26 NATURE 
| May 8, 1873 
dise therefore does not act where it is not. Itsets the air next 
it in motion by pushing it, this motion is communicated to more 
and more distant portions of the air in turn and thus the pres- 
sures oh opposite sides of the suspended body are rendered 
vnequal, and it moves toward the disc in consequence of the 
excess of pressure. The force is therefore a force of the old 
school, a case of vis a tergo, a shove from behind.” 
It has been customary with me for several years, when occa- 
sion invited it, to demonstrate to my musical friends the physical 
ection existing in the sounding organ-pipe, toshow them (taking 
upa chance wood-shaving lying on the floor of the workshop or 
a strip of tissue paper) that, heterodox though the teaching be, 
the stream of air at the mouth of the organ-pipe constitutes a 
free-reed—visibly ;before them the film-like wood-shaving is 
drawn into the motion of the air, and the beautiful curve of the 
reed’s swing displays itself beyond dispute ; then to show them 
that the air-moulded tongue obeys every law of the free-reed, 
has its own definite rate of vibration, that the current is so 
directed that it shall fass not sészke the lip, that it is an air- 
moulded or aéroplastic reed as definitely fashioned in substance, 
strength, proportion, and form, as metal reeds are to produce a 
required and determinate rate of vibration. First, the velocity 
of current, a constant upward force; then, the periodicity of 
yibration as a secondary mode of its activity. The aéroplastic 
reed forming with the pipe a system of transverse vibration asso- 
ciated ii tegindiva vibration, and possibly another phase of 
vibration across the width of the reed enabling it to synchronise 
with the harmonic range of the pipe; the principle of action of |. 
the whole being termed, in my non-academic phraseology, suction 
by velocity ; but if more exact expression is found its explana- 
tion should imply, or better still, include the axiomatic phrase 
of Sir W. Thomson, ‘‘in a moving fluid the pressure is least 
where the velocity is greatest.” To state the existence of an 
air-moulded free-reed is to give the key to its nature. Flutes, 
flageolets, whistle-pipes, disc-whistles, form one group with 
organ-pipes ; all are of one type. Then there is another group 
of free-reeded instruments including the vocal organs, the 
trumpet, bassoon, oboe, harmonium, and the like, the only dis- 
tinction between the two groups being that the one possesses 
reeds of air of definite pitch; and the other possesses reeds of 
grosser substance, whether it be membrane wood or metal, 
alike of definite pitch, but in every one the degree of elasticity 
or pliancy in the substance determines how much of that pitch 
shall be maintained as the work is done. Velocity is power, 
and in every conjunction of reed and pipe the reed is the domi- 
nant. Most distinctly it should be recognised that the air-reed 
does work and expends power in doing it. A rod or a string 
delivers up under a single blow the whole vibrating energy it is 
capable of—not so the air-column inthe organ-pipe, which needs 
to be beaten the precise number of blows requisite for the pitch 
of tone elicited. 
Reeds of the oboe are as truly free-reeds as are the vocal 
cords. The stream of air does not necessarily pass down the 
organ-pipe, but in the oboe it is essential it should pass down 
the pipe. The action of this orchestral instrument is best ex- 
plained under the law of ‘‘least pressure,” showing an identity 
in principle but with difference of mode; instead of the stream 
with a lapping action as an air-tongue at the mouth of the organ- 
pipe, we have an air-current passing between two sensitive reeds 
down a narrow straw-like tube into the main body of the pipe. 
The velocity in the little tube immediately causes ‘‘ least pressure” 
in the interior, effecting approach and closure of the pair of lip- 
like reeds, and so on, a perpetual renewing and breaking of con- 
tacts, the periodicity of such movement being determined by the 
sensitiveness of the reed in relation to theair-tube through which 
the impulses must move before the ‘‘ dispersion of the vibrations ” 
into the air ve/ieves the reed and fixes the eriod ot its stroke. In 
further proof that the flue organ-pipe is a free-reed instrument, 
compare the flute, its representative, with the oboe and clarionet. 
