Compton generator: Difference between revisions

Content deleted Content added

Inline

Revision as of 19:01, 14 September 2019

A Compton generator^[1]^[2] or Compton tube^[3] is an apparatus for experiment to demonstrate the Earth's rotation, similar to the Foucault pendulum and to gyroscope devices.^[4]

Explanation of apparatus

A Compton generator is a circular hollow glass ring tube shaped like a doughnut, the inside of which is filled with water.^[1] If the ring lies flat on the table, the water in the ring is stationary, and it is then turned over by rotating itself 180 degree around a diameter, such that it again lies flat on the table surface, which is horizontal. The result of the experiment is that the water moves with a certain constant drift velocity around the tube after the doughnut has been rotated. If there were no friction with the walls, the water would continue to circulate indefinitely.^[1]

The ring used in the initial experiment was made of one inch brass tubing bent into a circle eighteen inches in diameter, where the windows were placed the tube was constricted to a diameter of about three eights of an inch.^[5]

Compton used small droplets of coal oil mixed in the water to measure the drift velocity under a microscope.^[6]

Analysis

Assume the diameter of the glass tube is much smaller than the diameter of the ring, and $R$ is the radius of the ring, $\omega$ is the Earth rotation rate and $\lambda$ is the latitude.

Initially the ring is horizontal and the water is stationary. Second the ring is then quickly rotated by 180° around its East-West diameter and stopped, such that it again lies flat on the table surface, which is horizontal. At this time, the velocity $v_{th}$ of the water in the tube is given by
$v_{th}=2\omega R\sin \lambda$

Note that a rotation from the vertical to the vertical position produces the velocity $v_{tv}$ of the water in the tube is given by
$v_{tv}=2\omega R\cos \lambda$

Experimental verification

Compton used this measured drift velocity to determine his latitude to within 3% accuracy.^[6]

References

^ ^a ^b ^c Analytical Mechanics, p. 280.
^ Classical Mechanics, p. 365.
^ Blackie's Dictionary of Physics, p. 72.
^ A laboratory method of demonstrating the Earth's rotation 1913, p. 803.
^ A determination of latitude, Azimuth, and the length of the day independent of astronomical observations 1915, p. 110&111.
^ ^a ^b Analytical Mechanics, p. 281.

Bibliography

Journal

Compton, Arthur Holly (1913). "A laboratory method of demonstrating the Earth's rotation". Science. 37: 803–806.
Compton, Arthur Holly (1915). "A determination of latitude, Azimuth, and the length of the day independent of astronomical observations". Physical Review. 5 (2): 109–117.
Compton, Arthur Holly (1915). "Watching the Earth revolve". Scientific American Supplement. 79: 196–197.

Books

Hand, Louis N. (1999). Analytical Mechanics. Cambridge University Press. ISBN 978-0521575720.
Taylor, John R. Classical Mechanics. S.Chand & Company Ltd. ISBN 978-1891389221.
Blackie's Dictionary of Physics. S.Chand & Company Ltd. 2000. ISBN 978-8121942379.

[FOOTNOTEAnalytical_Mechanics280-1] Analytical Mechanics, p. 280.

[FOOTNOTEClassical_Mechanics365-2] Classical Mechanics, p. 365.

[FOOTNOTEBlackie's_Dictionary_of_Physics72-3] Blackie's Dictionary of Physics, p. 72.

[FOOTNOTEA_laboratory_method_of_demonstrating_the_Earth's_rotation1913803-4] A laboratory method of demonstrating the Earth's rotation 1913, p. 803.

[FOOTNOTEA_determination_of_latitude,_Azimuth,_and_the_length_of_the_day_independent_of_astronomical_observations1915110&111-5] A determination of latitude, Azimuth, and the length of the day independent of astronomical observations 1915, p. 110&111.

[FOOTNOTEAnalytical_Mechanics281-6] Analytical Mechanics, p. 281.

[1]

[2]

[3]

[4]

[5]

[6]

