DETERMINATION OV HIGH TEMPERATURES BY REFRACTED RAYS. 465 



by careful filing and polishing on the end of a narrow pencil of the same 

 substance. This little knob of lime was then gradually heated, carefuUy 

 turning it round, up to incipient fusion in the oxyhydrogen flame, so as to 

 allow contraction to take place. With care in this way, it is possible to get 

 a very uniform sphere having a surface of about one square centimetre. The 

 pyrheliometer was filled with bisulphide of carbon, for the purpose of 

 registering minute alterations of temperature. The experiments were made 

 at two distinct temperatures, viz. at a low visible red heat and at the 

 maximum temperature of the oxyhydrogen flame. The mean of these 

 experiments has given, for radiation per square centimetre per minute 

 at about 700° C, from 20 to 25 gramme-units per minute, and at 2000° C. 

 maximum temperature from 2000 to 2500 gramme-units — the ratio of the 

 amounts being as 1 to 100, very difi'erent from the calculated result. The 

 law of Dulong and Petit, therefore, gives a far too rapid increase for the total 

 radiation ; and if we assume the law to be true in order to define temperature, 

 the results arrived at are always too low. 



If the total amount of radiation at different temperatures is tabulated, 

 using a thermoelectric pile and an apparatus similar to the one employed for 

 light-intensities, it is found that the curve of increase may be very accurately 

 represented by a parabolic curve. The empirical formula of this curve is 



580° + »3 X 46° = «^E, 



where R is the total radiation at 668° C, and 580°C. + 7i3 x 46° C. is equal 

 to the temperature of the substance. If we calculate the total radiation from 

 the above formida at 2000° C. as compared with that at 668° C, it is in the 

 ratio of 1 to 112. Regarding these comparisons, they appear fairly within 

 the limits of experimental errors. We would anticipate that a similar law 

 would hold alike for heat-rays and light-rays. 



Assuming these laws to be approximately correct, it is interesting to find 

 what hypothetical temperature in the case of a solid or fluid substance would 

 correspond with the luminosity and total radiation from the sun. 



From the experiments of Fizeau and Foucanlt*, the luminous intensity of 

 the sun is found to be 146 times that of the lime-light. A temperature of 

 13,000° C, according to the formula given above, would give 144 times the 

 luminous intensity at 2000° C. 



From the observations of PouiUet, the total radiation from 1 square centi- 

 metre of the sun's surface in 1 minute was 85,000 units, and cannot well 

 exceed 100,000 units. At a temperature of 11,000° C, according to the 

 above formula for total radiation, the amount would be 50 times that at 

 2000° C. Now we have found above that a square centimetre of lime at 

 2000° C. emits 2000 gramme-units per minute, so that a temperature of 

 11,000° C. would be sufficient to evolve 100,000 gramme-units, as much 

 heat as is produced by the sun. The recent observations of Soret (' Biblio- 

 thuque Universelle,' 1872) prove that the total radiation of the sun is between 

 50 and 60 times that of lime heated to 2000° C. in the oxyhydrogen flame. 

 The estimate of 100,000 gramme-units per minute from the sun is therefore 

 not too great, seeing that it is just 50 times the amount actually emitted by 

 observation at 2000° C. 



Expenments luith Electric Arc. — The experiments formerly detailed to the 

 Association on the specific heat of carbon up to a temperature of 2000° 0, 

 naturally suggested the attempt to define by observation the temperature of 



* Ann. de Cliim. et de Phys. 1«44. 



1873. 2 H 



