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investigatio inventionem." Hugo de S. Victore.

" Cur spirent venti, cur terra dehiscat, Cur mare turgescat, pelago cm- tantus amaror, Cur caput obscura Phoebus ferrugine condat, Quid toties diros cogat flagrare cometas; Quid pariat nubes, veniant cur fulmina ccelo, Quo micet igne Iris, superos quis conciat orbes Tarn vario motu."

J. B. PineW -ji Mazonium.




Dr. R. Konig on Manometric Flames. ("With a Plate.) ~1

Prof. A. M. Mayer on an Acoustic Pyrometer. (With a Plate.) 18 Mr. H. A. Smith on the Chemistry of Sulphuric Acid-manu- facture 23

Mr. R. Moon on the Definition of Intensity in the Theories

of Light and Sound 38

Dr. A. Stoletow on the Magnetizing-Function of Soft Iron, especially with weaker decomposnig-powers. (With a Plate.) 40

M. E. Hagenbach's Experiments on Fluorescence 57

Notices respecting New Books :

Prof. A. M. Mayer's The Earth a Great Magnet 65

War Department Weather Maps. Signal-Service, United- States Army 66

Mr. J. N. Lockyer's The Atmosphere of the Sun 66

Proceedings of the Royal Society :

Mr. A. Liversidge on Supersaturated Saline Solutions . . 67

On the Distribution of Magnetism, by M. Jamin 76

Relation between the Pressure and the Volume of Saturated Aqueous Vapour which expands in producing Work with neither addition nor subtraction of Heat, by H. Resal .... 77 On the Definition of Temperature in the Mechanical Theory of Heat, and the Physical Interpretation of the Second Fun- damental Principle of that Theory, by E. Mallard 77

On Electro-magnetism, by M. Treve 80


Dr. W. M. Watts on the Spectrum of the Bessemer-flame. (With Two Plates.) 81

Prof. A. M. Mayer on the Experimental Determination of the Relative Intensities of Sounds ; and on the Measurement of the Powers of various substances to Reflect and to Transmit Sonorous Vibrations 90

Mr. I. Todhunter on the History of certain Formulae in Sphe- rical Trigonometry 98

Mr. R. Moon on the Law of Gaseous Pressure 100


Page Dr. R. Konig on Manometric Flames. (With a Plate.) .... 105 Mr. 0. Heaviside on the best Arrangement of Wheatstone's Bridge for measuring a given resistance with a given Galva- nometer and Battery 114

Mr. H. A. Smith on the Chemistry of Sulphuric Acid-manufac- ture 121

Mr. J. A. Wanklvn on Fractional Distillation 129

Proceedings of the Royal Society :

Dr. W. Huggins on the Spectrum of the Great Nebula in Orion, and on the Motions of some Stars towards or

from the Earth 133

Mr. J. N. Lockyer's "Researches in Spectrum Analysis in

connexion with the Spectrum of the Sun 147

Proceedings of the Geological Society :

Mr. "W. J. Sollas on the Upper Greensand Formation of

Cambridge .• 148

Dr. G. Henderson on Sand-pits, Mud-volcanoes, and Brine-pits met with during the Yarkand Expedition of

1870 149

Mr. W. B. Dawkins on the Cerviclse of the Forest-bed of

Norfolk and Suffolk 149

Mr. W. B. Dawkins on the Classification of the Pleisto- cene Strata of Britain and the Continent by means of

the Mammalia 150

On the Invention of the Water Air-pump, by H. Sprengel . . 153 Report on the Researches of M. Arn. Thenard concerning the Actions of Electric Discharges upon Gases and Yapours,

by Edm. Becquerel 154

On the great Barometric Depression of January, by W. R„ Birt. 156 On the Thermal Effects of Magnetization, by J. Moutier .... 157

Encke's Comet 159

On the Intensity of Sound and Light, by Henry Hudson, M.D., M.R.I.A ." 160


Prof. Everett on the Optics of Mirage 161

Mr. R. H. M. Bosanquet's Correction to a Paper " On an Ex- perimental Determination of the Relation between the Energy and Apparent Intensity of Sounds of different Pitch " . . . . 173 Dr. J. Hopkinson on the Effect of Internal Friction on Reso- nance 176

