THE 
^iistinguislied into negative, local, plane, 
and solid. A negative theorem is that which 
expresses the impossibility of any asser- 
tion ; as that the smn of two biquadrate 
numbers cannot mrfke a square number. A 
local theorem is that which relates to a 
surface ; as, that the triangles of the same 
base and altitude are equal. A plane theo- 
rem is that which cither relates to a rectili- 
near surface, or to one terminated by the 
circumference of a circle ; as that all angles 
in the same segment of a circle are equal. 
And a solid theorem is that which considers 
a space terminated by a solid line ; that is, 
by any of the three (ynic sections, ^e. gr. 
this ; that if a right line cut two a.symptotic 
parabolas, its two parts terminated by them 
shall be equal. 
THEORY, in general, denotes any doc- 
trine which termhiates in speculation alone, 
without considering the practical uses and 
application thereof. 
THERMOMETER, an instrument for 
measuring the degree of heat or cold in any 
body. The first form of this instrument for 
measuring the degrees of heat and cold, was 
the air tliermometer. It is a well known 
fart that air expands with heat so as to oc- 
cupy more space than it does when cold, 
and that it is condensed by cold so as to oc- 
cupy less space than when warmed, and 
that this expansion and condensation is 
greater or less according to the degree of 
heat or cold applied. The principle then 
on which the air-thermometer was con- 
structed is very simple. The air was con- 
fined in a tube by means of some coloured 
liqnor ; the liquor rose or fell according as 
the air became expanded or condensed. 
What the first form of the tube was, cannot 
now perhaps be well known ; but the fol- 
lowing description of the air-thermometer 
will fully explain its nature. Jt consists of a 
glass tube, B E, (Plate Miscel. XVI. fig. 4.) 
connected at one end with a large glass ball, 
A and at the other end immersed in an open 
vessel, or terminating in a ball,.D E, with a 
narrow orifice atD ; which vessel or ball con- 
tains any coloured liquor that wdll not easily 
freeze. Aquafortis tinged of a fine blue co- 
lour with a solution of vitriol or copper, or 
spirit of wine tinged with cochineal, will 
answ'er this purpose. But the ball. A, must 
be first moderately warmed, so that a part 
of the air contained in it may be expelled 
through the orifice, D ; and then the liquor 
pressed by the weight of the atmosphere 
will enter the ball, DE, and rise, for 
THE 
example, to the middle of the tube at C, at 
a mean temperature of the weather ; and in 
this stale the liquor by its weight, and the 
air included in the ball, A,&c. by its elasti- 
city, will counterbalance the weight of tl/e 
atmosphere. As the surrounding air be- 
comes warmer, the air in the hall and upper 
part of the tube, expanding by heat, will 
drive the liquor into the lower ball, and 
consequeMtly its surface will descend ; on 
the contrary, as the ambient air becomes 
colder, that in the ball is condensed, and 
the liquor pressed by the weight of the at- 
mosphere will ascend ; .so that the liquor in 
the tube will ascend or descend more or less 
according to the state of the air contiguous 
to the instrument. To the tube is affixed 
a scale of the same length, divided upwards 
and downwards from the middle, C,iuto 100 
equal parts, by means of which the ascent 
and descent of the liquor in the tube, and con- 
sequently the variations in the cold or licat 
of the atmosphere, may be observed. 
The air being found improper for measur- 
ing with accuracy the variations of heat and 
cold according to the form of the thermome- 
ter which was first adopted, another fluid 
was proposed about the middle of the se- 
venteentli century by the Florentine Aca- 
demy. This fluid was spirit of wine, or 
alcohol, as it is now generally named. The 
alcohol being coloured, was inclosed in .i 
very fine cylindrical glass tube previously 
exhausted of its air, having a hollow ball 
at one end. A, (fig. 5.) and hermetically 
sealed at the other end, D. Tlie ball and 
tube are filled with rectified spirit of wine 
to a convenient height, as to C, when the 
weather is of a mean temperature, which 
may be done by inverting the tube into a 
vessel of stagnant coloured spirit, under a 
reeeiver of the air-pump, or in any otlier 
way. When the thermometer is properly 
filled, the end D is heated red hot by a 
lamp, and then hermetically sealed, leaving 
the included air of about one-third of its na- 
tural density, to prevent the air wliid) is in 
the spirit from dividing it in its expansion. 
To the tube is applied a scale, divided from 
the middle, into 100 equal parts, upwards 
and downwards. As spirit of wine is capa- 
ble of a very considerable degree of rare- 
faction and condensation by heat and cold, 
when the heat of the atmosphere increases 
the spirit dilates, and consequently rises in 
the tube; and when the heat decreases, the 
spirit descends, and the degree or quantity 
of the motion is shown by a scale. 
This was evidently an improvement on 