So little is understood concerning the nature of these wind 
instruments, that, whenever in the science of acoustics they are 
referred to, it is stated that the clarionet is a closed pipe, and 
the oboe an open pipe; that the former produces the series of 
uneven harmonics and the latter the even series, and the expla- 
nation given is that the tube of the one is cylindrical, and the 
tube of the other is conical. 
explain. It is true that the clarionet gives in relation to its length 
the pitch corresponding to that of a closed pipe, whilst the opve, 
though of similar length (scale of key allowed for), is of the 
pitch of an open pipe, with relative harmonics ; yet this difference 
The explanation does not really | 
arises not in any degree from the shape of bore cylindrical or 
conical. As well denominate the oboe ‘‘a closed pipe” if 
structure is compared ; the one is not more a closed pipe th: 
the other, the true cause of the diversity is in the raté of reed- 
vibration of the clarionet being only half the rate of that natur: 
tothe oboe. The proof is clear and open to anyone intent to 
observe. Place the obos head on the clarionet-tube, and you 
will get from this same tube only the two-feet tone instead of the 
four-feet tone, and with this transformation of pitch the series of 
harmonics previously wanting. Place the flute-head on the 
clarionet-tube and the same results follow; showing that the 
velocity of vibration originates with the reed, and that the flute 
rightly considered is a free-reeded instrument. 
The experience of years justifies me in presenting these conclu- 
sions, and should they not be disproved, questions will suggest 
themselves whether physicists should not look to the disturbance 
of the equilibrium of air-pressure as the chief element in deter- 
mining the pitch of sounds produced in organ pipes ; whether 
the long conserve doctrine of ‘‘ the column of air within being 
alone the cause of sound ” has not been detrimental to investiga- 
tion as was in older times the doctrine that ‘‘nature abhors a 
vacuum,” which, as Whewell points out, retarded science a 
century by pre-occupying men’s minds against observation; a) 
whether it is not through the presence of the law of ‘*least 
pressure ” that vibration of any kind becomes possible. 
HERMANN SMITH 
The Hegelian Calculus 
YESIERDAY evening a copy of Nature for the roth instant, 
sent to my late address at Piershill, reached me here. The 
sender annexes the initials W. R. S.—those, presumably, of Mt. 
W. R. Smith. It was only thus that I became aware of that 
gentleman’s letter on *‘ The Hegelian Calculus,” in said issue ; 
and, as I am called upon by name therein, I should be obliged 
if, in an early number of the valuable publication referred to, 
you would kindly allow me insertion of this explanatory word 
in return. : 
In my rejoinder, mentioned by Mr. Smith as appearing in the 
current number of the Forfnighily, and which (rejoinder) treats, 
as Mr. Smith truly says himself, his own paper in the same 
pages ‘‘asa virtual concession of the entire case,” I speak 
thus :— 
‘*He that, with whatever tincture of mathematics, will but 
cast a single glance into the situation as it veritably is, will per 
ceive at once that Mr. Smith’s present paper is of such a 
character as not to demand any further answer from me, It is 
of such a character, however, that it may be put on the level of 
a business transaction, and if Mr. Smith can persuade any com= 
petent mathematician—say the greatest alive, Sylvester, hé 
being at once mathematician, metaphysician, and German 
scholar, and at the same time wholly unknown to myself—if, I 
say, Mr. Smith can persuade any such competent expert to seé 
in this matter with Mr. Smith’s eyes, I shall consent to be 
mulcted in what pecuniary penalty this expert may please.” 
Of course with reciprocity in the other event. I hepe Mr. 
Sylvester will kindly pardon me for having thus, almost invo- 
luntarily, made free with his name; but, if I could say the 
above then, certainly not less can I say the above: now—after 
this letter of Mr. Smith’s. The ‘‘ characier” in allusion is one, 
I believe, hitherto unexampled in literary controversy, and suclhy 
that, as I also believe, the most important interests call forth 
thorough understanding of it. It is m consequence of this 
“character” that, as I have intimated, I caunot, with any 
respect to myself, enter into further direct relations with Mr. 
Smith, and that I must confine myself to what has been said 
above. All, for that part, may be confidently left to time. 
Napoleon snipped off, and put in his pocket the alleged gold 
tassel, assured that use would disclose the tinsel in suspicion, 
So, as regards the—to me—extraordinary operations of Mr. 
Smith—not but every Kener must see what is concerned at a 
glance—I can leave them fearlessly to the intromissions of the 
public. 
Further proceeding, let me intimate in conclusion, however 
formidable it may look, must, so far as [ am concerned, be: 
arranged by a friend on the one par, and a friend on the other.. 
Longer to trouble the public with these alcercations can only 
seem to itimpertinent. I, at least, shal! be satisfied if it will 
but consider the result in the end, 
Edinburgh, April 18 J. HUTCHISON STIRLING 
—_ ~ As tr at Ses Ton” Pee ett. 
