SAFE CURRENT LIMIT OF CONDUCTORS. BY JOHN T. SPRAGUE, This subject has been very thoroughly examined both by mathematicians and practical engineers, and much information has been published, while much is no doubt held as a useful trading property. My present purpose is not to add an actual contribution of my own to the stock of knowledge, but to put the work of others into a form which appears to me to convey the facts in the simplest possible form, alike to the eye and to the mind. The problem to be dealt with is the amount of heat generated by the current, and the rate of its dissipation by the processes of transmission (or conduction), radiation and convection. We have to find out the conditions under which these two just balance, so as to produce a defined rise of temperature which shall do no damage. It is clear that no formula whatever can do this for all cases, unless we can introduce some variable element, a constant for each case, But we can discover a law which the practical man can modify as his experience teaches him. Two very natural ideas were at first accepted: 1. That the conductor should increase in the ratio of the current. 2. That bare wires would cool more rapidly than those cased in badly-conducting materials. But both these ideas soon proved erroneous. The first did not allow for the number of diagrams and curves showing the actions, which are worthy of close study by those who desire to understand the whole subject, but he did not give the one curve which makes the law clear at once, and it is to supply this that I am now writing. The law of conductance is that every part of a conductor carries equal current, except in the variable periods with intermittent currents-that is to say, that if we define our unit wire as having the area of one circular mil the conductance will vary as the number of these unit wires, which is given for round wires by d2. Then what we require to know is, what is the number of such unit wires which will carry one ampere of current under given ditions. The safe limit was set at various figures2,000, 1,000 amperes per square inch. But 1,000 amperes per square inch means 1,273 circular mils per ampere, while we know that a wire of 200 circular mils will carry an ampere current with very little heating. In the accompanying diagram I have given the curve derived from Mr. Kennelly's experiments, and this curve shows how the circular millage must be increased as the cooling powers "reduce by enlarging the wires. The horizontal scale gives the currents as ordinates of the curve, and the vertical scale gives the millage as the abscissæ. For any current the square root of these two multiplied together gives the diameter required. fact that as the conductor and its conductance increased as the square of the diameter, while its surface only increased as the diameter simply, the cooling powers rapidly diminish in ratio to the heating actions. The second left out of sight the fact that the non-conducting covering rapidly enlarges in surface, and so increases the power of heat diffusion. It is now recognised that encased wires may carry a much larger current at the same temperature as bare ones, because the covering disposes of some 25 per cent. more heat than the bare wire can. On the other hand, the bare wire may often permit a very much higher temperature than the covered one. The formula C2 varies as d3 or C=d, which was first devised, I think, by Prof. Forbes, who also showed that it was not strictly correct; it amounts to saying that the diameter of the wire must increase as the current, and not the square root of the diameter, which is the law of conductance. Prof. Forbes applied various constants to this law relating to the functions of heat, and worked out many valuable formulæ and tables. Several others have taken up the subject and done good work, but the most complete study of the whole matter that I am acquainted with is that of Mr. A. E. Kennelly in a paper read to the Edison Convention in August, 1889. He experimentally tested the rate of heating in various conditions in such a manner as to test the correctness of the theoretical data adopted by Prof. Forbes, and it must be admitted that these data, while subject to much modificatiou, proved very fairly trustworthy. Mr. Kennelly gave a For currents up to 120 amperes, curve 1 applies. For currents up to 1,200, curve 2 is on one-tenth the scale as to amperes. They show the conductor needed if the limiting rise of temperature is to be 10deg. C. in the case of copper wires of 98 per cent. conductivity enclosed in casings. This is the average temperature which ensures compliance with the regulation that conductors shall not rise more than 150deg. F. with double the normal current. Line 3 marks 1,000 amperes per square inch, and shows that for currents under 300 amperes it is wasteful of copper, and for higher currents it may become unsafe. The dotted line 4 is calculated from the figures of Prof. Forbes for a bare wire suspended in air and permitting a rise of 25deg. C. It shows in a very striking manner how fairly the theoretical data and the law of C2 a d3 apply to the facts. The curves all demonstrate also the advantage of using small conductors, and especially strips rather than wires, under conditions which permit diffusion of heat, rather than single large inasses of metal. Thus, to carry 1,000 amperes, 1,000 × 2,160 = 2,160,000 circular mils; but four wires each carrying 250 amperes means 4 x 250 x 1,370 = 1,368,500 circular mils, or little more than half the weight of copper. From the curves shown in the diagram it is easy to trace out such others as would meet any requirements, or to extend the curve 2 to any desired amperages. INSTITUTION OF ELECTRICAL ENGINEERS. At a meeting of the Institution