@@ Line 1: / Line 1: @@
 {{short description|Physics apparatus to demonstrate rotation of Earth}}
 [[File:Watching the Earth revolve, Fig-4.jpg|thumb|Arthur Compton was experimenting by the Compton Generator.]]
-A '''Compton generator'''{{sfn|Analytical Mechanics|p=280}}{{sfn|Classical Mechanics|p=365}} or '''Compton tube'''{{sfn|Blackie's Dictionary of Physics|p=72}} is an apparatus for experiment to demonstrate the [[Earth's rotation]], similar to the [[Foucault pendulum]] and to [[gyroscope]] devices{{sfn|A laboratory method of demonstrating the Earth's rotation|1913|p=803}}.
+A '''Compton generator'''{{sfn|Analytical Mechanics|p=280}}{{sfn|Classical Mechanics|p=365}} or '''Compton tube'''{{sfn|Blackie's Dictionary of Physics|p=72}} is an apparatus for experiment to demonstrate the [[Earth's rotation]], similar to the [[Foucault pendulum]] and to [[gyroscope]] devices.{{sfn|A laboratory method of demonstrating the Earth's rotation|1913|p=803}}
 == Explanation of apparatus ==
 [[File:A Determination of Latitude, Fig1.jpg|thumb|Constraction of Compton generator.]]
-A Compton generator is a circular hollow glass ring tube shaped like a doughnut{{sfn|Analytical Mechanics|p=280}}.The inside of the ring tube is filled with water{{sfn|Analytical Mechanics|p=280}}. If the ring lies flat on the table, the water in the ring is stationary, and it is then turned over by rotating itself 180 degree around a diameter, such that it again lies flat on the table surface, which is horizontal{{sfn|Analytical Mechanics|p=280}}.The result of the experiment is that the water moves with a certain constant drift velocity around the tube after the doughnut has been rotated{{sfn|Analytical Mechanics|p=280}}.If there were no friction with the walls, the water would continue to circulate indefinitely{{sfn|Analytical Mechanics|p=280}}.
+A Compton generator is a circular hollow glass ring tube shaped like a doughnut, the inside of which is filled with water.{{sfn|Analytical Mechanics|p=280}} If the ring lies flat on the table, the water in the ring is stationary, and it is then turned over by rotating itself 180 degree around a diameter, such that it again lies flat on the table surface, which is horizontal. The result of the experiment is that the water moves with a certain constant drift velocity around the tube after the doughnut has been rotated. If there were no friction with the walls, the water would continue to circulate indefinitely.{{sfn|Analytical Mechanics|p=280}}
-The ring used was made of one inch brass tubing bent into a circle eighteen inches in diameter{{sfn|A determination of latitude, Azimuth, and the length of the day independent of astronomical observations|1915|p=110}}, where the windows were placed the tube was constricted to a diameter of about three eights of an inch{{sfn|A determination of latitude, Azimuth, and the length of the day independent of astronomical observations|1915|p=111}}.
+The ring used in the initial experiment was made of one inch brass tubing bent into a circle eighteen inches in diameter, where the windows were placed the tube was constricted to a diameter of about three eights of an inch.{{sfn|A determination of latitude, Azimuth, and the length of the day independent of astronomical observations|1915|p=110&111}}
-Compton used small droplets of coal oil mixed in the water to measure the drift velocity under a microscope{{sfn|Analytical Mechanics|p=281}}.
+Compton used small droplets of coal oil mixed in the water to measure the drift velocity under a microscope.{{sfn|Analytical Mechanics|p=281}}
-The experiment consists of laying the tube flat on a table until the water in it came to equilibrium, then slowly (in about 3 seconds) rotating it about an east-west axis until it had turned 180° and wasagain lyingflat on the table{{sfn|Analytical Mechanics|p=281}}.
 == Analysis ==
 Assume the diameter of the glass tube is much smaller than the diameter of the ring, and <math>R</math> is the radius of the ring, <math>\omega</math> is the Earth rotation rate and <math>\lambda</math> is the latitude.
-Initially the ring is horizontal and the water is stationary. Second the ring is then quickly rotated by 180° around its East-West diameter and stopped, such that it again lies flat on the table surface, which is horizontal. At this time, the velocity <math>v_{th}</math>  of the water in the tube is given by.
+Initially the ring is horizontal and the water is stationary. Second the ring is then quickly rotated by 180° around its East-West diameter and stopped, such that it again lies flat on the table surface, which is horizontal. At this time, the velocity <math>v_{th}</math>  of the water in the tube is given by
 {{indent|4}}<math>v_{th} = 2 \omega R  \sin \lambda</math>
-Note that a rotation from the vertical to the vertical position produces the velocity <math>v_{tv}</math> of the water in the tube is given by.
+Note that a rotation from the vertical to the vertical position produces the velocity <math>v_{tv}</math> of the water in the tube is given by
 {{indent|4}}<math>v_{tv} = 2 \omega R  \cos \lambda</math>
 == Experimental verification ==
-Compton used this measured drift velocity to determinehis latitude{{sfn|Analytical Mechanics|p=281}}. He was measured to within 3% accuracy on his laboratory, which is pretty good for such a simple device{{sfn|Analytical Mechanics|p=281}}.
+Compton used this measured drift velocity to determine his latitude to within 3% accuracy.{{sfn|Analytical Mechanics|p=281}}
 == References ==