On a Paradox i?i the Calculus of Functions. 443 



As the iodate of ammonia is not noticed in any work with 



;vh.ch I am acquamted, I think it right to observe here that 



f l/Jr?-^ '^'^^^^^''"f g'-^""!^'- powder, possessed of but 



if Ln ;^^ '\"^^l ^' P''^P^'-^^ by saturating the solution 



of the muriatic and iodic acids with pure ammonia, when it will 



aril r;i' '""'•■f t"e'"^'"i"S dissolved. I find that iodic 

 acid ,s decomposed by sulphocyanic acid and the sulpho- 

 cyanates of potash and soda; and also that saliva, in conse- 

 quence probably of the sulpho-cyanate of potash i contains, 

 decomposes iodic acid and produces with it and starch a blue 

 piecipitate not to be distinguished from that produced under 

 smiilar circumstances by morphia. The importance of this 

 discovery in a medico-legal point of view is considerable, since 

 iodic acid IS now very much rehed upon as a test for morphia. 

 I am, Gentlemen, yours, &c. 

 Roebuck Place, Great Dover Road, Lewis Thompson, 



. Southwark. M.R.C.S. 



1^X^X11 Explanation of a remarJcable Paradox in the Cal- 

 culus of Functions, noticed by Mr. Babbage. By John T 

 Graves, Esq., M.A., of the Inner Temple. 



[Continued from p. 34], and concluded.] 

 UAVING thus proved that 



_ -^cos-i y 



we have seen in what manner it follows that 



IS ane-Iogofx. g.E.D. ^ 



Let / ^f + z' 4- ^^ — L= rn<-i .y , , . , 



I call the_o:^.log of . of the 0- order) be denoted by 



Doiit /" ""^ r "'■ J' '' P'"'" '^^' ^h^" ^- is real and 

 posi ive, I a: resolves itseli in point of quantity (as it ought to 

 do, li our notation be consistent) into' the arithmetical^^log 

 or ^, l^ollowing the same notation, ^ 



1 . 



V,/TJ^ ~ ^^-1 VT^cos;^ :7^. (16.) 



3G'2 



