PROFESSOR AT BONN 157 



may be cited : (i) when two rays of light pass in opposite 

 directions through any number of simple refracting media, 

 and coincide in one of these media in a straight line, the}' must 

 coincide in all; (2) if the pupil of the observed eye is to be 

 luminous, the, image of the source of light on its retina must 

 wholly or partially coincide with the image of the observer's 

 pupil ; (3) if in a centric system of refracting spherical surfaces, 

 the refractive index of the first refracting medium be n v and 

 that of the last n. 2 , and there be in the first, vertical to the 

 axis of the system, and close to the axis, a surface-element 

 a, and in the last a similar element ft, then when a has the 

 illumination nf . H, and ft has the illumination n% . H, as much 

 light falls from a upon ft as from ft upon a; this law, applied 

 to the problem of luminosity in the eye, tells us that the 

 quantity of light which falls from any surface-element of the 

 retina of the observed eye into the eye of the observer is 

 equal to the illumination of the retinal element by the source 

 of light, multiplied by the quantity of light that would fall 

 upon that retinal element from the pupil of the observer, if 

 its illumination were unity. By these laws he succeeded in 

 establishing a general method for determining the illumination 

 of any spot of the observed retina, as seen by the observer 

 with the ophthalmoscope, and on this again he founds his 

 comparison of the various forms of the ophthalmoscope. The 

 historical evolution is everywhere traced out in its smallest 

 details, with a careful summary of the literature of the 

 subject. 



Meantime his acoustic observations widened in import, and 

 a most valuable series of physiological discoveries in optics 

 and acoustics followed in quick succession. 



On May 18, 1857, he writes to du Bois : 



'I have gradually accumulated a considerable amount of 

 material for the reform of physiological acoustics, and am waiting 

 for instruments to carry it out. I will mention one fact that has 

 interesting bearings on nerve physiology, i. e. that the fibres 

 of N. acitsticus, " which perceive the higher tones, must be 

 capable of distinguishing as many as 150 alternations of rest 

 and excitation (150 vibrations) per second from a continuous 

 excitation, whereas in the optic nerve and in muscle, a rhythm 

 of 10-15 P er second acts as a continuous excitation. This 



