December 3, 1915] 



SCIENCE 



803 



measuring radiant energy by the pyrlieliometer, 

 we are dealing with the transition at a surface 

 from radiant to thermal energy. What be- 

 comes of the thermal energy afterwards — 

 whether it is distributed to a large or a small 

 volume — does not concern us. The idea of 

 volume is already implied in the definition of 

 the calory which is the thermal effect of a heat 

 unit (equivalent to an equal amount of radiant 

 energy) upon unit volume of water. 



The consequences of this mistake are mo- 

 mentous. Whole tables of figures covering 

 several pages have been obtained with this 

 erroneous transformation factor. Other insidi- 

 ous errors may be traced to this misconception. 

 Eor instance, on page 126 we read : " The 

 Kurlbaum coefficient of the Stefan formula for 

 a perfect radiator is taken at Y.68 X 10"^^ 

 (C. G. Min. C°)= 5.32 X lO"" joules per square 

 meter per sec, so that the air radiates at six 

 times the rate of a perfect radiator in the 

 ether." Six times more than perfection is a 

 rather large order. 



In transforming the coefficient in the Stefan 

 Law (on p. 279) by a formula with Planck's 

 constants in C.G.S. units. Professor Bigelow 

 has incorrectly divided by the number of ergs 

 in a joule (10'), obtaining (p. 280): Sigma = 

 5.1210X10-'^ in C.G.S. mechanical units, 

 where the exponent should be — 5. His value 

 in M.K.S. mechanical units on this page is 

 sigma = 5.1210 X 10"^^, which involves an 

 additional error in the logarithmic work. The 

 correct value (after a small change in the 

 adopted basal number), namely, sigma = 

 5.510 X 10-= (M.K.S.) is indeed given at the 

 bottom of the page, but it has not been used 

 on page 126, where still a new error appears. 

 Evidently, the author's ideas on this subject 

 are considerably mixed. 



On page 370, the energy of solar radiation 

 " used in heating " the atmospheric stratum 

 " above 38,000 meters," is said to be " the true 

 albedo of the earth's atmosphere," which im- 

 plies that the author has a very obscure idea 

 of what astronomers mean by " albedo." This 

 is surprising, since he has given a correct 

 definition of the word on page 277. 



From what precedes, it results that the nu- 



merical values of thermal quantities in 

 Tables 84 and 86, which are said to be in 

 " gr. cal./cm.2 min." should all be multiplied 

 by 100, in which case the sum of the " atmos- 

 pheric thermal quantities attributable to solar 

 radiation " would not bear the remotest resem- 

 blance to the " solar constant," an assumption 

 which is fundamental to Bigelow's entire argu- 

 ment ; nor would the so-called " total atmos- 

 pheric radiant energy " be " equivalent to 

 the ' solar constant ' at the distance of the 

 earth" (p. 385), since, even were the equiva- 

 lence merely one of ultimate derivation, other 

 factors must be considered, for example, the 

 loss of solar radiation by reflection in passing 

 through the air, which does not enter into the 

 thermodynamic equation, notwithstanding the 

 author's assertion (on p. 262) that the albedo 

 of the earth " can be found indirectly by 

 thermodynamic computations." 



The summation of atmospheric thermal 

 quantities from the surface to 35,500 meters is 

 said to " give the amounts measured by the 

 pyrheliometer " (p. 379) ; but the " free heat " 

 (Qi- — Qo) ill each 1,000-meter layer, has been 

 stated for unit mass (since the dimensions of 

 heat, work and inner energy are given as [L^] 

 on page 376, instead of [ML^T-^I, which re- 

 quires that both M and T shall be unity), and 

 therefore the numerical values should be mul- 

 tiplied by the density of the layer in trans- 

 forming them to mass measurement. More- 

 over, (Qj — Q„) is due to a flux of long dura- 

 tion and therefore should be averaged, rather 

 than summed, in order to compare it directly 

 with the solar radiation at a given moment. 

 Finally, although neither an average nor a 

 sum of these quantities is exactly equal to 

 the simultaneously exhibited solar radiation, 

 the free heat, though derived from solar radia- 

 tion, has no immediate connection with the 

 solar radiation at the midday observation to 

 which 2(Qi— Qo) is incorrectly equated, for 

 it continues by night as well as by day and 

 represents the accumulated result of many days 

 of sunshine, as the writer of this notice has 

 shown in a paper " On the Solar Constant."^ 



1 American Journal of Science, Vol. XXXIX., 

 p. 201, February, 1915. 



