Dec. 25, 1879] 



NATURE 



181 



which is, neglecting the constant coefficient of amplitude, 

 geometrically represented by another harmonic curve of 

 identical form, but shifted on so that it begins at a point a, 

 or a quarter of the length of the curve O o from the origin. 

 In this second curve the heights of the ordinates represent 

 the varying velocities of the diaphragm, the velocity being 

 nothing at a when the displacement at A is a maximum, 

 and being at a maximum at b when the diaphragm in 

 flying back passes through its point of rest or has no dis- 

 placement. Now of these two curves the former corre- 

 sponds in phase to the movement of the diaphragm of the 

 transmitting telephone, while the second curve corresponds 

 to the variations of velocity, and therefore of the current 

 transmitted, and consequently also corresponds to the 

 motions of the diaphragm of the receiving telephone. 

 Hence it is easy to understand that there exists a differ- 

 ence of phase of one-quarter of an undulation between the 

 movements of the diaphragms of the transmitting and 

 receiving telephones, which will be either a retardation or 

 an apparent acceleration of phase according to the sense 

 in which the transmitted currents traverse the coil of the 

 receiving telephone. These considerations apply only to 

 the telephone of Bell or its modification by Gower, in 

 which the vibrations of the transmitting diaphragm gene- 

 rate the current. They do not apply to the transmitters 

 of Edison and Hughes, which merely regulate the current. 

 In these instruments the strength of the current is pro- 

 portional to the displacement, not to the velocity j hence 

 there is no retardation of phase. 



The memoir of Helmholtz, which, by introducing certain 

 considerations respecting the mutualinductiveactions exer- 

 cised upon one another by the individual turns of wire in the 

 coil of the telephone, arrived at a somewhat different con- 

 clusion, and was principally devoted to the question of the 

 timbre of the transmitted sounds. The previous researches 

 in physiological acoustics of this distinguished physicist 

 had shown that differences of phase affecting individual 

 tones of a compound "clang" do not produce any effect 

 which the ear can detect. This important law the present 

 writer has, however, shown elsewhere to be true only when 

 one ear receives the sound, and to hold no longer in the 

 case of binaural hearing. The equations of Helmholtz 

 indicated the unexpected result that the difference of 

 phase between the vibrations of transmitter and receiver 

 was a quantity so small that practically it might be alto- 

 gether disregarded, and he arrived at the conclusion that all 

 sounds were transmitted by the telephone with an equal 

 proportionate degree of intensity independent of their pitch, 

 and therefore with unaltered timbre. Here again, how- 

 ever, the writer of this article has shown that the relation 

 between the thickness and diameter of the vibrating 

 diaphragm affects the distribution of the magnetism in- 

 duced in it by the magnet, as to whether it is lamellar or 

 radial in character, and that this distribution has influence 

 on the timbre of the sound emitted by the receiving 

 telephone, the notes of higher pitch being better given by 

 the disk in whose magnetisation the lamellar distribution 

 preponderates, while the lower ones are better given with 

 a preponderating radial magnetisation. The whole ques- 

 tion of timbre of the emitted sounds requires further 

 careful study. 



The experiments which M. Konig has executed entirely 

 confirm the a priori reasoning of du Bois-Reymond as to 

 the existence of a difference of phase. Instead of using 

 two vibrating diaphragms, Dr. Konig takes two tuning- 

 forks accurately tuned to unison, each of them being 

 placed in front of the magnet of a telephone whose disk 

 has been removed, and which are united in the usual 

 manner by wires. The first of the forks being set into 

 vibration with a violin-bow, the second immediately begins 

 to vibrate. The phase of each of the forks is next ob- 

 served. This has been done in several ways : firstly, by 

 direct comparison of each fork in turn with the vibration- 

 microscope ; secondly, by applying the well-known optical 



method of Lissajous, compounding together the two vibra- 

 tions rectangularly by throwing a ray of light on to small 

 mirrors attached to the two forks, and reflected from one to 

 the other and then on to a screen. The figure thus pro- 

 duced exhibited unmistakably a difference of phase of an 

 exact quarter of an undulation. A further experiment on 

 compound tones was made with the same general arrange- 

 ments ; two forks, differing by three octaves, being made 

 to take up, one as transmitter the other as receiver, 

 sounds whose higher vibrations were eight times as rapid 

 as the fundamental tone. Here again the difference of 

 phase experimentally found for the higher tone was one 

 quarter of a vibration. 



Incidentally two very important facts have been ob- 

 served by Dr. Konig.. In experimenting he found that a 

 tuning-fork, vibrating in front of the magnet of a tele- 

 phone whose circuit is closed, comes to rest in a much 

 shorter time than the same fork vibrating freely away 

 from the telephone ; also that this weakening of the 

 sound is greater in proportion as the distance of the fork 

 from the pole of the magnet is smaller, and also is greater 

 for small amplitudes of vibration than for large ones. 

 These results are not without interest in their bearing 

 upon Mr. Edison's recent attempt to construct a dynamo- 

 electric machine, in which the moving parts should be 

 attached to a large vibrating tuning-fork instead of to a 

 rotating axis. Doubtless the inventor's idea was to get 

 rid of the friction accompanying rotation ; for, as the 

 vibrations of the tuning-fork are very nearly simple har- 

 monic motions, and as the simple harmonic motion is the 

 only type which can be propagated without loss by friction 

 through a body, the motions of whose parts are coincident 

 in phase, it might be anticipated that there would be less 

 waste of energy in a " harmonic" engine than in a rota- 

 tory one. The important fact however remained behind 

 that by far the greatest part of the work of driving a 

 dynamo-electric machine was not spent in overcoming 

 friction, but in doing the work of moving closed con- 

 ductors across a magnetic field, a work which, to produce 

 an equal amount of current, requires equal power, whether 

 the motion be one of rotation or of " harmonic " vibration . 

 Many years ago Foucault demonstrated the reality of this 

 resistance to motion by spinning his gyroscope between 

 the poles of an electromagnet ; and with a Gramme 

 machine, and also with a Holtz machine, the increased 

 effort necessary to sustain rotation when work is being 

 done is a familiar fact. Dr. Konig has now demonstrated 

 the existence of a similar phenomenon in the case of the 

 vibrations of the tuning-fork, which comes much sooner 

 to rest when it is doing electrical work than when it is 

 doing no work. Silvaxus P. Thompson 



ON THE EOCENE FLORA OF BOURNE- 

 MOUTH 

 C\~^ several previous occasions these columns have 

 **-* called attention to the eocene plant remains ob- 

 tained at Bournemouth. The Palrcontegraphical Society 

 has undertaken their publication, but as this must be 

 spread over many years, it may not be undesirable to 

 note from time to time the principal additions to the flora 

 as they come to light. 



The specimens which I have collected this year may 

 reach about a thousand. Among the more important are 

 two from the marine beds east of Boscombe. One is 

 a portion of the stem of a cactus measuring two feet 

 three inches by three inches, showing eighty bosses of 

 spines cleared from the matrix. A section which I have 

 made of this presents a flattened ellipse in which the 

 pulp is replaced by sand and the woody stem has sunk 

 down to the lower side, though still preserving the 

 characteristic radiating structure. The cuticle is now- 

 thin and glossy black, and bears the spines, varying from 

 two to a dozen on each boss, arranged in the usual spiral 



