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to the case of an observer moving upon a locomotive, with a velocity of a hundred feet per second, and listening to a sound whose origin moves at the same rate toward him,

he finds the observed sound 0.8 times as loud as when both are at rest. A method is also explained by him, showing the possibility of testing his conclusions by experiments on the heat received and sent by moving bodies. — Poggendorff Annalen, CLII., 535.

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THE THEORY OF RESONATORS, Lord Rayleigh contributes an extract from a forthcoming work by himself on acoustics, in which he submits a new theory of the action of resonators, and opposes emphatically the general statement that a resonator augments the body of sound by offering a column of air which is capable of vibrating in unison with the original sounding body. The exceptions to this rule, he thinks, are very important in a theoretical point of view; and he prefers to reverse the statement, and to say that the neighborhood of a resonator in unison with a sounding body diminishes the loudness of the latter. The resonator, in fact, instead of augmenting the effect of a source of sound, annuls it altogether, so far as external space is concerned, by absorbing the condensations and rarefactions into itself.-- Phil. Magazine, p. 419.

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VIBRATION OF MEMBRANES. In a paper read before the London Mathematical Society, Lord Rayleigh demonstrates the theorem that an increase in the dimensions of a vibrating system is attended by a rise in pitch. For instance, if the system consists of a uniformly stretched membrane, with a fixed edge, it follows that any contraction of the boundaries must cause an elevation of pitch. If the membrane be uniform, of given density and given tension, the frequency of vibration is a function of the size and form ; and if the form is invariable, the frequency varies as the linear dimension. The pitch of the vibrations of a regular polygon is intermediate between those of the inscribed and circumscribed circles. When the area of the membrane is given, it is easy to see that any projecting corners tend to raise the pitch, thus among rectangles of a given

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area the square gives the gravest tone, and any membrane
not a circle is higher in pitch than the circle of equal area.
In estimating therefore the lower limit to the pitch of a reg.
ular polygon, it is best to substitute for it a circle of equal
area.- Proc. London Mathematical Society, V., 9.

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Messrs. Lockyer and Roberts have attempted to investi-
gate the nature of the absorption spectra of the least fusible
metals, for which purpose they employed the oxyhydrogen
blowpipe to volatilize the substances. Their experiments,
conducted at these high temperatures upon more than twenty
metals, go far, they think, to support the conclusions which
they had previously drawn from experiments at a lower ten-
perature on more easily volatilized metals, viz., that in pass-
ing from a liquid to the most perfect gaseous state, vapors
are composed of molecules of different orders of complexity,
and that this complexity is diminished by the disassociat-
ing action of heat, each molecular simplification being mark-
ed by a distinct spectrum.

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· The variations in the spectra of gases have been usually
supposed to depend to a certain extent upon the temperature
at which the light is produced. Wüllner has advanced the
theory that the spectrum depends upon the nature of the
electric spark; but Goldstein has recently advanced opposite
views, to the effect that the different order of spectra are en-
tirely independent of the form of the electric discharge by
which the light is produced. He states that he has been
able to secure a notable increase in the width of the lines of
the spectrum of hydrogen when the pressure has been less
than one one-hundredth part of a millimeter. His experiments
lead him to think that any given order of spectrum can be
produced, if we only have a sufficiently high temperature. —
19 C, VII., 444.

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For the purpose of observing the spectrum of stars or
other points of light, Zöllner describes a very compendious
instrument to be used in combination with the eye-piece of




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a telescope. He introduces between the ordinary eye-piece
and the eye of the observer a small tube containing a cylin-
drical convex lens of about four inches' focal length, for which
lens, under different circumstances, we may substitute other
lenses of different lengths of focus. Within the tube contain-
ing this lens, and between it and the eye, there is inserted a
second tube holding an ordinary direct-vision prism, such as
is made by Browning. The intensity of light in this ocular
spectroscope is so considerable that in combination with a
small portable telescope of one and a half inches' aperture it
shows distinctly the lines of stars of the first magnitude, and
of the crescent of Venus. It is peculiarly applicable to the
systematic observation of star spectra in which the main ob-
ject is to ascertain the typical constitution of the spectra.-
7 A, XLVIII., 156.

