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the resistances of the different branches of the bridge arrangement—under the limiting supposition, however, that the line used for duplex working was perfect in insulation, or, more generally, that the real conduction-resistance of the line could be neglected against the resistance of the resultant fault*.

It now remains, therefore, to investigate if the simple relations given are generally true; or if not, what they become an case the line has an appreciable leakage. In fact ths as teary the case of practical importance; since all overiand aes, exce ally long ones, even if constructed on the best known prinesun, will always have a very considerable leakage; ie, the rentace of the resultant fault (1) will generally be by no means very arre in proportion to the real conduction-resistance L of the ine. În order to obtain the best general soiation of the printem, ve must conduct the investigation with great tantan must be careful not to introduce beforehand any raton eseen the different variables, however convenient, thats 105 essarily a consequence of the paramount enndiron a le fud for duplex telegraphy, i. e. regularity of aguata.

usly minute t m the surface from large hydrocarb or I adopted a mical purity with prejudic those conclus investigation red by eyes train

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hus it will be seen that the present generainvest.gton be conducted somewhat diferently from the seca me in the First Part.

deman occup either support raw them altog

must, however, be understood from the beginning that,
er the best relations may be which should enst verween
ferent resistances of the bridge method when set in
et line, these relations must revert to the metal me
efore if we put i=x; and this fact affords a certain theca
e correctness of the new relations to be found.

heory of Duple


l solution of the first problem for the Braige Metrod nexed diagram ́p. 110, represents the general tase

om vol. xlviii. P therefore I shall refer in the present paper. investigation eral mathematical question when a so te wived fr

. p. 138) the be as Swan worked,

shed on spectrosco

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graphy has been stated as follows :

HITY OF SIGNALS-D and S are two functions which lly equal to zero when no variation in the øystem iccura

discoved, the spector any given variation in the system must se ta mail Smyth's communiend approximate rapidly towarda zero as le vratan

becomes smaller and smaker.


ese two functions D and S were expressed, my ve

regret that my duties)
ointed within a month
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is the only notice


EN 1 A

ion of the terms resultant fault."real conuer.on. * Iuction," "real insulation," "measured insulation. *.. frequent occurrence in this paper, see my 'Testing inH. Section I.

sequently it may be expected, from the symmetry, that minute exactness of the position is not of special importance. Putting,

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then, b=l―b=2 (7) reduces to

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which gives an infinite number of values of λ when A, λ are assigned.

I now assume A=7 (the reed the octave of the string), and

λ= as a pair of values such as may easily occur, and con

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venient for calculation, for the sake of seeing the general nature of the results to be expected.

The equation (8) can then be put in the form

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The numbers placed under the head,

in the Table which

follows, are approximate values of the first five roots of the above equation. Proceeding further, we should find a root lying between every consecutive pair of integers.

The second column contains the values of the ratios



to equal-temperament semitones; it gives the pitch of the note sounded with reference to the octave of the string.

The third column gives the pitch of the note sounded with reference to the lowest note of the combination, both in equaltemperament semitones and by description.

Pitch, in equal. Pitch, referred to lowest note of combination.

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Although it has not been possible to get a complete determination of the elements of any experiment, yet the following

observed successions of overtones may not be devoid of interest. There are four notes of the arrangement which I shall call I., and three notes of II. The pitch in semitones is appended for comparison. In both cases the point of attachment was nearly, though not exactly, in the middle of the string.

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Comparing these numbers with the overtones indicated in column 3 of the calculated Table, it will be seen that they follow, as far as they go, the general course indicated by theory in the hypothetical case assumed; and it may be inferred that this case furnishes a rough representation of the circumstances of the two experiments examined.

The above results are the only experimental ones which I know of.

The calculation of the length of the middle segment in the hypothetical case follows easily from the numbers in column 1 of the calculated Table. The fundamental, of course, has for its segment the whole string. In the other cases, expressing

7 in terms of


which is the length of each segment except the middle one, we get the middle segment at once, since we know the actual number of segments. (It is hardly necessary to remark that the numbers of segments in the successive overtones are the odd integers, by the symmetry.)

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So that, as the pitch of the note sounded rises, the reed diminishes more and more the segment to which it is attached, as compared with the others. Of course this remark is confined for the present to cases resembling the hypothetical case.

