PROFESSOR AT HEIDELBERG 191 



this final value, the negative with the period when it has 

 been exceeded, as always occurs in this case. The moment 

 of alternation between negative and positive images is found 

 by determining that value of /, at which s exceeds S. The 

 greater the excitation, and the less the fatigue deviates from 

 its final value, the longer will be the duration of the positive 

 image. A very brief period of excitation favours this. Further, 

 with otherwise similar conditions, it is favourable to the dura- 

 tion t of the positive image that the magnitude of intensity 

 of the persistent illumination shall be low, as is actually seen 

 in experiments in which the positive image is visible for the 

 greatest length of time upon the perfectly dark field. The 

 longer the time t, the smaller ' as follows from the exponential 

 quantities of the integrals ' will be the intensity of the nega- 

 tive image. In a wholly darkened field of vision, where the 

 retina is excited only by entoptic stimulation, the negative 

 image is only visible when the ratio between the final and 

 initial value of/ and the final value has become fairly large 

 in consequence of very strong illumination, or its prolonged 

 action. If we neglect the feeble intrinsic light of the retina 

 the course of the excitation will be quite independent of the 

 concomitant fatigue.' 



Helmholtz only began to develop the 'rise of excitation in 

 the recuperated eye' from the integral formulae. The ap- 

 plication of the relations found to the problem of intermittent 

 illumination leads to an expression for the strength of excita- 

 tion with persistent illumination of a given intensity, from 

 which Helmholtz concludes that the hypothesis made in 

 framing the differential equations is in agreement with the 

 well-known law, ' by which the apparently uniform brilliancy 

 of a periodically alternating illumination is equal to that which 

 would be obtained if the whole quantity of light in each period 

 were evenly distributed over the entire period/ 



During the summer, Part II of the Textbook of Physiological 

 Optics appeared. It was indeed ready before the death of his 

 wife, and on August 6 he sent a copy to Fechner, with the 

 following words : 



S* You will find the same subjects in this second part that you 

 lave dealt with lately in your own work. I had written the 

 :hapter on Intensity of Light, in all essentials, before I received 



