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Vectorial treatment of refraction of skew rays by a prism
NOTES FROM THE RESEARCH LABORATORY, EASTMAN KODAK COMPANY.* AN ELECTRICAL SOLUTION-MIXING DEVICE: By K. C. D. Hickman and D. Hyndman.
ELECTRICAL titration methods in general use employ electrodes immersed in the reacting liquids and give indications of hydrogen or other ion concentrations. T h e indications have been used by various workers to control automatically the mixing of the two reagents. Such electrical controls m a y be described as operating internally. The present m e t h o d uses externally gaseous indicators such as sulfur dioxide or ammonia, which it detects by an 'electric nose' placed over the reacting vessel. T h e variations in current actuate a valve which limits the particular solution in excess at t h a t moment. In this connection a special mechanism has been devised which requires so little energy for actuation that no amplification or relays are required on the electrical circuit for the 'nose' even t h o u g h thousands of gallons of solution be handled each hour. T h e device is useful both in acidimetry and in oxidation--reduction reactions, particularly with complex mixtures, since only the chosen volatile constituent can affect the control. VECTORIAL TREATMENT OF REFRACTION OF S K E W RAYS BY A PRISM. 2 By L. Silberstein.
TttE incident ray, of a n y orientation, being represented by the unit vector r, the refracted and ultimately emergent ray is expressed by the vector formula, r' = r q- gin1 q- g~.n2 * Communicated by the Director. ~Communication No. 321 from the Kodak Research Laboratories and published in Ind. Eng. Chem. 20: 2I 3. I928. Communication No. 333 from the Kodak Research Laboratories and published in J. Opt. Soc. Amer. I6: 88. 1928. 721
722
E A S T M A N KODAK COMPANY NOTES.
[J. F. 1.
(given some time ago in "Simplified M e t h o d " ) , where n l , n,2 are the normals of the two faces of the prism and gl, g2 are scalar factors; in obvious notation, gl = cos il - picos i~', etc. From this simple formula the two angular co6rdinates of the emergent in terms of those of the incident ray are now most directly deduced. If 0 be the inclination of the incident ray to the edge of the prism and 6 the angle between the first face of the prism and the plane through the edge parallel to the incident ray, then, for the emergent ray, 0' -- 0, and, the scalar g2 being readily eliminated, cos (6' -- ~) = cos (6 -- ~) -- gt sin c/sin 0, where ~ is the refracting angle of the prism. The factor gl is written explicitly in terms of incidence data. The advantages of the vectorial as compared with the usual t r e a t m e n t are brought out. The limiting condition, beyond which there is total reflection, is derived and discussed. CONTRIBUTION TO T H E THEORY OF P H O T O G R A P H I C EXPOSURE.~ By L. Silberstein.
IN the first part of the paper the original form of the q u a n t u m theory of photographic exposure and its several modifications are critically discussed. It is shown that none of them represents the photomicrographic findings with sufficient accuracy. The second and main part is devoted to nuclear theories, in which the element of chance is transferred from the impinging light to certain peculiarities of the grains themselves, viz., incipient nuclei haphazardly distributed among them. After a brief general introduction to such theories, a mathematical formulation of Toy's more or less qualitative theory is given. This is shown to lead to a formula which again deviates essentially from observed facts. Such being the case, an alternative type of nuclear theory of Communication No. 336 from the Kodak Research Laboratories and published in Phil. Mag. 5 : 4 6 4 • 1928.
ELECTRICAL titration methods in general use employ electrodes immersed in the reacting liquids and give indications of hydrogen or other ion concentrations. T h e indications have been used by various workers to control automatically the mixing of the two reagents. Such electrical controls m a y be described as operating internally. The present m e t h o d uses externally gaseous indicators such as sulfur dioxide or ammonia, which it detects by an 'electric nose' placed over the reacting vessel. T h e variations in current actuate a valve which limits the particular solution in excess at t h a t moment. In this connection a special mechanism has been devised which requires so little energy for actuation that no amplification or relays are required on the electrical circuit for the 'nose' even t h o u g h thousands of gallons of solution be handled each hour. T h e device is useful both in acidimetry and in oxidation--reduction reactions, particularly with complex mixtures, since only the chosen volatile constituent can affect the control. VECTORIAL TREATMENT OF REFRACTION OF S K E W RAYS BY A PRISM. 2 By L. Silberstein.
TttE incident ray, of a n y orientation, being represented by the unit vector r, the refracted and ultimately emergent ray is expressed by the vector formula, r' = r q- gin1 q- g~.n2 * Communicated by the Director. ~Communication No. 321 from the Kodak Research Laboratories and published in Ind. Eng. Chem. 20: 2I 3. I928. Communication No. 333 from the Kodak Research Laboratories and published in J. Opt. Soc. Amer. I6: 88. 1928. 721
722
E A S T M A N KODAK COMPANY NOTES.
[J. F. 1.
(given some time ago in "Simplified M e t h o d " ) , where n l , n,2 are the normals of the two faces of the prism and gl, g2 are scalar factors; in obvious notation, gl = cos il - picos i~', etc. From this simple formula the two angular co6rdinates of the emergent in terms of those of the incident ray are now most directly deduced. If 0 be the inclination of the incident ray to the edge of the prism and 6 the angle between the first face of the prism and the plane through the edge parallel to the incident ray, then, for the emergent ray, 0' -- 0, and, the scalar g2 being readily eliminated, cos (6' -- ~) = cos (6 -- ~) -- gt sin c/sin 0, where ~ is the refracting angle of the prism. The factor gl is written explicitly in terms of incidence data. The advantages of the vectorial as compared with the usual t r e a t m e n t are brought out. The limiting condition, beyond which there is total reflection, is derived and discussed. CONTRIBUTION TO T H E THEORY OF P H O T O G R A P H I C EXPOSURE.~ By L. Silberstein.
IN the first part of the paper the original form of the q u a n t u m theory of photographic exposure and its several modifications are critically discussed. It is shown that none of them represents the photomicrographic findings with sufficient accuracy. The second and main part is devoted to nuclear theories, in which the element of chance is transferred from the impinging light to certain peculiarities of the grains themselves, viz., incipient nuclei haphazardly distributed among them. After a brief general introduction to such theories, a mathematical formulation of Toy's more or less qualitative theory is given. This is shown to lead to a formula which again deviates essentially from observed facts. Such being the case, an alternative type of nuclear theory of Communication No. 336 from the Kodak Research Laboratories and published in Phil. Mag. 5 : 4 6 4 • 1928.