M. F. C. Henrici on the Action of Solid Bodies on [Gaseous]

Supersaturated Solutions 183

Mr. J. W. L. Glaisher on Arithmetical Irrationality 191

Mr. T. T. P. B. Warren on a Method of Testing Submarine Telegraph Cables during Paying-out 199


Page Captain Noble on the Pressure required to give Rotation to

Rifled Projectiles. (With a Plate.) 204

Mr. R. H. M. Bosauquet ou the Measure of Intensity in the

Theories of Light and Sound 215

Proceedings of the Royal Society :

Mr. J. Stuart on the Attraction of a Galvanic Coil on a

small Magnetic Mass 218

Messrs. J". N. Lockyer and G. M. Seabroke on a new

Method of viewing the Chromosphere 222

Mr. P. H. Wenhani on a new Formula for a Microscope

Object-glass 224

Proceedings of the Geological Society :

Prof. P. M. Duncan on Trochocyathus anglicus, a new

species of Madreporaria from the Red Crag 231

Col. A. L. Pox on the Discovery of Palaeolithic Imple- ments in association with Elejphas primigenius in the

High-terrace Gravels at Acton and Ealing 232

Mr. G. Busk on the Animal Remains found by Col. L. Pox in the High- and Low-level Gravels at Acton and

Turnham Green 233

Mr. R. H. Tiddeman on the Evidence for the Ice-sheet in North Lancashire and adjoining parts of Yorkshire and

Westmoreland 233

Prof. A. Gaudry on the Mammalia of the Drift of Paris

and its Outskirts 235

On the Action of a Conductor arranged symmetrically round

an Electroscope, by Ch.-V. Zenger 235

On the Heat of Transformation, by M. J. Moutier 236

Royal Astronomical Society 239

On the Determination of the Boiling-point of Liquefied Sul- phurous Acid, by M. Is. Pierre 240


The Marquis of Salisbury on Spectral Lines of Low Tempe- rature 241

Mr. 0. Heaviside on an advantageous Method of using the Differential Galvanometer for measuring small Resistances. 245

Prof. Everett on the Optics of Mirage 248

Prof. A. M. Mayer on a simple Device for projecting on a Screen

the Deflections of the Needles of a Galvanometer 260

Mr. L. Schwendler on Differential Galvanometers 263

Mr. J. C. Glashan on Eractional Distillation 273

Mr. C. Tomlinson on the Action of Solid Bodies on Gaseous

Supersaturated Solutions 276

Mr. A. E. Sundell on Galvanic Induction 283


Page Mr. A. S. Davis on the Vibrations which Heated Metals un- dergo when in contact with cold Material, treated mathe- matically 296

Proceedings of the Royal Society :

The President on a supposed Alteration in the Amount of Astronomical Aberration of Light produced by the Passage of the Light through a considerable thickness

of Refracting Medium 306

Dr. W. Huggins on the Wide-slit Method of viewing the

Solar Prominences 306

Mr. P. H. M. Bosanquet on Just Intonation in Music; with a description of a new Instrument for the easy control of all Systems of Tuning other than the ordi- nary equal Temperament of twelve divisions in the Octave. 307 Mr. P. Guthrie on a new Relation between Heat and

Electricity 308

M. A. 0. Des Cloizeaux on a new Locality of Ambly- gonite, and on Montebrasite, a new Hydrated Alumi- nium and Lithium Phosphate 309

Proceedings of the Geological Society :

Mr. P. T. Gregory on the recent discoveries of Tin-ore in

Queensland 311

Mr. G. H. P. Ulrich on some of the recent Tin-ore Dis- coveries in Kew England, ]S"ew South Wales 312

Messrs. W. J. Sollas and A. J. Jukes-Browne on the in- cluded Pock-fragments of the Cambridge Upper Green- sand 313

On the Electrical Pesistance of Metals, by M. Benoist .... 314 On the conditions requisite for the Maximum of Pesistance

of Galvanometers, by M. Th. Du Moncel 317

On Stratification in a Liquid in Oscillatory Motion, by J. Stefan. 320


Sir William Thomson on the Ultramundane Corpuscules of Le Sage, also on the Motion of Bigid Solids in a Liquid circu- lating irrotationally through perforations in them or in a Pixed Solid 321

