cation with the atmosphere is opened, restoring the external pressure, whereby the density within is increased from r to m. The density of the air which has re-entered will thus be diminished from e to m, and its mass will be m→ J.

Now, from what was formerly shewn of the air-thermometer, the heat evolved by the compression of the rarified mass r, will be to that absorbed by the dilatation of the re-entered mass log to (mr) log. Their difference or

m-r, as r log

m

r

log {(~)" (-)"}

may therefore represent the change of

temperature by the true scale, or the heat evolved by a mass of

air = 1, when its density is increased from unit to

But the mixed mass is m, and, therefore, the rise in its

1

temperature on the same scale, is = log { (7)"(-)'} =

m

Hence, i the rise of temperature in the mass m, reckoned on the common scale, is equal to what any mass of air at the temperature would undergo by increasing its density from unit

m

to

e

)=. Wherefore, if the specific heat of air under

m

a constant volume, be to that under a constant pressure, in the

constant ratio of 1 to 1 + x, we have i =

α

1+ a = (-1) =

o

from the law of Boyle. Hence, e=

To find the value of r when the surplus heat, or

ru.

d log {() =}

m

d m

= o. Hence, d m = 0,

x m

e

and, therefore, log-dr-dro; or hyp-log = 1, and

-This value of3r is independent of a. When r

and a are given, m may in every case be found, from the above formulæ, or from

#

value of m, but its minimum, answers to two different values of

r. For instance, r =

1

e. If three-fourths of the air be extracted from a close

vessel, and, after the temperature has settled, one-fourth be instantly restored, no change of temperature should ensue.

The law of temperature admits of a somewhat simpler investigation than was formerly given. Let t be the temperature, or rather the indication on the common scale of an air-thermometer, p the pressure, and the density of the mass of air; then a and b being constants, we have, as before, from the law of Boyle, pbę (1+at). Now, the specific heat under a constant pressure being to that under a constant volume, in the inverse ratio of the variations of temperature produced in these two different cases by equal variations in the quantities of heat, the following expressions respectively contain all the variables which enter into these specific heats, relatively to the ordinary graduation.

which are obtained from the above equation, by making p and

respectively to vary with t, whilst the other is constant. The variations of the quantities of heat being constant, and, as men

tioned above, the same in both terms, are omitted, as also the constant linear degree of the common scale.

Let the temperature be reckoned on AB, as on the common scale of an airthermometer commencing at A or 448° F; and let CF be a line of such a nature, that every ordinate as BC EF, &c. may be proportional to the specific heat of air under a constant

E

B

A

F

volume, at the respective temperatures B, E, &c. So at the intercepted areas will denote the corresponding variations in the quantity of heat under a constant volume. But if the specific heat of air under a constant pressure exceed that under a constant volume, in the constant ratio of K to 1, and if these ordinates be every where increased in that ratio, another line GD, passing through their extremities, must be of the same nature with CF, and the intercepted areas to the former as K to 1.

Again, let the specific heat of a mass of air under a constant pressure be BD x 1°; and let its temperature be raised from B to E under the same pressure; then the area BDGE will denote the increase of heat, and EG x 1 the specific heat under a constant pressure at the temperature E. Now EG: EF:: K: 1, wherefore EF x 1° is the specific heat of the dilated mass at the temperature E, under a constant volume. But EF x 1° would still have been the specific heat, had the air under its original volume been raised to the temperature E; and because EF: EG: 1: K, its specific heat at the temperature E under a constant pressure would have been EG x 1°, as before. Hence, the constant ratio of the specific heats renders them independent of the actual density or pressure, and, therefore

e

and

P

ар

are constant quantities. It thus appears, that the above expressions for the specific heats answering to a degree on the common scale, vary inversely as 1+ at; or, that any inate BD, or BC is inversely as AB, which is the well perty of the hyperbola; and, therefore, CF and hyperbolas, having A for their centre, and AE for We have, then, without going through the pr

ing a partial differential equation, arrived at the same construction as was used on page 337, vol. i., and which represents the relation between the common and true scales of temperature, viz. that when the variations on the latter are uniform, those on the former follow a geometrical progression.

On the Detection of Arsenic in cases of Poisoning. By J. L. BERZELIUS.

IN

cases of poisoning with arsenic, the individual may have taken the deadly poison either in the pulverulent form, or in a state of solution. In the first case, we can almost always detect visible particles of arsenic in the contents of the stomach, or on the inner coat of the stomach, where they are distinguished by dark red spots, on which they are to be looked for. The nature of these particles, although much under the one-tenth of a grain in weight, may be ascertained with great care and perfect certainty by the process or test of reduction. The following method I employ in the use of this test:-A glass tube, from one-tenth to one-seventh of an inch in diameter, is drawn out, at one extremity, into a fine point, from two to three inches in length, which ought not to be wider internally than the thickness of a coarse knitting needle, and is then hermetically closed at the extremity.

b a

The particle of arsenic (even the one-hundredth part of a grain in weight is more than is necessary), is moved upwards to a, and covered with charcoal powder, which has been previously exposed to the flame of the blowpipe, to drive off any moisture it might contain, to b. The tube is then brought, in a horizontal position, into the flame of a spirit of wine lamp; and in such a way, that a, where the grain of arsenic lies, remains beyond the flame. As soon as the charcoal at b is heated to redness, a is brought into the flame, by which the arsenious acid is converted into gas; and, during its passage through the glowing charcoal, is reduced. The metallic arsenic is condensed in the small tube, at the line

where it is beyond the flame, in the shape of a shining, dark metallic ring, which, by gentle heating, can be driven farther forward; and thus more is accumulated, by which it acquires a higher lustre. The small diameter of the tube prevents all circulation of air, so that no part of the metal is reduced. It only remains to determine the arsenic by its smell. This is effected, if we cut the tube between the charcoal and the metal, then heat it gently in the place where the metal rests, while we hold our nose over it but at a little distance.

The second case occurs, when no visible grains of arsenic are present, as in those instances where death has been caused either by solution of arsenic, or by finely pounded arsenious acid. When the poisoning has been caused by the solution of arsenic, it is often impossible to detect the arsenic, because, the solution has been carried off before death. If, however, some portion of it still remains, it is discovered by heating the contents of the stomach, at a boiling heat, with caustic potash, and then with muriatic acid. The filtered fluid is reduced, by evaporation, to a smaller volume; and, if necessary, again filtered, and then a stream of sulphuretted hydrogen passed through it. The fluid is now heated, to cause the precipitate to collect, or evaporated, if it does not subside until it does, and then filtered*. If the quantity of precipitate is so small that it cannot be mechanically removed from the filter, it must be removed from the paper by means of caustic ammonia, and the fluid evaporated in a watch-glass. The sulphuret of arsenic can be oxidized in two ways either it is dissolved in a little aqua regia, until all the arsenic is converted into arsenic acid, the fluid freed from sulphur, dried by a gentle heat, then the residuum dissolved in a drop of water, and supersaturated with lime-water: Or, better, we mix the sulphuret of arsenic with saltpetre and deflagrate the mixture at the end of a hermetically sealed glass-tube. We first melt a little saltpetre in the tube, and then gradually

* If the quantity of arsenic is very small, the fluid becomes yellow, without precipitation; but if it is then evaporated, the sulphuret of arsenic falls in proportion as the acid concentrates during evaporation. If the fluid becomes yellow, without any precipitation of sulphuret of arsenic, during the evaporation, it cannot be considered as a sign of the presence of arsenic. This colour almost always occurs when the fluid contains nitric acid, which reduced to the state of nitrous acid, colours the dissolved animal substances yellow.