Light, photometry and illumination : a thoroughly revedof ''Electrical illuminating engineering'' . gh S^ is equal to the luminous flux due toS2 passing through S^, the brightness being the same in each is analogous to the theorem that the magnetic flux due to a ILLUMINA TION CALCULATIONS 247 magnetic shell ^Sj, ^vliich passes through a second shell S^, isequal to that part of the magnetic flux S^ which passes throughS^, the strength of the shells being supiDosed the same. Or,again, the number of lines of force due to unit current in anelectric circuit S^ passing through aS, is equal
Light, photometry and illumination : a thoroughly revedof ''Electrical illuminating engineering'' . gh S^ is equal to the luminous flux due toS2 passing through S^, the brightness being the same in each is analogous to the theorem that the magnetic flux due to a ILLUMINA TION CALCULATIONS 247 magnetic shell ^Sj, ^vliich passes through a second shell S^, isequal to that part of the magnetic flux S^ which passes throughS^, the strength of the shells being supiDosed the same. Or,again, the number of lines of force due to unit current in anelectric circuit S^ passing through aS, is equal to the num])er oflines of force due to unit current in S^ passing through ^Sj. Itfollows from the above that in any closed surface of uniformbrightness the flux passing out from any portion S^ is equal tothat received from the remainder of the surface S^- A Hollow Sphere.^—(Rosa, Ref. Cit.) Suppose a hollowsphere (Fig. 148) of uniform surface having a coefficient of diffusereflection m, l — m= £* = illumination at S. E = mE = radiation from >S. h = — = brightness of Fig. 148.—The hollow flux falling on *Sj due to S is c //? _eSSiCos^<p mE SSj cos^ o But r =2a cos ^ r^ = 4a^ cos^ cp COS^ (p_ 1 ^ See Liebenthal, Praktische Photometric, p. 301. (170) (171) 248 LIGHT, PHOTOMETRY AND ILLUMINATION and this is the same for every element of the sphere. Hence everyelement illuminates all other elements equally. Therefore theindirect illumination of the sphere must be the same everywhere,no matter how unequal the direct illumination may be. That is,a light at L illuminates the sphere unequally, directly. Butthat part of the total illumination due to diffuse reflection, is,notwithstanding, everywhere equal. A light of mean spherical intensity / sends out An I lumens. Of this there is reflected, first, Anml lumens. Of this there is reflected, second, Axm^I lumens. Of this there is reflected, third, Ajzm^I lumens, and so the total a
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectlight, bookyear1912