M. H. C. Yogel on the Absorption of the Chemically Active Pays in the Sun's Atmosphere 345

Prof. A. M.Mayer on the Effects of Magnetization in changing the Dimensions of Iron, Steel, and Bismuth bars, and in in- creasing the Interior Capacity of Hollow Iron Cylinders. Part. 1 350

Dr. H. Hudson on the Intensity of Light &c 359

Mr. P. Moon on the Definition of Intensity in the Theories of Light and Sound 361

M. G. Quincke on Diffraction 365


Page Prof. D. Bierens de Haan on certain Early Logarithmic Tables. 371 Mr. J. W. L. Glaisher on Early Logarithmic Tables, and their

Calculators 376

Notices respecting New Books :

The Rev. T. W. Webb's Celestial Objects for Common

Telescopes 382

Mr. C. P. Smyth's Report presented to the Board of Visi- tors of the Royal Observatory, Edinburgh 382

Proceedings of the Royal Society :

Messrs. J. Dewarand W. Dittmar on the Vapour-density

of Potassium 384

Mr. C. Tomlinson on Supersaturated Saline Solutions . . 385 The Earl of Rosse on the Radiation of Heat from the Moon, the Law of its Absorption by our Atmosphere,

and its variation in amount with her Phases 390

Proceedings of the Geological Society :

Dr. H. A. Nicholson on the Geology of the Thunder-Bay and Shabendowan Mining Districts on the North Shore

of Lake Superior 391

Dr. J. W. Dawson on the Relations of the supposed Car- boniferous Plants of Bear Island with the Palaeozoic

Flora of North America 392

Mr. H. Woodward on Eocene Crustacea from Portsmouth,

and on a new Trilobite from the Cape of Good Hope. 393 Mr. S. H. Wintle on an extensive Landslip at Glenorchy,

Tasmania 393

On a new Determination of the Velocity of Light, by M. A.

Cornu 394

New Experiments on Singing Flames, byFr. Kastner 397

On a new Operation by which the Velocity of Projectiles can

be determined Optically, by Marcel Deprez 398

On the Development of Heat by the Friction of Liquids against Solids, by O. Maschke 400


Dr. H. Herwig on the Expansion of Superheated Vapours . . 401 Mr. 0. Heaviside on Duplex Telegraphy. (With a Plate.) . . 426 M. J. Jamin on the Theory of the Normal Magnet, and the

Means of augmenting indefinitely the Power of Magnets . . 432 The Hon. J. W. Strutt on the Law of Gaseous Pressure .... 438 Mr. H. Wilde on some Improvements in Electromagnetic In- duction Machines. (With a Plate.) .439

Mr. T. Muir on the first Extension of the term Area to the

case of an Autotomic Plane Circuit 450

Dr. J. Percy on a Crystallized Compound of Sesquioxide of Iron and Lime 455



Notices respecting !New Books :

Dr. J. Anderson's The Strength of Materials and Struc- tures 457

Mr. GL J. Symons's British Bainfall, 1872 459

"Weekly Weather Reports issued by the Meteorological

Office 460

Proceedings of the Greological Society :

Mr. H. Hicks on the Treinadoc Bocks in the neighbour- hood of St. David's, South Wales 460

The Bev. 0. Fisher on the Phosphatic Nodules of the Cre- taceous Bock of Cambridgeshire 461

Mr. "W. J. Sollas on the Ventriculitidse of the Cambridge

Upper G-reensand 461

American Astronomy 462

On the sudden Cooling of Melted Griass, and particularly on

" Bupert's Drops," by V. de Luynes 464

On a Method of measuring Induced Currents, by P. H. Bigelow. 467

Index . 469

PLATES. I. II. Illustrative of Dr. R. K6nig"s Paper on Manornetric Flames.

III. Illustrative of Dr. A. M. Mayer's Paper on an Acoustic Pyrometer, and Dr. A. Stoletow's on the Magnetizing-function of Soft Iron.

