THE MACH NUMBER

MACH, ERNST & SALCHER, P.

Photographische Fixierung der durch Projectile in der luft eingeleiteten Vorgänge. [In: Sitzungsberichte der kaiserlichen Akademie der Wissenschaften. Mathematisch-Naturwissenschaftliche Classe, 95. Band, IV und V. Heft. Jahrgang 1887 April und Mai. Zweite Abtheilung].

Wien, 1887. 8vo. The entire volume. Uncut and unopened in the orig. printed yellow wrappers, some soiling. Lacks upper part of spine, otherwise no tears, creases or lacks. Pp. 764-780 + one plate. [Entire volume: VIII, (2) pp., pp. 761-1120 + 3 plates, two of which are folded].

First edition of the seminal paper, in which Mach laid the basis for the principles of supersonics, determined the "sonic boom", demonstrated an object's speed relative to the speed of sound, now called the "Mach number" of an object, and presented the first photograph of a shock wave in front of an object moving at supersonic speed.

"Between 1873 and 1893 Mach and various collaborators, including his son Ludwig, devised and perfected optical and photographic techniques to study sound waves and the wave propulsion and gas dynamics of projectiles, meteorites, explosions, and gas jets. Stimulated by the remarks of the Belgian artillerist Henri Melsens, in 1881 Mach undertook to study the flight of projectiles by means of photographic techniques that he had already devised for other experiments in his Prague laboratory. His celebrated 1887 paper on supersonics was published jointly with P. Salcher of the Marine Academy of Fiume (now Rijeka, Yougoslavia) in the "Sitzungsberichte" of the Academy of Sciences of Vienna. The experiments described in this classic paper were carried out in Fiume with the support of the Austrian Royal Navy." (D.S.B., VIII: 597).

In this highly influential paper, Mach demonstrates, with the aid of his photograph of a bullet in flight and the shock wave produced by the gas around the tip of it (the first such picture in history), that the angle which the shock wave makes with the direction of its motion is related to the speed of sound and to the speed of the projectile. This angle is called the Mach angle (coined by Ludwig Prandtl in 1907). This discovery turned out to be of ground-breaking character, and in 1929 J. Ackeret suggested to use the term "Mach number" for the value of the ratio of the speed of an object to the speed of sound, recognizing the profound effect that this discovery had on aerodynamics for high-speed projectile studies. "The Mach number was introduced into the literature in English by the late 1930's and since the end of World War II has taken on considerable importance in theoretical and fluid dynamics." (D.S.B., VIII: 597).
Unlike most other units of measure, the number in this case comes after the name of the unit, making the second Mach number not "2 Mach", but "Mach 2". The "Mach 2" thus indicates a velocity of twice the speed of sound. Mach here also determines the effect of an object that travels past the speed of sound, namely the "sonic boom".

"By 1885 Mach had worked out the details of supersonic motion, along the way developing high-speed photographic techniques. Most importantly for engineers, Mach Number is the ratio of the speed of sound in the given medium to the speed of the projectile; his work is essential to modern aerodynamics, and through it the word 'Mach' has bizarrely entered into popular culture as an icon for razors, sound systems, fighter pilots, and high speed fuels." (Stanford Encyclopaedia of Philosophy).

The Austrian physicist and philosopher Ernst Mach was highly influential among his contemporaries and is famous for the impact he had on the Vienna Circle. Though his main contribution to physics lies in his seminal description and photographs of the shock waves and his descriptions of how passing the speed of sound compressed air in front of projectiles, his more general contributions to philosophy and science were also immense. He was an early devotee of an extreme form of positivism, and his passionate ways of expounding his theories and his success as a polemicist and popularizer influenced an entire generation of scientists towards a profound skepticism that even extended into the use of abstract mathematics as an element of physical theories. He was highly critical of physical science and tried to free it from all elements that were not verifiable by sensory experience.

"Ernst Mach (18 Februrary, 1838 - 19 February, 1916), made major contributions to, physics, philosophy, and physiological psychology. In physics, the speed of sound bears his name, as he was the first to systematically study super-sonic motion. He also made important contributions to understanding the Doppler effect. His critique of Newtonian ideas of absolute space and time were an inspiration to the young Einstein, who credited Mach as being the philosophical forerunner of relativity theory. His systematic skepticism of the old physics was similarly important to a generation of young German physicists." (Stanford Encyclopaedia of Philosophy).

Order-nr.: 37984