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Scientific American Supplement, No. 288 by Various

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L, upon it, then the lines of force and the equipotential planes will be
distorted, as shown in Fig. 3. If the hill or building be so high as to
make the distance H h or L l equal to e f (Fig. 2), then we shall again
have disruptive discharge.

If instead of a hill or building we erect a solid rod of metal, G H,
then the field will be distorted as shown in Fig. 4. Now, it is quite
evident that whatever be the relative distance of the cloud and earth,
or whatever be the motion of the cloud, there must be a space, g g',
along which the lines of force must be longer than a' a or H H'; and
hence there must be a circle described around G as a center which is
less subject to disruptive discharge than the space outside the circle;
and hence this area may be said to be protected by the rod, G H. The
same reasoning applies to each equipotential plane; and as each circle
diminishes in radius as we ascend, it follows that the rod virtually
protects a cone of space whose height is the rod, and whose base is the
circle described by the radius, G a. It is important to find out what
this radius is.

[Illustration: Fig. 5]

Let us assume that a thunder-cloud is approaching the rod, A B (Fig. 5),
from above, and that it has reached a point, D', where the distance. D'
B, is equal to the perpendicular height, D' C'. It is evident that, if
the potential at D be increased until the striking-distance be attained,
the line of discharge will be along D' C or D' B, and that the length, A
C', is under protection. Now the nearer the point D' is to D the shorter
will be the length A C' under protection; but the minimum length will be
A C, since the cloud would never descend lower than the perpendicular
distance D C.

Supposing, however, that the cloud had actually descended to D when the
discharge took place. Then the latter would strike to the nearest point;
and any point within the circumference of the portion of the circle, B
C (whose radius is D B), would be at a less distance from D than either
the point B or the point C.

_Hence a lightning-rod protects a conic space whose height is the length
of the rod, whose base is a circle having its radius equal to the height
of the rod, and whose side is the quadrant of a circle whose radius is
equal to the height of the rod._

I have carefully examined every record of accident that was available,
and I have not yet found one case where damage was inflicted inside this
cone when the building was properly protected. There are many cases
where the pinnacles of the same turret of a church have been struck
where one has had a rod attached to it; but it is clear that the other
pinnacles were outside the cone; and therefore, for protection, each
pinnacle should have had its own rod. It is evident also that every
prominent point of a building should have its rod, and that the higher
the rod the greater is the space protected.

* * * * *


Hantzel has communicated to the Saxon Royal Society of Science some
interesting observations on the production of electricity by light
in colored fluor-spar. The centers of the fluor-spar cubes become
negatively electric by the action of light. The electric tension
diminishes toward the edges and angles, and frequently positive polarity
is produced there. With very sensitive crystals a short exposure to
daylight is sufficient; by a long exposure to light the electric current
increases. The direct rays of the sun act much more powerfully than
diffused daylight, and the electric carbon light is more powerful even
than sunlight. The photo-electric action of light belongs principally
to the "chemically active" rays; this is shown by the fact that the
production of electricity is extremely small behind a glass colored with
cuprous oxide, and behind a film of a solution of quinine sulphate;
while it is not appreciably diminished by a film of a solution of alum.
The photo-electric excitability of fluor-spar crystals is increased by a
moderate heat (80 deg. to 100 deg. C.).

