392 
setting up of an area of maximum pressure upon the 
underside of the ogival head. This gives rise to a re- 
sultant disturbing couple, which, by reason of the sym- 
metry of the surface, has its axis parallel to the hori- 
zontal principal axis at the C.G., and this axis is directed 
rightwards. Since this disturbing couple has its axis at 
right angles to the axis of angular momentum, i.e. to the 
axis of figure, it causes a precessional motion of the axis 
in the plane of its own axis and of the axis of figure, so 
that this axis begins to turn itself slightly to the right 
of the trajectory, the rifling being taken to be right- 
handed. This action is a very small one, because the 
‘couple producing it is very small compared with the couple 
which is equivalent to the total angular momentum. The 
axes of angular momentum and of angular velocity being 
initially coincident with the axis of figure, while the axis 
of the disturbing couple is at right angles to it and parallel 
to one of the principal axes at the C.G., 
no effect upon the magnitude of either the angular 
momentum or the rotational velocity. It alters only the 
orientation of the axis of angular momentum, and leaves 
it coincident with the axis of figure. 
Now this deflection of the axis to the right causes the 
left side of the head of the shot to experience a greater 
normal pressure than the right, and so gives rise to a 
second disturbing couple, of small magnitude relatively to 
the whole angular momentum, about an axis parallel to 
a principal axis at the C.G. and directed downwards, very 
nearly, if not exactly, in the vertical plane through the 
axis of the shot. The effect of this is to bring about a 
precessional motion of the axis in this plane, directed 
downwards, so that the nose of the shot begins to dip 
towards the tangent to the trajectory. This couple has, 
otherwise, exactly the same effects on the motion of the 
axis “as the other one, and since both couples are very 
small in comparison with the total angular momentum, it 
is permissible to combine their effects after considering 
them separately. It thus appears that the axis acquires 
a small precessional motion about the tangent to the 
trajectory, and that the excess of pressure upon the left 
of the head will cause the trajectory itself to be bent to 
the right, bringing about the well-known rightward crift 
of the shot. If the rifling be left-handed the shot will 
drift to the left, but the nose of the shot will, as befcre, 
dip towards the trajectory. 
Any device that throws the C.G. well towards the base 
of the shot will have the effect of adding to the magni- 
tude of the first of the above two couples. A smaller 
deviation of the axis from the trajectory will then afford 
a larger disturbing couple, and the rightward precessional 
motion will be more quickly established. In consequence 
of this the rightward drift will be diminished. A lons, 
hollow bullet of thin steel, the rear half having a smaller 
diameter than the front half, and this rear half being filled 
with lead, and also coatéd exteriorly with lead so as to 
take the rifling, may, on this theory, be expected to have 
less drift than the ordinary bullet, whereas a_ bullet 
weighted towards the head would have more. 
J. W. SuHarpe. 
this couple has 
Woodroffe, Bournemouth. 
The Problem of the Random Path. 
THE following illustration of Prof. Karl Pearson's 
““Random Path ’’ problem may be of interest. 
Mr. Kipling in his story, ‘‘ The Strange Ride of 
Morrowbie Jukes,” gives the following directions for find- 
ing the safe path across a quicksand, which directions 
are supposed to have been found by the hero of the story 
in the coat of an earlier victim :— ; 
“Four out from crow-clump; three left; nine out; 
two right; three back; two left: fourteen out; two left; 
seven out; one left; nine back; two right; six back; four 
right; seven back.’? 
These numbers were probably taken at random, and it 
will be noted that seventy-five paces are taken, and the 
final position is only seven paces from the original 
position. 
This is a rather curious confirmation of Lord Rayleigh’s 
solution of the problem. i 
Recrnatp A. FESSENDEN. 
NO. 1947, VOL. 75] 
NATURE 
| FEBRUARY 21, 1907 
SPEECH CURVES. 
R. SCRIPTURE since 1901 has worked with 
zeal and energy at experimental phonetics, and 
he has published several valuable papers, as well as 
a large volume treating generally of the subject. The 
work has been carried on with the aid of the Carnegie 
Institution of Washington at Yale, Munich, Berlin, 
and Zurich. It has been an expensive research, as 
in addition to costly apparatus a staff of clerks was 
required for computation. A perusal of this mono- 
graph proves that Dr. Scripture has shown great 
ingenuity in the construction of recorders and in 
overcoming technical difficulties that can be fully 
appreciated only by those who have made excursions 
into this field of research. His experimental method 
has been to transcribe on smoked paper the curves 
of speech both from the gramophone of Berliner an 
the phonograph of Edison. E 
On the disc of the gramophone the curves produced 
by sound vibrations are not indentations in the bottom 
of a groove or furrow, as in the tracing on a phono- 
graph cylinder, but they are horizontal, as if they 
were drawn on the plane of a sheet of paper. 
Further, it is interesting to note that in the gramo- 
phone record the depth of the groove is constant, 
whereas in that of the phonograph the downward 
movement of the recording disc bearing the cutting 
tool is diminished, in consequence of increasing re- 
sistance, in comparison with the upward movement. 
Each instrument has its own peculiar quality of tone, 
and, except in very fine modern instruments, natural 
sounds are more or less falsified. This falsification 
Dr. Scripture shows is due to a distortion of the 
waves by the bending of the diaphragm, and not to 
nodal vibrations such as occur on Chladni’s plates. 
His best tracings were taken from gramophone 
records, by using either a simple or a compound 
lever, which at one end travelled slowly over the 
record, and at the other recorded the waves on a 
moving strip of smoked paper. 
There is no special novelty in this method except 
that it has been applied to the gramophone, and that 
the mechanical arrangements have been of the finest 
quality. It gives one a notion of the delicacy of the 
method when it is stated that 1 mm. of the tracing = 
0-0004 sec. The vertical magnification by the use of 
a simple lever was 300 times, but Dr. Scripture 
adds :—‘t The future of the method lies in the de- 
velopment of a compound lever.’’ Great care was 
taken to identify any portion of the record on the 
smoked paper with the corresponding part of the 
surface of the gramophone plate. This was accom- 
plished by a very ingenious device. The reproduction 
of the curves for printing was done by etching on 
zinc. An example of a tracing of the sounds of an 
orchestra is shown in Fig. 1, and the following is 
Dr. Scripture’s description :— 
“‘ The curve in Fig. 32 [Fig. 1] is from the record of a 
note from an orchestra. The most prominent vibration is 
one whose wave-length is 3 mm.=o-oo012 sec., that is, about 
the note xe Another prominent feature is the group- 
ing of these vibrations in threes, indicating a tone with a 
period of 9 mm.=0-0036 sec., or a note about ee There 
is one which reinforces every sixth vibration of the high 
note and another that coincides approximately with every 
ninth; the former would correspond to c° Z, the latter 
to g-" fF. The combination of all these notes—each com- 
prising a fundamental with overtones—produces a very 
complicated curve. From such vibrations, however, the 
ear can pick out not only the component notes, but also 
the characteristic tones of the piano, violin, &c.’’ (p. 33). 
1 “Researches in Experimental Phonetics: the Study of Speech Curves.” 
By Dr. E. W. Scripture. Pp. 204. (Washington, D.C.: Published by the 
Carnegie Institute of Washington, 1906.) 
