DECEMBER 6, 1889.]

637

Multiplying 37,875 (the cir. mils.) by 10,000 (the length of the circuit in feet), by 0000006044, gives the price of the copper at 20 cents per pound, equal to $228.92.

To construct a cumulative dynamo to maintain a constant E.M.F. at the motor terminals, it should be over-compounded for the resistance of the line, the series coil of the dynamo and the armature. Suppose that the resistance of the armature and the series coil together is one ohm, the drop at the dynamo terminals, due to the internal resistance of the dynamo, would be 82.8 volts. Therefore, to maintain a constant potential at the dynamo terminals, irrespective of the external circuit, we would have to proportion the ampère turns of the series coil so that the increase in the strength of the field would be such that the armature would develop 1,082-8 volts when supplying 82.8 ampères, the speed remaining constant. The line, A B, then, in fig. 4, would represent the voltage at the dynamo terminals under varying loads if the series coil had no effect at all, while the line, A E, would represent the number of volts actually developed in the armature when the series coil is proportioned to maintain a constant E.M.F. at the dynamo terminals of 1,000

Pressure wires should be run from the "bus" wires n the district station to a voltmeter in the main enerating station, so that the pressure at the district tation may be read at any time by the attendant in the main station. If for any reason this pressure should ary, a hand regulator should be provided in the shunt ield circuit of the generator to regulate the pressure at he district station.

By using the "box" or "crib" system of wiring, a arge district may be wired for a small initial cost, aving scarcely an appreciable drop of potential and needing no equalisers. This is effected by connecting he positive wires together and the negative wires ogether at each junction box, thus forming a network of positive and a network of negative wires. Should particular portion of the circuit be overloaded the current can flow through all the wires in both the posiive and negative networks, and supply all the current needed with scarcely a perceptible drop of potential. It also allows a larger district to be wired for the same nitial cost of copper than could otherwise be covered. Referring once more to the example, we find that Hividing 1,000, the voltage at the motors, by 80, that

volts, as shown in line, A D. The shunt field should be of such strength that the armature will develop 1,000 volts on open circuit, while the series coil will cause the armature to develop an increased number of volts, represented by ordinates included between the lines, A E and A D, corresponding to their respective ampère loads. Now, if the dynamo is over-compounded so as to maintain a constant E.M.F. of 1,000 volts at the motor terminals, it must be over-compounded for the resistance of the external and internal circuits, and the ordinates between the axis of X and the line A C would represent the voltage at the dynamo terminals under varying loads, while the ordinates between the line, A C and A D, would represent the compounding necessary to make up for the losses in the external circuit. But the ordinates included between A E and A D represent the compounding necessary to make up the losses in the internal circuit; therefore, the total compounding necessary to maintain a constant E.M.F. at the motor terminals would be the sum of the two; and, adding the ordinates of the triangle, A DE, to the respective ordinates of the triangle, A D C, we obtain the line, A H, which represents the total number of volts

638

developed in the armature under varying loads. Now, if it took 1,250 ampère turns of series coil to cause an increase in the strength of the field sufficient to overcome the drop in the internal circuit only, and maintain a constant E.M.F. at the dynamo terminals, the series coil would have 15 turns of a wire. To maintain a constant E.M.F. at the motor terminals, the ampère turns would be proportional to the increase in the voltage; or we should have

x =

82.8: 332.8 : : 1,250 x,

or a 5,145 ampère turns, which would require 62 turns of wire in the series coil, provided the machine was working below saturation and the shunt-field separately excited. If, however, the shunt-field is excited by the generator itself, the increase of ampère turns in the shunt-field, due to the increased current flowing through it under the higher voltage, should be subtracted from the total number of ampère turns obtained above, and a series coil laid out having a number of ampère turns equal to this difference.

THE law of the heating of conductors by current, which for a given rise in the temperature of the conductor, gives current diameter diameter, was very clearly set forth in the ELECTRICAL REVIEW in 1882,* and has since been the subject of very careful experimental investigation by Prof. Forbes, Mr. Preece, and others. The law is arrived at in a very simple manner. assumes that the loss of heat from a conductor is proportional to its surface, or what amounts to the same thing, the loss of heat per unit of surface is constant for all sizes. When a constant temperature is arrived "Electric Lighting by Incandescence," by H. R. Kempe.

