312

We do not hesitate to say that the declarations made in good faith to the Council are, for all that, contrary to the truth, and we address ourselves to you, M. le Président, to protest in the most formal manner against the wording of the famous note sent to the Director of Works. Here are the facts in their scrupulous exactitude:

We had been officially convoked by the Commission of the Halles Centrales to make experiments on August 6th at MM. Weyher and Richemond, at 9 o'clock in the morning precisely. We declare here that, having waited up till noon, not a single member of the Municipal Council presented himself. There were, therefore, no official experiments with our dynamo. It appears to be necessary to attribute the cause to the Syndic, who forgot to send carriages to the members of the commission. On the 6th we went to MM. Potier, Carpentier, and Hospitalier, apprising them of the situation; and as MM. Weyher and Richemond had themselves some experiments to make, we informed these gentlemen that we could no longer trespass on their kindness, having awaited five weeks the decision of the Council. On this declaration, MM. Potier and Carpentier decided to come the next day, August 7th, in the afternoon. We forthwith telegraphed to all the members of the commission, informing them that we should be at their service on the 7th, from 9 o'clock in the morning. M. Dumay alone came. We worked from 9 in the morning till 12.15, then from 1.50 till 5.50 in the evening; or seven hours and not two, as stated in the note sent to M. Alphand. MM. Potier and Carpentier came at 2. On the 8th the measuring apparatus was taken to M. Carpentier to be calibrated. On the 9th, the diagrams of the steam engine were sent to M. Potier. On the 12th, M. Potier caused us to be asked by M. Lafargue for the constant quantities of the exciter. Finally, we may state that, on the 14th, no report had been lodged by the eminent professors who much wished to be present at our experiments. This is, M. le President, the absolute truth. Is it possible to admit that on the 10th such an irregular declaration could have been made? The machine constructed for 170,000 watts and not for 220,000, could only be worked by an engine of 150 horse-power, kindly placed at our disposal by MM. Weyher and Richemond.

No one is ignorant of the fact, and the Administration less than others, we are pleased to believe, that about 400 horse-power of steam is necessary to produce 220,000 watts. Our experiments proved that the dynamo produced 83,000 watts and not 60,000, that is to say, the maximum the steam engine was capable of. Further on, it is stated that the Ferranti machines, already bought moreover, were made by Cail. Now, according to information, no machine has been made at the Cail factory.

It

As regards the Ferranti transformers, the matter is still more grave. The only transformer which can legally work in France is that of M. Lucien Gaulard, who died at St. Anne, overcome with bitterness and chagrin, which ended by disturbing his reason. would really seem that the death of this man of genius was not sufficient to disarm the hatred of his enemies and spoliators. The Municipal Council will doubtless require some light to be thrown on this subject. During a night surprise on December 30th, 1888, the Ferranti tender was passed. The next day, the 31st, MM. Paulard, Dumay, Joffrin, Faillet, Patenne, &c., protested in the name of French interests. On the declaration of M. Alphand, that no dynamo had been purchased, the Council decided that the preference should be given to French trade.

Confiding in this vote and declaration, we did not fear to enter into considerable expense, and our experimental machine, though weak through hurry, is superior in yield to all the other machines of the same nature, and costs much less, 24,000 frs., instead of 33,000 frs. asked by Mr. Ferranti. On August 10th, 1889, it was declared that Ferranti machines had been purchased long since. If that fact be true, what becomes of the vote of the Council, of which we speak above, and its laudable determination to give preference

[SEPTEMBER 20, 1889.

to French industry? Where are the particulars of the yield of the Ferranti machine to be found? Who was present at these experiments? Are experiments simply imposed on Frenchmen? and are foreigners exempt therefrom? The surprise of December 30th, 1888, failed; that of August 10th, 1889, has succeeded.