The note employed may be either the fundamental or any one of the overtones. As these are in general all inharmonious to each other, only one can be used at a time. But it is probable that, in particular cases, some two or more may become harmonious; and they would then be capable of combining in a true periodic motion.

XIII. Carbon and Hydrocarbon in the Modern Spectroscope. By W. MARSHALL WATTS, D.Sc., Physical-Science Master in the Giggleswick Grammar School*.


N the January Number of the Philosophical Magazine appears a paper with the above title by Professor Piazzi Smyth, which calls for a few words from me by way of explanation.

1. Professor Smyth inquires "why, since for cometary work the reference-spectrum should be of feeble intensity, I do not examine it in that shape, viz. as given by the blue base of the flame of a small alcohol lamp, or the all but vanishing globule of flame when a common gas-light is on the point of going out from inanition?" The answer is simple, that with a spectroscope of six prisms the loss of light is so great that in the spectrum of a blowpipe-flame there would not be more than one line (5165.5) bright enough to be measured, and it was my object to employ as large a dispersive power as possible in order to secure as great accuracy in the determinations as I could.

The same reason explains why, "although the spectrum consists notably and notoriously of five bands, viz. the orange, citron, green, blue, and violet," I only give measurements for three of the bands: the orange and violet bands were not bright enough to be measured accurately.

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2. An equally simple explanation solves the "strange problem' why the lines 5165·5 and 5585·5 are the best-determined. 5165.5 happens to fall close to the magnesium-line b, whose wave-length we know with great accuracy from the labours of Ångström.

5585 5 happens to be exactly coincident with an iron line in the solar spectrum. The first band of the citron group, although brighter than the second, does not fall near to any marked line in the solar spectrum which could be used as a reference-line; and its determination is therefore not quite so exact.

* Communicated by the Author.

3. Chemical Parentage of the Spectrum under discussion.-I freely admit the force of Professor Piazzi Smyth's remarks on the difficulty of volatilizing carbon; but that does not appear to me to affect the experimental evidence for my assertion that "this spectrum is the spectrum of carbon, and not of a hydrocarbon or any other compound of carbon." That evidence is very simple; this spectrum can be obtained alike from compounds of carbon with hydrogen, with nitrogen, with oxygen, with sulphur, and with chlorine.

Whether or not the spectrum is produced by the vapour of carbon is another question; but if this spectrum is, as Professor Piazzi Smyth asserts, that of a hydrocarbon, will Professor Piazzi Smyth explain how it is possible to obtain it from cyanogen, a compound of carbon and nitrogen, when no hydrogen is pre sent? I have just repeated the experiment with cyanogen for perhaps the fiftieth time. Dry mercuric cyanide was heated in a test-tube, and the gas evolved was dried by passing through a tube containing phosphoric anhydride; it then passed through a tube provided with platinum wires, the end of which dipped below warm and dry mercury. On passing the discharge from an induction-coil between the platinum wires a spark was obtained which gave the spectrum in question brilliantly, the gas being decomposed and carbon being deposited.

Professor Piazzi Smyth says that in May 1871, in a paper sent to the Royal Astronomical Society, he " gave such extracts from the authorities on either side as showed that the spectroscopists declaring for pure carbon, in opposition to those pronouncing for carbohydrogen, were blundering little less than the perpetual-motion men of last century." Permit me to quote from a paper communicated by myself to the Journal of Science for January 1871:

At first sight it would appear that carbon is an element unlikely to yield a discontinuous spectrum, inasmuch as it is not known in the gaseous condition; and that if we obtain discontinuous spectra from carbon compounds, they must be due to some compound of carbon. Thus the bright blue lines observed by Swan (1856) in the spectrum of the Bunsen-flame might be supposed to be more probably due to carbonic oxide or carbonic acid than to carbon itself. But we find that these same lines occur not only in the spectrum of the flame, but also in the spectra obtained by passing the electric spark either through carbonic oxide, or olefiant gas, or cyanogen, and the lines thus found to be common to compounds of carbon with different elements must of course be due to carbon itself. Whether they are really produced by carbon in the gaseous state is a question which cannot yet be certainly decided. If the carbon is in the solid

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