March 3, 1870] 
INEATEO Fee 
457 
of the gases on the enclosing wall. Kirchhoff deduced 
the consequences of this theory mathematically, and 
pointed out that the diminution of velocity must vary 
inversely as the square root of the number of vibrations 
in the sound propagated ; that is to say, that the velocity 
of sound could not be uniform for different notes. See- 
beck shows that the loss is inversely as the cube of the 
square root of the number of vibrations ; so that we can 
scarcely attribute the result entirely to the loss of heat by 
friction of the enclosed gas on the walls of the tube. On 
the other hand, his results completely establish the fact 
of a difference in the speed with which different notes of 
music are propagated in tubes. 
The magnificent and laborious work of M. Regnault 
on the velocity of sound in pipes, appeared while Seebeck 
was occupied in these investigations. He points out, 
that since the sounds which Regnault studied, such as 
explosions of gunpowder and so on, are due to violent 
and complicated disturbances, however important it may 
be to study them in a practical view, they are not likely 
to give us accurate and delicately differenced results. 
Where the sound contains a mass of irregular notes, no 
effect due to difference of note can be observed. The 
method of generation compels the air to move at first in 
all directions in the tube. Such sounds fall into the sea 
of air like a mass of stone dropped from a great height 
into the water. The waves which they generate can only 
reduce themselves to regularity at some distance from 
the disturbance and their propagation must be irregular 
till that distance is reached. On the other hand, a 
regular pulsation, such as would be produced by the 
timed advance and retrogression of a piston at the 
end of the cylinder, gives waves which are regular and 
regularly propagated from the beginning. It is in con- 
sequence of this delicacy in the character of his experi- 
ments that Seebeck has attained his results. 
He makes one of Ko6nig’s tuning-forks sound at the 
open mouth of a cylindrical pipe, the other end of which 
is stopped by a moveable piston. A short distance from 
the mouth of this pipe there is an opening, connected with 
an indiarubber tube which can be carried to the ear. 
If, by the motion of the moveable piston, this opening be 
made to correspond exactly to a “ventre” in the standing 
wave which is generated in the air of the tube, it is easy to 
measure, with great accuracy, the length of that standing 
wave, which corresponds to the precise number of vibra- 
tions of the tuning-fork. The extreme difference in fifty 
experiments for the same note, appears to have been 
about one five-hundredth of the whole amount. 
The results are the following, the velocities being re- 
duced from the experiments to those at 0° C.: 
Diameter of Number of vibra- 
Velocities reduced to 0°, 
ipe in tions per second 
cabins, injmetres|per second: in Bore sounded. 
Ie 2 » 34 + « 322°90 31886 317°26 2 « 512, 384, 320, 256 
ho 6 Cro A o ertievl epee Rey eer cree) o 
Bee) te) L755) eee) 390192) 420186) 320/24) 527/82 4 
4. « « 2910 . » 326°10 326°72 325°36 324°54 « o 
If we compare these numbers with that for the speed of 
propagation in free space, as given by Schréder von der 
Kolk, which is 332°77, we see (1) that they are wnzformly 
and considerably /ess, (2) the divergence zs greatest 71 
narrow tubes, with the exception of that where the tube 
was 29 millimetres in diameter, which was in all probability 
too wide to have the mass of air at its end uniformly 
affected by the vibrating tuning-fork ; (3) the notes which 
travel slowest are the /ow motes. This difference is by far 
the greatest in the case of the narrow tube of an eighth of 
an inch in diameter, amounting to nearly 1 in 60 of the 
whole amount for the notes ¢ and c.. 
The author discusses the further question, whether the 
nature of the enclosing tube produces any effect. In 
a tube, the inside of which is sheet copper, which has 
nearly 17mm. diameter, the velocity is as low as it is in 
a glass tube of gmm. Where the friction is raised to a 
maximum by coating the inside wall of the tube with 
flannel, the velocity is reduced to 293'7 metres per second 
in a tube of 13 mm. diameter. 
The same subject is treated fully by Herr Schneebeli, 
in a series of experiments published in Poggendor‘if’s 
Annalen in February of last year; but those which we 
have described appear to us to have conducted their author 
to more valuable and interesting results. 
WILLIAM JACK 
An Fatroduction to the Study of Chymistry. Written for 
the People by Cuthbert C.Grundy. Pp. 108, (London: 
Simpkin, Marshall, and Co.) 
We remember when at school being called upon to 
admire the beauties of Schiller’s Wzthelm Tell. Our 
impressions of that play were then by no means com- 
plimentary to some of the principal personages: so far 
as we could see Melcthal, Stauffacher and the rest of 
the members of the three Cantons apparently dil 
nothing but meet clandestinely (when the weather was 
favourable) to talk much treason and fine sentiment, 
generously leaving most of the hard work to be per- 
formed by Tell (who being lowly-born was perhaps not so 
free of speech). All this was doubtless wrong and absurd ; 
but we are reminded of these early impressions by the 
character of much of what is being said and done in 
reference to the education of the masses in the present 
movements. There is a wonderful disparity in the 
proportion of Tells to our ideal Melcthals and Stauf- 
fachers. Possibly, if certain noisy persons would but 
show their earnestness in the practical manner of Mr. 
Grundy, the wheels of progress would not drag so heavily. 
In a modest little preface, Mr. Grundy informs us 
that his book is mainly intended for those among the 
great body of the people who desire knowledge, but 
have little time and only limited means for acquiring 
it. Occasionally, for example, when defining and illus- 
trating the phenomena of latent heat, the author lays 
himself open to the charge of sacrificing precision of 
knowledge to clearness of statement. This fault is not 
unfrequently met with in manuals of this character : surely 
the two are not incompatible. Why does Mr. Grundy 
prefer the more antiquated form of styling the science? 
The generally accepted w@rd is undoubtedly more correct: 
Kopp has satisfactorily shown this in his recently pub- 
lished “ Beitrage zur Geschichte der Chemie.” 
On the whole, however, we can congratulate Mr. Grundy 
on having succeeded in explaining in clear and simple 
language the fundamental principles of chemical philo- 
sophy. ats 18, I 
UIP IGM ETAS HO) TIGER, IFIOVEION 
[The Editor does not hold himself responsible for opinions expressed 
by his Correspondents, No notice ts taken of anonyniois 
communications. | 
On Professor Tyndall’s Exposition of Helmholtz’s 
Theory of Musical Consonance 
In the course of a re-perusal of Helmholtz’s ‘‘ Ton-empfin- 
dungen,” it occurred to me to compare the theory of consonance 
and dissonance, there propounded, with the exposition of that 
theory presented in the Lectures on Sound of Professor Tyndall. 
The result of the comparison is the present paper, in which I 
shall endeavour to show that Professor Tyndall’s version of the 
theory is radically different from the original, and erroneous. 
Helmholtz determines the consonances of two sme tones by 
reference to their combination-tones. That of the first order 
suffices for the octave; those of the first and second order deter- 
mine the f/th and fourth. The remaining consonances—major 
and minor sixth and major and minor third, do not, according to 
him, admit of determination from two simple tones and their 
combination-tones, but require the addition of a third primary 
simple tone. 
* “Ton-empfindungen,” pp. 301-303, 306-307. _ I shall in the fellowing re- 
ferences use ‘‘ H.” to denote this work, and “ T.” for Prof, Tyndall's lectures. 