Thus, in defiance of a deliberation and a vote of the Council, orders were given to a foreigner, and in order to excuse itself it has been declared that our dynamo machine is bad, and that without a regular report from the commission nominated for that purpose, on a simple vote, the author of which it would be interesting to know, as it would be interesting to seek the names of the influential personages who so energetically upheld the interests of the Ferranti firm. A singular way to favour national industries! In the People's House, from the top of the Municipal tribune, we have been awarded a brevet of incapacity, we, the founders of the first central electrical station in France (Tours, 1885), one ruins us, one pays dearer, but, en revanche, one licenses publicly counterfeit to the benefit of foreigners, who take from us at one and the same time our labour and our industrial honour. That is, M. le Président-the result of the sitting of August 10th.

We therefore declare to you, Monsieur le Président, that in the name of French industry, that in the name of our poor and regretted friend, Gaulard, that in the name of right and justice, we are decided to fight to the end. We shall seize the Ferranti apparatus, we shall deliver public lectures, we shall invite all those interested, all French workmen, and shall defy the author of the famous note, which has surprised the good faith of the Director of Works, to dare, in public, to uphold the declaration made to the Municipal Council. Still, before going to such extremities, we address this appeal to the equity of the Municipal Council, to the well known fairness of its president. We will, therefore, still hope that this denial of justice will not be allowed to be carried out; this denial of justice which may to-morrow, under other forms, attack the whole French industry.

It is in this hope that we have the honour to be, Monsieur le Président, yours, &c.,

DANDEU and NAZE.

This is a very pretty quarrel as it stands, and now the next move is eagerly awaited from the other side.

ELECTRIC LIGHTING AT HOVE.

A SPECIAL meeting of the Hove Commissioners was held last week, to consider the advisability of applying to the Board of Trade for a Provisional Order under, and in accordance with, the Electric Lighting Acts, 1882 and 1888, to authorise the supply of electricity, by the Commissioners, for public and private purposes within the town of Hove. Mr. Woodruff moved that the Town Clerk be instructed to apply for a Provisional Order. He reminded the members that after what was said at the recent inquiry held upon the subject at Brighton, they were virtually pledged to do something in the matter. He thought that the House to House Electricity Company, and the Local Electric Light Company ought not to be allowed to obtain the necessary authority to supply electricity to the people of Hove. He knew that the London promoters of the House to House Electricity Company had organised, he believed, some twenty companies in the Metropolitan district, and ten or eleven subsidiary companies. Those companies had applied to the Board of Trade for electric lighting powers the same as they had asked for at Hove in no less than 224 districts. He contended that such a speculative Company was not likely to give satis faction in lighting their town. The electric light was rapidly advancing, and was within measureable distance of becoming financially successful, and in apply ing for a Provisional Order they were only doing what

SEPTEMBER 20, 1889.]

many towns had done before them. This year a total number of 480 applications for electric lighting powers had been made to the Board of Trade, and out of that number 40 had been applied for by local authorities. He should not say that it would be advisable for the Commissioners to supply the electric light. What they wanted to do was to obtain the Order and hand it over to some safe and reliable Company on terms advantageous to the ratepayers of Hove. The motion was

duly seconded, and General Sir C. Shute expressed a hope that if the Order were obtained it would not be made an excuse to delay giving the town the benefit of the electric light. Hove had about the worst and most expensive gas supply in the United Kingdom, and he thought there was no place better adapted for the electric light. The motion was carried.

313

gas, but in a large installation, such as one of 2,000 lights, electricity would be cheaper than gas. He firmly believed that before many years had passed electricity would be employed for both lighting and domestic purposes. True it was that millions every year were realised out of the by-products of gas making, and many scientific engineers believed the gas engine to be the engine of the future. Gas would be produced much cheaper and better in years to come, and both that and petroleum would make very good illuminants, yet he still thought they could look forward to the time when their dwellings would be warmed, ventilated and illuminated by electricity.

ELECTRIC LIGHT POSTS AND WIRES AT EXETER.

