20 PHYSICS 



at 2,500,000. The newer determinations * of the temperature of the 

 surface are, to be sure, in better agreement. Le Chatelier finds it to be 

 7600; Paschen, 5400; Warburg, 6000. Wilson and Gray publish 

 as their corrected result 8000. The estimate of the internal temper- 

 ature is of a more speculative character. Schuster's computation 

 gives 6,000,000 to 15,000,000; that of Kelvin, 200,000,000; that 

 of Ekholm, 5,000,000. 



Another interesting illustration of the dangers of extrapolation 

 occurs in the history of electricity. Faraday, starting from data con- 

 cerning the variation between the length of electric sparks through 

 air with the difference of potential, made an interesting computation 

 of the potential difference between earth and sky necessary to dis- 

 charge a cloud at a height of one mile. He estimated the difference of 

 potential to be about 1,000,000 volts. Later investigations of the 

 sparking distance have, however, shown this function to possess a 

 character quite different from that which might have been inferred 

 from the earlier work, and it is likely that Faraday's value is scarcely 

 nearer the truth than was the original estimate of the temperature of 

 the sun, mentioned above. 



Still another notable instance of the errors to which physical re- 

 search is subject when the attempt is made to extend results beyond 

 the limits established by actual observation occurs in the case of the 

 measurements of the infra-red spectrum of the sun by Langley. His 

 beautiful and ingenious device, the bolometer, made it possible to 

 explore the spectrum to wave-lengths beyond those for which the law 

 of dispersion of the rock-salt prism had at that time been experi- 

 mentally determined. Within the limits of observation the dispersion 

 showed a curve of simple form, tending apparently to become a 

 straight line as the wave-length increased. There was nothing in the 

 appearance of the curve to indicate that it differed in character from 

 the numerous empirical curves of similar type employed in experi- 

 mental physics, or to lead even the most experienced investigator to 

 suspect values for the wave-length derived from an extension of the 

 curve. The wave-lengths published by Langley were accordingly ac- 

 cepted as substantially correct by all other students of radiation; but 

 subsequent measurements of the dispersion of rock salt at the hands 

 of Rubens and his co-workers showed the existence of a second sudden 

 and unlooked-for turn of the curve just beyond the point at which the 

 earlier determinations ceased; and in consequence Langley 's wave- 

 lengths and all work based upon them are now known to be not even 

 approximately accurate. The history of physics is full of such ex- 

 amples of the dangers of extrapolation, or, to speak more broadly, of 

 the tentative character of most of our assumptions in experimental 

 physics. 



1 See Arrhenius, Kosmische Physik, p. 131. 



