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Volume 33, 1900
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Art. XLIV.—Researches into the Action of Fusible Cutouts.

[Read before the Wellington Philosophical Society, 12th March, 1901.]

Plate XIV.

The following is an account of the general results of researches (as yet incomplete) which I have been making into the behaviour of tin wires exposed to the heating effect of electric currents. These researches are the outcome of my experiences as fire underwriters’ electrical inspector here, it having been borne upon me that the action of fusible cutouts (or fuses) was not at all satisfactory.

Since the underwriters have become responsible for the design of these fittings it appeared desirable to make a few experiments on the subject. These soon led to the conclusion that the tables at present in use (quoted in the rules I am working under as well as in all the electrical pocket-books I have seen, and due to Sir W. H. Preece,* and commonly called Preece's tables) are erroneous, the error with the larger wires being, according to my experiments, as much as 90 per cent., or probably more with very large wires, the error being that the fusing-currents are given too great. This appears an extraordinary statement, but I think I shall be able to show how it is that this error has hitherto escaped the notice of practical men. It will be also suggested, as the result of experiments, that tin is probably a thoroughly reliable material for the construction of fuses, under proper design, of course.

I found it necessary to establish the physical properties of the tin I was using, the more especially as practical men assured me that my wire was made of an alloy of tin and lead. Accordingly I submitted the fuse-wires A and B to a careful approximate analysis. Taking SnO2 as 78.66 per cent. metal, I obtained, with both A and B, a percentage of tin of 99.5 per cent.; the impurities, roughly estimated as sulphides containing two-thirds of metal, gave 0.3 per cent. impurities with sample B, and about half this amount in the case of sample A. Sample A is certainly the purer of the two, and it will be noticed in the table of specific resistances that it has the higher conductivity—about 3 per cent. higher. It also has a higher fusing-point; but, still, the values of the fusing-currents observed were practically identical.

[Footnote] * Proc. Roy. Soc., 1884, No. 231; 1887, December; 1888, April.

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These results are sufficient to show that my metals are “commercial pure tin.” It would have been interesting, no doubt, to have made a complete analysis of the metals; but for this purpose what is really required is the specific resistance and the fusing-temperature of the material, and to this I accordingly devoted my attention. Here sundry difficulties cropped up. The first determination of the specific resistance (ρo) gave a value about 25 per cent. less than that of Matthiessen, the English standard. My values will be seen to be of the order of 10.6 × 10 − 6 ohms per cubic centimetre at 0° C. for tin wire, confessedly impure, hard-drawn into wire of about 36 mils; Matthiessen gives the numeric as 13.19 for “tin, pressed.” Matthiessen's value I find to be confirmed by Fleming;* my own value, approximately, by Kirchoff and Hausemann—10.67 at 15° C. (10.018 at 0° C., reducing by my formula for temp. coef.); Lorenz, at 0° C., 10.781 (taking mercury as 94.074); Becquerel (1846), given by Weiller (1885), 11.6 (cf. with mercury), 94.079; 10.71 (cf. with silver), 150. Tin pure; banca drawn into wire, 9.821.

A similar disagreement is apparent with regard to the temperature coefficient, the authorities I have been able to consult giving as follows (writing, instead of the usual formula, the coefficients for the temperature divided by 100, which gives handier numbers and is more convenient for my purposes):—

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Matthiessen, [1 + 0.3628 (t/100) + 0.0636 (t/100)2], from 0° to 100°: calculated by myself from his conductivity coefficient at 0°, 50°, and 100° C.

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Fleming, about [1 + 0.4085 (t/100) + 0.0345 (t/100)2], from 0° to 200°: calculated from the curves given (Elect.: 3rd July, 1896, p. 30), P at 0° = 13.1; 100° = 18.9; 200° = 25.6.

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Lorenz, [1 + 0.432 (t/100)]: calculated from values at 0° and 100° of conductivity.

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Benoït (1873), [1 + 0.4028 (t/100) + 0.05826 (t/100)2]

My own value for fuse-wire A (annealed) is—

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[1 + 0.421 (t/100) + 0.0398 (t/100)],

the curve fitting the equation very well indeed. My value, however, is dependent upon the thermometer errors very largely, especially the quadratic term. Since 0° and 100° are the fiducial points, it is better to take the change of resistance for this range. Thus we have—

[Footnote] * Friday Evening Discourse, Roy. Inst., 5th June, 1896.

