the light of the star has to traverse before reaching our spectroscopes. When, however, the region of combustion had encroached sufficiently to reverse the metallic lines, these would shine out with much greater brilliancy than the nonmetallic lines, and we should have a background of continuous spectrum crossed by the bright lines of the metals of smallest vapour-density. Such stars would only be expected among those which are, so to speak, in the latest phase of their "chemical period." It is significant that y Cassiopeia, B Lyræ, ß and Argo, three stars which show bright lines in their spectra, all have sufficiently complex spectra to warrant the belief that they have entered upon a late phase of their existence. Before the actual reversal of the metallic lines there must exist a period in the life-history of many stars when the temperature and extent of the zone of combustion is such as to obliterate the dark lines of those metals which will ultimately appear as bright lines. Such appears to be the case with the hydrogen in a Orionis; and according to the present views it might perhaps be predicted that this star will sooner or later show a permanent hydrogen-spectrum of bright lines. It is conceivable that in certain cases the composition of a star's atmosphere may be such as to permit a considerable amount of cooling before any combination took place among its constituents; under such circumstances a sudden catastrophe might mark the period of combination, and a star of feeble light would blaze forth suddenly, as occurred in 1866 to Coronæ Borealis. In other cases, again, it is possible that the composition of a star's atmosphere may be of such a nature as to lead to a state of periodically unstable chemical equilibrium; that is to say, during a certain period combination may be going on with the accompanying evolution of heat, till at length dissociation again begins to take place. In this manner the phenomena of many variable stars may perhaps be accounted for. On the whole, the possibility of actual combustion taking place in the atmosphere of a slowly cooling star previously at a temperature of dissociation does not seem to me to have had sufficient weight attached to it; and in concluding, I would point out the important factor which is thus introduced into calculations bearing upon the age of the sun's heat in relation to evolution.

London, June 6, 1878.

IN

VII. Notice of Researches in Thermometry.

By EDMUND J. MILLS, D.Sc., F.R.S.*

N the course of some researches, commenced some years since, which required a series of accurate measurements with the mercurial thermometer, I had occasion to make a somewhat minute inquiry into the properties of that instrument. The publication of the completely reduced results has been delayed by ill-health and pressure of other work; my present wish is to indicate them, as they may be of interest to those who are engaged in observations of temperature.

I. If an old thermometer be immersed in boiling water, its zero descends. In the course of two or three years, at the ordinary heat of the air, the zero may attain its original position, subject to some slight oscillations according to the season of the year. If a represent the time in months, y the remaining depression, and (A+B) the total depression, the equation to the ascent is

Aa depending on the diameter, BB on the length of the bulb. In the case of a spherical thermometer, A is very nearly equal to B. The probable error of a single comparison of theory with experiment, in a fairly favourable instance, does not exceed 00:01 C.

II. For other temperatures than that of boiling water, other depressions occur; the connexion between these depressions and the temperature seems to follow a compound-interest law, similar to the preceding.

III. If, however, a considerable elevation of temperature be effected, then the zero no longer falls, but rises. In various lead-glass thermometers this phenomenon usually commences at 120°-150°, the bulb collapsing to such an extent as to raise the zero sometimes 8°. At some point, which we may take roughly as not less than 100° higher than the last, the zero is again depressed, as might, in fact, be expected from the then sensible tension of mercury vapour, aqueous vapour, residual air, and other foreign bodies in the tube.

ÍV. I have made a large number of comparisons of the mercurial with the air-thermometer. The maximum difference between the two, between 0° and 100°, is at about 33°; neglecting Poggendorff's important correction (as is usually done), it lies at about 50°. It is convenient to use a glass helix, instead of a bulb, for the body of the air-thermometer; in this way convection of air is avoided.

* Communicated by the Author.

V. The effect of external pressure on a thermometer's bulb is directly proportional to the pressure as far as about 140 atmospheres. The ascent of the zero of a thermometer on keeping is consequent on a change of state in the glass, being the same whether the thermometer be open or closed, and therefore independent of atmospheric pressure.

VI. When all corrections are made, every individual thermometer has specific characters whereby it differs from all other thermometers.

VII. A number of bodies have been rigorously purified, and their fusion-points determined, with a good second place of decimals, in terms of the air-thermometer: these points range from about 35° to 121°. The possession of these bodies, which can always be preserved without risk, will enable any observer to obtain standard points within that distance, and save a vast amount of tedious experimentation.

