413 



KNOWLEDGE. 



October. 19in. 



Density which is produced if dc\elopinent is prolontjcd to 

 the limit. 



It will be seen that (for a non-fogging platel the Density for 

 a given exposure to light reaches a limit. This limit is 

 generally reached in about ten times the usual time of 

 development, that is to say, in about that time further 

 increase in the Density by increase of developing time will be 

 so small that it may be disregarded. 



The relation between the Density produced iwith a given 

 developing time! and the exposure, is also exponential, but of a 

 far more complex form. 



The relation is shown in the figure below. 



D 



FiGUKi; 1. 



This curve, which, of course, possesses an inflection point, 

 can in practice be divided into three portions. 



These portions were termed by Hurter and Driffield: — 



(1) " The period of under exposure." Here D increases 



more rapidly than log. E (for the lower portion, D, 

 is proportional to l-'l. 



(2) "The period of correct exposure." Here D is 



proportional to log. E. 



(3) "The period of o\er exposure." Here D increases 



less rapidly, and finally reaches a limit (eventuallv 

 re versing). 



We are not now concerned with the properties of this cur\e 

 as a whole, interesting as that subject is, but only with the 

 " period of correct exposure," because it is only for densities 

 falling within this period that the relations to exposure are 

 sufficiently simple to be trustworthy as a basis for the 

 measurement of intensities. 



For this period the relation between D and log. E is 

 approximately linear, and we may write the equation — 



D = 7 (log. E — log. i) where 7 = tan D. 



7 was called by Hurter and Driffield the development 

 factor, while i. the exposure corresponding to log. i. was 

 termed the inertia, being taken as a measure of the 

 iiisensitivciicss of the plate, the Hurter and Driffield speed 



number being defined bv them as . 



i 



It is found that for developers without bromide the value of 



it is unaffected by the time of development, 7 increasing 



proportionally to the Density, so that 7 = C (1 — e^*") where 



C is the maximum steepness of gradation which the plate can 



attain. 



It is this maximum steepness of gradation (or 7oo as it niav 

 be termed! by which the gradation of a plate is defined. Soft 

 working plates have low 7oo's (from 1'2 to I'yi. hard working 

 plates high 7oo's (from 2'5 to 4'0). 



In order, therefore, to find the relation between two 

 intensities of radiation all that is theoreticallj- necessary is to 

 measure the densities produced on a plate which has been 



developed to a known 7. or for a known time if k and 7oo are 

 known. 



Practically, however, there would be too much uncertainty 

 introduced if measurements were made in that manner, and 

 the following example will explain the method of procedure in 

 practice. It was desired to measure the relative intensity of 

 the Sodium lines Di and Dj in a number of light sources in 

 order to find whether the ratio was dependent on the source, 

 .Arc. flame, spark and vacuum tube spectra were used. 



The spectroscope was a reflecting grating Littrow spectro- 

 graph of eight feet focal length, the separation for the D lines 

 in the first order being about 1 mm. 



The slit was opened until the two lines just touched one 

 another, each being about 1 mm. wide. 



Plates were then obtained which were fully sensitive to the 

 spectral region concerned and which were coated on patent 

 plate glass. This is absolutely necessarj- ,as the errors 

 introduced by ordinary glass are very considerable. The 

 plates were cut from large plates, the edges being first cut oft' 

 and thrown away. A colour screen was then prepared which 

 passed only the narrow portion of the spectrum which had the 

 D lines at the centre of it. and this screen was placed in front 

 of an acetylene standard light and some of the plates exposed 

 to this behind a rotating sector wheel so that a series of 

 increasing exposures were impressed upon them. Whenever 

 now a spectrum negati\e was exposed one of these " sector 

 strip " negatives was developed with it. for the same time, in 

 the same dish. 



The Density of the spectral lines and also of the \arious 

 sectors of the negatives exposed behind the sector wheel to 

 the standard light were measured by means of a photometer, 

 the Density due to glass and gelatine being subtracted, and a 

 curve showing the relation between the Density and logarithmic 

 exposure of the sector strip negative was plotted. 



Into this curve were interpolated the Densities of the spectral 

 lines and the corresponding exposures were read oft' on the 

 abscissa. (Figure 2). 



LogE 



FlCUKK 2. 



It will be obser\ed that this method avoids all possibility of 

 error in development and also allows for deviation of the cur\e 

 from a straight line. 



The shape of the plate curve depends to some extent upon 

 the wavelength of the light, for w hich reason the colour screen 

 was employed in exposure. 



The result of the measurements made was to show that — 



'd. 



— = r41 and is independent of tlie source 



Hi 



The agreement of the measurements made in this way was 

 within 1 —2"... 



It must be noted, however, that all the precautions 

 are necessary. Mere measurements 

 quantitative measurements of intensity 

 interpolated into a 



given 

 Density are not 



....... „ „ _. unless they are 



...,^.^._ „ .. curve produced by known increments of 



exposure to the same kind of radiation. 



