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discharge within the allowable limits, i.e. down to the point where
each cell gives 1.85V. This affords an opportunity for another
illustration of the working of Ohm's Law. Suppose that the owner
desires to buy a small generator for charging these cells. Now the
pressure of the three cells, as stated above, is 6V, and this pressure
is a 'back E.M.F.' in direct opposition to the pressure of the generator.
If therefore the latter were incapable of a greater pressure than 6V
the two pressures would exactly balance, and no current would
flow. In point of fact the generator pressure would, towards the
end of the charging process, have to rise nearly to 9V in order to
force 4A through the cells. There is no contradiction of Ohm's Law
here; the effective pressure E is in this case the difference between
the two opposing pressures of generator and cells, and it must be
sufficient to overcome the resistance R made up of the internal
resistance of the cells and the external resistance of the circuit.
Returning, after this digression, to the consideration of ampere-
hours, let us assume that the applied pressure in any particular case
is sufficient to overcome the opposing pressure of the cell or plating
bath, etc., so that a current will flow through the latter; the total
electro-chemical effect of this current then depends on the number
of ampere-hours. For example, the international definition of an
ampere, already referred to in § 1, states that under the conditions
laid down it will deposit silver from silver nitrate at the rate of
0·001 118 of a gramme per second, or 4·024 8 grammes per hour.
term ampere-hour is the practical unit of quantity of electricity.

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21. Electro-chemical Equivalent. The weight of a metal electrically deposited from a solution per ampere-second or coulomb is called the 'electro-chemical equivalent' of the metal. The value of this function is constant for any particular substance, but different elements have widely different electro-chemical equivalents.' Hydrogen has a chemical equivalent of 1 and an electro-chemical equivalent of 0.000 010 38 gramme or 0.010 38 mg. per amperesecond. The weight in milligrammes of any other element liberated per ampere-second from a solution or 'electrolyte' will be found by multiplying the figure 0·010 38 by the chemical equivalent, or combining weight, of the element. The chemical equivalent is generally, but not in all cases, the atomic weight divided by the valency. Thus in the case of silver, which is univalent and has an atomic weight of 107-67, the chemical equivalent is also 107-67. The electro-chemical equivalent will therefore be 0.001 118 gramme or

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1.118 mg. per ampere-second or coulomb. The following table gives the value of these functions for a number of elements :

TABLE 2.- Electro-chemical Equivalents.

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In the case of any particular element the quantity decomposed from its solution per second is proportional to the current.

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22. Permanent and Electro Magnets. The familiar horseshoe' magnet is constructed of hardened steel, and when once magnetised retains its power of attracting iron or steel more or less indefinitely. It is used in certain classes of electrical measuring instruments and in' magneto' generators, etc. Annealed iron, on the other hand, is incapable of retaining magnetism, although it can be very powerfully magnetised by suitable means involving the expenditure of power. If a number of turns of insulated wire are wound round a soft iron

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core, and a current is then passed through this magnetising coil' the core becomes strongly magnetic for so long as the current is flowing. By varying the intensity of current the strength of the magnetism can be altered; in the case of alternating current the magnetism is constantly altering (§ 23). When the current ceases the magnetism almost entirely disappears. Into the elements of magnetism it is not necessary to go, as this knowledge is assumed ; it must however be pointed out that a magnet must necessarily always have a north-seeking pole and a south-seeking pole, whatever its shape or construction. If it is an electro-magnet the relation between the polarity and direction of the magnetising current is fixed, and will be seen at once from fig. 1, from Professor Thompson's Elementary Lessons. It matters nothing whether the turns are wound right or left-handed, or what the shape of the iron core is.

N

Fig. 1.-Polarity of electro-magnet.

The arrows show the direction of the current, from to, or positive to negative.

A wire, whether straight or bent into a loop, always creates a magnetic field around it when it is carrying a current, and an iron core serves to augment the strength of this magnetic field. In considering the field created by a wire Maxwell's 'corkscrew rule' is useful, and it will be found to apply to the conditions shown in fig. 1. The rule runs: The direction of the current (from + to --) and that of the resulting magnetic force (from N. to S.) are related to one another as are the rotation and forward travel of an ordinary right-handed corkscrew. An alternative means of memorising the relationship between polarity and direction of current circulation is provided by the fact that arrow-heads (directed outwards) on the tails of the letters N. and S. indicate the direction of current rotation producing north and south polarity respectively.