* * * * *


The January and February numbers of the _Elektrotechnische Zeitschrift_
contain a number of articles on this interesting subject by several
eminent electricians. Professor Foerster, director of the observatory in
Berlin, points out the great importance of the careful study of earth
currents, first observed at Greenwich, and now being investigated by a
committee appointed by the German Government. He further points out,
according to Professor Wykander, of Lund, in Sweden, that a close
connection exists between earth currents, the protuberances of the
sun, and the aurora borealis, and that the nearly regular periodical
reappearance of protuberances in intervals of eleven years coincides
with similar periods of excessive magnetic earth currents and the
appearance of the aurora borealis. The remarkable disturbing influences
on telegraph wires and cables of the aurora borealis observed from the
11th to 14th of August, 1880, have been carefully recorded by Herr Geh.
Postnath Ludwig in Berlin, and a map of Europe compiled, showing the
places affected, with the extent to which telegraph wires and cables
were influenced and disturbed. Although the aurora was but faintly
visible in England and Germany, and in Russia only as far as 35 deg. north,
disturbing influences were reported from all parts of Europe, the
Mediterranean, and Africa, and even Japan and the east coast of Asia.
As far south as Zanzibar, Mozambique, and Natal disturbances were also
noticed. They were in Europe most intense on the morning of August 12,
when they lasted the whole day, and increased again in intensity toward
eight o'clock in the evening, while they suddenly ceased everywhere
almost simultaneously. Scientific and careful observations were only
taken at a few places, but the existence of earth currents in frequently
changing direction and varying intensity, was noticed everywhere. Long
lines of wires were more affected than short ones, and although some
lines--for instance the Berlin-Hamburg in an east-west direction--were
not at all influenced, no general law was noticed according to which
certain directions were freed from the disturbing influence. While, for
instance, the Red Sea cable was not noticeably affected, the land
line to Bombay, forming a continuation of this cable, was materially
disturbed. The Marseilles-Algiers cable, so seriously influenced in
1871, showed no signs at all, but as may be expected, the north of
Europe suffered more than the south, and in Nystad, Finland, the
galvanometer indicated an intensity of current equal to that of 200
Leclanche cells.

Since thunderstorms are generally local, it is only natural that their
effect upon telegraph cables should also be confined to one locality.
Numerous careful observations, carried out over considerable periods of
time, show that the disturbing influences of thunderstorms on telegraph
lines are of less duration and more varying in direction and intensity
than those of the aurora borealis. Long lines suffer less than short
lines; telegraph wires above ground are more easily and more intensely
affected than underground cables. It is, however, possible, that this is
mainly due to the fact that in the districts where strict records were
kept, in the German Empire, most of the long lines are underground
cables, while most of the short local lines are overground wires. The
results of the disturbances varied; in Hughes's apparatus the armatures
were thrown off, lines in operation indicated wrong signs, dots became
dashes, and the spaces were either multiplied in size or number,
according to the direction of the earth currents induced by the
thunderstorms. Since these observations extended over nearly 2,000
cases, some conclusions might fairly be drawn from them. For the purpose
of a more complete knowledge on this subject, Dr. Wykander recommends a
series of regular observations on earth currents to be carried out at
different stations, well distributed over the whole surface of the
globe, these observations to be made between six and eight A.M., and at
the same time in the evening. Special arrangements to be made at various
stations to record exceptionally intense disturbances during the
phenomena of the aurora borealis, notice to be taken of time, direction,
intensity, and all further particulars. Since this question appears to
bear a considerable amount of influence on underground cables, it is one
that deserves serious attention before earth cables are more generally
introduced; there can, however, be little doubt that they are not nearly
so much exposed as overhead wires to disturbing influences of other
kinds, such as snow, rain, wind, etc., while they certainly do
suffer, though perhaps in a less degree, by electrical

* * * * *


[Footnote: A communication to the Sheffield Photographic Society in the
_British Journal of Photography_.]

It is quite possible that in the remarks I propose making this evening
in connection with the photographic art I may mention topics and some
details which are familiar to many present; but as chemistry and optical
and physical phenomena enter largely into the theory and practice
of photography, the field is so extensive there is always something
interesting and suggestive even in the rudiments, especially to those
who are commencing their studies. Although this paper may be considered
an introductory one, I do not wish to load it with any historical
account, or describe the early methods of producing a light picture, but
shall at once take for my subject, "The Photographic Image: What It
Is," and under this heading I must restrict myself to the collodion and
silver or wet process, leaving gelatine dry plates, collodio-chloride,
platinum, carbontype, and the numerous other types which are springing
up in all directions for future consideration.

