ISI'S ©TJ TOfE lXG«yftlTHM OF IMAGINARY iQUAKTITIBS. 



pnthealgo- "^qv, f/^^ 117 — 44 V —■ 1 =3 — 4 \/— 1 



rithm of 



imaginary 

 quantities. 



and ^— 117 + 44 V— 1 = 3 + 4 \/— 1 



'as will be-found by invslotivn. 



And consequently their sum is equal to 6 as it ought to 

 be, and we may therefore fairly conclude, that we are right 

 in our operation on the first formula. But with regard ~to 

 our second expression, it is the same as that with which we 

 begun, and is therefore equal to 1-87938, and not l-53206f), 

 as it ought to have been, had we been correct in the opera- 

 tions on the second formula; and htnce we may conclude, 

 with equal certainty, that some mistake has crept in unob- 

 served in the latter case, notwithstanding we huve proceeded 

 by parallel steps in both examples. 



The questions, therefore, that I have to propose to mathe- 

 matiota!>s,«Fe as foUows : 



1. What co?\stitutes the errours in the operation on the 

 latter formula? 



2. Howare such errours tobe guarded againft in other. cases .^ 

 The latter ©f these questions is equally important with 



the former ; as there are various other formulce of a similar 

 description, which, should they arise in any investigation, 

 when we have not the means of checking the result as in 

 the examples above, much uncertainty must necessarily at- 

 tend tbe conclusions thence deduced. 



The manner in which I have introduced these., questions 

 may appear somewhat novel in the present day, but it was 

 not uncommon at the time when the scicHces were most 

 successfully cultivated in this country, and when they were 

 making those rapid advances, which have immortalized the 

 names of several distirxguished English mathematicians and 

 philosophers. 



I have only now to observe, that, should no answer appear 

 to these ques,tions within three months, T will then, through 

 ithe medium of your Journal, publish my explanation ; but 

 I am not without hopes of seeing the subject elucidated by 

 ^ more able hand than, jSir, 



Your obedient Servant, 



MATHEMATICUS. 



