two coatings of a charged pane, we shall find that there is a small amount of positive electricity on one side un-neutralised by induction, and therefore free. The amount of this depends on the thickness of the glass.

If then we hold the finger to this side, taking care that the other coating is insulated, we shall obtain a small spark from it. As soon as this has passed, a similar amount of negative electricity will be set free at the other side, and we can then draw a spark from that; in this way, we may continue drawing off the charge, drop by drop, as it were, tiil it is all gone. If a Leyden jar be placed on an insulating stand, we may discharge it in a similar way.

Two interesting experiments may be tried as illustrations of this-one with the pane, the other with the jar. Make two feet of gutta-percha, or some insulating material, so that the pane may stand vertically. Having charged it, take a piece of wire and place a pith-ball on each end; then bend it almost round, so that when it rests on the upper edge of the pane the balls may each be about an inch from the coating. The side on which the excess exists will first attract the ball nearest to it, and thus part with its excess of electricity; the other ball will then be attracted by the other side, and in this way the wire will rock backwards and forwards till the charge is dissipated. This is called the electric pendulum.

A

To show the same thing with a Leyden jar, we must fix a bell on the wire just below the ball. metal support, A (Fig. 16), carrying a similar bell at the same height, must be fixed on a stand, and connected with the outer coating of the jar by a piece of wire or tinfoil, B. The upper part of this support has a bent wire fixed to it, from which a small ball is suspended by a thread of silk. If now the jar be charged, this ball

will be alternately attracted and repelled by the bells, and thus will continue to ring them till the jar is discharged.

If a jar be charged, and allowed to stand, the electricity in it will be slowly dissipated, chiefly owing to the moisture in the air, which acts as an imperfect conductor. This may be partly obviated by coating the surface of the glass with shellac varnish, and thus hindering the deposit of damp which usually forms on it. When, however, it is desired to preserve a charge for any length of time, the construction of the jar is slightly altered. The rod is not fixed to the cap, but passes through a glass tube fixed in it to the bottom; and when the jar is charged, it may be inverted, and the rod allowed to fall out. When the charge is required, the rod must be carefully dropped in again. In doing this, however, it is advisable to take the precaution of placing it first upon some non-conducting substance. Theoretically, there is no limit to the size of the jar that may be employed. In practice, however, many inconveniences attach to the use of those which are very large. The tension of the electricity frequently becomes so great in them, that if there be a flaw or thin place in the glass it will pierce it; and if it be made thick, to guard against this danger, the induction is considerably weakened. The plan therefore adopted is to employ a number of small jars, and connect them together so as to form a battery. They are usually placed in a tray lined with metal, so as to connect their exterior coatings, and a wire is brought from this to one of the handles; the knobs are also connected together by wires passing through them. (Fig. 17.)

Various batteries of great size and power have thus been made at different times: for all ordinary purposes, however, from four to nine jars, holding about five or six pints each, will be amply sufficient.

It is important to be able to estimate with some degree of accuracy the intensity of the charge in a jar, and different means of attaining this end have been devised. The simplest is by means of the quadrant electrometer A (Fig. 17), which is shown on one of the knobs of the battery. It consists of a thick brass rod, surmounted by a knob, and bearing on one side a semi-circular graduated scale, usually made of bone or ivory. At the centre of this is suspended a thin wood rod, carrying & pith-ball on its further end. As the charge increases, this ball becomes more and more repelled, and the angle shown on the graduated arc increases, thereby giving a rough indication of the intensity of the charge. It must be remembered, however, that it is the intensity, and not the quantity, of the electricity that is indicated. If the same amount of electricity be distributed over jars or batteries having double the amount of coated surface, the electrometer will only show one-half the intensity. Still, the instrument is very useful, especially if it is made with

the rod somewhat smaller at the lower end, so that it will fit into the prime conductor or any other piece of apparatus. A better way of regulating the intensity of a shock is by means of Lane's discharging electrometer, which is represented in Fig. 18. It depends for its action on the fact that the distance through which a charge will dart between the balls, or, as it is called, the striking distance, is, for small charges, directly proportional to the intensity of the charge; that is, if double the amount of electricity be present on the same surface the striking distance will be twice as great.