Now, in an ordinary pencil, pen and ink, or sepia sketch we have a
deposit of a dark, non-reflecting substance, which gives the outline of
a figure on a lighter background. The different gradations of shade
are acquired by a more or less deposit of lead, ink, or sepia. In
photography--at least in the ordinary silver process--the image is
formed by a deposition of metallic silver or organic oxide in a minute
state of division, either on glass, paper, or other suitable material.
This is brought about by the action of light and certain reagents. Light
has long been recognized as a motive power comparable with heat or
electricity. Its action upon the skin, fading of colors, and effect
on the growth of vegetable and animal organisms are well known; and,
although the exact molecular change in many instances is not clearly
understood, yet certain salts of silver, iron, the alkaline bichromates,
and some organic materials--as bitumen and gelatine--have been pretty
well worked out.

It is a remarkable and well-known fact that the chloride, iodide, and
bromide of silver--called "sensitive salts" in photography--are not
susceptible (at least only slowly) to change when exposed to the yellow,
orange, and red rays. The longer wave lengths of the spectrum, as you
know, form, with violet, indigo, blue, and green, white light. The
diagram on the wall shows this dispersion and separation of the
primitive colors. These--the yellow, orange, and red-- are called
technically "non actinic" rays, and the others in their order become
more actinic until the ultra violet is reached. The action of white
light, or rays, excluding yellow, orange, and red, has the effect of
converting silver chloride into a sub-chloride; it drives off one
equivalent of chlorine. Thus, silver chloride, Ag_2Cl_2=Ag_2Cl+Cl.
When water is present the water is decomposed. Hydrochloric acid, HCl,
hypochlorous acid, HClO is formed.

The iodide of silver in like manner is changed into a sub-iodide; but
with water hydriodic acid is formed unless an iodine absorbent be
present--then into hypoiodic acid. The silver bromide undergoes
a similar change. When with light alone, a sub-bromide,
Ag_2Br_2=Ag_2Br+Br, and with water hypobromous acid. It is important
to bear this in mind, as one or other, and frequently both iodide and
bromide of silver, is the sensitive salt requisite or used in producing
the invisible image.

The theory regarding these sensitive salts of silver is that, being very
unstable, _i. e._, ready to undergo a molecular change, the undulations
produced in the ether, which pervades all space, and the potential
action or moving power of light is sufficient to disturb their normal
chemical composition; it liberates some of the chlorine, iodine, or
bromine, as the case may be. This action, of course, applies to light
from any source--the sun, electricity, or the brighter hydrocarbons,
also flame from gas or candle, whether it comes direct as rays of white
light or is reflected from an object and conducted through a lens as a
distinct image upon the screen of a camera.

I have no time to speak on the subject of lenses, only just to mention
that they are, or ought to be, achromatic, so as to transmit white light
and of perfect definition, and the amount of light passed through should
be as much as possible consistent with a sharp image--at least when
rapid exposure is attempted.

I shall touch very lightly on the manipulative part of photography, as
that would be unnecessary; but a brief account of the chemicals in use
is essential to a right appreciation of the theory of developing the
image. In the first place, our object is to get a film of some suitable
material coated with a thin layer of a sensitive salt of silver--say
a bromo-iodide. By mixing certain proportions of ammonium iodide
and cadmium bromide, or an iodide and bromide of cadmium with
collodion--which is pyroxyline, a kind of gun-cotton dissolved in ether
and alcohol--a plate of glass is coated, and before being perfectly dry
is immersed in the nitrate of silver bath. The silver nitrate solution,
adhering and entering to a slight extent the surface of the collodion,
becomes converted by an ordinary chemical action of affinity into silver
iodide and bromide.

The ammonium and cadmium play a secondary part in the process, and
are not absolutely necessary in forming the image. The plate is now
extremely sensitive to light. When we have entered it into the dark
slide and camera, and then exposed to light, the change I mentioned
has taken place. The film is transformed into different quantities of
sub-iodide and sub-bromide of silver, according to brilliancy of light.
In addition, there is on the plate an amount of unchanged silver nitrate
which becomes useful in the second stage, or development. The image is
not seen as yet, being latent, and requiring the well-known developing
solution of sulphate of iron, acetic acid, alcohol, and water.
Practically we all recognize the effect of a nicely-balanced wave of
developer worked round a plate. The high lights are first to appear as a
darker color, till the details of shadow come out; when this is reached
the developer is washed off. The chemical action is briefly thus, and
it can be shown by solutions without a photographic plate, as in a test
tube: Pour into this glass a solution of silver nitrate, AgNO, and add a
solution of ferrous sulphate, FeSO_4. The ferrous sulphate combines
with the nitric acid, forming two new salts--ferric nitrate and ferric
sulphate. The silver is deposited. Any other substance which will remove
oxygen from silver nitrate without combining with the silver would do
the same, and metallic silver would be thrown down. The formula, as
shown on the diagram, explains the interchange.