on Thursday, November 12, there was an exceedingly interesting preliminary to the reading of the paper, part of which we gave last week, and which we conclude elsewhere. As we say, the usual preliminary business was agreeably diversified. The president announced that the council had elected Mr. Jacob Brett an honorary member of the Institution, in recognition of his valuable services in connection with the introduction of submarine telegraphy. He also announced two very interesting donations-viz., an excellent portrait in oils of Mr. Jacob Brett, painted and presented by Miss Alice Bolton, of 49, Blomfield-road, Maida vale; and seven volumes of manuscript letters and manuscripts formerly belonging to the late Sir William Fothergill Cooke, relating to the introduction into England of the electric telegraph by himself and his partner, the late Sir Charles Wheatstone, presented by Mr. Latimer Clark, pastpresident. Mr. CLARK, in acknowledging the vote of thanks to himself, and in seconding a similar vote to Miss Bolton, made some very interesting remarks, as follows: I have great pleasure in seconding this motion, but before referring further to the subject I feel bound to return my thanks for the kind way in which you have accepted from me the letters, documents, and papers of the late Sir Wm. Fothergill Cooke, which I have had the honour to present to the Institution. Anyone who looks into these letters will find their perusal very interesting, and I can vouch for the fact that they are historically extremely valuable, because they relate to the history of the introduction of the electric telegraph into this country at a date so early that it is not possible that anything earlier can be discovered. We owe it to the business aptitude and energy of Sir William Cooke, assisted by his partner, Wheatstone, that the electric telegraph was introduced on the railways of this country at a very early date, and before it was taken up by other countries, so that Great Britain will for all time to come claim the honour of having first introduced the electric telegraph into practical use, as it can also claim the first invention of electric telegraphy through the celebrated letter of " C. M." in the Scot's Magazine of 1753. Although I knew Sir William Cooke extremely well and for a great number of years, it was a long time before I could induce him to entrust to me the valuable papers he had in his possession. For many years I used on every opportunity to urge on him that they should be deposited in some public institution, and it was only some 10 years ago that he at last consented to place them in my hands, as part of a large collection of works which I had been accumulating, and which I assured him would sooner or later find their way to some public library. When I did obtain possession of them a great many were found missing, in spite of every search he could make. They now comprise seven volumes, containing all kinds of documents of a legal or business nature and a great many private letters. Perhaps the most interesting part of the collection is a series of private letters to his mother and his brother detailing the inception and early development of his ideas. He was most affectionately attached to his mother, and his letters to her abound in expressions of filial love which are quite touching. They were written in the old days of high postage rates, and as was customary in those days, they were crossed and recrossed in such a way that it is difficult to read them, and would be still more difficult to find space for an additional 20 words in any of them. Our honorary solicitor, Mr. George Bristowe, has very considerately made a copy of all those portions which relate to the electric telegraph, and this will be found in a separate volume. He has done this not only with a view to their more easy perusal, but he was impressed with their historic value, and he kindly undertook this duty with a view to their safe preservation from fire or other accident, deeming it unsafe that only one copy should be in existence. I will venture to read an extract from the first letter to his mother, dated April 5, 1836, because it is always interesting to trace the first movement in a path from which such mighty results are afterwards destined to emanate : "Heidelberg, April 5, 1836. "My Dearest Mother,-You must know that for some weeks past I have been deeply engaged in the construction of an instrument which I believe may prove of sufficient importance, should I succeed in bringing it to practical perfection, to merit a visit to London. Determined to satisfy myself on the working of the machinery before I went any further, I prepared to make a model, and being unable to obtain the requisites at Heidelberg, I sought them at Frankfort. Whilst completing the model of my original plan, others on entirely fresh systems suggested themselves, and I have at length succeeded in combining the utile of each, but the mechanism requires a more delicate hand than mine to execute, or, rather, instruments which I do not possess. These I can readily have made for me in London, and by the aid of a lathe I shall be able to adapt the several parts, which I shall have made by different mechanicians for secrecy sake. Should I succeed, it may be the means of putting some hundred pounds in my pocket. As it is a subject on which I was profoundly ignorant till my attention was casually attracted to it the other day, I do not know what others may have done in the same way; this can best be learned in London. You see, I am very mysterious at present, and think it very prudent to continue so. Nevertheless to you, dearest mother, if it were your wish, my plan and instrument should be explained now, though I think without better drawings than I could