This distance varies, too, inversely as the amount of surface over which the charge is distributed. Thus, if one jar has twice the surface of another, and the same amount of electricity be passed into each, the striking distance of the first will be only one-half that of the second. These results will easily be understood if we recollect that it is always intensity, and not quantity, that is shown; just as a thermometer shows the intensity and not the quantity of heat, for there clearly is a larger quantity in a gallon of water at the temperature of the body than in a cupful at the boiling-point, and yet the thermometer shows a much higher temperature if immersed in the latter.

The electrometer consists of a metal tube, A, which fits on to the rod of a jar or battery, and carries at one side a curved rod of glass, B. At the end of this is fixed a second tube, c, with a brass wire, terminated at one end in a ball, D, and at the other in a ring, passing through it. When this is attached to a jar, the ball D may be brought within any desired distance of the knob, and a chain is then attached to the ring and connected with the outside. When the jar is sufficiently charged, the electricity darts between the balls and discharges it. If it be desired to pass this shock through the body, or through any substance, the two sides of it are connected by brass chain or wire with the ring and outer coating respectively, and the shock passes as before.

There are one or two other forms of discharging electrometer which are sometimes used, and which depend on the attraction of the knob of the jar for a balanced metal rod. We need not, however, stop to explain them here.

In all these the shock is given as soon as the necessary charge is communicated; this is sometimes rather a disadvantage, and may be obviated by the use of a unit jar, which consists of a small Leyden jar exposing about six inches of coated surface on each side. This is supported on an insulating stand, so that its exterior is in contact with the knob of the jar to be charged. A rod and ball are also connected with its outside coating, and brought within striking distance of its inner rod. The jar is now brought to the conductor of the machine, and as it becomes filled a corresponding amount of electricity passes from its exterior into the large jar. This continues till the unit jar is fully charged, when it discharges itself, and the same process is repeated. In this way, by counting the number of discharges of the small jar, we ascertain the number of units of electricity contained in the large

one.

As we now clearly understand the construction and action of the Leyden jar and battery, we may notice some of the effects produced by the electric shock. We will look at the physiological effects; and the first which we observe is the peculiar sensation experienced when the charge is allowed to pass through the body. The sensation varies, of course, with the intensity of the shock, and is most strongly felt at the elbows and across the breast. If the shock of a large battery be taken dangerous results may ensue, especially if

the electric fluid pass through any vital portion; but with ordinary charges no ill effects whatever seem to be produced; in some cases it even appears to be beneficial. The effect of a very strong charge is seen when a person is struck by lightning, death being frequently caused by it. The action appears to be

mainly on the nervous system. If we pass the shock through small animals, such as birds or mice, they will be killed instantaneously, and larger animals have been killed by shocks from powerful batteries. There is, however, nothing further to be learnt by these experiments, and it is therefore cruel and needless to repeat them.

The electric fluid, in its passage through living or dead bodies, also causes convulsive contractions of the muscles. Its physiological effects will, however, be seen much more clearly when we come to treat of Voltaic Electricity, and we may therefore leave further notice of the matter till then

In studying the effects produced by electricity, we need some method of conveniently holding an object while the shock is passed through it, and this is afforded us by a very useful piece of apparatus, known as Henley's Universal Discharger. The construction and mode of using this will be understood by

reference to Fig. 19, which represents the charge from a battery being passed through a bird by means of this discharger.