When the developer is poured over the plate it attacks first the free
silver nitrate, and causes it to deposit extremely fine particles of
metallic silver. The question arises: How is it these particles arrange
themselves to form an image? This is explained by the physical movement
known as molecular attraction or affinity. These particles are attracted
first to the portions of the plate where there is most sub-iodide and
sub-bromide. In the shady parts less silver is deposited. When the image
is once started it follows that particles of silver produced by the iron
developer will cause more to fall down on the face of those already
present, and the image is, of course, built up if the silver nitrate
be all consumed on the plate. The developer then becomes useless or
injurious. The presence of acetic acid checks the reduction of the
silver, and the alcohol facilitates the flow when the bath becomes
charged with ether and spirit.

The molecular attraction just mentioned is made plainer by reference to
the simple lead tree experiment. We have here in this bottle a piece
of zinc rod introduced into a solution of acetate of lead. A chemical
change has taken place. The zinc has abstracted the acetic acid and the
lead is deposited on the zinc, and will continue to be so until the
solution is exhausted. The irregularities of surface and arborescent
appearance are well shown. If the change were rapidly conducted the lead
particles would from their weight sink directly to the bottom instead
of aggregating together like ordinary crystals. I have constructed a
diagram of colored card, which will perhaps more clearly demonstrate
the relation of the different constituents. The lower portion (Fig. a)
represents a section of the glass plate or support, the collodion film
(Fig. b) having upon its surface a thin layer of bromo-iodine silver
(Fig. c), which, when exposed to a well-lighted image, as in a camera,
changes into different gradations of sub-bromide and sub-iodide, as
indicated by irregular, dark masses in the film. The dotted marks
immediately above these are intended for the silver deposit (Fig.
d)--clusters of granules, more abundant in the well lighted and less
in the shaded parts of the picture, corresponding to the amount of
sub-bromide and iodide beneath.


d Silver deposit--Image, c Sub-bromide and sub-chloride (gradations of),
b Collodion film--Substratum, a Section of glass plate--Support.]

The next point to consider is that of intensification--a process seldom
required in positive pictures, and would not be needed so often in
negatives if there was enough free silver nitrate on the plate during
development. The object, as we all know, in a wet-plate negative is to
get good printing density without destruction of half-tone. It is a
rule, I believe, in an over-exposed picture to intensify after fixing
the image, and in an under-exposed picture to intensify before fixing.
Whichever is done the intention is similar, namely, to intercept in a
greater degree the light passing through a negative, so as to make a
whiter and cleaner print. The usual intensifier--and, I suppose, there
is no better--is pyrogallic acid, citric acid, water, and a few drops of
silver nitrate solution. Pyrogallic is the most active agent, and might
be used alone with water; but for special reasons it is not desirable.
As a chemical it has a great affinity for oxygen, and will precipitate
silver from a solution containing, for instance, nitrate of silver. It
also combines with the metal, forming a pyrogallate--a dark brown, very
non-actinic material. The use of a few drops of AgNO_3 solution is very
evident. A deposit is added to the image already formed. Citric acid is
the retarder in this case. Alcohol is unnecessary, as the film is well
washed with water before the intensifier is used, consequently it flows
readily over the plate.

As regards fixing, or, more properly, clearing the image: it is the
simple act of dissolving out or from the film all free nitrate,
chloride, iodide, or bromide. Cyanide of potassium does not attack the
metallic deposit unless very strong. It has then a tendency to reduce
the detail in the shadows.


* * * * *


[Footnote: A communication to the Photographic Society of Ireland.]