[Footnote] † Trans. R.S L., 1862.

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Matthiessen .4264 Change in resistance of 1 unit between 0° and 100° C.
Fleming .443
Lorenz .432
Benoït .460
My own value .4478*

Matthiessen's value for the temperature coefficient is usually given as 0.00365 per degree at ordinary temperatures. This value, as may be seen by differentiating the formula I have given, is the rate of change of ρo at 15° C.

Further research is evidently required to set up a standard for “pure tin.” I am at present engaged in testing some samples of commercial tin, some results for which will be found in a table printed herewith.

To add to the confusion, I find that at a temperature be-ween 170° and 190° the resistance of a sample of tin (hard-drawn sample A) increases 3.6 per cent., the highest temperature reached being 200.7° C. Upon reheating to 214.8° a further small increase (0.6 per cent.) occurred, making a total of 4.2 per cent. on two “annealings.”

Upon another sample the effect of fusing the wire (laid flat on asbestos) was tried. The resistance at 15° C. increased 5.1 per cent. It will be observed, however, that commercial tin does not vary much in the different samples I have tested. This will be noted as a point of great importance in estimating the reliability of tin as a fuse material, other essential points being thermal conductivity, emissivity, and fusing-points. I have not yet examined either of the former two quantities very closely; but, as far as sundry fusing-tests indicate, the change in thermal conductivity is very small after “annealing” the hard-drawn wire. As to emissivity, I hope to have something to say about this later on, meanwhile I include figures showing the effect on the fusing-current for one or two sizes of wire of shellacking and of thoroughly oxidizing the surface of the wire (by dabbing with nitric acid). It will be seen that a 10-per-cent. margin would about cover the effect of shellac or white oxide with these sizes. This is another point to be noted with regard to reliability.

As to fusing-points, a table is given of sundry samples, but the results are, owing to uncertainty in temperature standards, not absolute. Callendar and Griffiths give the fusing-point as 231.68° C. Still, the comparison shows that the variation which we may expect is very small. The standard thermometer has been sent to Kew.

The foregoing leads to the conclusion that there is no standard to which I can refer my wire for comparison with that used by Sir W. Preece. The only way in which the

[Footnote] * Thermometer errors included; correct value probably less.

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two can be compared is by the values of the fusing-currents themselves. Here there is some slight difficulty, owing to an alteration of the values assigned to the fusing-currents in the ratio of 1,800.6 to 1,642 between the years 1887 and 1888. This is referred to as a verification of the “dimensions of the currents as detailed in my paper read on the 22nd December, 1887,” but whether it is a recalibration of standards, the result of further tests, or a recalculation of means does not appear. I have taken it that the means have been recalculated.

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(1) Diameter of Fuse wire. (2) Fusing-currents calculated from Sir W. Preece's Formula. (3) Fusing-currents observed by Sir W. Preece. (4) From My Experiments.
8 1.43
10 1.64 2.55 2.0
14 2.8 3.244 3.1
18 4.0 4.095 4.1
20 4.65 4.675 4.65
26 7.0 6.570 6.2
30 8.5 8.656 7.25
33 9.9 9.430 8.1
36 11.25 11.60 8.85
40 13 13.14 9.9
50 18.4 * 13
100 52 * 31
150 95 * 50.5
157.4 102 * 53.5

My tests (column 4) are of tin wires, very long, horizontal, in free air, and tested with alternating current of 80 periods.

The agreement of Sir W. Preece's experimental results with his law is remarkably good, except, as he pointed out at the time, for the fine wires, which are of not much importance. But my results, while agreeing well with those of Sir W. Preece from 14 to 20 mils, show a decided divergence at the largest observed value, and a very serious divergence from the calculated figure for the largest wire which I tried.

The difference between my value and Sir W. Preece's for the largest wire he tested is about 32 per cent. With regard to this I have firs to remark that I have found, for the particular dimensions referred to, a cooling effect from the terminals of about 4 per cent., which, applied to Sir W. Preece's

[Footnote] * Apparently not observed.

