March 23, 1899] 



NA TURE 



495 



formula representing as closely as possible the results of experi- 

 ment. It is then assumed that the formula may be "extra- 

 polated," or used to estimate the temperature of a radiating 

 source of known intensity beyond the range of the observations 

 on which it was founded. This is a perfectly justifiable method, 

 and may lead to very good results if the empirical law happens 

 to be correct ; but if the formula happens to be unsuitable, it 

 may lead to the most remarkable conclusions. 



Law of Radiation, 



The curves shown in Fig. i illustrate some of the typical 

 formula; which have either been ])roposed for the law of radi- 

 ation, or been deduced from the results of modern experiments 

 over the experimental range of the gas thermometer, extending 

 to 1200° C, to which trustworthy determinations of temper- 

 ature on the theoretical scale are at present restricted. In 

 order to obtain a comparison of the formula; themselves, apart 

 froiTi other issues, the results of different observers are reduced 

 to a common hypothetical value, lo watts per square centi- 

 metre, for the radiation from a black body at 1000° C. 



Excluding the law of Newton, which applies only to small 

 differences of temperature, and also the law of Dulong and 

 Petit, which was founded on observations over a very limited 

 range with mercury thermometers, and is obviously inapplicable 

 at high temperatures, there is a certain family resemblance 

 between the remaining curves ; but the differences between 

 them are still so considerable that, if sufficiently accurate 

 measurements of temperature were available, it .should be possible 

 to decide with certainty which of the formula was the most 

 correct. A fairly close agreement is seen to obtain between 

 the formula proposed by Weber and the curves representing the 

 results of the recent experiments of Bottomley, Paschen and 

 Petavel. But, on the other hand, there is strong evidence, both 

 experimental and theoretical, in favour of the fourth power law 



LAW or RADIATION BoTTOMLEviBs«5 7n.scHi 



200' 



- Formulae of radiation. Experimental range. 



proposed by Stefan, which differs materially from that of Weber ; 

 and many supportersmay be found, especially among astronomers,' 

 for the very different formula of Rosetti. 



Results of Extrapdation. 



The importance of choosing a correct formula is most easily 

 realised by reference to Fig. 2, which represents the results of 

 extrapolation as applied to deducing the probable temperature 

 <if the sun. On the scale of Fig. 2, the dimensions of the ex- 

 perimental range of Fig. i are reduced to the thickness of the 

 Ime at the lower left-hand corner of the diagram. The line at 

 the top represents the intensity of solar radiation, which is 

 taken at 10,000 watts per square centimetre in round numbers. 

 The points at which the various curves meet this line show the 

 corresponding values of the solar temperature. 



The estimates of one million degrees and upwards, which 

 were current in many of the older books on astronomy, were 

 deduced from the law of Newton, and are obviously out of the 

 <luestion. The celebrated formula of Dulong and Petit gives 

 results between 1500" and 2000° C, according to the data 

 assumed, and evidently errs too much in the other direction. 

 At the same time, it must be observed that the recent formula 

 NO. 1534, VOL. 59] 



of Weber gives a result which is very little higher. Paschen 

 considered that his results lent support to Weber's formula, and 

 disagreed entirely with Bottomley's. But, according to the 

 writer's reductions, they agree very closely with Bottomley's, 



Fig. 2. — Temperature oi tlie sun by extrapolation. 



and are best represented by the formula ET'". The experi- 

 ments of Petavel agree most nearly with a fifth power law. 

 On the other hand, the experiments of Wilson and Gray, in 

 which the temperature was measured by the expansion of a 

 platinum strip, instead of by the increase of its electrical re- 

 sistance, appear to be in exact confirmation of the fourth power ' 

 law of Stefan, and give a much higher result for the solar 

 temperature. The formula of Rosetti is approximately a third 

 power law at high temperatures, and would not be admitted 

 as probable, at least by physicists, at the present time. 



The various formula above mentioned, together with the 

 methods employed and the results deduced, are summarised 

 in the following table. 



Table I. — Law of Radiation. 



* Formulae deduced by the writer from the observations. 

 The above table is not intended to be e.^haustive, but merely 

 as a comparison of typical formulae, reduced to a common 

 standard. It does not contain the results of photometric 

 investigations. 



The Necessity of More Accurate Measurements of Temperature. 

 The conclusion to be derived from the above illustrations 

 appears to be that in order to arrive at any certain knowledge 

 with regard to the law of radiation, and the measurement of 

 such extreme temperatures as those of the arc, and of the sun, the 

 first step must be to secure a higher order of accuracy in the 



