370 Observations on the value of the cipher, ^x. [Oct. 



novelty of its cliaracter, it cnnnot Init give an additional 

 degree of interest ; and emboldened by this considera- 

 tion, I flatter myself that I can hardly fail of success in 

 niy present attempt, so great is my confidence in the 

 polite indulgence which I may expect at your hands. 

 If then the fate of this attempt be equally auspicious 

 with that of my former essays, this will be my third 

 article in your journal, in reference to each of which 1 

 am almost painfully sensible, that the nature of my sub- 

 ject on each of these occasions, will gain me but little 

 credit as an utilitarian. 



I can assign no satisfactory reason for my choice in 

 this respect; but this is certain, that it should be other- 

 vrise if I could help it : this however is not the case at 

 present, and hence my present subject of nothing, the 

 most unpromising perhaps in the world. 



According to arithmeticians a cipher is an arithmeti- 

 cal symbol, used for denoting the value of nothing, and 

 is denominated insignificant to distinguish it from other 

 figures. Hence a cipher added to, or subtracted from, 

 any number does not increase or diminish its value, so 

 that any multiple of the cipher is still nothing; but 

 there are cases, in which it acquires other properties ; 

 for example : 



Sine 900= 1. Cosine 90^ = 0 Tan 90'^ = infinity. 

 By the relation of trigonometrical lines, 



sin X ~ tan x cos x 

 therefore sin 90« = tan 90^ x cos 90^ 

 or 1 = infinity x 0 



We will now examine the value of the quotient ofthe 

 cipher. Any number divided by an unit does not change 

 its value, but when it is divided by a number greater or 

 less than one the value is decreased or augmented ; 

 therefore any number divided by a cipher increases its 

 value infinitely. Let x represent any number then 



