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nished room—under these conditions only did I carry out my research on the spectrum of carbon. The absence of Plates and measurements in my paper is not".... explained (in a memoir crowned by being printed in the Philosophical Transactions of the Royal Society of London) by its one chief burden (viz. putting pure carbon vapour for hydrocarbon) having been grateful to the then already formed prejudices of the secret committee who passed it,” but by the fact stated in my paper, that Professor Swan had already measured and recorded, confessedly with great accuracy, the position of the lines of the spectrum (observed by him in hydrocarbon flames*).

Spectral analysis brings to light marvellously minute traces of matter, traces difficult to remove even from the surfaces of apparatus, and still more difficult to extract from large volumes of other matter. Have I overlooked traces of hydrocarbons in some of my flames and tubes ? Scarcely; for I adopted all precautions known to chemists to obtain chemical purity and cleanliness. Again, other chemists, armed with prejudice against my conclusions, have ended by confirming those conclusions. Still here perhaps is room for sound original investigation; something new could hardly fail to be discovered by eyes trained to observe. Is it too much to expect that a gentleman occupying so high a position as Mr. Piazzi Smyth will either support his statements by such sound evidence or withdraw them altogethert ?

JOHN ATTFIELD.

THE

XV. On the General Theory of Duplex Telegraphy.

By Louis SCHWENDLERI.

[Continued from vol. xlviii. p. 138.] THE first part of this investigation concluded by giving

(Phil. Mag. vol. xlviii. p. 138) the best relations between * Had so good an observer as Swan worked, instead of the writer, in 1862, with the light just then shed on spectroscopy, I am sure he would have looked for the spectrum in flames not containing hydrogen, and would thus have discovered what I discoved, the spectrum of carbon.—J. A.

† The tone of Mr. Piazzi Smyth's communication renders desirable on my part an expression of regret that my duties in the department of chemistry to which I was appointed within a month of the publication of my research on the spectrum of carbon, have quite prevented me from carrying on similar researches. That regret is much tempered, however, by my belief that such work would have been done far less efficiently by me than by men like Plücker, Morren, Lielegg, Troost and Hautefeuille, and Marshall Watts. I am obliged to add that nevertheless my labours, from the promotion of original investigation in other directions, have neither been few nor unsuccessful. This is the only notice I can take of the personalities in Mr. Piazzi Smyth's paper.-J. A.

| From the Journal of the Asiatic Society of Bengal, vol. xliii. part 2, 1874 (read on the 4th of February, 1874). Communicated by the Author.

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 in case the line has an appreciable leakage. In fact this is clearly the case of practical importance; since all overland lines, especially long ones, even if constructed on the best known principles, will always have a very considerable leakage; i.e. the resistance of the resultant fault (i) will generally be by no means very large in proportion to the real conduction-resistance (L) of the line.

In order to obtain the best general solution of the problem, we must conduct the investigation with great caution; that is, we must be careful not to introduce beforehand any relation between the different variables, however convenient, that is not necessarily a consequence of the paramount condition to be fulfilled for duplex telegraphy, i. e. regularity of signals.

Thus it will be seen that the present general investigation must be conducted somewhat differently from the special one given in the First Part.

It must, however, be understood from the beginning that, whatever the best relations may be which should exist between the different resistances of the bridge method when used on an imperfect line, these relations must revert to the special one given before if we put i=00; and this fact affords a certain check upon the correctness of the new relations to be found.

General solution of the first problem for the Bridge Method.

The annexed diagram (p. 110) represents the general case; and to it therefore I shall refer in the present paper.

The general mathematical question which is to be solved for duplex telegraphy has been stated as follows:

REGULARITY OF SIGNALS.-D and S are two functions which must be rigidly equal to zero when no variation in the system occurs —and which for any given variation in the system must be as small as possible, and approximate rapidly towards zero as the variation in the system becomes smaller and smaller.

Further, these two functions D and S were expressed, say for station I., as follows ::

E'N 1 A
D'
E'N' u mine?

(III.) For a definition of the terms “ resultant fault," “ real conduction," “measured conduction,” “real insulation,” “ measured insulation,” &c., which will be of frequent occurrence in this paper, see my 'Testing Instructions,' Part II. Section I.

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matter, traces difficult to remove even from the surfaces of apy
paratus, and still more difficult to extract from large volume di
other matter. Have I overlooked traces of hydrocarbons in sond
of my flames and tubes ? Scarcely; for I adopted all procar

tions known to chemists to obtain chemical purity and de
ness. Again, other chemists, armed with prejudice against
conclusions, have ended by confirming those conclusions,
here perhaps is room for sound original investigation; some
new could hardly fail to be discovered by eyes trained to ok
Is it too much to expect that a gentleman occupying so
position as Mr. Piazzi Smyth will either support his state
by such sound evidence or withdraw them altogethert!

