Chapter 5

The rod to the left is provided with a steel pivot, and contains several apertures, into which a pin enters, thus rendering it easy to begin bouquets at different heights.

The bouquet is mounted upon the rod to the left, as shown in the figure. The pin passes through the rod and enters a loop formed at the extremity of the twine, and thus serves as a point of support, and prevents the bouquet from falling, no matter what its weight is. When the pin is removed in order that the bouquet may be taken out, the loop escapes.

At the lower part of the rod upon which the bouquet is mounted, there is a collar with three branches, by means of which a rotary motion is given to the flowers through the aid of the hand. The twine used for tying is thus wound around the stems. When the apparatus is in motion, the twine unwinds from the spool, and winds around the rod that carries the flowers, and twists about and holds every stem.

An experienced operator can work very rapidly with this little apparatus, which has been constructed with much care and ingenuity, and which enters into a series of special mechanisms that is always of interest to know about.

The manufacturer was advised to construct his apparatus so that it could be run by foot power, but, after some trials, it was found that the addition of a pedal and the mechanism that it necessitates was absolutely superfluous, the apparatus working very well such as it is.--_La Nature_.

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[Continued from SUPPLEMENT, No. 567, page 9057.]

RADII OF CURVATURE GEOMETRICALLY DETERMINED.

By Prof. C.W. MACCORD, Sc.D.

NO. VII.--PATH OF A POINT ON A CONNECTING ROD.

The motion of the connecting rod of a reciprocating steam engine is very clearly understood from the simple statement that one end travels in a circle and the other in a right line. From this statement it is also readily inferred that the path of any point between the centers of the crank and crosshead pins will be neither circular nor straight, but an elongated curve. This inference is so far correct, but the very common impression that the middle point of the rod always describes an ellipse is quite erroneous. The variation from that curve, while not conspicuous in all cases, is nevertheless quite sufficient to prevent the use of this movement for an elliptograph. To this there is, abstractly, one exception. Referring to Fig. 22 in the preceding article, it will be seen that if the crank OH and the connecting HE are of equal length, any point on the latter or on its prolongation, except E, H, and F, will describe an exact ellipse. But the proportions are here so different from anything used in steam engines (the stroke being four times the length of the crank), that this particular arrangement can hardly be considered as what is ordinarily understood by a "crank and connecting rod movement," such as is shown in Fig. 23.

The length DE of the curve traced by the point P will evidently be equal to A'B', the stroke of the engine, and that again to AB, the throw of the crank. The highest position of P will be that shown in the figure, determined by placing the crank vertically, as OC. At that instant the motions of C and C' are horizontal, and being inclined to CC' they must be equal. In other words, the motion is one of translation, and the radius of curvature at P is infinite.

To find the center of curvature at D, assume the crank pin A to have a velocity A_a_. Then, since the rod is at that instant turning about the farther end A', we will have D_d_ for the motion of D. The instantaneous axis of the connecting rod is found by drawing perpendiculars to the directions of the simultaneous motions of its two ends, and it therefore falls at A', in the present position. But the perpendicular to the motion of the crank pin is the line of the crank itself, and consequently is revolving about O with an angular velocity represented by AO_a_. The motion of A' is in the direction A'B', but its velocity at the instant is zero. Hence, drawing a vertical line at A', limited by the prolongation of _a_O, we have A'_a_' for the motion of the instantaneous axis. Therefore, by drawing _a_'_d_, cutting the normal at _x_, we determine D_x_, the radius of curvature.

Placing the crank in the opposite position OB, we find by a construction precisely similar to the above, the radius of curvature E_z_ at the other extremity of the axis of the curve. It will at once be seen that E_z_ is less than D_x_, and that since the normal at P is vertical and infinite, the evolute of DPE will consist of two branches _x_N, _z_M, to which the vertical normal PL is a common asymptote. These two branches will not be similar, nor is the curve itself symmetrical with respect to PL or to any transverse line; all of which peculiarities characterize it as something quite different from the ellipse.

Moreover, in Fig. 22, the locus of the instantaneous axis of the trammel bar (of which the part EH corresponds to the connecting rod, when a crank OH is added to the elliptograph there discussed) was found to be a circle. But in the present case this locus is very different. Beginning at A', the instantaneous axis moves downward and to the right, as the crank travels from A in the direction of the arrow, until it becomes vertical, when the axis will be found upon C'R, at an infinite distance below AB', the locus for this quarter of the revolution being a curve A'G, to which C'R is an asymptote. After the crank pin passes C, the axis will be found above AB' and to the right of C'R, moving in a curve HB', which is the locus for the second quadrant. Since the path of P is symmetrical with respect to DE, the completion of the revolution will result in the formation of two other curves, continuous and symmetrical with those above described, the whole appearing as in Fig. 24, the vertical line through C' being a common asymptote.

