﻿242 Intelligence and Miscellaneous Articles, 



of attraction, we may in the sequel dispense with any strict de- 

 monstration. Hence I will briefly state the more important of these 

 principles, adding now and then a short observation. 



In reference to the measure chosen, it must be premised that the 

 intensity of that source of light is taken as unit which at the unit 

 distance imparts to a perfectly white element of surface at right 

 angles to the line of junction the unit of brightness. Hence a lu- 

 minous point of the intensity i emits the quantity of light 4ni. The 

 surface is always to be supposed perfectly white. In the case of 

 actual surfaces (which are never quite white — that is, whose white- 

 ness, a, is always less than 1), the formula has simply to be mul- 

 tiplied by a. 



This being premised, the following principles hold good. 



(1) A luminous point of intensity i at a distance r imparts to an 

 element of surface, whose normal makes the angle a with the line 

 joining the element and the source of light, a luminosity 



tt i 



H= —cos a. 

 r 2 



(2) If a, b, c are the rectangular coordinates of the luminous 

 point, x, y, z those of the element of the surface, and if this is at 

 right angles to the axis of X, its brightness is 





r' r dx 



(3) If the element of surface in the point x, y, z, at right angles 

 to the X axis, is simultaneously illuminated by several sources of 

 light, all of which are on the same side of the element, its brightness 

 is 



dZ 1 



H — r 



dx 



dx 



The brightness H of any element (presupposing that all sources of 

 light are on the same side of the element) is 



„_dU 

 dn 



meaning by dn the element of the perpendicular to the element of 

 surface. 



From these principles the following result is obtained : — 

 Given any number of luminous points, the brightness of any 

 surface illuminated by them at any given place is obtained by re- 

 garding the luminous points as material, and their masses as propor- 

 tional to the intensities of the sources of light, next seeking the 

 potential function of these masses, and then forming the differential 

 quotients of the normals according to the element of surface. 



This principle holds, of course, only under the above-made limi- 