AT the last meeting of the Exeter Town Council Mr. Yelland asked the Borough Surveyor whether he did not consider that the electric light posts were in many instances erected too close to the buildings. In some cases they were but a few inches from the houses. Mr. Dunn moved that the Town Clerk be requested to make the necessary inquires in order that the Council might be satisfied as to the legality, or otherwise, of the present position of the electric light posts and wires. The motion having been seconded the Town Clerk said the Council must remember that the Exeter Electric Light Company was not a company working under a provisional order. The Surveyor said that the wires were very close to the windows in some instances, but that could not be well avoided. Mr. Alderman Daw asked whether the Surveyor knew that there were regulations passed by the Board of Trade to the effect that electric light wires should not be within six feet of any buildings. The Surveyor said he knew regulations were in force in London to that effect, but he did not know whether they applied to Exeter. The Council granted permission for the erection of posts, and no conditions were laid down. He thought the public in general might rest assured that the best thing in the matter had been done. However, no permission had been given for the construction of the so-called supports to the posts. Instead of supporting the posts they were doing the opposite thing. Communication was made by means of two wires to each house from the main wires and would run over the pathway. Dunn's motion, after further discussion, was then put and carried. Mr. Dunn gave notice that at the next meeting of the Council, as the Urban Sanitary Authority, he would move that notice be given to the Exeter Electric Light Company to determine the permission given them to erect electric light posts in the public streets at the earliest possible date.

Mr.

LONG-DISTANCE TELEPHONY IN NORTHERN EUROPE.

The Telephone Line between Stockholm and Gothenburg.

THE Construction of this line, which is 285 miles long, has lately been completed. It consists of four wires -two and two combined-in two separate circuits, and simultaneously available for conversation. The diameter of the wire forming the one circuit is 3 mm., and of the other 2 mm.; both are made of hard drawn copper wire, with a conductivity of 95 to 98 per cent. of that of pure copper. The wires are suspended on the same poles as the telegraph wires, and they follow the track of the railway. The metallic circuit formed by the wires, which are well insulated and nowhere in connection with the earth, is the means of excluding the sounds produced by currents passing through the earth and also atmospheric disturbances, and as regards the disturbances caused by induction from other wires on the same poles these have been entirely eliminated by continuous twisting of the wires round each other, so that they maintain the same mean average equality of distance between themselves and the disturbing wires. The currents in the latter will induce impulses of equal strength in each branch of the telephone circuits, and these impulses being in opposite directions (for the one wire is used for going and the other for returning) will neutralise each other perfectly, and the result is that no sound is produced in the telephones.

In practice, this arrangement of the wires was effected by placing the four telephone wires so that the supporting points on each pole form a square, and by putting the wires, which belong to one circuit, in the diagonally opposite corners of the square. If the two thick (3 mm.) wires be marked with 1 and 3, and the two smaller (2 mm.) ones with 2 and 4, the following will represent the relative positions of these wires on five consecutive poles, viz. :—

ƒ1-2

DOMESTIC LIGHTING.

AT the Royal Cornwall Polytechnic Society last week, Prof. Lambert, of the Royal Naval College, Greenwich, in the course of his lecture on "Domestic Lighting spoke of the necessity of abundant ventilation where gas was burnt. He explained that one ordinary gas burner vitiated the air quite as much as five persons, and a small gas stove as much as 20. He did not consider that water gas-would play any part in the future for illuminating purposes, but that it would be largely used in manufactories. With ordinary care petroleum. was a good illuminant and twice as cheap as gas.

Electricity was undoubtedly the light of the future, but in small installations he did not think it was likely to supersede gas or petroleum. The expenses attending a 30-lamp installation would be £81, against £38 for

On the fifth pole

14-3, or as on the first pole. The method adopted on the Stockholm-Gothenburg telephone line is, in short, exactly the same as that which for the last eight years or more has been in use by the General Post Office with so much success, and which was first proposed by Prof. Hughes and afterwards carried out practically by Mr. Moseley near Manchester.

