In the process of ebullition, the expansive action of the heat absorbed by the lower layers of the liquid increases until the superincumbent pressure, the cohesive attraction of the vessel for the liquid, and the effective attractions subsisting between the molecules of the liquid (represented by the ordinates between a and b, fig. 1), are overcome. When this point is reached at any part of the liquid stratum, the separated particles will expand rapidly into bubbles of vapor, in opposition to the pressure of the atmosphere, and the attractions denoted by the decreasing ordinates between b and c, fig. 1. The expansion should continue until the distance between the atmospheres of two particles increases to the limit Od, at which the repulsion attains to its maximum value; or rather to a limiting distance somewhat greater than Od, at which the repulsion due to the heat pulses present in the molecules, plus the molecular repulsion at that distance, is equal to the external pressure.

It cannot proceed further than this without a direct expendi ture of heat-force, which will raise the temperature of the vapor. The heat which becomes latent, as the phrase is, is expended in the act of expansion, and in forcing up the molecular atmospheres in opposition to the attractive action of the atoms and all compressing forces. The amount of work thus taken up by the atmospheres manifests itself also as work of expansion, since it is so much work of the atomic attraction and of the compressing forces neutralized. When the heat pulses are not wholly expended in this manner, a portion of them pass into the molecu lar atmospheres and elevate the temperature of the liquid. If the pressure upon the free surface of the liquid exceeds the pressure of the atmosphere, the molecular atmospheres are more compressed, the value of m becomes greater, and the ratio,

n

diminishes in consequence; from this cause the limit of the recess of the particles, Od, fig. 1, diminishes, and the maximum repulsion, dn, increases (see Table I). The resulting vapor has, therefore, at the same time, a higher tension and a greater density.

,,

According to the theoretical views now advanced, the "interior work" which Tyndall maintains is expended in the act of liquefaction, and also in that of vaporization, in "moving the atoms into new positions," or in conferring "potential energy' upon them, is consumed in each instance in pressing up the electric atmospheres that surround the atoms of the substance; and heat disappears in the process in proportion to the effect thus produced.

[To be continued.]

ART. VIII.-On the Improvement of the Elements of a Comet's Orbit: Brünnow's method; communicated by C. ABBE.

THE following method of conducting the computation of the elements of a parabolic orbit was taught by Dr. Brünnow in lectures at the University of Michigan in 1858; it is here faithfully reproduced from my notes taken at that time, and whatever of merit it possesses is of course due to my instructor. The formulæ are thrown into the natural order of computation, and they will thus be readily available to the computer. The present is quite a general method: it presumes a previous approximate knowledge of the orbit, and is suited to normal places or very exact observations, and is not limited to the use of three places. The intervals t"-t' and t-t are not restricted.

We use at least three complete observations, i. e., the times t, t, t'; the geocentric longitudes λ, A', A", and the geocentric latitudes B, B, B". We shall also need the sun's geocentric longitudes O, O', o", and the logarithms of the sun's geocentric distances R, R', R". From our previous knowledge of the orbit we shall have been able to correct our observations for velocity of light, aberration and parallax; they should be referred by proper corrections for nutation and precession to the same equinox.

We first may prepare the angles

O′′-0, 1-0, 1-O, the number R, and the logarithm of t"-t. Compute the number g and angle G from

(O'

R" cos (0-0)-R=g cos (GO)
R" sin (O"-O) g sin (G-O)

g and G are the distance and longitude of the first place of the earth as seen from the third.

Compute the numbers c and c" and logarithms C and C" from

cos B cos (-O):
= cos y

R cos y C
R sin

C

cos B" cos ("-") = cos y'

R" cos y c"

R" sin "C"

andy" are the angles at the earth between the sun and comet at the first and third observations.

From our previous knowledge of the orbit we now assume two values and ▲, of the distance between the comet and earth at the time t. It will be a little more convenient and elegant to assume log ▲ and log A+. The following_computation is to be made for each assumption. Compute log D and angles B and L from

A cos cos (G)+g= D cos B cos (L-G)
A cos sin (-G) =D cos B sin (L-G)
=D sin B

A sin ?

D, B, L, are the distance, latitude and longitude of first comet's place as seen from third earth.

Compute the number a and logarithm A from

sin "n* sin m

cos B" cos ("- L) = n cos m

n cos (Bm) = cos p
D cos y a

D sin

Compute the number r from

A-C

= A

r=+√(A−c)2+C2 = if we put tan x =

r is the heliocentric distance of comet at the first observation. We now desire to find r", which must be accomplished by a tentative process.

