December 17, 1891] 



NA TURE 



163 



convection, and conduction, and it was further necessary to 

 improve on the calculation one of us had published on this 

 subject in the Electrician for 1879, by taking into account the 

 fact that the emissivity, as well as the thermal and electric con- 

 ducting power, of the wire differed at different points in con- 

 sequence of the difference of temperature. 



Until we had completed the experiments described in this 

 paper, we could, of course, only employ in this calculation values 

 that we had guessed at as being something near the truth for 

 the emissivity of platinum wire for different diameters and at 

 different temperatures. Hence, after the completion of the ex- 

 periments, we took up the mathematical investigation again, 

 substituting for the emissivity such a function of the diameter of 

 the wire and the temperature of the point as we had experiment- 

 ally found it to be. Section IV. of the paper contains the in- 

 vestigation by which we finally arrived at the calculated dis- 

 tribution of temperature along the wire, and we have to express 

 our sincere thanks to Prof. Henrici (whom we consulted as to 

 the best method of practically solving the rather complex 

 differential equation arrived at) for the warm interest that he has 

 taken in the mathematical treatment of the subject, and for the 

 many suggestions which he has made, and which have enabled 

 us to arrive at the mathematical solution given in the paper. 



Each wire to be tested was stretched along the axis of a hori- 

 zontal water-jacketed cylinder 32 "5 cm. long, 7 62 cm. external 

 and 5 '8 cm. internal diameter, the inner surface of which was 

 blackened and kept at a constant temperature by a stream of cold 

 water flowing through the jacket. The rate at which heat was 

 lost by any one of the wires was measured tiy the product of 

 the current passing through it into the P. D. (potential difference) 

 maintained between its ends, while the ratio of the P.D. to the 

 current gave the resistance of the wire, and, thsrefore, its 

 temperature. Experiments were in this way made with various 

 currents flowing through each of the nine wires. 



As the variation of resistance with temperature is known to 

 vary with different specimens of platinum, experiments were 

 separately made to determine the actual law of variation of 

 resistance with temperature up to 300" C. for each piece of wire 

 that had been employed in the emissivity experiments. 



In this later determination various thermometers were used, 

 and the subsequent comparison of these thermometers with a 

 Kew standard thermometer involved a vast amount of labour, 

 from the fact that it is, or at any rate was not possible three 

 years ago, to purchase from the Kew Observatory a standard 

 thermometer reading from, say, 200' to 300" C, with a short, 

 wide chamber at the base in which the mercury expanded beljw 

 200' C. All that could be obtained was a long thermometer 

 which had been carefully tested between 0° and 100° C, and the 



remainder of whose tube had been simply calibrated for 

 uniformity of bore. The consequence was that when we 

 desired to compare one of our thermometers reading, say, from 

 200' to 300' C, with the Kew standard, their bulbs were very 

 far apart when both were immersed in the oil-bath, and with 

 1 the tops of the mercury columns just above the surface of the 

 I oil. A short description is given in the paper of the devices 

 employed to overcome this difficulty, and which enabled an 

 accurate comparison to be made between the thermometers. 



On examining the curves, accompanying the complete paper, 

 which show the emissivity for each temperature for each of the 

 nine wires, we see that — 



(i) For any given temperature the emissivity is the higher the 

 finer the wire. 



(2) For each wire the emissivity increases with the temperature, 

 and the rate of increase is the greater the finer the wire. For 

 the finest wire the rate of increase of emissivity with temperature 

 is very striking. 



(3) Hence the effect of surface on the total loss of heat (by 

 radiation and convection) per second, per square centimetre, per 

 1° C. excess temperature, increases as the temperature rises. 



On comparing the loss of heat from the wire of I '2 mils 

 diameter when at 300^ C. with that from the wire of 6 mils 

 diameter when at 15^ C, both being in an inclosure at 10' C, we 

 see that the former loses per square centimetre of surface per 

 second not 



300 — 10 



15 — 10 



or 58 times 



as much heat as the latter, as it would if the emissivity were the 

 same ; but, instead, 



60 X 58, or 3840 times 



as much heat ; arising from the fact that the emissivity — that is, 

 the number of calories (gramme C") lost per second, per square 

 centimetre of surface, per i" C. excess temperature — of the i 2 

 mil wire at 300° C. is 60 times as great as that of the 6 mil wire 

 at 15^, the emissivity of the latter wire varying very rapidly 

 near 15' C. 



From the curves which accompany the complete paper, each 

 curve giving the variation of emissivity with temperature for a 

 particular wire, the following table has been drawn up, giving 

 the emissivities of the various wires at eight useful temperatures, 

 and it will be observed that, in consequence of our investigation 

 having been made on wires of which the thickest was thinner 

 than the thinnest ever previously used in absolute determinations 

 of emissivity, the emissivities we have experimentally obtained 

 are far greater than any previously arrived at. 



Diameter of wire in 



0-008230 

 0-005950 

 o'oo2i93 

 0-002460 



0009560 

 o 005860 

 0003336 

 0-002660 



j°C. 



rso C. 



0-010300 



o 007500 



0-004086 



o 002806 



0010846 

 0-007900 

 0-C04552 

 o 002930 

 0*002804 

 0-002297 

 0-002053 

 0-001894 



0-011875 

 o 008600 

 0-005095 



O 0032 12 

 0-002939 

 0-002448 

 0002216 

 0-002027 



0012783 



o 009070 



0005379 



o 003460 

 o 003076 

 o 002586 

 o 002363 

 0-002136 



250° c. 



0013625 

 o 009480 

 0-005628 

 o 003666 

 0-C032I7 

 o 0027 1 8 

 o 002490 

 o 002224 



300° C. 



0014400 

 o 009850 

 0-005845 

 0003837 

 0-003352 

 o 002843 

 o 002608 

 0002286 



1 he wire of 4 mils diameter i* omitted from the table, as th; experiments showed that its specific resistance was much greater, its temperature 

 coefficient much smaller, and its emissivity much smaller than if it had been of platinum. This piece of wire probably, therefore, contained iridium 

 or silver. 



We find that the emissivity of thin platinum wires of different 

 diameters at the same temperature can be very fairly expressed 

 by a constant plus a constant into the reciprocal of the diameter 

 of the wire. For example, we find that 



At 100' C. ^ = 00010360 -t- 00120776/-', . , . . (i) 

 ,, 200 „ e - 00011113 + o-oi43028(/-', .... (2) 

 ,, 300 „ e - 0-0011353 + 0-016084 d"^, .... (3) 



where d is the diameter of the wire in mils, or thousandths of 

 an inch. 



The statement, not unfrequentiy made, that the current 

 required to maintain a wire of a given material at a given 



NO. I 155, VOL. 45] 



temper-iture above that of the surrounding envelope is pro- 

 portional to the diameter of the wire raised to the power 

 three halves, is equivalent to stating that the emissivity is 

 independent of the diameter. Now from the three forn.ulae 

 (l), (2), (3), given above for e, we may conclude — 



That for a temperature of 100° C. the value of d in the 

 formula 



e = 0-0010360 -I- 0-0120776^-^ 



must be something like 220 mils, or 56 mm., in order that the 

 neglect of the second term may not make an error in e of more 

 than 5 per cent., and something like 1-15 inch, or 293 mm., if 

 the error is not to exceed i per cent. 