XV. On the General Theory of Duplex Telegrafi

By Louis SCHWENDLERI.

Continued from vol. xlvii. p. 138.)
HE first part of this investigation concluded by

(Phil. Mag. vol. xlviii. p. 138) the best relaties
* Had so good an observer as Swan worked, instead of the
1862, with the light just then shed on spectroscopy, I ung
have looked for the spectrum in flames not containing hydney
thus have discovered what I discoved, the spectrum of carta

+ The tone of Mr. Piazzi Smyth's communication renden my part an expression of regret that my duties in the deg mistry to which I was appointed within a month of the research on the spectrum of carbon, have quite

prevented on similar researches. That regret is much tempered,

that such work would have been done far less effe
ke Plücker, Morren, Lielegg, Troost and Hate
s. I am obliged to add that nevertheless an
of original investigation in other directions,
ccessful. This is the only notice I can take
azzi Sm

per.-J. A.
Journ 1 siatic Society of Berg
he 4th

1874). Communica

I

carry out my e of Plates and ed (in a memi ansactions of t eden viz. port is been grateful cret committer paper, that Pa confessedly wc. spectrum ober

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

It now remains, therefore, to investigate if the ope reis. tions given are generally true; or if not, what they become a case the line has an appreciable leakage. In fact art the case of practical importance ; since all overland 18, este ally long ones, even if constructed on the best kons; will always have a very considerable leakage; i.e. the fiscales

La of the resultant fault (7) will generally be by no means they are in

In order to obtain the best general scisci de priem, from the surie proportion to the real conduction-resistance

Lt must be careful not to introduce betsenzi ni za aces of hydrocarbon e bust conduct the investigation to get 121.18

pen the different variables, boterer 0721LE $ 116 essarily a consequence of the paramoist anna eind for duplex telegraphy, i.e. regularity of path.a.

hus it will be seen that the present renenti mumkan riginal investiga be conducted somewhat differently to the in the First Part.

met nust, however, be understood from the bernaung da, wered by eyes train:

vellously minute to ract from larte scu

1: for I adopted a chemical purity se ed with prejudiz rming those concleum

i gentleman occupe woll either support ihdraw them altor

er the best relations may be which wonii sus serveen
ferent resistances of the bridge netard vien ut in m
et line, these relations must retert 33 the mesa ine
efore if we put i=1; and this fact afri, der an meca

correctness of the new relations to be buni.
al solution of the first problem for the Britse Muut

inexed diagram 'p. 110, represent the nemt ose;
therefore I shall refer in the present paper.
graphy has been stated as that:

SITY OF SIGNALS.-D and Susten penctions Thuck lly equal to zero when m caridiwa Mten

w Theory of Duplex
1. SCAWENDLER

Lis investigation leral mathematical question waien le kiveri ir

from vol. xlviii. p.

VII. p. 138) the bo
rver as Swan worked,
then shed on spectrosor
rum in flames not contar
iti I discoved, the specir for,

any giren sariatin in the mixtum nuL le 18 mul

vizzi Smyth's communi nd approximate rapists importa a tele voration

of regret that my duties appointed within a month um of carbon, have quite por S. That regret is much tim k would have been done fare

Morren, Lielegg, Troosia Stirred to add that neverthe tigation in other da

e the only noticed

becomes smaller and smaker,

jese two functions D and S were shuset, as
follows:
EN 1 N

***
E'N
ion of the terms resultant init.* * tel santner.nn. *
metion," " real insulation, *“ near marion"
frequent occurrence in this paper, te nylowing

Section 1.

Society

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

1
then, b=2-b=(7) reduces to

π
7 (A?-12) Ao tan =AA?

(8)

λ which gives an infinite number of values of 2 when A, no are assigned. I now assume A=1 (the reed the octave of the string), and

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

47' 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

ī

4
1 a
tan TT

1

*

2 The numbers placed under the head in the Table which

à 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.

1 The second column contains the values of the ratios reduced

À 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.

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

1. Equal-tem-
referred to

2
perament

Description.
semitones.

5868
1:441
2:357
3.295
4.25

- 9.230
+6:326
16.132
20.646
25.052

15.556 25.362 29.876 34.282

Flat major tenth.
Sharp minor sixteenth.
Flat two octaves and tritone.
Sharp two octaves and minor seventh.

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

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