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THE BEGINNINGS OF SPECTRUM ANALYSIS. According to Lockyer, the distinguished Swedish philosopher Angström, whose untimely death in June, 1874, was at the time chronicled by us, will be forever considered as the founder of spectrum analysis, although unfortunately the obstacles opposed by the language in which his first treatise was written, and by distance from the scenes of his investigations, for three years prevented even its existence from being known to the scientific world at large. His work,"Optiska Undersokningar,” published at Stockholm in 1853, was the first publication in which use was made of a principle already propounded by Euler, viz., that the particles of a body in consequence of resonance absorb principally those æthereal undulating motions which are impressed upon them. He also endeavored to show that a body heated until it glows emits the same kind of light and heat which it absorbs under other circumstances; he further stated that in many cases the Fraunhofer lines are the inversion of the bright lines which are observed in the spectra of various metals in the galvanic arch.-12 A, X., 377.

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Professor Thalen has published the result of an investiga-
tion into the spectra of the rarer metals yttrium, erbium,
didymium, and lanthanium. He has operated with large

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quantities of the metals of undoubted purity, and his results are the most reliable hitherto obtained. He has not only removed all doubt with regard to some 28 spectral lines that were hitherto known, but has increased the whole number of these lines peculiar to these metals from 160 to 590.

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LINES. The question has often been discussed whether it is temperature or pressure which causes the widening of the lines in the spectrum of any gas. The following considerations are adduced by Schuster as favoring the view that each separate molecule would show at all temperatures narrow lines only, but that the shocks of the other molecules cause the widening, which may therefore be considered as depending rather upon pressure than temperature. Frankland and Lockyer have found that if we increase the pressure of hydrogen while the electric current is passing through it, the lines begin to expand until the spectrum becomes continuous, and, finally, the current ceases to pass altogether, On the other hand, Gassiot has observed that if we diminish the pressure of hydrogen, its electric resistance diminishes, becomes a minimum, and then increases again. We are therefore compelled to accept Frankland and Lockyer's original conclusion that pressure and not heat is the cause of the widening of the line.- Rep. Brit. Assoc., 1873, 39.

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The committee appointed by the British Association to construct a catalogue of spectral rays state in their recent report that the whole of their work is now finished and ready for the printer, so far as regards the solar spectrum, while the positions of the metallic lines, as determined by Thalen, have been only partly reduced to uniformity with the rest of the work. The tables presented by them are constructed by throwing the solar lines into those groups which catch the eye in observing the spectrum, and the position of each line has been corrected for the dispersion of air. Both Kirch- hoff's and Angström's scales will be given with the adopted wave-lengths for each spectral line, so that it is hoped that, when these catalogues are printed, observers will find in them,

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in a collected form, the best materials which yet exist for the identification of lines, and for the reduction of fresh determinations to wave-lengths.-Rep. Brit. Assoc., 1873, 250.



In some remarks upon the optics of the spectroscope,

Mr. Sorby states that in the construction of a spectroscope the eye-piece should be of as long a focus as possible, so as to cause all the rays to enter the eye. All magnifying beyond this means loss of brilliancy; and if the spectrum appears insufficiently large, an increase in the size of the collimating and telescope lenses, together with the prisms, or an increase in the number of prisms, should be made, until the spectrum appears large enough to suit the requirements of the observer.-12 A, X., 469.

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ABBE'S REFRACTOMETER. The new instrument devised lately by Professor E. Abbe, of Jena, for the determination of the index of refraction of any transparent body, has received high encomiums, and promises to be of use in all optical researches. In principle it is, we understand, based upon the property of total reflection of light. Two similar right-angled prisms are so fixed that their hypothenuses are parallel and a slight distance apart. Between them is placed the liquid to be examined, and by measuring the angle through which this combination must be turned in order to secure the total reflection of a ray of light, we have the means of directly determining the index of refraction. In order to employ white light, and annul the indistinctness caused by the dispersion of light, a compensator is introduced, based upon a combination of flint and ground-glass prisms, and it is stated by Professor Waltenhofer that the execution of measurements with this instrument leaves nothing to be desired as regards rapidity, elegance, and accuracy.- Technische Blätter, 1874, 106.

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FLAMES, It has been ascertained that if nitrogen, hydrochloric acid, or carbon dioxide be passed into the flame of a Bunsen burner, it becomes non-luminous; but when any such mixture

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