make you would scarcely comprehend me. As I do not wish my motives for revisiting London to be generally known, you had better, in mentioning it to my friends at Berne, state that private business requires my presence, and allow them to ascribe to modelling or what they please the sudden change of my plans." This is a sample of the correspondence which goes on for a great many years. But besides these the collection comprises autograph letters from several very eminent persons, and many papers connected with the celebrated arbitration between himself and Sir Charles Wheatstone, and with the introduction of the telegraph and the formation of the Electric Telegraph Company, which was the first public company established for the purpose of telegraphic communication, and which opened its doors to the public on the 1st January, 1848, at which time about 1,500 miles of telegraph were in existence. Life is proverbially uncertain, and I have, therefore, had very great pleasure in confiding these papers and documents to the care of the Institution of Electrical Engineers, and I thank you sincerely for the kind way in which you have accepted them. I have now the pleasure of seconding the vote of thanks which has been proposed to Miss Alice Bolton, of 49, Blomfield road, Maida-vale, for her presentation to this Institution of the very artistic and excellent portrait of Mr. Jacob Brett, which we see before us. Its artistic merits are very obvious to us all, and I can testify to its being an excellent likeness, as I have had the pleasure and privilege of knowing Mr. Brett for a great many years. It represents him not so much as he is to-day, but rather as he was some four or five years since, when the portrait was originally painted. Mr. Jacob Brett is now 83 years of age, and I grieve to say he lies on a sick bed through an accident which occurred to him some time ago in getting out of a vehicle; one of his legs was injured, and as the wound has reached the surface of the bone it is extremely difficult to heal. It is a great pleasure to me to know that Mr. Jacob Brett has been elected one of the very few honorary members of this Institution, for I feel that in conferring honour on Mr. upon ourselves. Brett we have, perhaps unwittingly, conferred an honour I do not think it probable that many of those whom I see present with us this evening can be fully aware of the very important part which Mr. Jacob Brett and his brother, Mr. John Watkins Brett, have played in connection with the history of the introduction of the electric telegraph, and especially the submarine electric telegraph, into the country and into the world. That connection dates back to a past generation, and is much deeper and more important than the world generally is aware of. His brother (Mr. J. W. Brett) and Mr. Brett were close friends and partners, and worked together in all their undertakings. His brother had a considerable fortune, which he was always ready to lavish on the advancement of submarine telegraphy. They commenced their public labours in 1845, and it is through their energy and devotion to the subject that we as Englishmen can claim for ourselves the distinction of having been the pioneers in the introduction of submarine telegraphy, as we can equally claim to have been the first nation to invent the electric telegraph, and the first nation to introduce it into practical working. In order to be able to appreciate the early date at which they began their labours, I would remind you that in 1837 Cooke and Wheatstone exhibited the private working of their telegraph from Euston to Camden Town, and the public then for the first time became aware of the possibility of the introduction of the electric telegraph as a factor in daily life. During the ensuing years Sir W. Cooke, by his great business energy, succeeded in establishing telegraphic lines on many of our railways; as for example, the Norwich and Yarmouth line, the Dalkey atmospheric line, the Northampton and Peterborough, the SouthEastern, the Great Western, and others. But on January 1, 1845, an event occurred which startled the public mind contributed most powerfully to the advancement of the electric telegraph. On this date occurred the notorious. case of a murder of a woman at Slough, by the Quaker, John Tawell, and his arrest was effected by the telegraph. After he had left by train for Paddington, a description of the murderer was forwarded by telegraph, and on his arrival he was seen to enter an omnibus. A detective mounted on the roof, and after watching him through several streets in the City, followed him into a small eatinghouse in an obscure and narrow alley, and seated himself opposite to him. Having satisfied himself by observation that he was in the presence of the right man, he suddenly accosted him with the question, "Haven't you just come from Slough?" Tawell's astonishment and his haggard looks at once betrayed his guilt, and he was eventually condemned and hanged for the crime. This episode occurred in 1845, and made a great impression on the public mind, and I have no doubt had its influence on the two brothers Brett, for on the 16th of June of that year they registered the General Oceanic Telegraph Company. I shall have to refer later on to this company, but for the moment only call attention to its date and to the fact that the Electric Telegraph Company, the well-known pioneer telegraph company of Great Britain, was not registered until the 2nd of September in the same year. On the 23rd July, 1845, the two brothers laid before Sir Robert Peel and the Government their plans for uniting Dublin Castle with Downing-street, and also for a general system of oceanic and subterranean electric telegraphs, to include the United Kingdom and the colonies, together