The study of β-ray spectra has now advanced to that stage at which, for the majority of radioactive substances, the velocities of the homogeneous electrons forming the “lines” have been measured with a fair accuracy. The relative intensities of the “lines” have in the past been obtained by visual estimation of the photographic blackening of the plates on which they have been recorded, and it has become important to obtain more precise information on this subject. The most direct method of determining the relative intensities would be to count the number of, or measure the total charge carried by, the particles forming the lines. This is not practicable, to any high degree of accuracy, because of the small effects which are obtainable, and it is obvious that the photographic plate, in giving quite intense and sharp lines, in addition to a permanent record, presents many advantages. The use of this method, however, necessitates the calibration of the plate both for the variation of the blackening with exposure and also with velocity of the rays. The corresponding calibrations for ordinary light have now become a matter of routine, but since there has, as yet, been little systematic work on the behaviour of the photographic plate to β-rays, we have thought it best to record in this paper such experiments as we have found necessary before undertaking the main intensity problem. It is the dependence of blackening on exposure which is mainly treated in this paper, although we have in addition obtained some interesting results on the effect of β-particles of different velocities. In an investigation on the relationship between blackening and exposure
i. e
., the characteristic curve of a type of plate, it is first necessary to find the dependence of the blackening D on the time of exposure
t
, when the product of intensity I and time of exposure
t
is kept constant. If D is independent of
t
, when I.
t
is constant, then the Reciprocity Law of Bunsen and Roscoe is said to be valid for the plate. This law, although it has to be slightly modified for luminous radiation, has been shown to be true in the case of X-rays and also for heterogeneous β-rays. In all previous work on the photographic action of β-rays the particles were of heterogeneous velocities, but in view of the ultimate object of this investigation it was thought unsatisfactory to employ heterogeneous particles, and although the procedure was thereby made rather more laborious, beams of practically homogeneous particles, taken from the continuous β-ray spectrum, were used. It is in general important, when dealing with an unknown type of plate, after investigating the validity of the Reciprocity Law, to determine the variation of the characteristic curve with time of development, and thereby find the optimum value. Our general experience in photographing β-ray spectra had led us to employ a particular type of plate and method of development, and the main value of our experiments on the variation of the characteristic curve with time of development was that it indicated the error introduced into the value of the density for a given uncertainty in the time of development.
Local abelian Kato-Parshin reciprocity law: A survey