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figures, reduces the discrepancy to 28 per cent.; and, secondly, that unless the effect of time is carefully studied the observed values may be too great. As an instance, I may give my own experience. By applying current by slow increments (or what I then considered slow) to a wire of 100 mils I obtained a value for fusing-current of 44 amperes, against the value 31 which I subsequently found to be the true one, and 52 as given by Sir W. Preece's formula. Not only that, but I obtained a number of results all agreeing within about 2 per cent., which I, at that early stage, considered highly satisfactory. Upon going into the subject mathematically, however, I found that time was of the greatest importance, and, as indicated, convicted myself of the surprising error of 42 per cent. due to “personal equation.” I had discovered this before testing the smaller size, unfortunately, but will hazard the calculation that I would have erred 15 to 20 per cent. with a 40-mil fuse. Sir W. Preece, so far as I have observed, makes no mention of this source of error in his papers.

I have not yet quite finished my work on the cooling effect of terminals, but have got far enough to be able to give the length of fuse at which Sir W. Preece's values apply. The following are these lengths:—

Diameter. Mils. Amperes (Preece). Approximate Length in Inches.
100 52 3
50 18.4 3
40 13 2 ½
30 8.5 2 ½
20 4.65 *

Practical men will recognise in these lengths the ordinary lengths used, or rather longer, so that in practice, and unless the fuse is confined or the terminals get hot, Sir W. Preece's table gives a value of the fusing-current that will not fuse the wire. This is, I believe, the explanation of the fact that the error of Preece's tables has not hitherto been detected by practical men, who seem to have been satisfied that the troubles that have arisen have been due to faults due to the material tin.

Many engineers—not, I think, insurance inspectors—prefer copper as a fusing material. It is significant to note that in my preliminary experiments I tried copper fuses up to about 30 amperes, and found my figures agree with Sir W. Preece's, and that the cooling effect of the terminals is much less than with tin. This was to be expected, since the experimental figures go up to 53 amperes.

A practical point I should like to mention is the remark-

[Footnote] * Very long wire; 5 amperes, = 2 in.

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able effect of shellac upon fuse-wires, which was mentioned by Sir W. Preece. I have not yet fully examined the effect on the fusing-current; with a 100-mil wire, long, it increases the fusing-current about 14 per cent., and 10 per cent. with a 40-mil wire. I may here note that thorough oxidation of the surface has the same effect (about) as shellac upon the 100-mil wire.

If the plain fuse-wire simply stretches between its terminals the effect of fusion is first noticed by the centre melting and dropping into a catenary, which slowly increases in length until it reaches within, say, ½in. of the terminals (if the fuse is short), when it attains a dull-red heat (owing, no doubt, to the specific resistance of molten tin being probably about double that of the solid metal). Oxidation sets in, and after a few hours a thin wire will burn right through. If the wire is long enough, the catenary will increase in length till the weight breaks it off. By experiment I have found that this length is roughly represented (for sizes over 20 mils) by the formula—

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L D = 40, where L = length of catenary in inches, and

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D = diameter of wire in mils.

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Thus a 40-mil wire requires a length of 40/40 = 1 in. for its catenary, with, say, ½in. allowance at each end—2 in. in all— before it will break without getting red-hot. So with 20 mils the length required is 3 in., with a clear space of about 5/2in. underneath, to allow for the droop of the catenary. But if the wire is shellacked the effect is that upon fusion the shellac may be seen to dance about in a very lively fashion on the surface of the molten tin, which presents a mirror-surface, until a length of ¼in. is fused, when the wire snaps sharply, the molten material flying back and forming little beads on the unmelted end of the wire. (The voltage of the circuit was about 5 volts, alternating.) This observation seems to be of some practical importance, as I think it is generally understood that shellacking a fuse-wire is intended merely to prevent oxidation.

I may say that I consider the phenomenon to be due to surface-tension, and not prevention of oxidation, because while the before-mentioned catenary is forming, the tin wire breaks off in little avalanches as it melts into the catenary, the surface presenting momentarily the bright appearance of unoxidized metal.

I will now give a table of the properties of my materials so far as I have determined them at present. I have to thank Professor T. H. Easterfield for the determination of the specific gravities of the materials, an operation requiring great skill and care to insure accuracy. I have applied the corrections

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for specific gravity of water by Volkmann's table, and for air by Regnault's figure, and for dilatation at 0.000063 per degree. The specimens were about 35 mils diameter, varying about 0.2 mil from the mean at most as tested by a micrometer, the diameter being obtained from the lengths and weight, and the lengths about 5 ft. or 6 ft. The wires generally stretched about one-thousandth after coiling round a 3 in. drum. The mean length was taken. Without going into detail, I may say that I believe each measurement to have been accurate to 1 in 1,000, which is quite sufficient for the purpose.