It

(DECEMBER 6, 1889

That is to say, in order to maintain a given temper ture (1) in conductors of different diameter, the curre in each must be proportional to (diameter), or (2) different currents the diameters must be proportionalt (current).

The assumption that the loss of heat is proportion to the surface is, however, only true in certain cases, A conductor may loose heat in three ways: by conduction through its extremities, by convection and by radiation The loss of heat is strictly proportional to the surfe only when radiation is the ruling factor. Short leng of wire are very much affected by the cooling through large terminals, as in the case of ordinary "cut-onta The experiments of Mr. Preece, who used the same pair of massive terminals and the same length of win in each case, show that the constant, a, (c = a d1) en scarcely be called constant under these conditions Convection does not seem to be proportional to surface. Therefore the only case where this law can be strictly true, is when the conductor is of considerable lengt compared with its diameter, or the supports are very small, so that the conduction from the ends is a very small proportion of the total loss of heat and when there is no convection. That is, the conductor must be in a vacuum. These conditions are very nearly filled in the case of a filament of an ordinary incandescen lamp. Large current lamps, however, such as are made for series lighting, and which require large radiating lumps at the joint of the carbon and leading-in wires in order to keep the joint cool, must, if the filament i short, be an exception; the radiating lumps acting in the same way as the binding posts of a safety cut-out. The writer has found this law of great use in calculating the diameters for lamp filaments, and some time ago in orde to ascertain how close the actual results were to the calculated values, he took very careful measurements of 30 lamps. The lamps were taken from six different batches and tested at 3 watts per C.P. by three different observers.

a is taken from the No. 1 lot of lamps and = 9.73. The crosses mark the position of each batch d lamps, as determined by the actual measurements of the current and diameters. It will be seen that the actual results lie very close to the calculated, showing that lamp filaments, at any rate within these limits of diameter, certainly do follow the c law, and that the radiation per unit of surface is the same for all the diameters. Although, at the time, the writer did not take any observations below 7 mils., he has since done so low as 5 mils., and found the same agreement betwee the calculated and observed values. By means of this la it is thus very easy to estimate the correct diameter for a filament of an incandescent lamp of any voltage and candle-power. A different constant will, however, be required for different efficiencies. In order to make lamp of certain volts and C.P. at a certain efficiency, is only necessary to calculate the current which lamp will take, and the equation d a c gives the

=

DECEMBER 6, 1889.]

Both the constants, a and b, can be determined at O same time and for all efficiencies, from measurents taken from one or more lamps. Their value pends on the nature of the surface of the filamentemissivity, its specific resistance, the temperature, , watts per C.P.-and the units employed. Of course, same constants will only be applicable to filaments de by the same process. This method of calculating O size of a filament is only really useful in the case of ments which do not require flashing; although it y be used to indicate about the size to give to a shed filament. When the process of flashing is reted to it gives a wide range to the possible diameter a filament. The emissivity may be made to vary ry much-as much as 50 per cent.-and what might called the specific resistance of the filament, may be duced any amount down to, at any rate, th. It is as quite possible to have two filaments of exactly the ne length and diameter and at the same temperature ., same watt per C.P.), yet giving a very different ount of light. Or, to put it another way, two filaents may give the same C.P. at the same volts and effincy, and yet be of very different dimensions. So ry largely are the emissivity and resistance of a filaent changed by flashing, even when done very slowly d in an exceedingly rarefied gas, that it is easier to lamps uniform one with another by simply selectg the filaments by measurement than by attempting make them all alike by flashing.

With a really good filament the only advantage of shing is that the same diameter of filament may be ade to do duty within certain limits for different rrents. As a flashed filament has usually a much aller emissivity and a lower resistance than an unshed one, it must be longer to give the same C.P. at e same volts and efficiency, and as certain users of e electric light will insist that they get more light om a long filament than a short one-no matter what emissivity and diameter may be-it might in such ses be considered wise to make filaments as long as ssible. The remark, however, does not apply at e present time in this country, as customers have no oice. If the filament is inferior to start with-for stance, if it shows bright spots or otherwise lights up evenly-of course flashing is advantageous in corcting these faults, as also it is if the filament is soft, rit may then be given a hard coating of flashed rbon, which will protect it from disintegration. In many cases it is quite possible to have the same ameter for a flashed or unflashed filament for the me volts, C.P. and efficiency. Take the case of a

