gent of any arch and of its supplement to the whole circum. ference, or 360 degrees, are equal and contrary to one an other, or the one negative of the other.

Let t, u, w, be put for the tangents of the three arches A, Demonstrations B, C respectively, and r for the radius, and for the whole

circumference. Then A+B+CO, and Co-A+B.

By trigonometry, t, A+B=

r2 xt+u
p2-tu

,and the tang. C=tang.

(0-A+B)=-tang. A+B, by what has been said above.

Thereforet, A+t, B+t, Cort+u+w=t+u

=tux

r2xt + u

r2-tu

; butt and u are the expressions for the tan

r2xt+u r2-tu gents of A and B respectively, and

sion for the tangent of C, or for w. Therefore, r2 ×t+u+w, or the square of the radius multiplied into the sum of the three tangents of A, B, and C-tuw, or the product of the tangents. Q. E. D.

V.

On the apparent Radiation and Reflection of Cold by means of two concave metallic Mirrors. In a Letter from Mr. JOHN MARTIN.

SIR,

To Mr. NICHOLSON,

facts not suffi

THERE are many phenomena, exhibited to the notice Some chemical of the chemical philosopher in the course of his arduous ciently explainresearch, that are not so well understood as perhaps the ed. present state of science might lead him to expect. Some of these phenomena have hitherto been totally inexplicable; others have not been explained with all the clearness and perspicuity that could be wished. Among the number of Apparent radithe latter may be ranked the apparent radiation and reflection of cold by means of two concave metallic mirrors.

ation and reflection of cold.

The cold body supposed to receive heat

from the ther

mometer.

heat.

This curious fact, notwithstanding we are so well ac quainted with the laws that govern heat during its passage through and impingency upon bodies, has never, I believe, been illustrated with sufficient clearness.

The explanations that have hitherto been given rest principally for support on the supposition, that the thermometer placed in the focus of one mirror acts as a heated body, and that the heat radiating from it is transmitted to the cold But this cannot body in the opposite focus. The thermometer, however, give out radiant is in fact not a heated body, since it is not hotter than the surrounding atmosphere, and consequently cannot radiate caloric: but it is said, the surrounding air becomes cooled, and consequently the thermometer in respect to it is a hot body, and radiates caloric accordingly. This however does not explain olearly why the thermometer should be reduced to a temperature lower than the air which surrounds it, which will be found to be the case; or at least, it leaves too much to be supplied by the imagination. I trust I shall be able to render this matter clearer.

Another mode of accounting for it.

How this is effected.

There are only two ways, in which heat can be made to move in one direction through any given body, we will suppose a wire Ax y B; one is the application of a superior temperature to B, causing the heat to move on towards A by the conducting power of the wire, and the tendency of the caloric to establish an equilibrium; the other is, to reduce the temperature at A, and thus cause a partial vacuity of heat, which must of necessity be filled up by a fresh quantity from toward x, which will receive again a fresh supply from toward y, and that from towards z, &c., and by this means induce a current of heat from B to A, till an equilibrium is established. It is upon this principle, the filling up of partial vacuities of heat (if I may be allowed the expression), that the rational explana tion of the phenomenon in question can be grounded. Fact puts this sufficiently beyond a doubt, and it now remains to show how it is effected.

It will scarcely be necessary to mention in this place, that, when a particle of heat impinges upon a plane re flecting surface, it is thrown off in an angle equal to that

with which it is thrown upon it. Now, on the contrary,
if a cold body, b, Fig. 5, Pl. 9, be brought near a plane
reflecting surface, as particles of heat are entering into that
body in all directions from the surrounding air, some par-
ticles of heat must be entering into it in the direction ab,
consequently the point a of the reflecting surface must be-
come cooler, or, to use my former expression, a vacuity
of heat will be there formed: now it may be demonstrated,
that this vacuity or space will not be supplied by heat mov-
ing in the direction xa, ya, or z a, but will be supplied
by heat moving in no other direction than ca, which heat,
striking against the point a, will be thrown off into the
body b; the angle cad being equal to the angle b a e, and
bodies will move in the direction in which they meet with
the least resistance; for if heat were to come from any
other direction but ca, it would not be reflected towards
the body b, but elsewhere, and consequently, to join the
current of heat a b, it must again change its course. Hence
it follows, that, when a cold body is brought near a plane
reflecting surface, in proportion as the surrounding air be-
comes cool, heat will enter into that body in right lines
tending to its centre; the plane reflecting surface will have
its temperature lowered, and particles of heat will strike.
upon every part of it in such directions, as to be thrown
off in right lines to the cool body.

a concave sur

face.

The application of this fact to the explanation of the This applied to phenomenon in question will be readily perceived, substituting concave reflecting surfaces instead of plane ones: the heat enters into the cold body placed in the focus of one mirror (B. fig. 6) from the surrounding air in all di rections, consequently every point of the surface of the mirror, a, b, c, d, &c., becomes cooled, and those points can only receive a fresh supply in parallel rays, in a direct course from the opposite mirror, because only such rays (striking against so many imaginary tangents a, b, c, d, of that mirror) can be thrown off towards the body B; the opposite mirror therefore becomes cool, and for the same reason the whole surface of it must be supplied by heat from the thermometer T, which consequently must become cooler than a body placed any where in its neighbourhood.

If you think proper, an insertion of this explanation in your valuable Journal will greatly oblige,

Old Broad Street,

Sir,

Your most obedient Servant,

JOHN MARTIN.

19 July, 1808.

Balance leve!

VI.

Description of a Balance Level, useful for laying out Land for Irrigation, for Roads, and other Purposes. By Mr. RICHARD DREW, of Great Ormond Street*.

SIR,

HEREWITH HEREWITH you will receive a Balance Level, of my useful in drain- invention, which I have satisfactorily used on several gentleing and watering land. men's estates in Devonshire, where I have been employed to drain and carry water to irrigate meadow land. I have made several for persons in that county, whose employment is to drain and irrigate land, and they have found it to answer their purpose better than the spirit or water level, it being more portable and ready to the sight.

Method of using it.

I have lately used it on Mr. Satterley's farm, at Hastings, to carry the water of his closes over several acres of dry ground. Dr. De Salis, who has seen it, advised me to send it to the Society of Arts, &c., that they might judge of its merits.

I am, Sir,

Your obedient Servant,

RICHARD DREW.

Explanation of the Method of using the Instrument.

Set it on a triangular staff, and point it at the object staff, which is held by another person at a distance; move the level on the joint, until the inner tube plays clear within

* Trans. of the Society of Arts for 1807, p. 22, The Society voted Mr. Drew ten guineas for this invention,

the