RES 
^raically, the method is this: First, the 
•given quantities are distinguished from those 
•that are sought; and the former denoted 
by the initial letters of the alphabet, but 
the latter by the last letters. 2. Then as 
many equations are formed as there are un- 
^known quantities. If that cannot be done 
from the proposition or data, the problem is 
• indeterminate ; and certain arbitrary as- 
sumptions must be made to supply the de- 
fect, and which can satisfy the question. 
When the equations are not contained in 
the problem itself, they are to be found by 
particular theorems concerning equations, 
j-atios, proportions, &c. Since, in an equa- 
tion the known and unknown quantities are 
mixed together, they must be separated 
in such a manner that the unknown re- 
main alone on one side, and the known 
ones on the other. This reduction, or sepa- 
ration, is made by addition, subtraction, 
multiplication, division, extraction of roots, 
and raising of powers ; resolving every kind 
of combination of the quantities, by their 
counter or reverse ones, and performing the 
same operation on all the quantities, or 
terms, on both sides of the equation, that 
the equality may still be preserved. 
To resolve a geometrical problem alge- 
braically. The same sort of operations are 
to be performed as in the former article ; 
besides several others, that depend upon 
the nature of the diagram, and geometrical 
properties. As, 1. The thing required or 
proposed, must be supposed done, the 
diagram being drawn or constructed in all 
its parts, both known and unknown. 2. We 
must then examine the geometrical rela- 
tions which the lines of the figure have 
among themselves, without regarding whe- 
ther they are known or unknown, to find 
what equations arise from those relations, 
for finding the unknown quantities. 3. It 
is often necessary to form similar triangles 
and rectangles, sometimes by producing of 
lines, or drawing parallels and perpendicu- 
lars, and forming equal angles, &c. ; till 
equations can be formed from them, includ- 
ing both the known and unknown quantities. 
Resolution, in chemistry, &c. the re- 
duction of a mixed body into its component 
parts, or first principles, by a proper analy- 
sis. The resolution of bodies is effected by 
divers operations, as distillation, sublima- 
tion, fermentation, precipitation, &c. See 
Distillation, Sublimation, &c. 
Some logicians use the term resolution 
for what is more usually called analysis, or 
file analytic method. 
RES 
Resolution of forces, or of motion, is the 
resolving or dividing of any one force or 
motion, into several others, in other direc- 
tions, but which, taken together, shall have, 
the same effect as the single one ; and it is 
the reverse of the composition of forces or 
motions. 
RESPIRATION, in animal economy. 
The absolute necessity of respiration, or of 
something analogous, is known to every one ; 
and few are ignorant that in man, and hot- 
blooded animals, the organ by which respira- 
tion is perfoi jned is the lungs. N ow respira- 
tion consists in drawing a certain quantity of 
air into the lungs, and throwing it out again 
alternately. Whenever this function is sus- 
pended, even for a very short time, the 
animal dies. The fluid respired by animals 
is common atmospherical air; and it has 
been ascertained by experiment, that no 
otlier gaseous body with which we are ac- 
quainted can be substituted for it. All the 
known gases have been tried ; but they all 
prove fatal to the animal which is made to 
breathe them. Gaseous bodies, as far as 
respiration is concerned, may be divided 
into two classes: — 1. Uurespirable gases. 
2. Respirable gases. The gases belonging 
to the first class are of such a nature, that 
they cannot be drawn into the lungs of an 
animal at all; the epiglottis closing spasmo- 
dically whenever they are applied to it. To 
this class belong carbonic acid, and pro- 
bably all the other acid gases, as has been 
ascertained by the experiments of Pilatre de 
Rosier, who went into a brewer’s tub while 
full of carbonic acid gass evolved by fer- 
mentation. A gentle heat manifested itself 
in all parts of his body, and occasioned a 
sensible perspiration. A slight itching sen- 
sation constrained him frequently to shut 
his eyes. When he attempted to breathe, a 
violent feeling of suffocation prevented him. 
He sought for the steps to get out; but not 
finding them readily, the necessity of breath- 
ing increased, lie became giddy, and felt a 
tingling sensation in his ears. As soon as 
his mouth reached the air he breathed 
freely; but for some time he could not 
distinguish objects: his face was purple, his 
limbs weak, and he understood with diffi- 
culty what was said to him. But these- 
symptoms soon left him. He repeated the 
experiment often ; and always found, that 
as long as he continued without breathing, 
he could speak and move about without in- 
coiiveuience ; but whenever he attempted 
to breathe, the feeling of sutiocatioii came 
on. For the lungs of animals suffocated by 
