86 



NA TURE 



\_Nov. 26, 1 1 



dependence on temperature of radiation of heat from the 

 same surface — namely, that the radiation is in proportion 

 to the fourth power of the absoUite temperature. This 

 law was deduced originally from certain experiments of 

 Prof. Tyndall on radiation from a heated platinum spiral 

 {Pogg. Atin., Bd. c.xxiv., quoted by WuUner, " Exp. 

 Physik," Bd. iii. 1885). The law has been also con- 

 sidered by other writers, including Christiansen {Ann. 

 del- PhysUc und C/icmie, Bd. xix. 1883), and they have 

 adduced experiments which seemed to them to confirm it. 



The method of experimenting which I employ makes 

 it easy to test the truth of such a law, and in fact to find 

 the law, and 1 have accordingly made the necessary 

 calculations for the former purpose. 



In my experiments a current of known strength is 

 passed through the wire under examination, and the 

 increase in the resistance of the wire due to heating by 

 the current is determined while the current is passing 

 through it. When the temperature of the wire has be- 

 come constant, the heat generated by the current (which 

 can be calculated in absolute measure) must be equal to 

 that emitted by the surface of the wire plus that lost at 

 the ends of the wire by conduction. The temperature of 

 the wire at the moment is also ascertained from its resist- 

 ance (as was done by Siemens in his experiments on 

 resistance of platinum wire at different temperatures, 

 Prcc.K.S., vol. xix. p. 443). I have recently been experi- 

 menting on platinuni wires in a high vacuum down to 

 about 1/20 BE. (one twent\--millionth of an atmosphere), 

 as was described to the British Association at its meeting 

 at Aberdeen. 



The results quoted in Table I. below- were obtained 

 with a straight platinum wire about half a metre long, 

 004 cm. in diameter. It was contained in a glass 

 tube about o'6 cm. in internal diameter, and was sealed 

 into the tube at the two ends, the exhaustion being made 

 by a small side tube. The exhaustion at the time of the 

 experiment, as measured by a McLeod gauge, was 1/15 M. 

 The temperature of the room during the experiment was 

 15° C. 



The following two tables show the results of the ex- 

 periment, and also a comparison of these results with 

 the increase of emissivity with absolute temperature 

 calculated according to Stefan's supposed law. Four 

 cases have been taken which are numbered in the 

 first column of each table. For these the current, C, and 

 the resistance of the platinum wire, R, as found by expe- 

 riment, are gi\'en in the second and third columns of 

 Table I. The energy lost by the wire, C-R, called e in 

 Table II., and the estimated temperature Centigrade are 

 given in the fourth and fifth columns of Table 1. The 

 temperature of the surroundings at the time of the experi- 

 ment was 15° C. In the second table, the second, third, 

 and fourth columns show the absolute temperatures of 

 the wire and surroundings, and the energy lost, e, or C-R. 

 Column 5 shows the ratios of the energy lost in the 

 several cases to that lost in Case i, taken as unity. Ac- 

 cording to Stefan's law the heat emitted from the wire 

 ought to be given by 



W = A(S^ - T<), 

 where S is the absolute temperature of the wire, and T 

 that of the surroundings. Hence if Si, Tj denote those 

 temperatures in Case No. i, and if the heat emitted in 

 this case be taken as unity, the heat emitted with any 

 other temperatures, S and T, would be 



g4 _ ^4 



Si' - Ti'- 



This ratio, for the temperatures of the several cases, is 

 given in the sixth column of Table II. ; and it will be 

 seen by comparison with Column 5 of that table that the 

 increase of loss of heat with increase of temperature does 

 not follow any such exceedingly rapid law. 



Table I. — Rdsulls of Experiment 



Tempera- j, ^;,i, 

 M— , Lent.- ^f^;^, 



Resistanci 



C 

 I xo'i69 



2'2X •169 



65 X -169 



R 



1-087 

 1-371 



C=R 



1-087 



6-636 



78-12 

 9S-06 



■ 25 

 . no 



( Wire per- 

 . 525* I ceptibly red 



( in the dark 



( Wire dis- 

 . 550 \ tinctly red 



( hot 

 jstimate of temperature 



• Temperature 525° taken according to Draper's 

 of a body just visible in the dark. 



Table II. — Comparison of Experimental Results with Calcula- 

 tion in accordance with Stefan's Laiu 

 Absolute Absolute 

 tempera- tempera- Energy j,^,;^ r^,;„ 



:ofs 



Itted 



A comparison between the last two columns shows the 

 enormous discrepancy between the results calculated 

 from Stefan's law and those obtained by experiment. 



I am now waiting for the use of a secondary battery, 

 which I expect to have in a very short time, to determine 

 the ratio between the energy lost at dull red heat, say 

 550' C, and that lost at bright white heat (1200° C. 

 according to Draper), for the case of an incandescent 

 lamp. Already, however, we know enough of the be- 

 haviour of incandescent lamps — for example, in the case 

 of an eight-horse-power gas-engine, developing five-horse- 

 power of electric energy, and feeding 50 sixteen-candle- 

 power lamps — to be able to say that it does not require 

 ten times as much work to keep the lamps at white heat 

 as it does to keep them at dull red heat. 



November 16 J. T. Bottomlev 



ELLIPTIC SPACE 



ELLIPTIC geometry is more general than ordinary 

 geometry. It refers to a three-dimensional space 

 of a more general type than ordinary space. The ordinary 

 mathematics supposes a more or less plausible assumption 

 or axiom which reduces elliptic space to a special type. 

 The present little paper is intended to illustrate the un- 

 artificial character of the elliptic geometry and to indicate 

 the analytical nature of the axiom which the Euclidian 

 geometry requires us to introduce. We investigate the 

 measurement of distance on which the theory of elliptic 

 space chiefly depends. 



It is requisite to observe carefully the definitions which 

 are made, and to refrain from the introduction of any 

 notions not explicitly conveyed by the definition. Let us 

 consider a " point " whose co-ordinates are .r,. -fj, .1-3, .r4. 

 It is not necessary to think of these co-ordinates as 

 related to any geometrical scaffolding of tetrahedra or 

 the like. It is in fact desirable to attach no geometrical 

 import to the words, and merely to think of the word 

 "point" as implying the four magnitudes just written. 

 A second " point," y, will be similarly denoted by y^ y„, 

 I':,, j'4, and we define that the point x is distinct from _;', 

 unless in the case where 



J'l y-i J'3 yi 

 If X be a numerical magnitude 



x\ + Xj'i, .r„ -J- X)'.,, .1-3 + ^'i, ^'4 + ^yj 

 will also denote a point, and then, it being assumed that 

 .r and y are distinct, we have a multitude of points corre- 



