210 On Arithmetical Complements. 
bitants. At all events, it is, as far as I can learn, sooner or later 
destructive to Europeans in anywise affected with coughs, colds, 
or hemorrhages from the lungs; and speedily so, to such as are 
at all predisposed to or affected with, tubercles or vomice. Va- 
rious are the calamitous instances that could be adduced, both 
in the navy and army, of the rapid progress and fatal termination 
of this, even amid the prevalence of other disorders peculiar to 
the climate. I have had some cases of pneumonia; and have 
at present one of vomice, which originated in a voyage to Green- 
land about eighteen months ago. I have also in my mind at 
this moment the particular case of a captain of foot, who was 
cut off in the flower of his age, at Montreal, in the winter of 
1815, by this disease, aggravated as it strikingly was by the per- 
nicious influence of the climate. Indeed, the peculiar suscepti- 
bility of the body to be acted upon by the relaxation or particu- 
lar action of the exhalants, from a temperature so varying, is 
SS 
XXXII. On Arithmetical Complements. By Mr. PETER 
NICHOLSON. : 
I HAVE been greatly surprised to find that the use of arithmeti- 
cal complements has been entirely confined to logarithms, and 
that they are treated as if they only resulted from the properties 
of those artificial numbers. But whoever has much practice in 
finding the roots of equations by approximation, or in any other 
way, must have felt the confusion of so many changes of signs 
which require the negative and affirmative numbers to be added 
together separately, and then their differences to be taken: 
whereas, if we were to use not arithmetical complements, but. 
numbers found in a similar manner, we need only add the whole 
together in one compact sum. . 
And thus it may be seen that arithmetical complements are a 
branch of common arithmetic, and not at all peculiar to, though 
very useful in, logarithms, nor their uses entirely confined to lo- 
arithms, but are equally useful in arithmetic and algebra. 
Let —31416 be a negative number : subtract each figure from 
10, and carry unity to the next figure ; set the results in a row 
one after the other, proceeding from the right hand to the left, 
and prefix unity with a negative sign before the first figure. 
This simple operation may be done at sight, without putting the - 
one number under the other, thus, 168584, where only the first 
figure is negative. tik 
This number now found is not the arithmetical complement, 
but equivalent to the number itself: for 168584=—100000 
+68584= —31416, sb 
The 