The instruments at work on these telephone circuits are those of the firm L. M. Ericsson & Co., of Stockholm, whose microphone transmitters are well known, and which were described in the ELECTRICAL REVIEW of August 3rd, 1888. P. C. D.

September 14th, 1889.

314

THE BRITISH ASSOCIATION.

THE DESIGN OF TRANSFORMERS. Paper read before Section G of the British Association, September 16th, 1889.

By JAS. SWInburne.

So much has been already said on the design of transformers, and so many calculations have been made, and so many formulæ given, that it would seem at first sight as if there was little that could be added.

The greatest change that has taken place recently in the practice of transformer design has been the substitution of a continuous iron core interlinked with the copper coils, for a straight core with wires wound on it, as in the Ruhmkorff coil, and the secondary generators of MM. Gaulard and Gibbs. The idea in making this change is that the continuous iron core needs fewer current turns to produce a given induction, and this is generally considered to be of the first importance. With the object of getting the necessary excitation as small as possible, makers give the iron core as large a cross-section and as short a length as possible; and the tendency of designers is to increase the iron and diminish the copper of their transformers. The question of loss of power in heating of the cores does not appear to receive enough attention, and the object of this paper is to point out that many common designs produce very inefficient transformers, and that in many cases a particular form of "open circuit" transformer is the best.

If a transformer, with a full load output of 1,000 watts has a loss of 50 watts in the copper and 150 in the iron, its full load efficiency is 83.5 per cent. But suppose it is put in a house wired for, say, 17 lamps, the full load is on only very occasionally; about half the lamps being the usual maximum. Some authorities take it that the average is equal to all the lamps on one hour a day; others say three or even five hours a day. If the full load is on two hours a day, and the transformer stands idle, merely keeping its iron hot all the rest of the time, its average efficiency is only 35 per cent. Many will at once say that the loss of 150 watts in a 1,000-watt transformer is absurd, and that modern transformers work at something like 98 per cent. full load efficiency. The figures generally given by makers are so obviously impossible, that one is driven to conclude that the loss in iron is not measured.

As a matter of fact, the measurement of this loss is no easy matter. Before bringing forward a paper like this, it might be said that I ought to produce a number of accurate data, giving the loss at various inductions, at various frequencies. Unfortunately, I cannot do so. We must, therefore, rest content with Prof. Ewing's determination of the curve of a single specimen of iron magnetised very slowly. No doubt it is perfectly accurate, but we want a great many curves taken with different samples of commercial iron, and perhaps different frequencies.

It is commonly assumed that a low induction should be used in transformers, because the heat lost per c.c. of iron per cycle is then less; but it is forgotten that more iron is then needed. The volume of iron needed does not vary inversely as the induction, it increases quicker, as the iron is bent round the wire coils. The copper coils have also to surround more iron if its section is increased, and this entails more loss over resistance. On the other hand, the loss per c.c. of iron increases more quickly than the induction, but not much more quickly, so that it may often be advisable to use a high induction.

Before going farther, it will be well to explain some of the terms used in this paper. The square root of the mean square of the electromotive force is called the virtual electromotive force; so that an electrometer or non-inductive voltmeter measures the virtual electromotive force. The square root of the mean square of the current, or the current as measured by a dynamometer, is called the virtual current. Thus the product of the virtual electromotive force and virtual current on a non-inductive resistance give the real power, and so on. Roughly speaking, the virtual current and electromotive force may be taken as 10 per cent. greater than the mean electromotive force. Similarly, the virtual induction is measured by the virtual electromotive force it produces. The mean induction need never be considered, as the question of heating depends on the maximum induction. The virtual induction is thus a maximum of about 10 per cent. less than would be necessary to give the corresponding mean electromotive force. The maximum induction again depends on the maximum excitation, and not on the mean excitation. To get a maximum induction of 1 needs a maximum current of 1; it needs a mean current of about or

