212 Dr. Hi Airy on a distinct [Feb. 17, 



which determines the function E(.r), a rational and entire function of the 



?'th degree. 



I conclude this paper with a proposition of much importance in the 

 theory of linear differential equations, 

 Let 



d n y d n ~ ] ij d n ~ 2 y 



+ ^^s^ + ^^ss4+ • • • +^=° 



be any linear differential equation. Then in general this equation will not 

 admit a solution of the form y=f(e*). For then, putting for (x) succes- 

 sively # + 2-*, cc-\- 4-/, . . . , we should have 



*" ( ' T) ~dr r + < w +9 "-~ J*"- 2 + — ' 



tn(*+4*i)^§£ +^_ l(x+4lri) ^p + . . .=o. 



And these equations can be indefinitely continued. It will be observed 



P % u 



that this solution does not comprise integrals of the form q € "> where — is 

 a rational function. 



February 17, 1870. 



Dr. WILLIAM ALLEN MILLER, Treasurer and Vice-President, 



in the Chair. 



The following communications were read : — 



L "On a distinct form of Transient Hemiopsia." By Hubert 

 Airy, M.A., M.D. Communicated by the Astronomer Royal. 

 Received January 6, 1870. 



(Abstract.) 



From a comparison of the different accounts of " Hemiopsia, ,, " Half- 

 vision," or " Half-blindness," given by Dr. Wollaston (Phil. Trans. 1824, 

 p. 222), M. Arago (Annales de Chimie et de Physique, torn, xxvii. p. 102), 

 Sir David Brewster (Phil. Mag. 1865, vol. i. p. 503, and Transactions of 

 Royal Society of Edinburgh, vol. xxiv. part 1), the Astronomer Royal 

 (Phil. Mag. July 18G5, vol. ii. p. 19), Professor Dufour (in a letter to the 

 Astronomer Royal), Sir John Herschel (Familiar Lectures on Scientific 

 Subjects, p. 406, Lecture IX., and private letters), Sir CharlesATheatstone 

 (in a private letter), Mr. Tyrrell (On the Diseases of the Eye, 1840, vol. ii. 

 p. 231), and the author of this paper, it is plain that there are different 

 forms of transient Hemiopsia, irrespective of the wide primary distinction 



