C. D. Shane

LIMB-DARKENING AND THE ABSORPTION COEFFICIENT

A detailed interpretation of the spectra of the sun and stars requires a knowledge of the absorption coefficient in the atmospheres of these bodies. We should like to be able to calculate this coefficient for any wave length in terms of the temperature, pressure, and chemical composition at any point in the atmosphere of a star. Some progress has been made in this direction through the work of a number of astronomers, but despite a great amount of endeavor our knowledge of the absorption coefficient is far from satisfactory. At present the theoretical determinations are found in some respects to indicate results that differ notably from observation. As the theory is improved in the future we must supply numerous observational tests of its validity. It is the purpose of this paper to discuss in an elementary fashion one type of test that can be applied to theories of the absorption coefficient, namely, the observation of limbdarkening in the sun and stars. The theory of limb-darkening was placed on its present basis largely through the work of Lindblad and Milne in papers published from 1920 to 1923. The physical picture of limb-darkening is rather simple. Radiation that emerges from an absorbing stellar atmosphere will on the whole originate in regions of greater depth and therefore higher temperature if viewed normally to the stellar surface than if viewed tangentially. In other words, radiation from the center of the stellar disk corresponds roughly to a higher temperature than that from the limb. We should therefore expect under all conditions to find the limb fainter than the center. In addition, the limb should in general be redder than the center though this need not always be the

THE DETERMINATION OF TIME FROM SHADOWS SHOWN ON A PHOTOGRAPH

From time to time the astronomer is called upon to furnish certain astronomical data in connection with court trials. Some years ago the Chief Justice of the California Supreme Court called upon the authors to inquire if it were possible to calculate the time of day from shadows appearing in certain terrestrial photographs. These photographs had been submitted in connection with the Mooney case. They were taken of the preparedness day parade from the top of the Meadowbrook Building and show Mooney on the roof of the adjoining Eilers Building. It was claimed that a clock appearing in the pictures indicated the times when they had been taken. The original pictures were small and considerable doubt existed that the face of the clock could be read. The original films and pictures were lost and only enlargements were available in later years. In these enlargements it certainly is not possible to read the times directly. A flag on lower Market Street completely obscured the clock on the Ferry Building which otherwise should have shown the time. Fortunately the Sun was shining when the pictures were taken so that various objects cast distinct shadows. It appeared possible to use the positions of these shadows for time determinations. The methods employed for this purpose are described in the present article. The problem of determining the time from shadows would be a simple one if the positions of an object and its shadow could be located. Then the time could be determined from the distance of the shadow measured from a point vertically beneath the object casting it or from the azimuth of the shadow as seen from the object. A careful inspection of the photographs revealed a single object and its shadow for this purpose, namely, a trolley pole at the corner of Mason and Market streets. There were two reasons for rejecting this object. From the photographs it was difficult to locate the point on the sidewalk where the end of the shadow fell and there was no assurance that the