639

100 volt 20 C.P. lamp at 3 watts per C.P. It would be 167 ohms resistance, and wonld take 6 ampère. The diameter in a certain make of carbon would be 7 mils., and when unflashed would be 4.7 inches long to give the required result. Now this carbou, when flashed, would have its emissivity reduced, say, in the ratio of 14 to 10. Therefore for the same diameter, in order to 14 still give 20 C.P., it must be lengthened to 4.7 x = 6.6 inches. It will have now a correspondingly increased resistance of 234 ohms; but, by the flashing, this may be reduced to 167 ohms, and without perceptably increasing the diameter. Therefore 6.6 inches of this filament when flashed will be the exact equivalent of 4.7 inches unflashed.

10

The process of flashing does not, as is sometimes supposed, deposit carbon in the pores of the filament. A good filament practically has no pores. It is only an exterior coating which is deposited.

There is on this account a disadvantage in flashing in the case of very thin filaments, such as must be used for low C.P. high volt lamps. When the current is switched on to one of these lamps suddenly, it frequently happens that a small portion of the flashed deposit, perhaps th inch long, will be detached, and in a quiet room a distinct click may be heard when this happens.

On examining the lamp a gap in the flashed coating will be seen, the original black filament showing through. A bright spot is formed here where the filament will soon break. Probably the filament proper becomes hot and expands before the flashed coating, and to such an extent as to cause the coating to break. At any rate, it does not occur in lamps with thick filaments, which take an appreciable time to get hot after the current has been turned on. This is a fruitful cause of breakage in flashed filament lamps of say 100 volts, 8 C.P.

An unflashed filament with a highly polished black surface, which at 3 watts per C.P. gives, say, 14 C.P., if very slightly flashed, just enough to make the surface appear white instead of black, and without any perceptible thickening, and still retaining its polished appearance, will now at 3 watts per C.P. give only 10 C.P. There is a still greater difference in emissivity between the white shiny surface and a black dull surface, such as is often seen in the filament of a lamp which has been running a long time, and it is this which causes the greater part of the falling off in light of old lamps. A flashed filament with a smooth whitish surface, after a certain length of time, gradually loses its polished appearance, and eventually turns to a dull black, with the result of increasing its emissivity perhaps 50 per cent. As the amount of heat now generated in the filament is certainly no more than it was originally, it will be radiated much more freely, and therefore at a much lower temperature. The other, and usually lesser, causes of the falling off in C.P. are the blackening of the globe by particles of carbon thrown off from the filament and the consequent rise in resistance of the filament due to this throwing off.

Mr. Preece, in a lecture before the Royal Society, December, 1887, gave the results of numerous experiments he had made to ascertain the current required to fuse wires of various metals in air, both with short lengths of wire, as used in cut-outs, and therefore subject to much cooling from the terminal posts, and with wires six inches long where the terminal cooling was negligible. The wires experimented on ranged from 4 mils. to 40, and for each diameter Mr. Preece gave the value of the constant a, in the equation c = a d1. There is a large variation in the value of a in the case of the cut-outs, as might be expected. And on examining the tables of constants for the 6 inch lengths, they are also seen to vary considerably, especially for diameters below 15 mils. The value of a rises very much as the wires get smaller, below about 15 mils. Mr. Preece has taken the mean, for each metal, of all the values obtained for a, and has calculated therefrom the fusing currents. These calculated values, however

640

do not agree closely with the actual results. In a subsequent lecture, however, a few months later, he gives corrected values for a, which are smaller than the former values, and are evidently obtained by omitting the high values for the smaller wires. The currents calculated from these constants agree much more closely with the observed values, and no doubt give about the correct value. Though from accidental variation in the emissivity or the specific resistance of the different samples of wire or from some other cause, the actual fusing current may differ as much as 20 per cent. from the calculated. This may be readily seen by plotting on squared paper the values calculated from the "final values of a," and the actual values as given. It would seem unnecessary to calculate such constants to five figures.

In a paper also before the Royal Society in April, 1884, Mr. Preece gave the values of fusing currents for very small platinum wires in air, from 0.5 mil. to 3 mils. diameter, and instead of following the d law the currents were almost exactly in direct proportion to the diameters. It is thus evident that even if the ca d law is correct for conductors over about 20 mils. diameter in air, it is certainly not correct from that size downwards.