1

2

π

64, or a virtual current of about or about 7. But a maximum induction of 1 is equal to a virtual induction of about 1.1, so that a virtual induction of 1 needs a virtual exciting current of about 64. As an example, suppose a long core of one centimetre cross-section wound with wire; and suppose with a direct current one ampère per centimetre produced an induction of 10,000. If the direction of magnetisation alternated perfectly uniformly at a frequency of 2,500 per second, it would induce one volt per turn of wire round it. But if the magnetisation does not increase and decrease perfectly uniformly, the mean electromotive force will

[SEPTEMBER 20, 1889.

remain one volt per turn, but the virtual electromotive force will be greater. Take now the case of an alternating current, and find what virtual exciting current will be needed to induce one virtual volt per turn at a frequency of 2,500. The virtual induc tion needed will be 9,000. This will need a maximum exciting current of 9, or a mean current of 9 x 64, or a virtual current of .9 x 7, or of '64. If the direct exciting current of 1 lost 1 watt in a given length of wire, the corresponding alternating current will lose only about 4, or less than half.

In making calculations to find the proportions which give highest efficiency it is clear that the interlinked coils must be as in the figure, in which the single link may be either the

FIG. 1.

copper or the iron. If the cross sectional area of the single link is equal to that of the pair, the pair will have less volume. If the waste of power per cubic centimetre of iron is greater than that of the copper, the wire will take the form of the pair of links, and the single link will be the copper wire. To get the best result the cross-section of the coil and core will be very nearly, but not quite, square. In the following calculations they have been assumed to be square, which can make no perceptible difference in the efficiency, and makes the calculations easier by removing two variables. The problem now proposed is: Given the desired output of the transformer, to design it to give the highest efficiency. Call the side of the section of the iron core a, and the side of the section of the copper core z. All the other dimensions of the transformer depend on x and z. We now have to find the loss in the transformer in terms of known quantities and of x and z, and have then to choose ≈ and z so as to make this loss as small as possible.

The waste in the iron core is equal to the waste per cubic centimetre of iron multiplied by the volume of the iron. Call the loss per cubic centimetre at the induction and frequency under consideration, l. Then

Power spent in core = 1 x2 (4 z+2x)

The loss in a cubic centimetre of copper varies as the square of the current density. The most economical current density ought, properly speaking, to be determined by taking the current density as a variable; but it is generally so high that the coils would get hot. At first sight it may seem strange that a piece of apparatus that gets hot can be more efficient than one that keeps cool; but it must be remembered that the temperature depends on the facility for dissipating the heat, and a large transformer can lose more heat by radiation and convection than a small one, and can thus keep cool, though less efficient. Similarly a dynamo that gets hot is not necessarily inefficient. Heating is inadmissible on the score of durability and safety, so a current density must be assumed that will not cause excessive rise of temperature. The current density can generally be settled beforehand, as the size of the coils will be roughly known, and a safe density can be taken. If the loss per cubic centimetre of copper, with a current density of 1 ampère per square centimetre, is called p, the loss per cubie centimetre of copper is p d2, d being the density in ampères per square cm. As the output is known, and the current density is assumed, and the thickness of insulation is also known, the proportion of copper to the whole volume of the coil is known. Call this k.

The loss in the copper is then k z2 p d2 (4 x + 4), so the total loss in the transformer is

41 x2 + 21 æ3 + 4 k p d2 x z2 + 4 k p d2 x3.