Assume a value, A", of the distance of third comet from third earth. Compute the number r" from

With the r and thus found we compute logarithm x from Lambert's equation, as follows:

logu is tabulated with argument 7. (See Davis's Gauss Theoria.)

x = nu (r"+r)

If this value of x does not agree with that found from

we must then assume another value of A" and renew the computation of x. A few trials will give the required value of a". x is the chord between the first and third places of the comet.

We are now able to find the heliocentric distances r and r". latitudes b and b', and longitudes I and l", of the first and third positions of the comet, from the following formulæ :

A cos B cos (-O) - Rr cos b cos (1-0)

A cos sin (-O)

rcos b sin (1-0)

A sin B

=r sin b

* Sign of n is plus.

and

A" cos B" cos ("-") — R" = "' cos b" cos (l" —O")
A" cos B" sin ( — O")

="cos b" sin ("—")
=r" sin b"

A" sin 8" The values of r and r" found from these formulæ must agree with those found previously.

Having now the heliocentric coördinates of the comet for the times t and t", we are able by well known formulæ to find the elements of the orbit, and from these elements we compute the latitude and longitude for the time t'. A comparison of these results with the observed 8' and ' will show that

From as many such equations as we choose to employ we may determine x, and a new computation assuming log A+ as the logarithm of the distance between first comet and first earth, will lead to our desired improved elements.

ART. IX.-Notes on the Platinum Metals, and their Separation from each other; by M. CAREY LEA, Philadelphia.—Part I.

(I.)

FEW branches of inorganic chemistry present difficulties comparable with those involved in the study and separation of the platinum metals. Their close analogy with each other, and the remarkable manner in which the relations of each to chemical reagents are controlled by the presence of the others, give rise to difficulties in their detection and separation which are only by degrees being surmounted. Much time and unwearied labor on the part of the chemist are required to reach results which when obtained appear insignificant in proportion to the effort which they cost, and it may in fact be said that the platinum metals constitute a chemistry in themselves, governed by special rules and to be studied by special methods. Each step in the simplification of the processes by which the separations are effecte, each decisive reaction by which the presence or absence of a member of the group may be certainly inferred, is so much gained toward conquering a complete knowledge of these rare and interesting bodies.

AM. JOUR. SCI.-SECOND SERIES, VOL. XXXVIII, No. 112,-JULY, 1864.

For much the better half of all we know upon this subject, we are indebted to Dr. Claus, whose method of separation I have followed up to a certain point, and then have diverged from it, with I think some advantage. I propose to introduce the use of oxalic acid, as an agent in effecting the separation, in the manner which I shall presently describe.

From my friends, Prof. Booth, of the U. S. Mint, and Mr. Garrett, I received the material upon which I have worked. This was Californian osmiridium, which had already undergone a preliminary fusion with nitre and caustic potash.

This material was next boiled with aqua regia to extract all the soluble portions, the residue was then ignited with nitre and caustic soda,' the fused mass was heated with water. From the resulting solution small portions of osmite of potash crystallized out. The metallic oxyds were next precipitated, and this precipitate, together with the portions insoluble in water, was boiled again with aqua regia, ignited again, &c. These ignitions, in addition to that which it had undergone before coming into my hands, still left a small portion of unattacked residue.

The boiling with aqua regia was continued for a very long time in order to get rid as thoroughly as possible of the osmic acid; in all, this treatment was extended over two hundred hours. Even this however still left osmium in the solution, in easily recognizable but in comparatively small quantity. The greatest advantage was found throughout the whole of this part of the operation from the use of the blowing apparatus, which I described in a former number of this Journal, and with the aid of which all inconvenience from the fumes of osmic acid was avoided. The apparatus was constantly swept clear by a powerful air-current, and the osmic acid was removed as fast as it volatilized. The treatment which the ore had undergone before it was placed in my hands, had removed the greater part of the osium; a portion of what remained had separated out as osmite of potash, and it was not deemed worth while to attempt to save the little that remained. It would be easy, however, in operating upon fresh material with the aid of this blowing apparatus, to conduct the osmic fumes through an appropriate reducing agent, and at the same time to sweep out every trace which escaped reduction. As the ignition of the ore with alkaline nitrate and caustic scarcely drives off any osmium, and as almost all inconvenience in manipulating the resulting solutions can be avoided by throwing down the metals with alcohol from

Attention is necessary to the order in which these substances are employed. If the caustic soda is melted first, it attacks the iron vessel strongly and may even go through. If added last, it causes sudden and violent effervescence, with danger of boiling over. Therefore, place the nitre first in the vessel, and when it is fused, add the caustic soda. When a red heat is attained, add the osmiridium by degrees.