HA RD WICKE' S SCIENCE- G OS SIP. 



53 



ray L E. Such a pencil has the form of a cone, of 

 which the luminous point L is the vertex, and LE 

 the axis. The peculiarity about it which we have 

 first to notice is, that the intensity of the illumina- 

 tion on a give?i surface, varies inversely as the square 

 of the slant distance from the source of light. 



If a cross-section of the cone-shaped pencil were 

 made at any point B, in a plane at right angles to 

 the axis, that section would evidently be a circle 

 having A B for its diameter. Take L d equal to three 

 times L B, and at D suppose another cross-section to 

 be made. It will again be a circle, with the 

 diameter c D ; and because L D has been taken equal 

 to three times lb, c d (as may be geometrically 

 proved) will be equal to thrice A B. Also, because 

 the areas of circles are to one another as the squares 



If the point L be supposed to move along N D 

 towards N, f will move in the opposite direction 

 towards F ; and when L has become infinitely 

 distant, f will coincide with F, the incident rays 

 having become parallel (compare Fig. 158, Nov. 

 1886, p. 249). Again, if L be supposed to move 

 along nd towards c, f will advance towards L, and 

 at C they will meet. If L continue to move towards 

 F, f will leave C and move away in the opposite 

 direction towards N. The points L and f will, in 

 fact, have changed places, f occupying the first 

 position of L, when L reaches the first position of 

 f. When L comes to the principal focus F, there 

 will be no point f, the reflected rays having become 

 parallel. If L passes F towards D, the reflected rays 

 will be divergent. 





Fig. 23. 



of their diameters, the area of the section at B is to 

 that of the section at D as I 1 is to 3 2 , or as 1 to 9. 

 That is to say, the rays have so spread themselves 

 by divergence, as to cover at c D nine times the space 

 which they covered at A B ; and the intensity of the 

 illumination on any given portion of the section at 

 D is therefore, only 1th of that on the same extent of 

 surface at B. 



In Fig. 22 we have a section of the small concave 

 mirror previously represented, whose centre of 

 curvature is c, and principal focus F. Let L be a 

 luminous point, beyond c, in ND the principal axis 

 of the mirror; and L A B be a simple divergent pencil 

 emanating from L and falling upon the mirror A B. 

 The rays will be reflected with a fair amount of 

 exactness \.of a point in the principal axis between 

 F and c. 



Any change therefore in the position of L, involves 

 a corresponding change in the position of f, and this 

 relation between the two points is expressed by 

 calling them conjugate foci of the mirror. The 

 number of conjugate foci is infinite. 



On page 250 of the vol. for 1886, it was explained 

 why the principal focus F cannot be employed by the 

 microscopist. The focus_/j in any of its positions on 

 nd, the principal axis of the mirror, is equally 

 unavailable, and for the same reasons. He cannot 

 place his lamp in line with the principal axis of the 

 mirror, so as to represent the point L in the figure. 

 The incidence of the pencil must necessarily be 

 oblique. 



It would be convenient now to show by several 

 figures, as was done for parallel rays (vol. for 1886, 

 p. 250), the alterations made in the distance of the 