IV. V. Illustrative of Dr. W. M. Watts's Paper on the Spectrum of the Bessemer-flame.

VI. Illustrative of Captain Noble's Paper on the Pressure required to give Rotation to Rifled Projectiles.

VII. Illustrative of Mr. O. Heaviside's Paper on Duplex Telegraphy.

VIII. Illustrative of Mr. H. Wilde's Paper on some Improvements in Electromagnetic Induction Machines.


Vol. 44, page 522, line 5 from bottom, for therefore read therefor.

Vol. 45; page 160, for paragraph 3 of Mr. Hudson's paper (commencing "This point" &c.) substitute-.

This point can be easily tested experimentally as regards sound. Thus a tense string with amplitude of vibration =2 ought to become inaudible at twice the distance at which it ceases to be heard with amplitude =1, if the square of the amplitude be the correct assumption. The relative distances at which the sounds should be inaudible ought to be as 1 to 070715, if the simple amplitude (not its square) be correct.

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Mag. S.4. Vol. 46.PIJM.


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1. On Manometric Flames. By Dr. Rudolph Konig [of Paris)*. [With Two Plates.]

IN the beginning of 1862 I invented a new method of ob- servation, which had for its object to make apparent the sounding air-waves, or, what is the same thing, the changing density of the atmosphere while penetrated by sounding vibra- tions, or while itself in a state of vibration, in the same way as acoustic experiments were able to show clearly the vibration of bodies which produce the vibration of the atmosphere.

The first apparatus founded on this method was shown in the London Exhibition of 1862; and since that period I have invented a whole series of apparatus on the same principles : a short description of some has appeared in PoggendorfPs Annalen for 1864 ; and others are briefly sketched in my Catalogue of 1865.

The following pages are designed to explain all these appa- ratus, as well those which have been added since the publica- tion of my Catalogue, as also the experiments in connexion with them.

The small instrument, on the use of which my method is founded, and to which I have given the name of Manometric Capsule } consists of a cavity in a wooden plate, whose orifice is closed by a thin membrane. Illuminating gas may be intro- duced into this cavity through a pipe a second pipe, termina- ting in a gas-burner, giving means for exit and ignition.

Now, if the air before the membrane be rendered suddenly of

* Translation, communicated by the Author, from Poggendorff's Annalen, vol. cxlvi. p. 161.

Phil. Mag. S. 4. Vol. 45. No. 297. Jan. 1873. B

Dr. U. Konio; on Manometric Flames.


a greater density, the membrane will of course be driven inwards, and thus expel the gas and cause the flame to rise quickly. If, on the contrary, the air be suddenly rarefied, the membrane becomes drawn outwards, the space within momentarily in- creased, the gas expanded, and the flame lowered.

A membrane is known to possess, like every other elastic body, only a definite series of notes ; and thus we should suppose that the manometric capsule would only show an effect when the note acting upon it agreed with one of the notes of its membrane.

But this is not the case ; for besides the vibration which a body makes under the influence of its elasticity, any motion whatever can be forced upon it if only the active force be much greater than the resistance which it can offer.

For example, let us take a long thin string, tuned to the funda- mental note of 100 vibrations, and place its centre in firm con- nexion with the prong of a strong massive tuning-fork of 110 vi- brations ; it will then clearly move to and fro 110 times in unison with the vibrations of the tuning-fork, although in accordance with its nature it could only execute 100, 200, 300, &c. vibra- tions. In point of fact it does not truly vibrate, but is only mechanically drawn to and fro.1 This is also the case with the manometric capsule, as it is so constructed that the resistance offered to the condensation and rarefaction of the atmosphere must be considered very trifling, indeed almost nil. One and the same capsule is thus equally effective for every note ; also different capsules, whose membranes have not been tuned in unison, nevertheless give the same results under the influence of the same note.

If out of several capsules which are fed by the same gas-reser- voir you set one in activity, the flames in all the others are set in motion. Thus, if the membrane be pressed into the capsule, the pressure will not only drive the flame higher from the exit- pipe, but will also spread its influence through the entrance-pipe to the general reservoir, and thence to the other capsules, the flames of which become prolonged, although in a less degree. Of course, a pressure in the contrary direction produces an opposite effect. If, therefore, several capsules are to be em- ployed at the same time, this mutual influence must be annulled.

I at first sought to attain this end by placing between the re- servoir and the capsules long thin india-rubber tubes; but this did not act quite satisfactorily.