Few of those who work with gelatine dry plates seem to be aware of the
great beauty of the transparencies for lantern or other uses which can
be made from them by ferrous oxalate development with the greatest ease
and certainty.

I think this a very great pity, for I hold the opinion that the lantern
furnishes the most enjoyable and, in some cases, the most perfect of all
means of showing good photographic pictures. Many prints from excellent
negatives which may be passed over in an album without provoking a
remark will, if printed as transparencies and thrown on the screen, call
forth expressions of the warmest admiration; and justly so, for no
paper print can do that full justice to a really good negative which a
transparency does. This difference is more conspicuous in these days of
dry gelatine plates and handy photographic apparatus, when many of our
most interesting negatives are taken on quarter or 5 x 4 plates the
small size of which frequently involves a crowding of detail, much of
which will be invisible in a paper print, but which, when unraveled or
opened out, as it were, by means of the lantern, enhances the beauty of
the pictures immensely.

When I last had the pleasure of bringing this subject before the members
of our society, it may be remembered that I demonstrated the ease
and simplicity with which those beautiful results maybe obtained, by
printing in an ordinary printing frame by the light of my petroleum
developing lamp, raising one of its panes of ruby glass for the purpose
for five seconds, and then developing by ferrous oxalate until I got the
amount of intensity requisite. On that evening, in the course of a very
just criticism by one of our members, Mr. J. V. Robinson, he pointed out
what was undoubtedly a defect, viz., a slightly opalescent veiling of
the high lights, which should range from absolutely bare glass in the
highest points. He showed that, in consequence of this veiling, the
light was sensibly diminished all over the picture. This veiling of the
high lights was a serious disadvantage in another important particular,
inasmuch as it lessened the contrast between the lights and shadows of
the picture, thereby robbing it of some of its charm and deteriorating
its quality.

Since that evening I have endeavored, by a series of experiments, to
find out some means by which this opalescence might be got rid of in the
most convenient manner. Cementing the transparency to a piece of plain,
clear glass with Canada balsam, as suggested by Mr. Woodworth, I found
in practice to be open to two formidable objections. One of these was
that Canada balsam used in this manner is a sticky, unpleasant substance
to meddle with, and takes a long time--nearly a month--to harden when
confined between plates in this manner. The other objection was of
extreme importance, namely, that, in consequence of commercial gelatine
plates not being prepared on perfectly flat glasses in all cases, I
found that, after squeezing out the superfluous balsam and the air
bubbles that might have formed from between the two plates, they are
liable to separate at the places where the transparency is not flat,
causing air bubbles to creep in from the edges, as you may see from
these examples. I, therefore, have discarded this method, although it
had the effect desired when successfully done.

I have hit, however, upon another way of utilizing Canada balsam, which,
while retaining all the good qualities of the former method, is not
subject to any of its disadvantages. This consists in diluting the
balsam with an equal bulk of turpentine, and using it as a varnish,
pouring it on like collodion, flowing it toward each corner, and pouring
it off into the bottle from the last corner, avoiding crapy lines by
slowly tilting the plate, as in varnishing. If the plate be warmed
previously, the varnish flows more freely and leaves a thinner coating
of balsam behind on the transparency. When the plate has ceased to drip,
place it in a plate drainer, with the corner you poured from lowest, and
leave it where dust cannot get at it for four or five days, when it will
be found sufficiently hard to be put into a plate box. The transparency
may be finished at any time afterward by putting a clean glass of the
same size along with it, placing one of the blank paper masks sold
for the purpose--either circular or cushion-shaped to suit the
subject--between the plates, and pasting narrow strips of thin black
paper over the edges to bind them together. This method is very
successful, as you may see from the examples. It renders the high lights
perfectly clear, and leaves a film like glass over all the parts of the
transparency where the varnish has flowed.

In order to avoid the risk of dust involved in this process, I tried
other means of arriving at similar results and with success, for the
plates I now submit to you have been simply rubbed or polished, as I
may say, with a mixture of one part of Canada balsam to three parts of
turpentine, using either a small tuft of French wadding or a small piece
of soft rag for the purpose, continuing the rubbing until the plate is
polished nearly dry. This method is particularly successful, rendering
the clear parts of the sky like bare glass. I have here a plate which is
heavily veiled--almost fogged, in fact--one half of which I have treated
in this way, showing that the half so treated is beautifully clear,
while the other half is so veiled as to be apparently useless.