Anderson's College, Glasgow.

VIII. On the Relation between the Notes of Open and Stopped Pipes. By R. H. M. BOSANQUET, Fellow of St. John's College, Oxford.

To the Editors of the Philosophical Magazine and Journal. GENTLEMEN,

IT

T has long been known to practical men that, if an open pipe be stopped at one end, the note of the stopped pipe is not exactly the octave below the note of the open pipe, as it should be according to Bernouilli's theory, but the stopped pipe is somewhat less than an octave below the open pipe; in ordinary organ-pipes the difference is said to be about a major seventh instead of an octave. It has occurred to me lately that the theory of this phenomenon is not generally known; and the following account of it, with some of its applications, may be of interest. I should mention that the investigations were made some time ago, before the publication of my Notes on the Theory of Sound, in the Philosophical Magazine last year; and they were not mentioned there only because the methods depending on them proved of insufficient accuracy for the purpose then in view.

Consider a cylindrical tube open at both ends. Let its length be l, and its diameter 2R. Then the effective (or reduced) length of the pipe is 1+2a; where a is the correction for one open end, which formed the subject of the investigations contained in Nos. 5 and 6 of my "Notes" (Phil. Mag. [V.] vol. iv. pp. 25, 125, 216).

Now suppose a flat stopper, fitting airtight, to be applied at one end of the tube. It may then, according to the ordinary theory, be regarded as equivalent to the half of an open pipe whose middle point, or node, coincides with the face of the stopper, the effective length measured from the node being 1+a. The length of the corresponding open pipe would be double of this, or 2(1+a). The ratio of the notes is consequently (+2a): 2(1+a), which may be put in the form

α.

1 1+2a
X

2 7+a

that is to say, the interval in question differs from an octave by the interval whose ratio is (+2a): (1+a).

The following experiment was made with an iron cylindrical tube, 4.9 inches in length and 2 inches in diameter. The notes were determined, as in my former investigations, by blowing short jets of air against the edges. The tube was stopped by standing it upright on a flat surface, and applying a little oil round the edge in contact with the surface. The notes of the pipe, open and stopped, made with one another the interval of a minor seventh; i. e. they deviated from the octave by a whole tone. The ratio (98) was determined with some slight accuracy by comparison with the notes of my enharmonic organ. The tuning of this instrument is not, however, sufficiently stable to base very accurate work on. Then

The value of a for this tube was formerly determined at 635 R (Phil. Mag. vol. iv. p. 219). The tube has been shortened by about 1 inch since; but this cannot affect the correction. İt appears then that the present process presents general correspondence with the result of the former investigation; but the numerical values of a do not coincide very exactly.

When I originally investigated this subject some time ago, I anticipated that I should be able, by observation of the in

terval between open and stopped pipes, to determine & in an accurate manner. For this purpose I constructed many pipes, in which the interval in question was as nearly as possible of definite magnitude, generally a semitone less than the octave; but the method proved too inaccurate to be of any real use. An excellent and perfect tonometer is required to measure the intervals accurately; and if we have that, it can be applied to the solution of the problem with greater advantage in other ways. The present method, however, is quite sufficient for the approximate demonstration of the value of a.

There are difficulties in the way of the exact application of these principles to ordinary organ-pipes. First, it is impossible to blow an open and stopped pipe in a similar manner with the same mouthpiece. The pitch varies considerably with the force of the blowing; and the two notes produced with different blowing are not comparable. Again, there is a considerable correction of unknown amount to be taken account of, due to the closing-in of the mouth-end of the pipe.

We may, however, partly get over these difficulties. In the first place, it is possible to arrange a pipe so as to blow the fundamental when open and the twelfth when stopped, without variation of the wind. Secondly, the correction due to the closing-in of the parts round the mouth can be determined for pipes of given shape by sawing one of them across so as to leave a plain circular end. The correction due to the difference in pitch +a (correction for circular end) gives the total value of the correction for the mouth.

The following is an example:-Organ-pipe 9.5 inches from upper lip to open end; diameter 95 inch. When arranged so as to blow the fundamental when open and twelfth when stopped, the twelfth was 2 commas of the enharmonic organ sharper than the note corresponding to the fundamental. Taking these to be true commas, which they are very nearly, we may take the resulting interval to be 40: 41.

The correction for the mouth was determined by sawing across a similar pipe; it is roughly

Phil. Mag. S. 5. Vol. 6. No. 34. July 1878.

F