Mr. Bernstein has published an interesting table (Centralblatt für Elektrotechnik and Industries, March, 1889), showing the energy per unit of surface required to maintain a temperature showing a dull red glow in the dark (526° C.), for platinum wires ranging from 3.55 to 10 mils. under different pressures from atmospheric pressure down to the most perfect vacuum he could obtain. The observations he gives are plotted below. Curves from Bernstein's Table, showing energy per unit of surface required to maintain temperature of 526° C.

They show that with a perfect vacuum the energy per unit of surface is precisely the same for all the sizes of wire. This means that the law ca d is true, even for these small sizes of wire, when in a perfect vacuum. With a poor vacuum, however, there is at once double the power per unit of surface required in the case of the 3.55 mil. wire as with the 10 mil, while at atmospheric pressure there is 2 times the amount.

According to this, in the case of two wires of the same length, one 3.55 mils. and the other 10 mils. diameter, at atmospheric pressure, the smaller wire will require energy in the proportion of 3.55 x 2.5 = 8.9 units, as against 10 for the larger one, to raise it to the same temperature.

(To be continued.)

ON THE HEATING OF CONDUCTORS BY ELECTRIC CURRENTS.*

By A. E. KENNELLY.

I.

ALTHOUGH the best economical dimensions of a conductor employed to transmit power are determined by Sir William Thomsom's law that that portion of the cost rate depending directly upon the cross sectional

Abstract of report read before the Edison Convention at Niagara Falls, August, 1889, and published In the Electrical World.

[DECEMBER 6, 1889.

area of the conductor should equal the average em rate of the power it absorbs in its duty, and although at the existing prices of copper and of power, such a conductor must be very heavily loaded to acquire dangerously high temperature; yet not only may limits of safe capacity be strained by occasional pre sure, but it is well known that in practice, economy not the only factor that determines a conductor's S since the necessity, for example, of maintaining a cstant difference of potential over an entire network of electric light mains under wide variations of load, may sometimes clash with the conditions of economy their transmission, or even of safety in their tempen tures.

Notwithstanding the consequent importance of complete knowledge of the safe carrying capacity conductors under all practical conditions of service, the subject has not, apparently, received the attention : deserves, and the simplicity of the law which deter mines the generation of heat in an active conductor seems to have caused the complexity of the h governing the dissipation of that heat, and thus the limiting temperature, to escape the full notice of pras tical men. The most important published contribution to the subject appear in two papers, one by Mr. W.E Preece, to the Royal Society, in March, 1888, and the other by Prof. G. Forbes, to the London Institution d Electrical Engineers (March, 1884). The former deals principally, however, with the fusing currents of wire for different metals and diameters, while the latter 3 almost exclusively devoted to the theoretical treatme of the subject. Had the experimental data of Prof Forbes's paper been as exhaustive as its mathematica investigation was complete, there would probably ha been little left to add or amend from an engineering point of view; but the vital numerical coefficiente adopts are taken from experiments on the emission & heat, which, however accurate and valuable in the selves, are not fairly applicable to the conditions of conducting wires, and which, in their published form tend rather to conceal than to elucidate the principis underlying the subject. The fact remains that none the existing text books or tables up to the present dat give, with any pretension to accuracy, the carrying capacity of wires consistent with safe temperatures, clearly tabulated form, or any clear conception of the variation the limit undergoes with change of envirus ment empanelled, free, or out of doors. In addition this, the rule of the British Board of Trade for insta lations within doors has been pointed out by Prot Forbes and others to be very uneconomical for smal wires, and actually unsafe for wires of a certai thongh perhaps unusual, diameter.

FIG. 1.

To determine some of these unknown quantities, a particularly with a view to obtaining the necessa data for the fire insurance offices, the Edison Electr Light Company, of New York, recently instituted series of experiments at the laboratory of Mr. T. Edison, in Orange, N.J., and with their permission the results obtained are now published. Not only ha satisfactory general rules been arrived at for the s carrying capacity of conductors, but the numerical e efficients in the formulæ given by Forbes have be determined with a fair practical degree of accura while the field has been opened for further useful a vestigation.