In order to find the radius of curvature at any point on the generated curve, it is necessary to find not only the location of the instantaneous axis, but its motion. This is done as shown in Fig. 25. P being the given point, CD is the corresponding position of the connecting rod, OC that of the crank. Draw through D a perpendicular to OD, produce OC to cut it in E, the instantaneous axis. Assume C A perpendicular to OC, as the motion of the crank. Then the point E in OC produced will have the motion EF perpendicular to OE, of a magnitude determined by producing OA to cut this perpendicular in F. But since the _intersection_ E of the crank produced is to be with a vertical line through the other end of the rod, the instantaneous axis has a motion which, so far as it depends upon the movement of C only, is in the direction DE. Therefore EF is a component, whose resultant EG is found by drawing FG perpendicular to EF. Now D is moving to the left with a velocity which may be determined either by drawing through A a perpendicular to CD, and through C a horizontal line to cut this perpendicular in H, or by making the angle DEI equal to the angle CEA, giving on DO the distance DI, equal to CH. Make EK = DI or CH, complete the rectangle KEGL, and its diagonal ES is, finally, the motion of the instantaneous axis.

EP is the normal, and the actual motion of P is PM, perpendicular to EP, the angle PEM being made equal to CEA. Find now the component EN of the motion ES, which is perpendicular to EP. Draw NM and produce it to cut EP produced in R the center of curvature at P.

This point evidently lies upon the branch _z_M of the evolute in Fig. 23. The process of finding one upon the other branch _x_N is shown in the lower part of the diagram, Fig. 25. The operations being exactly like those above described, will be readily traced by the reader without further explanation.

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AUTOMATIC COMMUTATOR FOR INCANDESCENT LAMPS.

Incandescent electric lighting, already pushed to such a degree of perfection in the details of construction and installation, continually finds new exigencies that have to be satisfied. As it is more and more firmly established, it has to provide for all the comforts of existence by simple solutions of problems of the smaller class.

Take for example this case: Suppose a room, such as an office, lighted by a single lamp. The filament breaks; the room becomes dark. The bell push is not always within reach of the arm, and it is by haphazard that one has to wander around in the dark. This is certainly an unpleasant situation. The comfort we seek for in our houses is far from being provided.

M. Clerc, the well known inventor of the sun lamp, has tried to overcome troubles of this sort, and has attained a simple, elegant, and at the same time cheap solution. The cut shows the arrangement. The apparatus is connected at the points, BB', with the lighting circuit. The current entering by the terminal, B', passes through the coils of a bobbin, S, before reaching the points of attachment, a and b, of the lamp, L, the normally working one. Thence the circuit runs to B. Within the coil, S, is a small hollow cylinder, T, of thin sheet iron, which is raised parallel with the axis of the bobbin during the passage of the current through the latter. At its base the cylinder is prolonged into two little rods, h and h', which plunge into two mercury cups, G and G'. The cut shows that one of the cups, G', is connected to the terminal, B', and the other, G, to the terminal, a', of the other lamp, L'. An inspection of the cut shows just what ensues when an accident happens to the first lamp while burning. The first circuit being broken at ab, the magnetizing action of the current in the bobbin ceases, the cylinder, T, descends, and the rods, h and h', dip into the mercury. It follows that the current, always starting from the terminal, B', will by means of the cups, G and G', pass through the lamp, L', to go by the original return wire to B.

The substitution of the lamp, L, for L' is almost instantaneous. It can scarcely be perceived. It goes without saying that such an arrangement of automatic commutation is applicable to lamps with two or more filaments of which only one is to be lighted at a time. The apparatus costs little, and can be made as ornamental as desired. No exaggeration is indulged in if we pronounce it simple and ingenious. It may be used in a great variety of eases. The diameter of the wire is 55/100 (22 mm.), its length eighteen meters (60 feet), its resistance one ohm; ¾ ampere is needed to work it, and less than a watt is absorbed by it.--_Electricite_.

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DEFINITIONS AND DESIGNATIONS IN ELECTROTECHNICS.

We may discourse for some time to come upon the uniformity of electric language, for universal agreement is far from being established. An important step toward the unity of this language was taken in 1881 by the congress of Paris, which rendered the use of the C.G.S. system definitive and universal. This labor was completed in 1884 by the meeting of a new congress at Paris, at which a definition of the C.G.S. and practical units was distinctly decided upon. That the unit of light defined by the congress has not rapidly come into favor is due to the fact that its practical realization is not within everybody's reach.