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Table of Specific Resistance of Tin Wires Hard-drawn.
Description of Material. 1. Specific Gravity at 0° C. II. III. Specific Resistance, Microhms per C.C. IV. Fusing-point, Centigrade (approx.). V. Diameter from Volume and Length. VI. Diameter by Micrometer, with Variation from Mean.
0° C. 15° C.
Fuse-wire (sample A)— Ingot.
No. 1 7.2880 10.969 11.672 224.6 224.2 20.48 35.25 35 circ. +0.27 −0.13 +0.2 −0.2
No. 2 7.2790 10.951 11.653
No. 3 7.2863 10.928 11.628
Fuse-wire (sample B) 7.3000 11.263 11.984 223.5 223.0 35 circ.
Ditto, purified by oxidation and reduction 7.2812 11.088 11.798 30.638 30.556 +0.3 -0.3
Fuse-wire (sample C) 7.3144 11.233 11.953 221.3 221.0 36.88 +0.43 - 0.12
Purchased as “chemically pure” (Merck) 7.2935 10.592 11.269 224.9 224.3 36.965 36.875 +0.13 -0.07
Australian tin 7.2833 10.944 11.645 224.6 224.2 35 585 +0.08 -0.12
Ditto, remelted in air 7.2914 10.835 11.529 35.7 +0.05 -0.1
Plumbers' “block” 7.3088 11.082 11.791 219.6 219.3 36.80 36.71 +0.19 -0.21
Cornish tin 7.3606 11.219 11.939 225.6 225.0 35.68 +0.02 -0.05
Fine fuse-wires drawn by the maker (nominal diameter)—
14.7 No. 2 No. 1 Assumed, 7.30 10.598 10.547 11.277 11.222 14.68 +0.07 -0.03
113 10.368 11.032 11.27 +0.05 -0.1
9.6 10.116 10.764 9.57 +0.08 -0.12
8 No.1 No. 2 10.118 10.030 10.767 10.690 7.96 8.01 +0.015 -0.01
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The resistances were measured near 15°, and corrected to zero by the formula given in the paper for 0° C. (col. II.). The temperatures in this are not corrected; the thermometer has been sent to Kew. The dimensions of the wires are reduced to 0° C. by the coefficient (linear) 21 × 10-6.

It will be observed that these figures, leaving out the very thin wires, which are perhaps abnormal, do not vary much (8.2 per cent.) from the value 10.4 × 10-6 ohms per cubic centimetre at 0° C—that is to say, the common impurities do not much affect the conductivities apparently; also, that the materials probably the most pure have the highest conductivity, which is usually the case with metals. The agreement with the Continental authorities is very fair, but with the English there is a very decided disagreement.

The values for specific gravity agree very well with those of Matthiessen, which I calculate to have been 7.282, the only notable exception being the “Cornish tin,” which gives a value about 1 per cent. high.

It is now necessary to refer to the results of previous experimenters, and here is the chief difficulty in making original researches of this kind in Wellington. Beyond the “Transactions and Proceedings of the Royal Society” (for which I am indebted to Sir James Hector), and a few years of the Electrician, which the Telegraph Department kindly gave me access to, a few works in the public libraries, and technical papers and works of my own, I found nothing available in Wellington. This seems to me a regrettable state of affairs. However, I think I am justified in asserting that Sir W. Preece's tables have never been effectively criticized. Dr. Bottomley, indeed, in a letter to the Electrician, * suggests that Sir W. Preece's figures were not in accord with some experiments of his. I may extract a sentence: “And I should expect that it would require currents greater for small wires and smaller for large wires than corresponds to the proportionality to dd, “which is what I have found. But in a postscript he adds that a difference in the conditions may alter the law in such a way as” would correspond to what Mr. Preece has found, though, of course, the subject will require investigation.” The effect of this criticism may be judged from the date (1884).

