128 Dr. S. P. Thompson on Photometry. 



Case (i) . To get some idea of the magnitudes involved, let 

 ns take a concrete case. Suppose the aperture to be a 

 hole 1 millimetre in diameter and the diaphragm 

 ■J millimetre thick; so that tan = 1. What will 

 the ratio be of the oblique to the central illumination 

 for a point P 2*5 centimetres from the centre X of a 

 screen which is itself at a distance OX= 50 centimetres 

 from the aperture ? As a Bunsen disk is seldom more 

 than 5 centimetres in diameter, this is rather an extreme 

 case. Here tan = 2-5-r-5O = O-O5. So = 2° 52', and 

 cos = O9975. Whence 7? = 0'935. 



Case (ii). Suppose the hole in the diaphragm to be still 

 1 millimetre in diameter, but the diaphragm to be 

 2*5 millimetres thick. Here tan = 5. Taking 6 as 

 before, we get rj = 0*684. 



Case (iii) . Suppose, on the other hand, that the hole is made 

 in metal foil only O'l millimetre thick, or that, having 

 been pierced through thicker metal the edge has been 

 cut away by countersinking, leaving only a narrow rim 

 0*1 millimetre in thickness. In this case tan</> = 0'2. 

 In the case where thin foil is used there is a consi- 

 derable risk of the metal buckling with heat : and it 

 would be quite possible, from this cause alone, that 

 the axis of the aperture should become oblique by as 

 much as 10° from the axis of the photometer. As- 

 suming then = 10°, the ratio of the central illumina- 

 tion, as thus perturbed by the error of centering, to 

 its unperturbed value will be 97 = 0*940. 



From all this it may be concluded that unless due care be 

 taken in the selection and proper centering of the diaphragm, 

 errors of several per cent, may arise in the photometric 

 measures executed with its means. The errors arising from 

 thickness of the diaphragm diminish, whilst those arising from 

 defect of centering are increased, as the distance from the 

 photometer-screen to the aperture is increased. In the above 

 investigation no account has been taken of the effects of 

 diffraction, which in the case of ver}^ minute apertures might 

 become important. 





