. Amer. Math. Soc. 2 (7): 151–157. doi:10.1090/s0002-9904-1893-00129-8.
^Wilson, Edwin Bidwell (1917). "Review: Report on Gyroscopic Theory by Sir G. Greenhill" (PDF). Bull. Amer. Math. Soc. 23 (5): 241–244. doi:10.1090/s0002-9904-1917-02930-8.
External linksedit
Wikisource has original works by or about: Alfred George Greenhill
Quotations related to Alfred George Greenhill at Wikiquote
Alfred George Greenhill. The First Century of the ICMI (1909 - 2008)