I attained my object, however, by the use of accessory cap- sules, through which I permitted the gas to pass before I con- ducted it into the manometric capsule ; they are constructed like the others, each consisting of a cavity closed by a thin membrane.

Dr. E/. Konig on Manometric Flames.

If the pressure derived from the manometric capsule pass through the entrance-tube towards the gas-reservoir, it will be annulled when entering the accessory capsule by the yielding of the membrane.

Practice shows that we may put into the strongest motion one of several flames isolated in the foregoing manner without in any way affecting the rest.

Proof of the different condition of the Air in the Nodes and Ventral Segments of a sounding Air-column.

In order to show the changing density of the air in the nodes and its fixed condition in the ventral segments of a sounding air- column generally, I make use of an open organ-pipe, which is so constructed that either its fundamental tone or its first harmonic or overtone, the octave, can be sounded at will (fig. 1). At the node of the fundamental and the two nodes of the octave are three orifices in one side of the pipe ; Fig. 1.

over these three manometric capsules are so placed that the orifices are exactly closed by the membranes, being of the same diameter; a common reservoir, provided with accessory capsules, feeds the three flames, the length of which can be regulated by cocks.

If, now, we give to the three flames an equal height of 15 to 20 millimetres, and sound the octave, then the two exterior flames will be put into such violent motion that they will appear prolonged, narrow, quite blue, and without illuminating power, on account of the considerable amount of air which they draw with them in their flickering up and down, whilst the middle flame will remain almost still and bright, being placed at the centre of a ventral segment, where the air is only gliding to and fro.

At the sounding of the fundamental the middle flame is at the node, and therefore vio- lently agitated ; the two exterior ones, which are then between the node and the centres of the ventral segments at the ends of the pipe, show only a weaker motion. As in this case it is only a question of different intensity of motion in the individual flames, it is better here to make use of smaller flames, when the middle one becomes quite blue, while the exterior ones remain bright. If we give the


4 Dr. R. Konig on Manometric Flames.

flames the length of only 8 to 10 millims., on sounding the fun- damental the middle flame will be extinguished, on sounding the octave the exterior ones will disappear.

These experiments may also be made with a closed organ- pipe which can be sounded on its fundamental and its first over- tone. One of the flames must then be at the end of the pipe, where the node of the fundamental, as well as one of the nodes of the overtone, are found.

If the flame be shortened, on sounding the fundamental the end flame will be the first to go out, aud then the middle one, because the latter is nearer to the node than to the ventral segment in the mouth of the pipe.

But on sounding the first overtone, the 12th of the fun- damental, the middle flame remains unchanged, while the two exterior ones become extinguished.

Comparison and Combination of several Tones.

These experiments have only shown the general working of whole series of consecutive vibrations ; if, however, we allow the flame to be reflected by a rotating mirror, we see all phases of their motion side by side, and we can then not only examine the number of vibrations and the ratios of different tones, but also observe the images made by the combination of several tones.

The apparatus which serves for these investigations consists of a set of organ-pipes, each of which is provided at the node of its fundamental with a manometric capsule. This can be con- nected by means of an india-rubber tube with gas-burners, which are placed on a special stand (fig. 2).

Before these gas-burners there is placed a revolving mirror, made of four glass plates coated with platinum. The platinum surfaces are turned outwards, in order to avoid the confusing double images of the common mirrors, which is caused by re- flection from the two surfaces of the glass plates. A small wind- chest, for the reception of two organ-pipes, has two mouth- pieces, the larger of which serves to conduct the air from a bellows. Through the smaller one the gas is conducted to a com- mon receiver, provided with two cocks, which are joined by means of india-rubber tubing to the capsules of the organ-pipes.

The reflection of a flame at rest shows in the rotating mirror a band of light of the width of the height of the flame. If we, however, sound the organ-pipe in connexion with it, there appears in place of the band of light a series of regularly con- secutive flame-pictures, the tips of which are bent in a direction opposite to that in which the mirror is moving.