This magnetic effect in conductors is by no means negligible. A case cited in § 480 shows that it may have serious effects on overhead lines, and it frequently gives rise to errors in electrical instruments placed too near switchboard conductors carrying heavy currents.

It also causes the apparent rise of resistance known as skin effect (§ 400), which is most marked in steel conductor rails on electric railways.

The direction of a current is a matter of convention, for the work of the engineer is not seriously affected by the truth or otherwise of the modern electronic theory of matter, and it matters little to him whether there is an actual transfer of corpuscles or merely a molecular or ultra-molecular vibration around the conductor. The adopted convention arose from the consideration of the primary cell, and is explained in that relation in § 43. The positive pole of any other generator is taken to be that which behaves in the same way as the positive pole of a battery. Since the current in any conductor produces a magnetic field, it will, like any other magnet, deflect a compass needle to one side or the other according to its polarity. This property enables the conventional direction to be determined by Ampère's rule, viz.: Suppose a man swimming in the wire with the current, and that he turns so as to face the needle, then the North-seeking pole of the needle will be deflected towards his left hand. A useful old mnemonic in this connection is Crompton's SNOW rule; viz.: Place a compass needle under a wire placed in the meridian, and the current entering at South turns the North-seeking pole of the needle Over to West.

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Apart from the use of electro-magnets in dynamo-electric machinery and instruments, they are also used extensively for their direct effect in attracting iron or other paramagnetic metals; the practical applications vary from lifting magnets, for raising girders and the like, whether on land or below water, to the extraction of splinters from the human body. Until recently the latter use was mainly confined to the oculist, but of late giant electro-magnets, taking several kilowatts, have been used in hospitals for extracting shell splinters and ferro-nickel cased bullets. While iron and steel are by far the most important, there are other metals, especially nickel and cobalt, which are paramagnetic in a less degree; substances which are repelled from a magnet are called diamagnetic, and include bismuth, antimony, and many others.

With modern lifting. magnets it is possible to hold as much as 5 lbs. weight per watt of energy. The smaller sizes are capable of carrying twenty times their own weight; medium sizes up to about 3 feet diameter, ten times their own weight; and large sizes of 5 feet diameter, from five to seven times their own weight.

When lifting

scrap metal, about 10 per cent. of these solid weights can be raised. For special applications, such as plates and rails, batteries of several large magnets are employed. Hot steel ingots can be raised if the temperature does not exceed 700°F, above which their magnetic properties diminish rapidly. Above 1 100° or 1 200°F, iron and steel become practically non-magnetic.

23. Hysteresis. If the magnetising current is alternating (§ 54), then the core is alternately magnetised in one direction, demagnetised on the reversal of the current wave, and then magnetised in the opposite direction. These cycles continue so long as the current is maintained, and have the same periodicity as the current, i.e. generally 50 cycles per second (§ 55); but the magnetic changes lag slightly behind the current reversals. The abrupt reversal of the direction of the magnetism, involving a change in the molecular arrangement of the iron, involves also a certain expenditure of power known as the hysteresis watts.' The energy so wasted is proportional to the frequency, and heats up the iron core. Such losses occur in transformers and all alternating current machinery, and to a lesser degree in continuous current machines (see § 469 for transformer losses).

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24. Ampere-Turns. In any form of apparatus using electromagnets the phrase 'ampere-turns' is used for the product of the current in amperes and the number of complete convolutions or turns of the wire carrying it. This is the practical unit of magneto-motive force. The magnetising effect (up to a certain limit) depends on the number of ampere-turns; thus 100 turns of a wire carrying 1A will have the same magnetising effect on a bar of iron within the coil as a single turn carrying 100A; in each case there are 100 ampereturns. This holds good until the iron is approaching magnetic saturation.' In the case of a solenoid or a coil of wire without any magnetic core, the strength of the field produced is proportional to the current, i.e. to the number of ampere-turns, without any limit; but when an iron core is inserted in the coil this proportionality drops as the core becomes incapable of further saturation, until at last the increase is only that due to the coil alone. Thus according to the requirements of each case an electro-magnet may be designed to work either saturated, or approaching saturation, or at a point where the change in the current produces the maximum change in the field strength.

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