Mechanics of Luminosity. 385 



In order to find the total emitted brightness falling upon 

 the photometer, a curve was drawn with the times as abscissa?, 

 and the observed brightnesses 10 3 sin 2 a as ordinates. The 

 energy emitted during the time of illumination of a second 

 may be neglected. The area enclosed by the curve, the com- 

 mencing coordinate, and axis of abscissae, divided by 10 3 , gives 

 the total brightness radiated. In this way it was shown that 

 when the total evolution of light was compressed into 1 

 second, and whilst it remained constant, it would amount to 

 1-7 referred to the comparison lamp. The question now was 

 to determine the total brightness excited from the observed 

 brightness which corresponded to the energy of the rays 

 emitted in a definite direction, viz. towards the telescope, 

 which indeed corresponds to the energy of the rays emitted in 

 all directions. 



In fig. 5 let s be the slit through which the light falls upon 

 the plate of Balmain's luminous paint, B ; co the opening of 

 the screen so often mentioned, the opening of the objective, 

 e the distance from co, e the distance of the plate B from co. 

 The distance of B and co, and the breadth of the slit were 

 so chosen that rays from the phosphorescing surface should 

 certainly reach all points of the objective 0. In order 

 to show this, a narrow strip of looking-glass a inclined at an 

 angle of 45° to e was brought in front of the objective, and 

 the observer satisfied himself that the image of the diaphragm 

 which it reflected in the direction of the arrow was equally 

 bright, whether the strip was in the middle of the objective 

 or at its edge. 



The position of the Balmain's tablet at an angle of 45° 

 compensates the diminished excitation of each separate point 

 of the tablet in consequence of its inclination to the exciting 

 rays by the increased magnitude of the radiating surface, 

 because of its equally great inclination to the rays going to 

 the objective, if we assume that the radiating substance is 

 perfectly transparent to the phosphorescent light. 



The cone which has for vertex a point in the aperture of 

 the diaphragm co, and for base the objective 0, cuts out a 

 portion ft of the surface of the Balmain's luminous paint, 

 and from the projection of this upon the plane at right angles 

 to the axis of the cone, a portion /jl = Oe 2 /e 2 , which is to be put 

 instead of the surface /3, sending its rays into the objective. 



In our particular case the radius of the objective is 

 19 millim., e = 180 millim., e—6 millim.; consequently 



fi 2 .7r.(19) 2 1 _ . ir , 



/x = /Tq?Y\2 = 1 2o square millimetres. 



Phil. Mag. S. 5. Vol. 28. No. 174. Nov. 1889. 2 F 