Again, in 1892 Professor W. E. Ayrton, F.R.S., and Mr. H. Kilgour made a research into the emissivity of platinum wires up to 14 mils in diameter. They write: “In 1884 it was observed experimentally that, whereas the electric current required to maintain a thick wire of given material under

[Footnote] * 19th April, 1884, p. 541.

[Footnote] † Phil. Trans. Roy. Soc., 183A, 1892, 1892, p. 371, et seq.

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given conditions at a given temperature was, roughly, proportional to the diameter of the wire raised to the power three halves, the current was more nearly proportional to the first power of the diameter if the wire were thin.” Later on, on page 395, after pointing out that their formulæ for emissivity may not be safely extrapolated, they assert that to assume the emissivity to be constant would be to make “an error of hundreds per cent. in the case of some of them” (i.e., wires of diameters “from a small value up to 1 in.”).

This is an evident criticism of Sir W. Preece's work, but I am wholly unable to find any practical effect following from it. And, finally, Sir W. Preece's tables are quoted without remark in all the electrical pocket-books I have seen.

The crux of the whole question is the value to be taken for the emissivity which is concerned in the phenomena in the following manner:—

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Let C.= current in amperes,

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pθ = specific resistance at the temperature of fusion,

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∊ = emissivity in absolute measure or in gramme calories per second, per square centimetre, per degree (at the temperature of fusion),

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J = Joule's equivalent, gramme calories (Watt-seconds),

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D = diameter of wires,

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A = a constant,

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θ = elevation of temperature of wire at fusion,

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then fusion is reached if there is no cooling effect of the terminals in a wire when—

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C2 pθ/D2 = AJ∊θD;

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[or] C2 = AJθ∊/pθS3

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[or] C = D 3/2; √JAθ/pθ ∊

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Sir W. Preece assumes the quantities under the root to be a constant (1642, D being inches).

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If, now, we take my values for θ and ρθ to be correct, we may calculate the constant value for ∊ which is assumed by Sir W. Preece. It is—

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∊ = 0.00176 absolute units (approximately).

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Ayrton and Kilgour (l.c.) give the formula—

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∊ = 0.0011113 + 0.0143028 D - 1 mils for a temperature difference of 200° C. for platinum.

The accompanying diagram (Plate XIV.), of which the ordinates are values of ∊, the abscissæ values of 1/D in., shows clearly the relation between Sir W. Preece's law, Ayrton and

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Kilgour's law, and the approximate values of ∊ calculated from my results. The experimental values obtained by Ayrton and Kilgour are shown by circles.

It will be seen that my results agree fairly (considering a possible difference between the materials tin and platinum) with Ayrton and Kilgour's experimental results, but do not agree with the extrapolation indicated by the law of Ayrton and Kilgour given above, and that Sir W. Preece's constant value is incompatible with both.

My curve, it will be seen, agrees fairly well with a straightline law from 157 mils to 20 mils diameter of wire of the following form—

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∊ = 0.000314 + 0.031 D-1, 157 to 20,

the maximum error being about 8 per cent. at 97 mils (only 4 per cent. if the fusing-current is calculated from the formula, since the current is proportional to the square root of the emissivity). The figures are only provisional, but it is interesting to compare them with the Ayrton and Kilgour formula. However, I do not think that emissivity can be a simple function of the diameter. As the result of a consideration of the factors involved I fancy that the true curve will be found wavy or “kinky.”

Experiments upon-samples A and B, while giving results hardly distinguishable from each other, both agree in suggesting a kink in the curve at 97 mils.

Of the further work remaining to be done with fuses it will be observed— (1.) That a standard is required for the specification of tin wire (or whatever metal is selected) in the particulars of specific resistance, annealing coefficient, and temperature coefficient (or specific resistance at a temperature near fusing-point) and the fusing-point. At any rate, it should be decided whether a guarantee of “commercial purity” of metal is sufficient. (2.) That the cooling effect of terminals needs inquiry. I hope shortly to publish figures accounting for this factor; but a full theory of this phenomenon involves amongst other things thermal conductivity. This quantity, however, can, I think, be calculated in a form suitable for the purpose from the cooling-effect results. (3.) The effect of change from a horizontal to a vertical position of the fuse-wire must be studied. This should, however, be a small matter after the phenomena for horizontal wires have been determined. Corrections in the form of small percentages should cover it in practical cases. (4.) That then the phenomena of fuses in their porcelain boxes may be studied with some hope of success. This is the problem which I set out to solve; it is the practical

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problem which interests insurance companies, electrical engineers, and users of electricity alike.

