AT THE PHYSICO-TECHNICAL INSTITUTE 381 



on that also. You have already attacked it at many points, and 

 it is (as I have long felt) only the consequence of the remark- 

 able development of your scientific life, which is unique in the 

 history of the sciences, that it should, beginning at the right 

 hand with the most practical scientific medicine, advancing 

 through physiology to experimental and theoretical physics, 

 arrive finally at the extreme left of the abstractions of " pure " 

 mathematics. The wealth of practical experience, of sound and 

 interesting problems, which you will bring to mathematics, will 

 (like the work of the astronomers in the last century) give it a 

 new direction and a new impulse; whereas the one-sided 

 mathematical speculation that returns upon itself only leads to 

 sterile regions. Therefore come over to our side, honoured 

 friend, and impress the imperishable traces of your bold and 

 original progress upon the paths of pure mathematics, so that 

 the lines of the future may be indicated in this direction also/ 



At this very time Helmholtz was already midway in his 

 great mathematical investigations of monocyclic systems and 

 the principle of least action. 



The new edition of Physiological Optics compelled him at the 

 same time to examine a whole series of difficult optical prob- 

 lems, and restate the answers to them. On November 2, 1888, 

 he made a brief communication to the Physical Society ' On the 

 Intrinsic Light of the Retina ', published in an expanded form 

 in 1890 in the Zeitschrift f. Phys. u. Psych., with the title ' The 

 Disturbance of the Perception of the Least Differences of 

 Brightness by the Intrinsic Light of the Retina '. Helmholtz 

 finds that the intrinsic light is not equally distributed over the 

 fundus of the retina, but always appears to us in irregular 

 patches, and that what we generally perceive of this internal 

 retinal excitation, under normal conditions, with weak external 

 illumination, is only the local differences of brightness in the 

 patches ; and it is only under exceptional circumstances that we 

 can estimate the mean brightness of the fundus by comparison 

 with still darker fields. Helmholtz adduces a number of 

 highly interesting experiments, which show that the patchy 

 character of the intrinsic light is the chief obstacle to the 

 perception of very weakly illuminated objects, especially if they 

 are small, since these disappear between the patches of the 

 intrinsic light, and are confounded with them. His experiments 



