Chapter I: II (3)

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._

* * * * *

AN INTEGRATING MACHINE.

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

By C.V. BOYS.

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 required.

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 = cx² / 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 / x² 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 logarithms.

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 current.

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.

* * * * *

UPON A MODIFICATION OF WHEATSTONE'S MICROPHONE AND ITS APPLICABILITY TO RADIOPHONIC RESEARCHES.

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

By ALEXANDER GRAHAM BELL.

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.]

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.]

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 parts.

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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