If we place two burners in such a position that their reflections give two bands of light, one above another, and connect them

Dr. R. Konig on Manomstric Flames. 5

with two organ-pipes which together give the interval of the octave, the series corresponding to the higher tone gives double

Fig. 2.

the number of flames that the other one does, by which the vi- brations are shown to be in the ratio of 1 : 2 (PI. I. fig. 3) . If we take organ -pipes of other intervals, we get with the fifth three flames above two, with the fourth four above three, and so on. The rapidity of the motion of the flames allows their reflections in the mirror to be very sharply defined; but as they are of very short duration, it would be difficult in this experiment to observe trifling deviations from the purity of the intervals ; for although in point of fact it is easy to recognize that in one of the series there are almost always two flames when there is one in the other, yet it would be difficult to discover that about 200 in the one series coincide with about 101 in the other. These exact observations can be made with the greatest facility, how-

6 Dr. R. Konig on Manometric Flames.

ever, if we make the two capsules of the two corresponding organ- pipes act on the same flame.

If we sound two organ-pipes, exactly tuned to an octave, while the gas streams from their two capsules into the same burner, the flame has the appearance of containing within it a smaller one without motion. By the slightest discord, how- ever, the latter becomes flickering, and lengthens and shortens periodically within the greater one. Each of these double movements composed of ascending and descending shows a fluctuation, either the deviation of the upper tone by a double vibration, or of the lower by a single vibration from the pure interval of the octave.

The fifth (2 : 3) shows three, the fourth (3 : 4) four, the third (4 : 5) five points of flame one above another, whose mutual position remains unchanged with the perfect purity of the in- terval ; on the contrary, any deviation from this causes an up- and-down movement among them of each single point, which takes the appearance of a waving motion.

In all these intervals it is easy so to arrange the length of the flame that all the points may remain clearly bright and appear separated from each other by blue non-luminous parts of the flame. If, however, the ratios of vibration of the two tones becomes more complicated, it is often difficult to observe them exactly ; but even in this case the flame shows plainly whether the interval be pure or out of tune, as we have but to see whether the flame is at rest or in motion.

This property of the manometric flame, of showing the least deviation from the purity of the interval, makes it in many cases exceedingly useful in tuning, as it is not necessary that the two notes which are to be brought into tune should be produced by organ-pipes provided with capsules : the notes of any instrument may be used, if they are produced before two resonators in relation with them, which act on two manometric capsules whose gas-pipes end in the same burner.

The ratio 1 : 2 is the most convenient, on account of its easy examination ; so that if we want to tune a series of tuning-forks to the same note, it is better to choose the fork for comparison an octave lower or higher.

If we wish to observe the whole process of vibration in the above-mentioned flames on which two notes act at the same time, we must again employ the rotating mirror. The pure octave shows in it a series of flames, in which a shorter always follows a longer, and the shorter ones have all, like the longer ones, equal heights (fig. 4, PL I.). If any beats occur, the summits of the smaller as well as of the larger flames move up and down. However, these motions are opposed; so that in

Dr. It. Konig on Manometric Flames. 7

those positions where the long flames are at their longest, the short flames are at their shortest, and vice versa.

In fig. 4, PI. I. the picture of the seventh (8 : 15, or 8 : 16 1) shows this process, although in a very short period. The fifth (2 : 3) shows a period of three, the fourth (3 : 4) of four, the third (4 : 5) of five, and the second (8 : 9) of nine in the range of the increasing and then decreasing flames.

If the proportion is not of the form n : n + 1, then there takes place in the whole period not only a rise and fall of the flame-summits, but the curve connecting them shows as many elevations and depressions as the difference between the two ratios. For example, see the picture of the sixth (3 : 5) (fig. 4, PL I.).

The more complicated the interval of the two notes, the more carefully we must bring it into perfect purity of tune, until no further movement whatever can be discerned in the flame, because otherwise the recurring periods of the flame- pictures in the mirror suffer continual change by the change of phase, and in that case it becomes difficult to recognize them. But this exact tune becomes still more imperative if we wish to combine more than two notes while making them act on one flame. It will be remarked, besides, in these experiments, how difficult it is to retain absolutely constant notes with organ -pipes, even when we make use of a well-regulated bellows.

Coexistence of two Tones in the same Air-column,

The investigation of the combination of two related tones in one flame-picture is especially useful, because it teaches us from the flame-picture of a combination of tones, of which the com- ponents are unknown, to find the single tones of which it is composed.

