3l8 ELEMENTS OF ELECTRICAL ENGINEERING. 



conical intensities, R, R' ', R", R fn ', etc., at equal angular dis- 

 tances, <, are measured. On account of the rotation of the lamp 

 each setting of the photometer gives the average conical intensity 

 along a parallel of latitude, as it were. Each reading, R, R', R", 

 etc., represents, therefore, the conical intensity over a zone of the 

 reference sphere ; so that the readings must be multiplied by the 

 areas of the respective zones and the sum of these products 

 divided by the total area of the reference sphere to give the aver- 

 age conical intensity in all directions, which is equal of course to 

 the total light flux in spherical-units, hefners or candles as the 

 case may be. Thus the reading, R", Fig. 178, refers to the 

 spherical zone, ab, of which the area is sensibly equal to the 

 length of the arc, ab (= r$), multiplied by the mean circumference 

 (= 27rd = 27rrsin 6"), of the zone. The radius, r, of the refer- 

 ence sphere cancels out when one divides the above-mentioned 

 sum by the total area of the reference sphere (= 4?rr 2 ), as above 

 explained. 



Example. The conical intensities are given in Fig. 175 for 

 every 10. The area of each of the two polar zones corre- 

 sponding to conical intensities 3.0 and 6.6 is, IT x ($-$ of 2?rr) 2 ; 

 the area of each of the zones corresponding to conical intensities 

 5.0 and 7.0 is, 2irr sin 10 x (g 1 ^- of 2irr) ; the area of each of 

 the zones corresponding to conical intensities 7.5 and 8.1 is, 

 2irr sin 20 x (-$ of 27rr) ; and so on. A calculation of the 

 mean conical intensity in all directions from the data given in 

 Fig. 175 gives 13.33 spherical-candles as the light flux emitted 

 by the lamp. 



132. The Matthews integrating photometer. Two ingenious arrangements of 

 mirrors have been devised by Professor C. P. Matthews by means of which the light 

 flux from a lamp in spherical-candles can be determined by a single setting of a photo- 

 meter.* A photometer provided with such an arrangement of mirrors is called an 

 integrating photometer. The essential features of one of Professor Matthews' arrange- 

 ments are shown in Fig. 179. The lamp, Z, to be tested is rotated about the vertical 

 axis, VV y and a number of equidistant beams from Z, all lying in the plane, QL V y 



*The Integrating Photometer, C. P. Matthews, Transactions of American Insti- 

 tute of Electrical Engineers, Vol. XVI1L, pp. 677-697, 1901 ; Vol. XX., pp. 59-70, 

 1902. 