The work of unification should not come to a standstill on so good a road. How many times in scientific works or in practical applications do we find the same physical magnitude designated by different names, or even the use of the same expression to designate entirely different things!

The result is an increase of difficulties and confusions, not only for persons not thoroughly initiated into these notions, but also for adepts, even, in this new branch of the engineer's art. The effects of such confusion make themselves still further felt in the reading of foreign publications. Thus, for example, in Germany that part of a dynamo electric machine that is called in France the _induit_ (armature) is sometimes styled _anker_, and more rarely _armatur_. The _north pole_ of a freely suspended magnetized needle is the one that points toward the geographical north of the earth. In France, and by some English authors, this pole is called the _south_ one. Among electricians of the same country, what by one is called _electro-motive force_ is by another styled _difference of potential_, by a third _tension_, and even _difference of tension_.

Our confrere Ruhlmann, of the _Elektrotechnische Zeitschrift_, gives a still more remarkable example yet of such confusion. The word _polarization_, borrowed from optics, where it has an unequivocal sense, serves likewise to designate the development of the counter electro-motive force of galvanic elements, and also that essentially different condition of badly conducting substances that is brought about by the simultaneous influence of quantities of opposite electricity.

In Germany, the word _induction_, coupled with the word _wire_, for example, according to the formation of compound words in that language, may also have a double meaning, and it is by the sense alone of the phrase that we learn whether we have to do with an induced wire or an inducting one. The examples might be multiplied.

At its session of November 5, 1884, the International Society of Electricians, upon a motion of Mr. Hospitalier, who had made a communication upon this question, appointed a committee to study it and report upon it. The English Society of Electricians likewise took the subject into consideration, and one of its most active and distinguished members, Mr. Jamieson, presented the result of his labors at the May session of the society in 1885.

A discussion arose in which the committee of the International Society of Electricians was invited to take part. The committee was represented by its secretary, Mr. Hospitalier, who expressed himself in about these words: "The committee on electric notations presided over by Mr. Blauvelt has finished a part of its task, that relative to abbreviations, notations, and symbols. It will soon take up the second part, which relates to definitions and agreements." He broadly outlined the committee's ideas as follows:

In all physical magnitudes that are made use of, we have: (1) the physical magnitude itself, aside from the units that serve to measure it; (2) the C.G.S. unit that serves to measure such grandeur (granted the adoption of the C.G.S. system); (3) practical units, which, in general, have a special name for each kind of magnitude, and are a decimal multiple or sub-multiple of the C.G.S. unit, except for time and angles; (4) finally, decimal multiples and sub-multiples of these practical units, that are in current use.

The committee likewise decided always to adopt a large capital to designate the physical magnitude; a small capital to designate the C.G.S. unit, when it has a special name; a "lower case" letter for the abbreviation of each practical unit; and prefixes, always the same, for the decimal multiples and sub-multiples of the practical units.

Thus, for example, work would be indicated by the letter W (initial of the word); the C.G.S. unit is the _erg_, which would be written without abbreviation, on account of its being short; and the practical units would be the kilogrammeter (_kgm_), the grammeter (_gm_), etc. The multiples would be the _meg-erg_, the tonne-meter (_t-m_), etc.

Mr. Jamieson's propositions have been in great part approved. Some criticisms, however, were made during the course of the discussion, and it is for this reason that the scheme still remains open to improvements. The proposed symbols are as follows:

A.--PRACTICAL ELECTRIC UNITS.

Total resistance of a circuit. R Internal resistance of a source of current. r_{1} Resistance of the separate parts of a current. _r__{1}, _r__{2}, etc. Specific resistance. [rho] 1 ohm. [omega] 1 megohm. [Omega] Intensity of a current. C Magnitude of 1 ampere. A 1 milliampere. [alpha] Electro-motive force. E Magnitude of 1 volt. _v_ Capacity. K Constant of specific induction. [sigma] 1 farad. [Phi] 1 microfarad. [phi] Quantity of electricity. Q 1 coulomb. C Electric work (volt coulomb). _v_C Electric effect (volt ampere, watt in one second). W Horse power. HP

B.--MAGNETISM.

Pole of magnet pointing toward the north. N The opposite pole. S Force of a pole, quantity of magnetism. _m_ Distance of the poles of a magnet. _l_ Magnetic moment. M = _m.l_ Intensity of magnetization. J Intensity of the horizontal component of terrestrial magnetism. H

C.--ELECTRIC MEASUREMENTS.

