320 ELEMENTS OF ELECTRICAL ENGINEERING. 



and each representing a zone of the reference sphere,* are reflected to the photometer 

 screen, S, as shown. This photometer screen is stationary and the photometer setting 

 is made by moving the standard lamp nearer to or farther from the screen. 



If the beams of light from all of the mirrors struck the photometer screen at right 

 angles, the reading of the photometer would be the sum of the conical intensities of 

 all the beams, that is, the photometer reading would be proportional to the simple 

 average of the conical intensities of all of the beams. 



The spherical-candle power of a lamp is found, however, not by taking the simple 

 average of the conical intensities in various directions, but by taking what is called a 

 weighted average as explained in Art. 131. 



If the illumination of the screen by each beam alone were z'/z as large as it would 

 be if the beam struck the screen at right angles, z being the area of the equatorial 

 zone of the reference sphere which is associated with the beam that is at right angles 

 to VV, and z f being the area of that zone of the reference sphere which is associated 

 with any given beam, then the reading of the photometer, Fig. 179, would be the sum 

 2(z x //2) that is, the photometer reading would be proportional to the true spherical- 

 candle power of the lamp. In fact the reading of the photometer would be n times 

 the spherical-candle power (=r 2z'//4:rr 2 ), where n is equal to the ratio of the area of 

 the entire reference sphere, 47rr 2 , to the area of the equatorial zone, 2. The incomplete 

 reflection of light by the mirrors is considered later. 



If the photometer screen were entirely free from gloss an oblique beam of light 

 would produce a degree of illumination inversely proportional to the area of screen 

 over which unit sectional area of the oblique beam is spread, that is, a degree of 

 illumination proportional to the sine of the angle between the beam and the plane of 

 the screen. This is precisely the reduction of illumination specified above in terms 

 of the ratio z'/z. It is impossible however to make a photometer screen without 

 gloss, that is a screen that does not show regular reflection to some extent, and the 

 more oblique the incident light the larger the proportion of the light which is reflected 

 regularly and the less the proportion that is reflected diffusely by the screen. There- 

 fore the mirrors near the axis, W, in Fig, 179 must be somewhat nearer to L and S 

 so as to lessen the optical distance from L to S, and thus intensify slightly the beams 

 that strike the screen obliquely. 



The Matthews integrating photometer is adjusted as follows so as to eliminate 

 errors due to gloss of screen and errors due to absorption of light by the mirrors. Put 

 an auxiliary standard lamp in place of Z, cover all of the mirrors except the pair that 

 receives the horizontal beam from the auxiliary standard, that is mirrors 5 and $' in 

 Fig. 179, and take the reading /f of the photometer. Then cover all of the mirrors 

 except any given pair, turn the auxiliary standard lamp so that its standard face or 

 aspect is towards the uncovered pair, set the photometer arbitrarily at reading, kz f /z, 

 and adjust the uncovered pair of mirrors inwards or outwards until the screen shows 

 equal illumination on its two sides. Proceed in like manner with each pair of mirrors 

 until the adjustment is complete. 



* Compare Art. 131. 



| The quantity i// is the factor by which any reading of the photometer must be 

 multiplied to correct for loss of light due to incomplete reflection by the mirrors. 



