CORRESPONDENCE, 1846-55. 213 



example as to matter, though not as to form, if you choose a 1850. 

 better one. Closed windows may denote death or absence, &c. 

 But change it thus. A man who ties a ivliite glove on his knocker 

 enunciates that a child is born in the house. I believe there is 

 no ambiguity of meaning here. I hold that he does enunciate. 

 However, this is all for consideration. I remain, dear sir, 



Yours truly, 



A. DE MORGAN. 



To Sir John Herschel. 



Oct. 15, 1850. 



DEAR SIR JOHN, .... 



I always advance the following as the infinitely small quan- 

 tity which is the most puzzling of all. All others are mental 

 creations, but this one seems different. 



Let ifc be granted that a target which must be hit can be con- 

 ceived. It may be the whole enceinte of the room, ceiling, floor, 

 walls, &c. 



Let it granted that the fixing of an arrow with a mathemati- 

 cal point can be distinctly conceived. I don't ask for workman- 

 ship. 



Let A be a point in the target. Since some point must be hit, 

 and all are equally likely, there is some chance of hitting A that 

 is, it is not impossible to hit A, which is synonymous. 



But the chance of hitting a given point is certainly less than 

 any that can be assigned. 



Therefore there does exist in the mind an idea of a quan- 

 tity which, not being nothing, is less than any that can be 

 assigned. 



In geometry we do not meet the same difficulty, because we 

 learn (how correctly I give no opinion on) to know the point, line, 

 surface, and solids as different species of magnitude, but belief 

 cannot be subdivided into different species. Is not an expecta- 

 tion of hitting A homogeneous with that of hitting some point 

 within a given area ? 



I do not know whether you have returned. I hope all your 

 clan are well, and you yourself not disposed to give any hints 

 about your scientific life being terminated, as you did a while ago. 



Yours very truly, 



A. DE MORGAN. 



From my examination room, where I shall sit two hours and 

 a half more, without anything to do except just what I please, 



