558 Mathematical Correfpondence.On Imaginary Quantities. | (Sur. 
¢: unfortunate being to indufiry and repent- 
« ance.’? To fhow alfo how much this friend 
engroffed the fecret thoughts of his heart, even 
in his dying moments, after quitting the tene- 
ment to drown himfelf, he firft ftepped into the 
ground-floor of another tenement, and wrote the 
following lines ¢ *¢ O Lord! how weary lam 
« of life! If my acquaintance fhould hap- 
6* pen to fee this wiiting, he will remem- 
t€ ber, perhaps, the hand ef an o/d former 
s¢) acquaintance.’ 
«© Defpair pervades my foulettadeath I fly 
€€ for reliei.”’ 
Here then is the teftimony that this unfor- 
tunate perfon has fallen a victim to difappoint- 
ed friendfhip and defpair-. The fweeteft and 
gnoft engaging pleafures of life are thofe 
which {pring from our fecial connections ; and 
Jet ‘thofe who are joined in the bonds of parti- 
enlar friendfhip, be folicitous not to break off 
fo delightful an union. A true friend is one of 
the mof valuable blefiings this life can beftow ; 
and what greater fatisfaction can we experience, 
than that which arifes from our being connected 
with one to whom we can fafely difclofe the 
ynot fecret thoughts of our hearts, ‘Yielding 
then to the benign propenfity of returning a ge= 
ncrous and a good action, and beftowing a {mall 
pounty on an old friend in diitrefs, might have 
been the means (in the prefent cafe) of faving a 
foul from death; whereas, on the other hand, 
#f the pafe and unfriendly conduct of perfuns 
whom we have once loved, diffolve all the 
bonds of amity and friendfhip, aed fhow our 
@onfidence has been abufed, then are opened 
fome of the deepeft fprings of hitternefs in the 
human heart. If the unfufpecting friend be 
_ deferted in the hour of diftrefs by the friend in 
whom he trufted ; or in the mi@fi of his mif- 
gortunes meets with cold indifference, wherg 
& 
he expected to find the kindeft fympathy, and 
where the heart is fickened and wounded by 
the ingratitude or faithleffhefs of ene on whom 
it had leaned the whole weight of affection, 
where fhall it turn for relief ? 
Thope, Mr. Editor, there is not to be found 
an advocate for fuicide. A heart impreffed with 
a religious fear will fay, * how can I commit 
his great evil,-and fin againft God?” The 
Chriftian religion teaches us to fupport our- 
felves with fortitude under all our misfortunes 
and trials. From hardfhips and difficulties we 
derive an experience and fteadinefs, which 
teach us to act with propriety in the ftations 
wherein Providence has placed us. It is our 
duty t» acquiefce in what is allotted us; and 
our fole concern to acquit ourfelves well in our 
refpeétive flations, and fuftain Well our cha~ 
racters upon this ftage of life. Every one, 
therefore, ought to be fatisfied with his portion, 
and inftead of repining at the more liberal 
allotments of his neighbour, fhould be grateful 
for his own; for the wifdom of the fupreme 
Ruler of the world alone knows what is moft 
conducive to the well-being of the general fyfs 
tem, and to the particular welfare of indivi- 
duals. He afligns our ftation, and it is our duty 
to conform to it. 
T reraain, Mr. Editor, 
Your moft obedient, humble fervant, 
JosEPH James, 
Stoke Bifh p, near Brift:/, 
Nov. 22, 1797. 
P.S. I forgot to explain the meaning of the 
letter N. under mof of the fentences’ written on 
the wall; the gentleman who firft difcovered 
them, in copying them off, marked each fentence 
with N. (the initial of his own name) to prevent 
copying any of them twice. 

MATHEMATICAL CORRESPONDENCE, 
Eee EE 
To tbe Editor of tbe Monthly Mazazine, or 
SIR, 
PERMIT ‘me to fay a few words in reply to Parro-Cosa’s remarks on my paper, refpecting 
imaginary Quantities. 
“In the firft place, then, we will examine a few of Philo-Cofa's affertions, and fee how far 
pins = = eqs 278 
‘théy are agreeable to truth. He has afferted, that “ ,/——4 is a term which has no meaning yi 
‘that © —-a is an imaginary number;” that “ —-2 is no number at all;”’ and that “4/—a is 
“pothing at all’? Are thefe affertiuns generally truc ? I anfwer, they are not. Jf they are not 
gencrally, are they partially true ? I anfwer, that, independently confidered, they do not offend 
againft the truth. The terms —2, and 4/—-2, are general exprefhons, in which @ may be 
made to denote any thing. Of courfe, then, it follows, that if a, abfiadtly confidered, be 
yoade to fignify a thing of no meaning, the expreffion 4/ aa, will be ‘<a term which has no 
meaning.” In the fame point of view, “ —a may denote an imaginary number.” And Jaftly, 
if 2 is made to denote nothing, then will “ —a denote no number at all; and “ 4/—ea nothing 
at all: for furely the {quare root of nothing is nothing ; of a truth, cx mhilo nihil fit. But 
in the equations ba —=c¢ or —a==zcm—b, and 4/—a =4/c—4, wha is there that will fay, 
that *¢ —2 is an imaginary number,” .or that © it-is no number ar all?” and that ‘¢4/—a 
is a teym of no meaning,’’ or that it fignifies nothing at all?’? Here the term -~2 is as much a 
zeal quantity er-mumber as either d or ¢; and the term ¥/e-a has as much fignification as the 
ea) © 
3 : tera 
