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 LXXIV. Intelligence and Miscellaneous Articles. 



THE TANGENT PHOTOMETER. BY DR. FERDINAND BOTHE. 



Bunsen's photometer, and those constructed by Wight and Desaga 

 according to the same principle, depend, as is well known, on the 

 circumstance that a transparent grease-spot on a sheet of paper 

 disappears when both sides of the paper are illuminated with equal 

 brightness. In most cases the flame of the normal candle, serving 

 as unit of light, is directly compared with the light to be measured. 

 In Desaga' s instrument, in accordance with the principle of double 

 weighing, it is compared with a gas-flame burning inside a case, 

 which flame is adjusted to the normal candle. In all these instru- 

 ments a displacement of one or the other of the flames is necessary, 

 which carries with it many inconveniences. 



This displacement may be avoided by placing the screen on which 

 is the transparent spot so that it can be turned, and providing it 

 with an alidade, so as to read it off. The brightness of an illumi- 

 nated surface, independently of the intensity of the source of light 

 and the distance, depends upon the angle at which it is illuminated : 

 it is proportional to the cosine of the angle of incidence, to the 

 sine of the angle which the rays make with the face. If, then, two 

 sources of light to be compared are so placed that their rays cross 

 at right angles, and if the rotating screen be so placed that it is 

 lighted on both sides by these with an equal intensity of light, the 

 angle of irradiation of each must be equal (that is, 45°) if the spot is to 

 be invisible. With unequal intensity of light, the screen of the bright 

 flame must be turned towards and that of the weaker away from 

 their respective lights to produce disappearance in the spot. 



If the angle for the flame of the brightness (I) = a, it is for the 

 other, (I 1 ), = 90 — a, and we have the equations 

 I sin a=l! sin (90 — a), 

 I tan a=I 1( 

 Hence the intensity of the light of one source as compared with the 

 other may be measured by the tangent of the angle of rotation. 



The premisses for the accuracy of this method : — 



(1) Absolute transparence of the greased paper, 



(2) Perfectly scattered reflexion of light — cannot be assumed with 

 complete accuracy. The side directly illuminated always appears 

 brighter than the transparent spot ; and hence a double placing of the 

 screen and a twofold reading off are indispensable, the mean value 

 of which gives the true position, and therewith the true value of a. 



The errors arising from the circumstance that the quantity of 

 light not diffused, and also of the light passing through the paper, 

 at different angular positions of the screen must differ are usually 

 outside the limits of observation, and at most only deserve con- 

 sideration if the angle of inclination of the rays towards the surface 

 is on the one side a very small, and on the other a correspondingly 

 large angle, — a case which cannot occur in the practical use of the 

 instrument. 



It must finally be mentioned that, when there is a very great 

 difference of the intensities of light, the angle whose tangent is to 