I have tried to still further simplify this necessary clearing of those
plates, and find that soaking tor twelve hours in a saturated solution
of alum, after washing the hypo out of the plate, is successful in a
large number of cases; and where it is successful there is no further
trouble with the transparency, except to mount it after it becomes dry.
Where it is not entirely successful I put the plate into a solution of
citric acid, four ounces to a pint of water, for about one minute, and
have in nearly all cases succeeded in getting a beautifully-clear plate.
The picture must not be left long in the citric acid solution, or it
will float off; neither do I like using citric acid until after trying
the alum, for a similar reason.

I may mention that I recommend a short exposure in the printing-frame
and slow development, in order to get sufficient intensity. Of course
the exposure is always made to a gas or petroleum light. I also still
prefer the old method of making the ferrous oxalate solution, pouring
it back into the bottle each time after using, and using it for two
or three months, keeping the bottle full from a stock bottle, and
occasionally putting a little dry ferrous oxalate into the bottle and
shaking it up, allowing it to settle before using next time. By treating
it in this way it retains its power fairly well for a long time; and as
it becomes less active I give a little longer exposure, balancing
one against the other. Making the ferrous oxalate solution from two
saturated solutions of iron sulphate and potassium oxalate has not
succeeded so well with me for transparencies. The tone of the picture is
not so black as when developed by the old method; and I do not like gray
transparencies for the lantern. I also recommend very slow gelatine
plates, about twice as sensitive as wet collodion--not more, if I can
help it.

I have demonstrated, I hope to your satisfaction, the possibility of
producing lantern slides from commercial gelatine plates of a most
beautiful quality--ranging from clear glass to deep black, and
giving charming gradation of tones, showing on the screen a film as
structureless as albumen slides, without the great trouble involved in
making them. You must not accept the slides put before you this evening
as the best that can be done with gelatine. Far from it; they are only
the work of an amateur with very little leisure now to devote to their
manufacture, and are merely the result of a series of experiments which,
so far as they have gone, I now place before you.--_Thomas Mayne, T. C.,
in British Journal of Photography._

* * * * *


[Footnote: Read at a meeting of the Physical Society, Feb. 26.]


All the integrating machines hitherto made, of which I can find any
record, may be classed under two heads, one of which, Ainslee's machine,
is the sole representative, depending on the revolution of a disk which
partly rolls and partly slides on the paper, and the other comprising
all the remaining machines depending on the varying diameters of the
parts of a rolling system. Now, none of these machines do their work
by the method of the mathematician, but in their own way. My machine,
however, is an exact mechanical translation of the mathematical method
of integrating y dx, and thus forms a third type of instrument.

The mathematical rule may be described in words as follows: Required the
area between a curve, the axis of x and two ordinates; it is necessary
to draw a new curve, such that its steepness, as measured by the tangent
of the inclination, may be proportional to the ordinate of the given
curve for the same value of x, then the _ascent_ made by the new curve
in passing from one ordinate to the other is a measure of the area

The figure shows a plan and side elevation of a model of the instrument,
made merely to test the idea, and the arrangement of the details is not
altogether convenient. The frame-work is a kind of T square, carrying a
fixed center, B, which moves along the axis of x of the given curve, a
rod passing always through B carries a pointer, A, which is constrained
to move in the vertical line, ee, of the T square, A then may be made
to follow any given curve. The distance of B from the edge, ee, is
constant; call it K, therefore, the inclination of the rod, AB, is such
that its tangent is equal to the ordinate of the given curve divided
by K; that is, the tangent of the inclination is proportional to the
ordinate; therefore, as the instrument is moved over the paper, AB has
always the inclination of the desired curve.

