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tity of heat is in itself proportional to the work as soon as the initial temperature is regained, while the pressure and volume may have other values; as pure loss of heat it appears, it is true, only after a complete restoration of the original condition.p sdi skon

19 Let us now suppose that neither Mariotte's law nor the law of the invariability of the capacities is accurately true. If c and c' are subject to any small changes in consequence of changes of pressure or temperature, we may consider them as functions of p and v, and write equations (2) and (3) as follows:

-sysɔ odt szorgzo 19 (Sopdv + fo'vdp)

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ea The elusion mfddr = 2 (Sepdv + Sevdp),

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If now during the change there is only work consumed or work performed, if consequently pdv undergoes no change of sign, we may, by a known property of definite integrals, place the factors c and c-c' before the sign of integration, when the last equation will correspond with equation (4): only we now understand by c' and c-c' certain definite mean values between the greatest and least of those which these functions assume during the entire change. The validity of the relation between work and heat is consequently not changed by small variations in the capacities for heat. The proportional number itself is of course subject to simultaneous variations, which however are smaller than the variation in the capacities.

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If the gas be restored to its original volume, so that at any time pdu must change its sign, the proportional number is no longer necessarily a mean value of (c-c'); yet we see, by representing specially the heat conveyed during positive and negative work, that this number can differ but l but little from the values of its expression as long as the excess is not too small. If, however, there remains from a large amount of work only a small positive excess, it might be difficult to show that the proportional number could not differ considerably from the values of its expression.

Finally, if Mariotte's law be not strictly accurate, we may put pu+p for pv, and consider p as a small magnitude depending on p and v, which at the beginning of the motion is zero. In this case, in place of pdv and vdp, we shall have relatively

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pdv+ dv ; and vdp+

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The last magnitude is cancelled, and does not occur in the resulting equation. On the other hand, q now becomes

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Were ρ of the form (p)+x(v), the quantity added to q would (v), and would vanish after the restoration to the original volume. In general, however, p would produce a change in the quantity of heat, which evidently would be always small, inasmuch as a sudden or quick change in p is very improbable.-Poggendorff's Annalen, xcvii. p. 30, January 1856; and Silliman's Journal for May 1856.

EXPLOSIVE ACTION OF SODIUM ON WATER.

BY FREDERICK W. GRIFFIN, PH.D.

The action of sodium on water contained in a glass vessel is such an elegant proof of the composition of that liquid and other points, as to lead to its being occasionally introduced in lectures. I have, however, found the experiment liable to a grave accident, which ought altogether to banish it from public demonstrations. Some years ago, during my private course of lectures, I passed a piece of the metal, about a quarter of an inch square, into a tube filled with water, 18 inches in length by 1 in diameter. When the action was nearly over, a powerful explosion occurred, which forced the tube (weighing upwards of a pound) violently through my hand and dashed it to pieces against the ceiling. As I had often before performed the experiment with perfect safety, I presumed that air must have somehow got mixed with the hydrogen; the more so as, simply holding the sodium in the fingers, I had, to slip it under more quickly, brought the mouth of the tube very near the surface of the water. On all subsequent occasions I placed the sodium in a little tube closed at one end, which it almost filled, and stopping the mouth with the finger, opened it below the larger tube, which was kept at least a couple of inches under water, so that there was no possibility of letting in air by any sudden jerk or otherwise. All went off well for several times, till at a public lecture in Devonshire an explosion resulted more violent than the first, and the tube was blown into splinters which strewed the floor of one half of the room, and slightly wounded several persons. Since that occurrence I have relinquished showing this experiment in public at all, though numerous trials appear to prove that a piece less than a pea may be used with safety, though there is sometimes a slight concussion at the end. The cause of the detonation remains to be explained. In the last instance at any rate, it is quite certain that no explosive mixture with air was formed, and I have little doubt that the effect proceeds from the water round the sodium being thrown into the spheroidal state. This view seems confirmed by the fact, that at the first moment of contact a large quantity of gas is always liberated, but the action speedily becomes weaker, and the evolution of hydrogen extremely slow. In all probability the metal is then merely decomposing the atmosphere of aqueous vapour around it; and when the piece is small, it disappears tranquilly in this way; when it is larger, so that the action is prolonged, its temperature slightly falls, contact ensues, and a burst of gas and steam takes place with explosive violence. In both cases the tube was three-quarters full of gas, and

I noticed a sudden downward rush of the liquid the moment before the explosion.

The detonation, with occasional fracture of the vessel, observed by Wagner and Couerbe* to take place when sodium floating fused on water is struck with a spatula, probably proceeds from the same cause, the highly heated globule being forced mechanically into sudden intimate contact with the liquid.

While on the subject of sodium, I may add that when it is melted with a little naphtha in a sealed tube containing no air, it presents to the full extent the high lustre and mobility of mercury, from which indeed it cannot be distinguished by the eye; but as soon as it solidifies, it assumes a slightly crystalline and dead white surface, more nearly resembling frosted silver.

Bristol School of Chemistry,

June 19, 1856.

METEOROLOGICAL OBSERVATIONS FOR MAY 1856.

2.