The experiments were made on conductors unde three different conditions:

1. With insulated copper wires encased in woode panelling to represent house wires.

DECEMBER 6, 1889.]

2. With copper wires, both bare and covered, susnded on poles in the open air to represent overhead rvice.

3. With copper wires and strips suspended across a om to represent the conductors in an electric light ation, and also to form a connecting link between the vo previous conditions.

*

The elevation of temperature produced in the wires whose conductivity varied from 97 to 101 per cent.) as in every case determined from the increase of eir resistance observed after the experimental current ad been passed through them sufficiently long to actically attain a limiting permanent temperature. his period of time was found to be about ten minutes ith the panelled, and some two minutes with the spended wires. With the former, a steady increase resistance, which, according to theory would connue for all time, could be noticed for as much as 30 inutes, but it was estimated that the temperature evation reached in ten minutes was 97 per cent. of s full ultimate value, and the greater accuracy tained by longer intervals of flow would not have paid greater loss of time, especially as the quality of e wooden panel, its thickness, form and position, ould practically involve commensurate variation in sults.

641

to diameters of nearly half an inch, or from wires whose resistance per metre varied from 0.019 ohm to 245 microhms at zero C. All the resistances in the tests are expressed in legal ohms (106-0 centimetres).

The increase in the resistance of the wires due to their heating was determined in the cases of all but the very smallest by that very accurate null method, in which the variable potential difference between the ends of the tested wire is balanced against the constant potential difference between the ends of an invariable platinoid resistance in the same main circuit, as shown diagrammatically in fig. 3. This standard resistance was formed by a grid of 40 parallel platinoid wires, each eight feet (244 centimetres) long and 0.031 inch (0.79 centimetre) in diameter, stretched in a wooden frame between copper rods. The joint resistance of all these wires was 0·0499 ohm, and their large total surface of 374 square inches (2,410 square centimetres) and small coefficient of temperature variation (0.21 per cent.

DG

SR

FIG. 2.

Two 20-foot lengths of pine panelling were made of he cross sections represented in figs. 1 and 2, and in all he tests these panels rested with their broad bases on he wooden floor of the testing room. In the smaller ize, 12 wires, ranging from 00185 inch (0-047 centinetre) to 0.119 inch (0.302 centimetre) diameter, vere successively tested, one side only of the panel being occupied at one time. In the larger size, 12 arger wires were tested, ranging from 0.119 inch 0-302 centimetre) to 0-445 inch (1.131 centimetres) liameter, generally two at one time, one in each compartnent, so that the observations may be said to extend

FIG. 3.

D, dynamo; P.R, platinoid resistance; L.B, lamp bank; T.W, tested wire in panel; G.R, standard resistance of platínoid wire grating; R, rheostat; D.G. differential galvanometer.

per degree C.) effectually maintained the resistance constant within at least 0.1 per cent. under all current strengths employed, especially as with the stronger currents the grid was connected with its two halves in multiple by letting the current enter at a third copper rod in the centre and divide among the forty wires on each side, the total resistance in this condition being 0.0121 ohm.

The

To balance the potential differences supplied by the wire and the grid, a dead beat differential mirror galvanometer was employed. It was carefully adjusted for differential perfection, until five volts with its coils in opposition series produced a barely perceptible deflection. The resistances and balance of the coils (about 2,700 ohms each) were observed before and after each test. During the observations one of these coils was connected with the panelled wire, and the other in opposition with the platinoid grid. initial difference between the opposed currents thus acting on the needle when the first feeble current was sent through the main circuit, was reduced to vanishing point by inserting resistance in the circuit of preponderating influence. Under these conditions the resistance of the wire became determined, and its terminal potential difference exactly balanced on the galvanometer that from the grid. As the current in the main circuit was successively increased this balance became upset by the corresponding rise of temperature, resistance and terminal P.D. of the wire, necessitating readjustment of the inserted resistance, while the extent of this readjustment supplied all the data for the calculation of the change. This method was found to be very sensitive, and allowed the rise of temperature to be observed in a convenient manner for estimating the approach to limiting permanent state, while all slight variations of the dynamo testing current were eliminated, since their effect was equal and opposite on the galvanometer circuits. The temperature elevation was carried up to 100° C., except in the case of the largest wires.