58 POPULAR SCIENCE MONTHLY. 



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 hetween 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 discharge 

 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 appear- 

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

 numerous empirical curves of similar type employed in experimental 

 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 accepted 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 coworkers 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 exam- 

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

 tentative character of most of our assumptions in experimental physics. 



We have then two distinct sets of physical concepts. The first of 

 these deals with that positive portion of physics the mechanical basis 

 of which, being established upon direct observation, is fixed and defi- 

 nite, and in which the relations are as absolute and certain as those of 

 mathematics itself. Here speculation is excluded. Matter is simply 

 one of the three factors which enters, by virtue of its mass, into our 

 formulae for energy, momentum, etc. Force is simply a quantity of 

 which we need to know only its magnitude, direction, point of appli- 



