fiM 



BEFECTlVt ALGORITHM Or IMAOl»ARY QtTAKTITItS^ 



Then we have C n 



c r: 



Let r rr 



A = 



K ^ 

 n zz 



nv*J>rh 

 Hence ^—^ 



ifoot 



•865 

 •5 



6 in. ^ 

 1 ft. 

 3 ft. 



16 ft, (omitting th« /-jth) 

 1 i 



(^+2/) + 



ne 



Pr' 



4ir 



•OSt966s7 + -00187486 r: •03384173 ounces for there- 

 STstanceto a cylinder of the above dimensions, when moving 

 with the velocity of 1 foot per second. And therefore, as 

 the resistance to the same cylinder varies as the square of 

 the velocity, the resistjmce corresponding to any other ve- 

 locity will be had by multiplying the above by the velocity 

 (in £eet) squared. 



A qnafJrattc 

 equation ap- 

 |»arently with 

 t^ree roots. 



On the Defective Algorithm vf Imaginary Qvantities, In a 

 Letter from a Correspondent, 



To Mr. NICHOLSON. 



SIR, 



aN a mathematical investigation, in which I was lately en- 

 gaged, I fell upon a very, singular anomaly in the theory of 

 equations, which is nothing Icss^ than a quadratic equaiiofi 

 havinLJC (at least to all appearance) three roots, all different 

 from each other; whereas, according to received principles, 

 it can have only two. As this is a very Orange deviation 

 from what has been hitherto considered as a wtll established 

 theory, 1 am induced to request the publication of it in your 

 Journal, in hopes that some of your mathematical corres- 

 pondents may undertake to explain the difficulty, and res- 

 cue the theory of equations, and the present algorithm of 

 imagina.ry quantities, from the danger to which such ano- 

 malies rauft necessarily expose theoi ; particularly as there 



