October 4, 1901.] 



SCIENCE. 



539 



all concerned that they should everywhere fur- 

 nish good models. 



Let us first take the general law of inverse 

 square, on account of its widespread applica- 

 tion. We find the definition of ' Newtonian 

 Forces, the most familiar examples of which are 

 the mutual attractions of the sun and the 

 planets' (Webster, p. 113), followed by the 

 general expression for potential energy in such 

 cases (p. 114). The latter contains no indica- 

 tion of the factor which becomes gravitation 

 constant, or dielectric constant, or permea- 

 bility factor ; yet it has been stated previously 

 (p. Ill) that "Potential energy is defined as 

 work. The unit of energy is, therefore, the 

 erg.'" The medium-factors for electric and 

 magnetic phenomena are introduced later (p. 

 354), but the gravitation constant is nowhere 

 restored in the developments, so far as I am 

 aware. 



The potential function, or potential, is very 

 commonly defined as representing so much 

 work. Thus, " The potential at P is the work 

 done by the electric forces when the unit charge 

 is taken from P to an infinite distance " (Thom- 

 son, p. 27). Or we are told that the potential 

 function is obtained as a particular value of the 

 potential energy, when one mass-factor is unity 

 (Webster, p. 144). This is inconsistent with 

 the dimensions of potential as generally ac- 

 cepted, and as given by the authors themselves 

 (Thomson, p. 449 ; Webster, p. 559). It is con- 

 sistent, however, with their definition of field 

 as a force. The negative vector-parameter of the 

 potential function is " The strength of the field, 

 that is, the force experienced by a unit of mass, 

 concentrated at the point in question " (Web- 

 ster, p. 144). "The electric intensity [field] 

 is the force acting on a small body charged with 

 unit positive charge, when placed at this point ' ' 

 (Thomson, p. 13). But the dimensions of field 

 are not those of force. Electromotive force, as 

 difference of potential, is then of course work 

 also ; we find this explicitly stated (Thomson, 

 p. 282 ; Webster, p. 333). Current, again, is 

 work as well. " JF=,47ri. Thus the work [ Jl^] 

 done on unit pole, when it travels round a 

 closed curve, * * * is equal to 4wi, if i is the 

 strength of the current " (Thomson, p. 325). 

 Professor Webster gives this in the form i2 = Jw 



(p. 413). Here S2 is magnetic potential, /cur- 

 rent and 0) solid angle. 



The clue to all these confusions (except the 

 first) is the same elementary consideration. 

 There is a failure to distinguish, in the context 

 and in set terms, between a numerical equality, 

 and a ' physical equation ' in which the quan- 

 tities equated are of the same dimensions. But 

 a sense of such differences must be cultivated, 

 as a part of correct physical thought ; although 

 they may be ignored sometimes for the im- 

 mediate purposes of the mathematician or of 

 numerical determinations in the laboratory. It 

 is probable that repeated contact with state- 

 ments like those cited dulls our first impression 

 of the contradictions in them. In order to re- 

 store its vividness, we need only to construct 

 parallel instances, with which custom has not 

 familiarized us. Thus, density is mass ; that 

 is, the mass of a unit volume. In a similar 

 (numerical) sense, force, or momentum, or 

 kinetic energy is mass in special cases. I have 

 pointed out elsewhere (' Principles of Me- 

 chanics,' p. 242) that the true dimensional re- 

 lations for the electrical quantities can be 

 preserved very simply by defining field and 

 potential, respectively, as force and work per 

 unit (in the body afl^ected) of the measured 

 quality that is subject to the influences of the 

 particular field. There is no unclearness if the 

 (dimensional) division is indicated by this 

 verbal device or its equivalent. 



F. Slate. 



University of Califoenia. 



TRE BRITISH ASSOCIATION FOB THE AD- 

 VANCE3IENT OF SCIENCE. 



There is not much to add to the information 

 we gave last week in regard to the Glasgow 

 meeting of the British Association. The presi- 

 dent of the Association was directed to write a 

 letter to the American embassy in the name of 

 the Association, containing expressions of regret 

 on the death of President McKinley. 



The attendance was 1,912, distributed among 

 the different classes as follows : 310 old life 

 members, 37 new life members, 374 old annual 

 members, 131 new annual members, 794 associ- 

 ates, 246 ladies and 20 foreign members. This 

 is a smaller attendance than at the previous 