with the establishment of a system of postal telegraphs throughout Great Britain. That letter was printed in type by an electrical type machine patented by the Bretts, which was exhibited at 29, Parliament-street, and I well remember seeing it at that time. Copies of the letter were extensively distributed, and I believe that the instruments themselves are stil in the possession of Mr. Jacob Brett. In the following year, 1846, they applied to the French Government for a concession for a cable to be laid at their own expense from England to France, and in 1847 this concession was granted to Messrs. Brett by his Majesty Louis Philippe, and in 1849 was further confirmed by Louis Napoleon, the President of the French Republic. They also applied in this year for a Belgian concession, which was granted to them in 1852. In 1850 they laid down their first submarine line, the well-known single wire of guttapercha, which was successfully completed on the 28th of August, just in time to save their concession. That wire, as we well know, was so slight that it failed almost immediately, but it was followed in 1851 by a permanent cable of a very different character, which, subject to repairs, was working in portions for 20 years or more; in fact, no record exists of the date of renewal of the last remaining portions of it. This cable contained four conductors, and was armoured with stout iron wires in the usual manner; in fact, it formed the type for all future submarine cables. The success of the line enabled them to form, in 1852, the Submarine Telegraph Company, Mr. J. W. Brett himself being one of the directors, which proved one of the most prosperous and successful of cable companies, and has only recently passed into the hands of the British Government. In 1853 they laid the first Belgian line and formed the Mediterranean Electric Telegraph Company, followed by cables to Corsica, Sardinia, Algiers, and many other places, while they were incessantly active in pushing forward their great scheme for a line of cables across the Mediterranean to Egypt, the Red Sea, India, and Australia. Mr. J. W. Brett was also a director of the British and Irish Magnetic Telegraph Company, which, in combination with others, formed so powerful a rival to the old Electric Telegraph Company. Now, it must ever be a source of suprise that with such records as these the name of Brett should have been omitted or forgotten in 1866, when the somewhat lavish distribution of honours and titles was made in consideration of the splendid success of the Atlantic undertaking, and that surprise will not be diminished when I proceed to show you that Mr. J. W. Brett was himself the originator and one of the earliest and strongest supporters of that project. I have said that on the 16th June, 1845, Mr. Jacob Brett had registered at the Joint-Stock Company's office the General Oceanic Telegraph Company, the first telegraphic undertaking ever registered. I have seen the original certificate and receipt. But what is more curious is that even at that early date, the application goes on to say: "Object specified to form a connecting mode of communication by telegraphic means from the British Islands and across the Atlantic Ocean to Nova Scotia and the Canadas, the Colonies, and Continental Kingdoms." So that we are met by the extraordinary fact that the first telegraphic company ever registered in this country was formed, not with the object of erecting telegraphs on land, but for the purpose of laying a submarine cable across the Atlantic Ocean, and this at a period when the world at large had not even heard of submarine telegraphy. Later on, in 1855, we find Mr. J. W. Brett associated with Peter Cooper, Cyrus Field, Dudley Field, Prof. Morse, and other prominent names, in founding the New York, Newfoundland, and London Telegraph Company, and I have seen the receipt for the £3,000 which he contributed in 1856 as his share to the common fund. In October, 1856, we find the "Memorandum of Association of the Atlantic Telegraph Company" with a capital of £300,000, in 300 shares of £1,000 each; and again we find Mr. J. W. Brett's name at the head of the list with a subscription of £25,000, followed by the subscription of a like sum by Cyrus W. Field; and subsequently we find his name at the head of the list of directors of the Atlantic Telegraph Company, which was at first unsuccessful. It is most difficult to understand how such splendid services in the cause of electric telegraphy could have gone unrequited and unnoticed. One can only conjecture that he must have impoverished his fortune by his too great liberality in his efforts to advance the cause of submarine telegraphy, so that when the final victory was won, and the hour of triumph and reward came, he was unable to take his place in front, and was left aside unnoticed and forgotten. I feel very much gratified that this Institute should possess a portrait of the only survivor of the two brothers whose names will go down to posterity as those of the fathers of submarine telegraphy, and I have therefore the greatest pleasure in seconding the vote of thanks to Miss Alice Bolton. I can only regret that the very artistic portrait which she has presented to us this day cannot be seen by a wider circle, for it could not fail to add largely to her professional reputation. We also owe a debt of gratitude to her and her mother for the affectionate care with which they have assisted Mr. Brett during many long years of public neglect. As for Mr. Brett himself, I regret to say that he is in extremely straightened circumstances. He has for many years subsisted entirely on a pension of £100 a year which was granted to him from the Civil Service Fund, and he has no other means of subsistence. It will ever be