In this expression the extra loss of power due to the magnetising current in the primary coil is neglected, as it is exceedingly small. The magnetising current is itself small, and differs in phase, roughly, a quarter of a period. Thus, if the magnetising current were even 10 per cent. of the full load current, the full load loss in copper would only be about 1 per cent. more than here allowed. If B is the virtual induction in the core, and n the vibrations per second, 4 B, n x 10-8 2 is the electromotive force per turn of primary or of secondary wire. The total electromotive force is 4 By n x2 x 10-8 multiplied by the number of turns in the primary or secondary coil. The output of both coils, or twice the output of the transformer, or 2 P = 4 Br n z2 x 10→ multiplied by the ampère turns in both coils. The ampere turns = k d z2, so that

This can be solved as a cubic equation for each transformer wanted, or by trial. In practical work an exact solution of such an equation is not required, as any dimensions that even approximately fit the equation give sensibly the same efficiency. Thus a can be made a round number of millimetres, or of eighths of an inch. If a complete table of transformers is wanted it may be shorter to make a finite difference table increasing a2, the crosssectional area of the core by jumps of, say, two square centimetres. Or the table may be calculated directly with the aid of a slide rule. In practical work a great deal of time may be wasted, not on legitimate calculations, but on work containing clerical errors, and on trying to find out the mistakes and to see how they got there. Any one who is an inaccurate worker may therefore prefer to make a table in such a way that if the last term is right all the rest must be right too.

A complete set of closed circuit transformers was designed by me for Messrs. Crompton & Co., the waste in copper and in iron, and the cost of material and the efficiencies under various circumstances being worked out. In this case the loss in iron was assumed to be about half as much again as in this paper, as that seemed a fair margin for practical work, though it might not be assumed for argumentative purposes. Most of them were calculated for a frequency of only 33 per second; as I found that led to great saving in the manufacture of the dynamo, and led to small extra cost and loss of efficiency in the transformers, some of these tables may be shortly discussed before going farther. The induction is taken at 14,000, and the loss is taken at 14,600 ergs per c.c. per cycle, or '024 joules per cubic inch.

The tables were calculated with the object of being useful, so the dimensions are in inches; as in practice one always uses inches. When one's sole object is the advancement of science of course he rises to centimetres.

In Table I., the first column gives the number of 60-watt lamps. The second and third give the diameter or size of wire in inches in the primary and secondary coils. The dagger means that the wire is square. The fourth and fifth give k and b, which are mere coefficients as before. The column gives the side of the core, and z the side of the coil in inches. The next columns give the loss of power in watts. The cost of material in the last columns is in shillings, taking iron at 3d. and copper at 9d. a pound. Table I. is calculated for transformers on full load the whole 24 hours.

It must be borne in mind that these tables do not give sizes for actual transformers, but act as guides to give the dimensions that should be approached. For instance, the sizes of wires given are no particular wire gauge, and no room is left for cheeks or formers for the coils. The secondary wires would not fall into whole numbers of layers.

Table II. is calculated for 16 hours a day. That is to say, the transformer is supposed to have the secondary open a third of the time. The transformers have then to be re-designed, as the loss in iron becomes relatively more important. It will be noticed that the efficiency begins to fall off and the price to go up. If transformers from Table I. were used only 16 hours a day, the efficiencies would be lower than those in Table II. Tables III. to VI. need no further explanation. It is well to point out that a great deal depends on the way the time is estimated. Full load one hour a day is not the same as half load two hours a day. Half load two hours a day would have less copper waste, so to make the best transformer the copper would be increased and the iron lessened. These last transformers are really absurdities; the 50 lights in Table VI. has an average efficiency of only 60 per cent. and costs about £20 for material only. The E.M.F. has so far been assumed to depend only on the induction in the iron core, but when the core is so small and the coils are so large, this is no longer even approximately true, as will be explained later.

Table VII. is to show what may be gained by transforming from 1,000 to 50 volts instead of from 2,000 to 100. The difference is due to the difference of room taken up by the insulation. The table is made for 50-light transformers, designed for the various times of full load. The column of efficiencies at 2,000 and 100 volts is for transformers designed for these volts, not for the same transformers merely re-wound. The difference would be greater if the same transformer were used in each case. It will be seen

that the efficiencies and costs are very little reduced by using low tensions; but as the percentage fall of E.M.F. on the lamps is increased by using the most efficient transformer, it would be best not to design the low-tension transformer with a view to efficiency only.

