THE MICROSCOPE. 



still more clearly intelligible by reference to figs. 6 and 7, where 

 two lenses, L L and L' L', having equal focal lengths, are repre- 

 sented ; the same object, o ando', is placed 

 at the same distances from them, and equal 

 images of it, 1 1 and i' I', are produced at 

 equal distances from the lenses. The 

 angular aperture of L L, being L o L, is 

 greater than that of I/ L', which is I/ o' L' ; 

 and it is evident that a greater number of 

 rays issuing from the object, will fall upon 

 the lens L L, than upon L' L', in the 

 proportion of the square of the angular 

 aperture of the former to that of the latter ; 

 thus, if the angular aperture of L L be 

 twice that of i/ L', the number of rays 

 which fall on L L will be four times the 

 number which fall on I/ L'. 



Supposing, then, that all the rays which 

 fall upon each of the lenses, pass through 

 them, and are made to converge upon corre- 

 sponding points of the images 1 1 and i' i', 

 it is clear that each point of the image 1 1 

 will be more intensely illuminated than the 

 corresponding point of I' i', in the propor- 

 tion of the square of the angular aperture 

 of L L to that of L' L' ; and if these apertures 

 be in the proportion above supposed of two 

 to one, the several points of the image 1 1 

 will be four times more intensely illumi- 

 nated than those of i' i'. 



15. As a practical example of the effect 

 of the angular aperture upon the image, 

 we here give seven drawings made by the 

 late Dr. Goring, of the appearance of a 

 particle of dust, or a scale, as it is called, 

 of a butterfly's wing, viewed with the same 

 magnifying power, the angular aperture of 

 the lens being successively augmented. 

 When the aperture was reduced to the 

 smallest limit, the object appeared as re- 

 presented at A, fig. 8 ; when the aperture 

 was increased in the proportion of 2 to 3, 

 the object assumed the appearance repre- 

 sented at B, and, in short, by successively increasing the aperture, 

 it assumed the appearances shown in c, D, E, F, and G. It will be 

 12 