regarded as a matter of wonder to future generations that the rulers and merchant princes of the Victorian era, who have derived such splendid benefits from submarine telegraphy, should have permitted two of the noblest of the pioneers of electrical science to thus pass away unnoticed and almost unknown. Mr. Brett is, however, fortunately a man of happy and cheerful disposition, and feels amply repaid by the knowledge that the subject to which he devoted his early life has now become of almost infinite importance to mankind; that by day and night myriads of signals are ceaselessly flashing through every ocean, and bearing their priceless messages of love or of commerce, of peace or of war. It is a pleasure to feel that when he shall be called away to his last rest he will be sustained by the proud consciousness that he has been enabled to confer greater benefits on his country and on the world than any other man now living. Subway Inspector.-The London County Council have appointed Mr. F. McMahon, at present assistant inspector of subways, to the position of inspector of subways. = way, and found 103 volts. The circuit from this dynamo was then opened, and again closed by joining one end of it to the shaft, the other end to the commutator of an armature the insulation of which was to be tested. The volts were again read, the insulating material of the dynamo armature thus forming part of the circuit, which was made direct through G-the potentiometer rheostat having been disconnected. The reading on the volt scale was now 89.5-i.e., a current of 89.5 microamperes was passing through the circuit. The total resistance of the circuit was therefore including the insulation resistance + a few hundred ohms resistance of G2 and leads. 6. DESCRIPTION AND CALIBRATION OF INSTRUMENTS. Galvanometers.-As has been already mentioned, these are of the D'Arsonval type, which was chosen on account of its deadbeatness, and more particularly its independence of variations in the surrounding magnetic field. It is hardly too much to say that a system such as that described in this paper depends on the D'Arsonval galvanometer for its existence. The galvanometers are mounted on a stone supported on thick indiarubber rings, an arrangement which has been found to a large extent to stop the transmission of vibrations. The scales are at a distance of 5ft. from the galvanometers. Calibration of Galvanometer.-Fig. 1 shows the connections and general arrangement. A current is established by means of two or three secondary cells through two suitable rheostats, one having a fixed and the other a variable resistance, the latter made of mercury placed in grooves of a wooden trough with two copper slides. The strength of this current is varied by adjusting the mercury rheostat until the fall of potential across the fixed resistance "A" on the diagram, Fig. 1-the terminals of which are connected with two mercury cups on the instrument table, is equal to the E.M.F. of the standard cell. Paper read at last week's meeting of the Institution of Electrical Engineers, The balance is effected by placing a standard cell joined in between the two mercury cups, and adjusting the mercury series with a second galvanometer in opposition to the P.D. resistance until no deflection is obtained on the second galvanometer. The galvanometer to be calibrated forms with an adjustable resistance-box in series, and generally with a shunt across its terminals, a circuit between the same mercury cups. When no deflection is obtained on the second galvanometer, the fall of potential across the circuit of the galvanometer under calibration is equal to the E.M.F. of the standard cell. Clearly, therefore, the current in the galvanometer can be easily found by means of the formula, (5) As a practical matter, the values of R based on the use of a certain shunt are calculated beforehand, so that the current shall be 10, 20, 30. micro-amperes; and the observations are noted as shown on Table III., which gives the calibration of galvanometer No. 1,588, taken on the 22nd April last. In the circuit of the standard cell a key is used which has double contacts, and is connected with a high resistance (about 10,000 ohms) in such a manner that, when the key is depressed half way, this resistance prevents an injurious current from passing through the cell, whilst, when the key is completely depressed, after the balance has been very nearly established, the resistance is short-circuited, and so the full sensitiveness of the arrangement obtained. When the P.D. between the mercury cups is equal to the E.M.F. of the standard cell no current passes through the second galvanometer, the spot of which will move visibly for a current of 1-ten-millionth of an ampere. As the internal resistance of the standard cell plus the resistance of the galvanometer does not exceed 1,600 ohms, a visible deflection is obtained, one way or the other, if the balance is at fault to the 1 extent of × 1,600, or '00016 volt, which is about 011 per 107 cent. of the value of the standard cell. The mercury varying but little in resistance by temperature, and giving perfect joints with the copper slides, allows of the resistance of the mercury rheostat being adjusted with any desired accuracy, and remaining practically constant when once correctly adjusted. The delicacy of this electrical balance is so great that a movement of 1-64in. of one of the slides is sufficient to cause a deflection on the second galvanometer. This balance is tried for each reading when calibrating a galvanometer. TABLE III.-CALIBRATION OF GALVANOMETER No. 1,588, 22/4, 1891. Temperature of cell and instruments, 14 5deg. C. =1.4386 volts (legal). = 430-9 ohms 39 = 47.9 105 e R+1G E M.F. of cell, e (measured). = G. = micro-amperes. |