A passage to the trial of such a combination of tones as, e. g., each sound offers, is the combination formed by a fundamental with a known overtone in the same air-column. Very suitable for such an experiment is the above described closed organ-pipe with three flames, since the node of the fundamental as well as one node of the first overtone are situated at their ends.

If we blow the fundamental (1) very gently, the flame- picture in the mirror shows the vibrations of this tone ; if now we blow the overtone (3) strongly, each single vibration will be replaced by three flames. With a rather weaker blast both tones are produced together, and we always see three flame-summits over every fundamental flame (fig. 5, Plate I.) . Therefore several tones present at the same time in the air-column give exactly the same flame-picture as the combination of the same tones when each is produced by its own particular organ -pipe.


Dr. R. Konig on Manometric Flames.

Representation of Sounds,

The apparatus which is used for the representation of sounds consists simply of a manometric capsule, before the membrane of which there is a small cavity terminating in a short tube (fig. 6) . The sounds to be represented must be conducted into

Fig. 6.

this cavity with the smallest possibleloss of their intensity and without undergoing any change in their passage.

The sound-pictures of the combined tones of the same instru- ment are never all alike, but the deepest tones always show much larger and more complicated flame-groups for each single vibra- tion of the fundamental than the higher ones, because the high harmonic tones, which are to be heard in the sound of the deeper tones of the instrument, disappear more and more as the funda- mental ascends. Thus the higher the tone the smaller in com- parison are the dimensions of the means which produce it. The vibrations of all resounding instruments, however, take a simpler form if the dimensions of the latter are very small, because the different bodies lose their capacity of forming subdivisions in vibration, by which the accessory tones, if not exclusively, yet in many cases are chiefly produced.

A second reason, however, and that a very potent one, is this. If the tones are produced not so much by the elastic vibrations of a body as rather by gusts of air, as in the siren and pandean

Dr. R. Konig on Manometric Flames. 9

pipes, the upper notes which are contained in the sound of a lower note have so high a place in the scale for a high note that they produce no effect, either on the ear or on an artificial membrane.

The lowest note of the violin, for example, is g (192 vibrations),

and its 8th harmonic g (1536 vibrations) is within the range of the instrument. It is produced on the G-string by a length of 4, and on the E-string by about 13 £ centimetres. Nevertheless,

if we take this very g as fundamental tone, the length of string of its eighth harmonic on the E-string would be about 17 millimetres; and besides, with 12,288 vibrations, it would be already nearly two octaves above the highest notes used in music, which sufficiently explains why it is not heard in the

sound of g.

My success was but partial in the representation of violin sounds, owing to the high position of the notes of the instru- ment, since, with the exception of the notes from g to c on the G-string, I obtained only the fundamental vibrations for all the rest. In my endeavours to conduct the notes as loud as possible to the membrane I tried two methods. First, I connected the interior air of the violin with the small apparatus, by means of an india-rubber tube which I introduced into one of the /-shaped apertures of the violin ; and secondly, I pressed my stethoscope with its concave membrane on the bottom -piece of the violin, precisely under the sounding-post, and attached the india-rubber tube to the flame-apparatus. The results in the latter case were as follows.

On the G-string g showed the figure of the octave in weak wave-formed flames, which, as far as b, rose to sharply defined clearly cut flames. With c the latter fell quite suddenly into one single broad, short, and faint flame, in which I could perceive only the smallest trace of the octave when played forcibly. Already the D-string only showed simple flame series, which for d e f g were rounded, wave-like, and weak, but on play- ing a became again stronger. The a- on the A-string gave very high and deeply cut flames, b still stronger ones, which fell,

however, at c and became quite weak. Up to g and a on the E-string every trace was lost of the small flame-points which had appeared at the last overtones.

On the connexion of the interior air with the apparatus, the insensibly graduated picture of the octave from g changed into a single sharply defined flame at b ; this attained such an extra-

10 Dr. R. Konig on Manometric Flames,

ordinary height at c, as though it had been produced by the vibrations of an organ-pipe provided with a capsule at the node.

The note d also showed a series of high and sharply defined flames, which, however, quite disappeared at e to give place to the weak rounded-off waving lines as far as a.

