210 Dr. Fleming : Ratio between Mean Spherical and 

 entire surface of the circumscribing sphere is 



477T 2 I H \ 2 cot? 0d0 

 Hence by the definition of mean spherical candle-power 



Iq we have 



47rr 2 I s = 47n' 2 I 



h| cos 2 0dO, 



Jo 



or 



s=f c ° s2 ^=r(^>=i=° 



785. 



Accordingly for such a short straight filament the ratio 

 experimentally found by Mr. Dyke, viz., I s /Ih = 0*78, holds 

 good. 



Conversely, the fact that experiment shows that for any 

 incandescent lamp Is/Ih = tt/4 nearly, is a proof that the 

 cosine law of luminous radiation from the filaments in different 

 direction holds good, with considerable exactness. 



The departure from the above rule when the filament is 

 not short compared with the radius of the sphere can be found 

 as follows : — 



Consider a straight incandescent filament of length 21 the 

 half of which is represented by the line AB (see fig. 2) placed 



B 





Fig. 2. 







d 

 c 







^>> 





A 



< 



D 





>■ 



at a distance AP = D from a photometer-disk P, the filament 

 being parallel to the photometer-plane. Let an element of 

 length at C be denoted by dl. Let the angle APB subtended at 



