200 



SCIENCE. 



than those of the molecule. Granting the correctness of 

 the expression for argument's, sake I must confess that I 

 do not understand how the Professor gets the expression 

 E' — E=f given under 3, in his "Table of Forms of 



Energy." If e in the expression E == t is anything 



2 



it certainly must be the rat'o_ where E =^iZ- is the energy 



E 2 

 of agitation of an atom. By subtraction we obtain E' — 



E = 



in if 2 in Zr 



= — . (e — 1) and not £ as the Pro- 



believe that the equation E' = 



fesscr would lead us to believe. While I regard it simply 

 a gratuitous assumption to give the expression for the 

 total energy of an atom, and that for the total energy of 

 a molecule the same form — because we have no experi- 

 mental evidence whatever to justify us to believe that the 

 conditions of the atom resemble those of the molecule — I 



£ — in which e is inier- 

 2 



nal energy is utterly incorrect, e. in this expression is 

 not at all analogous to ft in y z ft mv' 2 the expression 

 for the total energy of a molecule as given by 

 Maxwell. Here ft is the numerical ratio of the total 

 energy to the energy of agitation, an abstract, 

 while e is internal energy, a concrete. Here let me ask 

 what is energy times energy. The form E' — E = e is 

 undoubtedly correct. From this by substitution we get 



T,} m v ' 2 , . 111 V 2 



E = + £ and net £ ■ 



2 2 



The statement " Latent heat, specific heat, and specific 

 inductive capacity, are all involved in (that factor?) e," is 

 certainly not correct. Latent heat is work performed 

 upon some body, and is, according to Clausius, partly in- 

 ternal and partly external. The external work is per- 

 formed upon surrounding material systems. The internal 

 work is, in general, composed of two parts — one ex- 

 pended upon the molecules in expanding the body from 

 one state of aggregation to another, the other part is ex- 

 pended upon the parts of the molecule. It is only this 

 last portion which can affect the atom as such, and which 

 can in any way be involved in £. Similarly we find that 

 specific heat is also work performed, and that, too, of a 

 complex nature. Specific inductive capacity seems to me 

 to belong to an altogether different class of phenomena. 



In regard to the ether the Professor makes some very 

 curious statements. He says that he knows nothing of 

 the specific properties of the ether, yet in the same sen- 

 tence is the statement " ether is not matter," as if this 

 were a generally accepted view. If the ether is not mat- 

 ter, what is it ? There are two ways of looking at mat- 

 ter — the subjective or metaphysical, and the objective or 

 physical. Metaphysically defined matter is anything 

 which has extension or occupies space. For the physical 

 definition I quote Maxwell' 2 : " Hence, as we have said, 

 we are acquainted with matter only as that which may 

 have energy communicated to it from other matter, and 

 which may, in its turn, communicate energy to other mat- 

 ter." Again, he says: " Energy cannot exist except in 

 connection with matter." Whether, then, we accept the 

 metaphysician's definition or the physicist's, we must regard 

 ether as matter; for it certainly has extension and occu- 

 .pies space, and it certainly receives from other matter, 

 transmits and imparts to other matter energy. That 

 Maxwell regarded ether as matter, appears from the fol- 

 lowing quotation, taken from the same work and page as 

 the preceding: "Hence, ... we conclude that the 

 matter which transmits light is disseminated through the 

 whole of the visible universe." The italics are mine. Pro- 

 fessor Dolbear, furthermore, tacitly assumes ether to have 

 mass, as will appear hereafter. 



Again, the Professor says : " Furthermore, as atoms 

 differ in mass so will their rates of vibration differ when 



a " Matter and Motion," p. 93. 



they possess the same absolute amount of energy. Ve- 

 locity, in this case, will be equal to amplitude a b, the 

 space point c passes over during one vibration. If m and 

 in' be two atoms of different masses having equal energy 



of vibration, thenE=2»-g= and that is 



2 2 m' v" 2 



the square of their velocities is inversely as their masses, 

 so that wave-length in the ether will vary as the mass of 

 the atom." This is certainly very curious logic and math- 

 ematics. The statement may be true, and the investiga- 

 tions of Lecoq de Boisbaudran even furnish some evi- 

 dence in its favor, but the mathematical proof offered by 

 the Professor does not justify any such conclusion, v 

 and v are, according to his own statement, amplitudes of 

 vibration; when, then, the atoms of different masses have 



equal energy, the proportion ^L = _^_ simply proves 



tri v 1 



that the squares of the amplitudes of vibration are in- 

 versely as the masses. In what manner the rate of vibra- 

 tion and wave-length in ether follows from this relation 

 of mass to amplitude the Professor does not make clear. 

 In order to make the above conclusion of Professor Dol- 

 bear correct, we must have the further condition, - — = — 



ifl n 



where n and it are the relative number of vibrations of 

 in and in' in equal times. One of the most funda- 

 mental equations of motion is unquestionably v = 



s 



T 



Hence, as the amplitude a b is a space passed over in a 

 given time, we can make it equal to v only by making t 

 unity. Similarly we can make the amplitude of 111 equal 

 to v' only by making t unity. If now we wish to com- 

 pare the velocities and masses of the two atoms we can 

 certainly not use different units of time to determine those 

 velocities ; and we get, according to the Professor's 

 statement, the self-contradictory result that two atoms, 

 which make each one vibration in equal times yet have 

 different rates of vibration. To make the problem more 

 general let us take two atoms of masses m and in'. 

 Let them make respectively 11 and n' vibrations of ampli- 

 tudes, a and a' in unit of time. The time of one vibra- 

 tion of in will be — and of ni , ~. Substituting 



n n 

 these values successively for t, and a and a' successively 

 for s in the equation of motion, we have 



a 1 , a' , , , • • v an 



v — : an and v =_ = a n combining — = , 



1 1 v a' n' 



or the velocities are proportional to the products of the 

 amplitudes by the number of vibrations in unit time. 

 Combining this with the Professor's proportion we have 



in a' 2 n" 2 



a- n 



To obtain from this the relation ,f — = ^L, 



?■ and X be- 



ing 



I'ave-lengths, we must fulfil the condition 



t * _ n 

 a' n* n 



a' 3 



.= . — If, then, two atoms of the masses in and 



a" 2 



n a 



m have equal energy, and the relation — = — 



11' a' 2 



holds 



and 11 , being the respective number of vibrations in unit 

 time, and a and a' corresponding amplitudes, the relation 

 X _ m 



For we will then have, as above shown, — =_ . . We also 



JL = in which "K and A' are wave-lengths will follow. 



have A 



and V = 



From these we obtain — = — 

 A n 



and, hence, 



in 

 m 