Table VIII. shows the effect of using transformers for time loads for which they are not intended. It is constructed for various 50light transformers. The power spent in the copper remains the same in each horizontal line. The waste in the iron during the whole day is concentrated into the hours of lighting, as before. Thus a full time 50-light transformer has an efficiency of 92 per cent. on full time, but only 44.2 per cent. with full load an hour a day. The 50 lighter, specially designed for one hour a day, has an efficiency of 60 per cent., but at 24 hours a day it only rises to 82.3 per cent. The fall of E.M.F. on the lamps is also quite out of the question.

Table IX. shows the percentage fall of secondary E.M.F. at full load. The table, like those before it, is for a frequency of 33. The last two columns show the advantage of using 80 per second. The loss in a 50-lighter is 2.76 instead of 3.42 per cent. in the case of 24 hours, and 14 per cent. instead of 19.5 for the one-hour trans

[SEPTEMBER 20, 1889.

former. The 1,000-lighter would be for sub-stations, and would never have its primary on and its secondary off, so it is taken for 24 hours only. The fall is 1.5 per cent. at 33, and 1·15 at 80. TABLE IX.-Fall of Sec. E.M.F.

2,000 p.p.m.

It is needless to remark that when the variation of terminal E.M.F. is great, it is very much more important than the efficiency of the transformer itself, as it affects the efficiency of the lamps, and thus of the whole system.

Table X. is for three transformers for a frequency of 80. The 1,000-lighter has an efficiency of 97.2 instead of 96-75, or an increase of 45 per cent. Its cost of material is £13 103., instead of £20 10s.

The efficiency of the full time 50-lighter is 93 against 92, and its cost of material is £1 13s. 6d., against £2 8s. 6d. This must, of course, not be confused with the cost of the transformer, which includes many other items.

Leaving these tables, as the induction might be considered too high, and as the loss might also be considered excessive, we may return to our equation:

The more usual frequency of 80 per second will be taken. The current density, d, will be taken at 150 ampères per square cm., which is about 1,000 per square inch. The primary will be taken at 2,000 volts and 1.5 ampères, and the secondary at 100 and 30. Allowing for double cotton insulation, and assuming the sectional area occupied by a wire to be the square of its over-all diameter, ⚫375.

k =

To find 1, the waste of power per c.c. of iron for any virtual induction, such as 10,000, we may take the loss per c.c. from Prof. Ewing, and multiply by the frequency; this allows a margin for the air spaces among the wires or plates, and comes about right with round wire. It is not likely that the iron used in commercial transformers is nearly so well annealed as Prof. Ewing's specimen, and it is generally handled a good deal in the workshops. A small allowance should also be made for Foucault currents. Some authorities would also make an addition for viscous hysteresis.

The specific resistance of copper is about 1.8 microhms. All the coefficients in the equation can now be replaced by numbers.

In the tables already given the induction was always 14,000; we will now work out some examples with low and high inductions for various time loads, but always, for ease of comparison, for 50 lamps, or 3,000 watts.

No. 1, with virtual induction of 7,000, designed for full load always on, has an efficiency of 95.2, and a drop of E.M.F of 2.3.

ם

FIG. 2.

FIG. 3.

The same transformer run at full load for two hours a day, or at half load for 8 hours a day, has an efficiency of 747. The figure is to scale.

No. 2, with same induction, designed for two hours a day, has 81.5 efficiency, and at full load always its efficiency goes up to 92. Its drop is no less than 7.3.

No. 3, with virtual iuduction of 10,600, designed for continuous load, has 95.1 efficiency, and at two hours a day, 72-5; drop 2-2,