I do not think it reasonable that private individuals should be expected to carry out work of this kind at their own expense, but I shall be content if I have been able to do something towards the conversion of the fusible cutout from an empirical makeshift to a scientific instrument.

In conclusion, I would like to thank Mr. Stuart Richardson, A.M.I.E.E., of the New Zealand Electrical Syndicate, for the loan of measuring-instruments and the use of standard instruments for the calibration of the same.

Note.—I have taken out values for emissivity from the research of J. E. Petavel (loc. cit.), and find that they agree very well with my curve. The points are marked in triangles on the chart. The following are the figures (emissivity at 200°C. of platinum wires):—

Diameter (Mils). e
44.15 0.001 in horizontal iron tube. Inch. int. Diam.
44.15 0.00108 in horizontal brass box, 1 ⅛ in. × 3in. × 3in.
23.7 0.00148 in horizontal brass box, 1 ⅛ in. × 3in. × 3in.

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Mr. Petavel also gives a figure from Dr. Bottomley's researches* of a vertical wire, which he calculates at about 11–8 mils, for which ∊ =0.8137/408 =0.001995, which value, plotted back on Mr. Petavel's curves, fig. 7 reduces to about 0.00165. Then, adding 30 per cent. (to express the difference between a wire vertical and horizontal, estimated from the same curves), we have ∊ = 0.002145. This value is plotted in a square, and is given for what it is worth.

Dr. Bottomley in this paper gives results, which I take as the lowest value of ∊ attained by himself, as 45 × 10—6, and as 30 × 10—6 by Schliermacher, in the best vacua obtainable.

I have taken a value of ∊ for a ½ in. copper rod at 200° C. from Mr. R. W. Stewart's results, for which ∊=0.000387, about; also a value from an engineering-book of ∊ = 0–000245 for a steam-pipe at about 150° C. These have been plotted in as figures of comparison; Mr. Box's formula (∊ = 0.00005710 × 0.0833 D-1), which is referred to by Professor Ayrton and Mr. Kilgour, for large cylinders at a temperature not given.

These results, plotted together, suggest a curve for ∊ of some fractional power of D-1, with zero at ∊=0-00005,

[Footnote] * Phil. Trans., 178a, 1887.

[Footnote] † Phil. Trans., 184a, 1893.

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about, for average surfaces. Such a curve sketched in gave the following trial ordinates:—

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D—1 Trial Value of ε. ε—0.00005. ε calculated.
0.2 0.00390 0.00385 0.00396
0.1 0.00255 0.00250 0.00257
0.05 0.00170 0.00165 0.001674
0.02 0.00095 0.00090 0.000956
0.01 0.00065 0.00060 0.00063
0.34 0.00553
1.0 0.010915

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Ayrton's formula gives 0.0154 for D-1 = 10.

The column “∊ calculated” is of values of ∊ calculated thus:—

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∊=0.00005 + 0.010865(D-1)635, D being mils.

As will be seen, the agreement is fairly good as a first approximation.

The corresponding curve has been traced (thin line), marked “B formula.” It will be seen to agree in a rough way with the data I have here collected, except for the copper rod and steam-pipe, and also with Professor Ayrton and Mr. Kilgour's results for wires finer than 2–7 mils, which could not be plotted on the diagram. It will be observed that Mr. Box's formula is parallel or tangential to it at 0.92 in. diameter, my own straight-line formula at about 50 to 70 mils, and the formula of Professor Ayrton and Mr. Kilgour at 7 or 8 mils (about the mean diameter of the wire used by them).

It would appear from Dr. Bottomley's and Mr. Schliermacher's researches that the radiation, or electro-magnetic emission, is not more than 0.00003 for silver or platinum tested in vacua. This is not of very different dimensions to the constant of Box's formula. Consequently, I take it, practically, the whole of the emission from ordinary fuse-wires is convective.

As this matter has been elaborated, I wish to again say that my figures are subject to correction, chiefly for thermometer error, especially for the three finer wires (those for which D-1 = 0.049, 0.068, and 0.1258), the physical constants of these wires not yet having been determined.