Galvanometer and its resistance. G Resistance of the shunt of a galvanometer. _s_ Battery and its internal resistance. B

For dynamo machines, the following designations are proposed:

The machine itself. D Positive terminal. +T Negative terminal. -T Magnet forming the field. FM Current indicator (amperemeter). AM Tension indicator (voltameter). MV Electro-magnet. EM Luminous intensity of a lamp, in candles. _c.p_. Resistance of the armature. R_{a} Resistance of the magnet forming the field. R_{m} Resistance of the external circuit. R_{o} Intensity in the armature. C_{a} Intensity in the coils of the magnet. C_{m} Intensity in the external circuit. C_{e} Coefficient of self-induction. L_{s} Coefficient of mutual induction. L_{m}

A primary battery would be represented as in Fig. 1, and a battery of accumulators as in Fig. 2.

In order to designate incandescent lamps, circles would be used, and stars for arc lamps. A system of incandescent lamps arranged in multiple arc would be represented as in Fig. 3.

Fig. 4 and the formula

R = B + Gs/(G + s) + r

would serve for the total resistance, R, of an electric circuit, upon giving the letters the significations adopted.

Such is, in brief, the present state of the question. The scientific bodies that have taken hold of it have not as yet furnished a fully co-ordinated work on the subject. Let us hope, however, that we shall not have to wait long. The question is of as much interest to scientific men as to practical ones.

A collection of identical symbols would have the advantage of permitting us to abridge explanations in regard to the signification of terms used in mathematical formulas. A simple examination of a formula would suffice to teach us its contents without the aid of tiresome explanatory matter.

But in order that the language shall be precise, it will be necessary for the words always to represent precise ideas that are universally accepted, and for their sense not to depend upon the manner of understanding the idea according to their arrangement in the phrase.

Nothing can be more desirable than that the societies of electricians of all countries shall continue the study of these questions with the desire of coming to a common understanding through a mutual sacrifice of certain preferences and habitudes.--_E. Dieudonne, in La Lumiere Electrique_.

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IMPROVED MICROSCOPICAL SETTLING TUBE.

By F. VANDERPOEL, of Newark, New Jersey.

In the February number of this _Journal_ the writer described a new settling tube for urinary deposits which possessed several advantages over the old method with conical test-glass and pipette. For several reasons, however, the article was not illustrated, and it is for the purpose of elucidation by means of illustration, as well as to bring before the readers of the _Journal_ two new and improved forms of the tube, that space in these columns is again sought. The first two of the figures, 1 and 2, represent the tube as originally devised; 1 denoting the tube with movable cap secured to it by means of a rubber band, and 2 the tube with a ground glass cap and stop cock. The first departure from these forms is shown at 3, and consists of a conical tube, as before, but provided with a perforated stopper, the side opening in which communicates with a side tube. The perforation in the stopper, which is easily made by a glass blower, thus allows the overflow, when the stopper is inserted into the full tube, to pass into the side tube. The stopper is then turned so as to cut off the urine in the latter from that in the large tube, and the latter is thus made tight. After allowing it to remain at rest long enough to permit subsidence of all that will settle, the stopper is gently turned and a drop taken off the lower end upon a slide, to be examined at leisure with the microscope. The cap, ground and fitted upon the lower end, is put there as a precautionary measure, as will be seen farther on.

The tube shown at 4 is, we think, an improvement upon all of the foregoing, for upon it there is no side tube to break off, and everything is comprised in a small space. As will be seen by referring to the figure, there is a slight enlargement in the ground portion of the stopper end of the tube, this protuberance coming down about one-half the length of the stopper, which is solid and ground to fit perfectly. The lower half, however, is provided with a small longitudinal slit or groove, the lower end of which communicates with the interior of the tube, while the upper end just reaches the enlargement in the side of the latter. Thus in one position of the stopper there is a communication between the tube and the outer air, while in all other positions the tube is quite shut. In all these tubes care must be taken to fill them _completely_ with the urine, and to allow no bubbles of air to remain therein.

The first of these settling tubes was made without the ground cap on the lower end, the latter being inserted into a small test tube for safety. At the suggestion of Mr. J.L. Smith the test tube was made a part of the apparatus by fitting it (by grinding) upon the conical end, and in its present form it serves to protect the latter from dust and to prevent evaporation of the urine (or other liquid), and consequent deposition of salts, if, for any reason, the user should allow the tube to remain suspended for several days.

These tubes will be found very useful for collecting and concentrating into a small bulk the sediment contained in any liquid, whether it be composed of urinary deposits, diatoms in process of being cleaned, or any thing of like nature; and, as the parts are all of glass, the strongest acids may be used, excepting, of course, hydrofluoric acid, without harm to the tubes.--_American Microscopical Journal_.

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[Continued from SUPPLEMENT, No. 594, page 9491.]