The part of the instrument that draws the curve is a three-wheeled cart
of lead, whose front wheel, F, is mounted, not as a caster, but like the
steering wheel of a bicycle. When such a cart is moved, the front wheel,
F, can only move in the direction of its own plane, whatever be the
position of the cart; if, therefore, the cart is so moved that F is in
the line, ee, and at the same time has its plane parallel to the rod,
AB, then F must necessarily describe the required curve, and if it is
made to pass over a sheet of black tracing paper, the required curve
will be _drawn_. The upper end of the T square is raised above the
paper, and forms a bridge, under which the cart travels. There is a
longitudinal slot in this bridge in which lies a horizontal wheel,
carried by that part of the cart corresponding to the head of a bicycle.
By this means the horizontal motion communicated to the front wheel of
the cart by the bridge, is equal to that of the pointer, A; at the same
time the cart is free to move vertically.

The mechanism employed to keep the plane of the front wheel of the cart
parallel to AB is made clear by the figure. Three equal wheels at the
ends of two jointed arms are connected by an open band, as shown. Now,
in an arrangement of this kind, however the arms or the wheels are
turned, lines on the wheels, if ever parallel, will always be so. If,
therefore, the wheel at one end is so supported that its rotation is
equal to that of AB, while the wheel at the other end is carried by the
fork which supports F, then the plane of F, if ever parallel to AB, will
always be so. Therefore, when A is made to trace any given curve, F will
draw a curve whose ascent is (1/K) f y dx, and this, multiplied by K, is
the area required.


Not only does the machine integrate y dx, but if the plane of the front
wheel of the cart is set at right angles instead of parallel to AB, then
the cart finds the integral of dx / y, and thus solves problems, such,
for instance, as the time occupied by a body in moving along a path when
the law of the velocity is known.

Some modifications of the machine already described will enable it to
integrate squares, cubes, or products of functions, or the reciprocals
of any of these.

Of the various curves exhibited which have been drawn by the machine,
the following are of special physical interest.

Given the inclined straight line y = cx, the machine draws the parabola
y = cx squared / 2. This is the path of a projectile, as the space fallen is as
the area of the triangle between the inclined line, the axis of x, and
the traveling ordinate.

Given the curve representing attraction y = 1 / x squared the machine draws the
hyperbola y = 1 / x the curve representing potential, as the work done
in bringing a unit from an infinite distance to a point is measured
by the area between the curve of attraction, the axis of x, and the
ordinate at that point.

Given the logarithmic curve y = e^x, the machine draws an identical
curve. The vertical distance between these two curves, therefore,
is constant; if, then, the head of the cart and the pointer, A, are
connected by a link, this is the only curve they can draw. This motion
is very interesting, for the cart pulls the pointer and the pointer
directs the cart, and between they calculate a table of Naperian

Given a wave-line, the machine draws another wave-line a quarter of
a wave-length behind the first in point of time. If the first line
represents the varying strengths of an induced electrical current,
the second shows the nature of the primary that would produce such a

Given any closed curve, the machine will find its area. It thus answers
the same purpose as Ainslee's polar planimeter, and though not so handy,
is free from the defect due to the sliding of the integrating wheel on
the paper.

The rules connected with maxima and minima and points of inflexion are
illustrated by the machine, for the cart cannot be made to describe a
maximum or a minimum unless the pointer, A, _crosses_ the axis of x, or
a point of inflexion unless A passes a maximum or minimum.

* * * * *


[Footnote: A paper read before the Philosophical Society of Washington.
D. C., June 11, 1881.]


In August, 1880, I directed attention to the fact that thin disks or
diaphragms of various materials become sonorous when exposed to the
action of an intermittent beam of sunlight, and I stated my belief that
the sounds were due to molecular disturbances produced in the substance
composing the diaphragm.[1] Shortly afterwards Lord Raleigh undertook
a mathematical investigation of the subject and came to the conclusion
that the audible effects were caused by the bending of the plates
under unequal heating.[2] This explanation has recently been called in
question by Mr. Preece,[3] who has expressed the opinion that
although vibrations may be produced in the disks by the action of the
intermittent beam, such vibrations are not the cause of the sonorous
effects observed. According to him the aerial disturbances that produce
the sound arise spontaneously in the air itself by sudden expansion due
to heat communicated from the diaphragm--every increase of heat giving
rise to a fresh pulse of air. Mr. Preece was led to discard the
theoretical explanation of Lord Raleigh on account of the failure of
experiments undertaken to test the theory.