A piece of hard wood is taken, about twenty inches long and six inches wide, and in the middle of it there is fixed a small table, which can be adjusted at a convenient height by means of a thumb-screw. The top of this table is usually made of a disc of glass fixed on by shellac, or else it has a strip of ivory inlaid across it. At each end of the board is fixed a glass rod, carrying at the top a revolving cap fitted with a compass joint, so that the wire passing through it may be inclined at any angle. The wires can also be slipped backwards or forwards, so that they may easily

insulating handle, as the electricity always chooses the best conductors, and if there be any distance between the knobs, or if a badly conducting substance be interposed, the electricity may travel through the body of the operator to the ground instead of passing through the discharger

The next class of effects we notice are the luminous. As already seen, whenever the spark traverses air a line of light is seen; when the two electricities from the opposite sides of a jar unite, the spark is much more luminous, being thicker and denser, because of the passage of a much greater amount of the fluid. This spark is almost instantaneous, so that if a dark room be suddenly illuminated by it, a rapidly revolving wheel in it will appear to be at rest. So instantaneous is it, that a printed bill has been fixed on to a wheel, and made to revolve several hundred times per minute, and yet a distinct photograph of it has been taken by means of the light from

the spark, the time required for its passage being so short that the light has faded before the wheel has moved through an appreciable space.

If the points be made nearly to touch, and the thumb pressed down upon them, it will appear to be rendered semitransparent, and the shock will not be felt. In a similar way the shock may be passed through eggs, oranges, etc., illuminating them. Some substances, too, remain luminous for some time after the charge has passed through them.

If we fix a ball to the plate of an air-pump, and connect it with the exterior of a jar, and then place over it an open receiver with a similar ball and rod passing air-tight through a plate at its upper end, we shall find that the spark will pass a much greater distance. In a long exhausted tube it will sometimes appear to dart along like a ball of light.

Similarly, if we exhaust a large globe having a wire and ball fixed tightly in each end, and connect the upper one B (Fig. 20) with the prime conductor, we shall find that, instead of the electricity passing along in a series of thin sparks, it will spread out and form a large faintly luminous space, having a violet tinge. On again gradually admitting the air by means of the stopcock, this space will grow smaller and smaller, till at last the narrow but bright sparks pass as before. Many similar experiments of great beauty may be performed by means of voltaic electricity, and it is believed that th beautiful phenomena of the aurora borealis, or northern lights, so frequently seen in high latitudes, may be attributed to a similar cause.

LESSONS IN ALGEBRA.-XXII.
SIMPLE EQUATIONS.

TWO UNKNOWN QUANTITIES.

IN our former Lessons on Simple Equations we gave the rules for solving those which contain only one unknown quantity; and, with the exception of one or two, the whole Centenary of Problems were solved by means of these rules. We proceed now to show how to resolve equations which contain two unknown quantities.

Cases indeed frequently occur in which two unknown quantities are necessarily introduced into the same calculation. EXAMPLE. Suppose the following equations are given, viz. :

Lastly, by substituting the value of y in the 1st equation, we have x+6=14; and x = 8. Therefore, 8 and 6 are the values of x and y.

In solving the preceding problem, it will be observed that we first found the value of the unknown quantity a in each equation; and then, by making one of the expressions denoting the value of xr equal to the other, we formed a new equation, which contained only the other unknown quantity y. This process is called extermination or elimination.

In the resolution of equations there are three methods of extermination, viz., by comparison, by substitution, and by addition and subtraction.

CASE I.-To exterminate one of the two unknown quantities by comparison.

RULE. Find the value of one of the unknown quantities in each of the equations, and form a new equation by making one of these values equal to the other. Find the value of the unknown quantity in this equation, by the rules formerly given. Then substitute this value of the one unknown quantity in either of the other equations, and resolving it by the same rules, the other unknown quantity will be found.

EXAMPLE.-Given x + y = 36, and values of x and y.

y=

12; to find the

h-d h2 + d

2h

2h

=

EXAMPLE (3). Given ax + by h, and x + y = d; to find the values of x and y.

Here, from the first equation, we have, by transposition,
ake= = h—by,
h-by

And a=

Again, from the second equation, we have, by transposition,

The rule given above may be generally applied for the exter mination of unknown quantities. But there are cases in which other methods will be found more expeditious.

=

EXAMPLE (4). Given hy, and ax + bx = y; to find the values of x and y.

As in the first of these equations is equal to hy, we may in the second equation substitute this value of x for itself. The second equation will then become, ahy + bhy = y2.

The equality of the two sides is not affected by this altera tion, because we only change one quantity z for another which is equal to it. By this means we obtain an equation which