Chiswick.-May 1. Overcast : cold showers, partly hail: clear and cold. Quite clear: cloudy: frosty at night. 3. Cloudy and cold: showery. 4. Overcast: cloudy: clear, with sharp frost at night. 5. Frosty early A.M.: cloudy and cold, 6. Fine: cloudy and cold: rain. 7. Cold rain. 8. Densely clouded: cold north wind. 9. Heavy clouds. 10. Uniformly overcast : fine. 11. Light haze : fine: cloudy. 12. Uniform haze: rain. 13. Rain: cloudy. 14. Heavy showers. 15. Fine: showers, with some hail. 16. Fine. 17. Cloudy. 18. Boisterous, with rain and hail. 19. Very fine. 20. Very fine: slight frost. 21. Fine: rain. 22. Rain. 23. Cloudy: fine. 24. Fine. 25. Cloudy: rain. 26. Fine. 27. Very fine heavy rain at night. 28. Cloudy: very fine. 29. Hazy: cloudy: fine. 30. Cloudy and cold. 31. Rain.

Mean temperature of the month
Mean temperature of May 1855

Mean temperature of May for the last thirty years
Average amount of rain in May

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50°.09
48.78
53 .55
1.852 inches.

19.

Boston.-May 1. Cloudy: rain and sleet P.M. 2, 3. Cloudy: rain and hail P.M. 4, 5. Cloudy. 6. Cloudy: hail and snow A.M. 7. Cloudy. 8. Cloudy: rain A.M. 9, 10. Cloudy. 11. Fine. 12, 13. Cloudy. 14. Cloudy: rain with thunder P.M. 15, 16. Cloudy. 17. Cloudy: rain P.M. 18. Cloudy: rain A.M. and P.M. Cloudy. 20, 21. Fine. 22. Rain A.M. and P.M. 23. Fine: rain and thunder P.M. 24. Cloudy: rain A.M. and P.M. 25, 26. Cloudy: rain г.м. 27. Fine: rain P.M. 28. Cloudy rain a.m. and P.M. 29. Cloudy 30. Fine. 31. Cloudy: rain P.M. Sandwick Manse, Orkney.-May 1. Bright A.M.: cloudy P.M. 2. Sleet-showers A.M.: cloudy P.M. 3-5. Cloudy A.M. and P.M. 6. Cloudy A.M.: clear P.M.

:

7. Clear A.M. and P.M. 8. Cloudy A.M.: clear P.M. 9. Clear A.M.: rain P.M.
10. Cloudy A.M.: drops P.M. 11. Drizzle A.M.: fog P.M. 12. Hazy A.M.: clear,
fine P.M. 13. Cloudy A.M. and P.M. 14. Cloudy A.M.: rain P.M. 15. Cloudy A.M.
drops P.M. 16. Bright A.M.: cloudy P.M. 17. Clear, fine A.M.: cloudy, fine P.M.
18. Showers, bright A.M.: showers P.M. 19. Cloudy A.M.: showers P.M.
Bright A.M.: clear P.M. 21, 22. Bright A.M.: cloudy P.M. 23, 24. Cloudy A.M.
and P.M. 25. Clear A.M. and P.M. 26, 27. Cloudy A.M. and P.M. 28. Bright A.M:
cloudy P.M. 29-31. Clear A.M. and P.M.

Mean temperature of May for previous twenty-nine years
Mean temperature of this month

Mean temperature of May 1855

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Average quantity of rain in May for fifteen previous years

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20.

47°-85
46.83
43.81

1.66 inches.

The great drought continues; the rain during the last three months being less than the average for May alone, which is our driest month, and not half the quantity that fell in March alone last year.

Gmelin, Handbook (Cav. Soc.), vol. iii. p. 75. Berzelius, Traité, vol. ii. p. 83.

Γ

Meteorological Observations made by Mr. Thompson at the Garden of the Horticultural Society at CHISWICK, near London; by Mr. Veall, at BOSTON; and by the Rev. C. Clouston, at Sandwick Manse, ORKNEY.

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THE

LONDON, EDINBURGH AND DUBLIN

PHILOSOPHICAL MAGAZINE

AND

JOURNAL OF SCIENCE.

[FOURTH SERIES.]

AUGUST 1856.

X. On a modified Form of the second Fundamental Theorem in the Mechanical Theory of Heat. By R. CLAUSIUS*.

́N my memoir "On the Moving Force of Heat, and the Laws which can be deduced therefromt," I have shown that the theorem of the equivalence of heat and work, and Carnot's theorem, are not mutually exclusive, but that, by a small modification of the latter, which does not affect its principal part, they can be brought into accordance. With the exception of this indispensable change, I allowed the theorem of Carnot to retain its original form, my chief object then being, by the application of the two theorems to special cases, to arrive at conclusions which, according as they involved known or unknown properties of bodies, might suitably serve as proofs of the truth of the theorems, or as examples of their fecundity.

This form, however, although it may suffice for the deduction of the equations which depend upon the theorem, is incomplete, because we cannot recognize therein, with sufficient clearness, the real nature of the theorem, and its connexion with the first fundamental theorem. The modified form in the following pages will, I think, better fulfil this demand, and in its applications will be found very convenient.

Before proceeding to the examination of the second theorem, I may be allowed a few remarks on the first theorem, so far as this is necessary for the supervision of the whole. It is true that I

* The present memoir appeared in Poggendorff's Annalen, vol. xciii. p. 481, and was referred to by the author in a letter lately published in this Magazine; it is also employed to a considerable extent in a memoir on the steam-engine by the same author, a translation of which will shortly

appear.

Phil. Mag. vol. ii. pp. 1, 102.

Phil. Mag. S. 4. Vol. 12. No. 77. Aug. 1856,

G

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