[Footnote 1: Amer. Asso. for Advancement of Science, August 27, 1880.]

[Footnote 2: _Nature_, vol. xxiii., p. 274.]

[Footnote 3: Roy. Soc., Mar. 10, 1881.]

[Illustration: Fig. 1. A B, Carbon Supports. C, Diaphragm.]

He was thus forced, by the supposed insufficiency of the explanation, to
seek in some other direction the cause of the phenomenon observed, and
as a consequence he adopted the ingenious hypothesis alluded to above.
But the experiments which had proved unsuccessful in the hands of Mr.
Preece were perfectly successful when repeated in America under better
conditions of experiment, and the supposed necessity for another
hypothesis at once vanished. I have shown in a recent paper read before
the National Academy of Science,[1] that audible sounds result from the
expansion and contraction of the material exposed to the beam, and that
a real to-and-fro vibration of the diaphragm occurs capable of producing
sonorous effects. It has occurred to me that Mr. Preece's failure to
detect, with a delicate microphone, the sonorous vibrations that were
so easily observed in our experiments, might be explained upon the
supposition that he had employed the ordinary form of Hughes's
microphone shown in Fig. 1, and that the vibrating area was confined
to the central portion of the disk. Under such circumstances it might
easily happen that both the supports (a b) of the microphone might touch
portions of the diaphragm which were practically at rest. It would of
course be interesting to ascertain whether any such localization of the
vibration as that supposed really occurred, and I have great pleasure in
showing to you tonight the apparatus by means of which this point has
been investigated (see Fig. 2).

[Footnote 1: April 21, 1881.]

[Illustration: Fig. 2. A, Stiff wire. B, Diaphragm. C, Hearing tube. D,
Perforated handle.]

The instrument is a modification of the form of microphone devised in
1872 by the late Sir Charles Wheatstone, and it consists essentially of
a stiff wire, A, one end of which is rigidly attached to the center of
a metallic diaphragm, B. In Wheatstone's original arrangement the
diaphragm was placed directly against the ear, and the free extremity
of the wire was rested against some sounding body--like a watch. In the
present arrangement the diaphragm is clamped at the circumference like
a telephone diaphragm, and the sounds are conveyed to the ear through a
rubber hearing tube, c. The wire passes through the perforated handle,
D, and is exposed only at the extremity. When the point, A, was rested
against the center of a diaphragm upon which was focused an intermittent
beam of sunlight, a clear musical tone was perceived by applying the ear
to the hearing tube, c. The surface of the diaphragm was then explored
with the point of the microphone, and sounds were obtained in all parts
of the illuminated area and in the corresponding area on the other side
of the diaphragm. Outside of this area on both sides of the diaphragm
the sounds became weaker and weaker, until, at a certain distance from
the center, they could no longer be perceived.

At the point where we would naturally place the supports of a Hughes
microphone (see Fig. 1) no sound was observed. We were also unable to
detect any audible effects when thepoint of the microphone was rested
against the support to which the diaphragm was attached. The negative
results obtained in Europe by Mr. Preece may, therefore, be reconciled
with the positive results obtained in America by Mr. Tainter and myself.
A still more curious demonstration of localization of vibration occurred
in the case of a large metallic mass. An intermittent beam of sunlight
was focused upon a brass weight (1 kilogramme), and the surface of the
weight was then explored with the microphone shown in Fig. 2. A feeble
but distinct sound was heard upon touching the surface within the
illuminated area and for a short distance outside, but not in other

In this experiment, as in the case of the thin diaphragm, absolute
contact between the point of the microphone and the surface explored was
necessary in order to obtain audible effects. Now I do not mean to
deny that sound waves may be originated in the manner suggested by Mr.
Preece, but I think that our experiments have demonstrated that the kind
of action described by Lord Raleigh actually occurs, and that it is
sufficient to account for the audible effects observed.

* * * * *

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