This sudden appearance of very high flames in the region of c~is explained by the circumstance that the lowest proper note of the interior air of the violin is precisely c. For the upper notes I obtained the same result as with the stethoscope ; that is to say, the notes a and b again gave much stronger vibra- tions than e f g, and than the upper c d e &c; so that the second peculiar note of the interior air, or rather of the whole system formed by the violin, seems to be in the region of a and b.

With regard to sound, we have in this case certainly been able only to make evident the transition from the figure of the octave to that of the simple note. The siren shows much better the gradual disappearance of the higher upper note from the musical sounds when their fundamental tone is raised. To this end I intercept the impulse above the open perforated plate by means of an arched aperture which expands into a small tube, and is placed immediately above a part of the apertures so as to permit them to affect the flame, while I cause the rotation of the plate to increase from its lowest to its highest swiftness by increased pres- sure of the air. The mirror then shows at the lowest notes very large and dense flame-groups; these change towards the middle of the great octave into more clearly defined and deep-slit waves, with at first five, then towards c and d with four flame- points. At g and a the number of the points falls to three, at c and d to two; and at a the last trace of the octave disappears from the sound; after this all the still higher notes only show single flame-pictures.

But the result of this experiment is essentially different if when a sounding-chest is fastened over the perforated plate. It first intensifies the upper harmonics of the sound, then the lower, and lastly the fundamental itself: this causes the flame-groups no longer to become simpler gradually and in accordance with the height of the notes, but to show rather sudden changes alter- nately rising and disappearing. Thus the sound of a siren, over the perforated plate of which a resonance-box giving the

note c was placed, after showing a few complicated and faint pictures when the plate was slowly rotated, produced on reach- ing the pitch c clearly a large flame in agreement with the fun- damental tone : this flame had four summits, derived from

Dr. It. Konig on Manometric Flames. 11

overtone 4, which coincided with the proper note of the sound- ing-chest. On turning the plate more rapidly, the flame- picture became simpler, until at / it became one single flame, so that the overtone 3 must be quite wanting in this sound of the siren. The ascending scale had scarcely passed / when there appeared between each two large flames a small but sharply defined flame, which quickly increased in size, and towards c reached nearly the height of the chief flames, where the effect of the resonance-box confirmed the fact of its being the overtone 2 of the sound of the siren. Above c the smaller flame leant always more towards the larger one, until at a it completely disappeared in it : after this again only single flames appeared (PL I. fig. 7).

In order to make the sound in these experiments act strongly on the capsule, I provided the resonance-box with a tube, and placed its interior in direct connexion with the flame-apparatus. These experiments, in which the air-impulses of the siren are prevented from passing immediately into the atmosphere, being compelled to pass through a resonator which remains unchanged for all the fundamental tones of sound, give a visible picture of the process of the formation of vocal sounds ; for it is known that the air contained in the cavity of the mouth, when speak- ing or singing the same vowel in different tones, is always tuned to the same note, so that the mouth must act on the air-waves produced in the larynx in the same way as the sounding-chest on the air-impulses of the siren. Nevertheless the series of flame-pictures of the same vowel, sung in the tones of two oc- taves, does not show such sudden changes as might have been expected without closer research.

In order to produce the pictures of the vowels, I sing them into a small funnel-shaped mouthpiece which is connected with the cavity before the membrane by a short india-rubber tube ; thus they reach the capsule with great intensity (fig. 6).

I had already in 1867 sketched and had painted the pictures of the vowels u} o, a, e, i sung to the notes of the two octaves from C to c. I proceeded in the following manner. In order to be sure that I had not changed the character of the vowel in the transition from one tone to another, I first verified the proper note of the mouth with the tuning-fork ; then, while I sang into the apparatus, an artist drew the picture which he saw in the mirror. I also drew the same picture independently : and if both our drawings were identical they were looked upon as correct ; if, however, there were discrepancies, I repeated the experiment until the error was discovered.

The five finished drawings (PI. II. fig. 8) were unfortunately

12 Dr. R. Konig on Manometric Flames.

too late for the Exhibition; but I was able to exhibit them at the Meeting of the Association of Natural Philosophers at Dresden in 1868. I delayed their publication until now because I wished to revise them with precision, but was always prevented by the