December 22, 1893.] 



SCIENCE 



339 



SCIENCE: 



Published by N. D. C. HODGES, 874 Broadway, New York. 



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THE CENTIMETEE GEIMME SECOND AND 

 THE CENTIMETRE DYNE SECOND SYSTEMS 

 OF UNrrS AND A NEW GEAVITATIONAL 

 EXPERIMENT. 



B. BEGINALD A. FESSENDEN, ALLEGHENY', PA. 



The C. G. S. system of units was undoubtedly a great 

 advance over previous systems, but it has at least one 

 serious disadvantage. This is the emj)loymeiit of the 

 gramme as one of the fundamental units. Mass is not a 

 fundamental conception, and has no claim to be put in the 

 same class as length and time. We can conceive of matter 

 as distinct from mass just as easily as we can conceive of 

 matter as distinct from electricity', and far more logically, 

 for each unit of matter is always associated with the same 

 quantity of electricity, while the amount of mass asso- 

 ciated with the unit of mattei", i. e., the atom, is more 

 than 200 times as great in the case of some kinds of 

 atoms as in others. 



There is, therefore, this theoretical objection. There is 

 also a practical one. Any system of units must be 

 logical, m that the dimensional formula for any quantity' 

 must be made up of such concepts only as are necessarily 

 associated with that quantity. This is not the case with 

 the C. G-. S. system. The dimensional formula for quan- 

 tity of electricity in the electrostatic system of units is 



L" T ~' M 's in which the concei^tion of mass is brought 

 in. Now, mass has no connection with electricity, so far 

 as we know at present; if thert were no such thing as 

 mass we should still have electricity, and therefore the 

 system of units which gives such a formula is defective. 



There is a second practical reason. This is, that in the 

 C. G. S. system of units it is much more difficult to see 

 readily relations between different quantities, and to in- 

 terpret them, than in a more theoretically perfect one, on 

 account of the fact that the M in the formula of a force 

 which has no necessarj- connection with matter may can- 

 cel out with an M which has a legitimate right to be 

 there For instance, suppose that, in working out a 

 problem, we get such a result as M/T, this may mean al- 

 most anything, i. e., it may be the product of various 

 things, and what these are is not readilj- apparent. 



As a matter of convenience, the writer has used a 

 system of units in which the dyne takes the place of the 

 gramme, and has found that there is a considerable ad- 

 vantage. 



In this system the unit of mass drops back into its 

 rightful place, and is a dimension of the same sort as the 

 unit of electricity or the unit of magnetism. GTavity is 

 treated as a separate substance, di'itinct from matter, but 

 reading in it in the same way as magnetism is supposed 

 to reside in iron, and unit quantity of gravity is defined 

 as that quantity which will attract equal quantity placed 

 at unit distance with unit force. The atomic weight of 

 an atom is its permeability to gravity, and corresponds to 

 j-i in magnetism. Lines of gravitational force are sup- 

 posed to radiate from a body char^-ed with gravity in the 

 same way as from a body charged with electricity or mag- 

 netism. 



Current of gravity is the quantity of gravity which 

 passes between any two points in unit of time, and unit 

 of gravitational potential causes unit current of mass 

 through unit resistance. 



To show the advantage of the C D. S. system over the 



C. G. S. system, the following table is sabjoined, which 



gives the principal dimensional formulae in Electricity, 



Magnetism, Heat and Gravity in both systems: 



C. D. S. Elec. Elec. 



Units. Gravity. Mag. Stat. Mag. Heat. 



Quantity /FL V^L V^L ^FU/T FL 



Current V^'L/T ^FL/T V^L T V^LVT^ FL/T 



Difference of 



Pot ... . ^/F ^F ^F VFT/L 1 



Resistance . . T/L T/L T/L L/T T/FL 



Capacity . . . L L L L'/T' FL 



C. G. S. Elec. Elec. 



Units. Gravity. Mag. Stat. Mag. Heat. 



Quantity . M ^U^M/T V^^/M/T ^L^lSl L^M/T^ 

 Current . .M/T ^I/'^M/T ^-L'^M/T ^L^M/T L'-'M/T' 

 Difference 



of Pot.. LVT^ VLV^/T VL^M/T ^U^M/T 1 

 ResistanceLVTM T/L T/L L/T T'L=M 



Capacity MTyL'^ L L LVT= L=M/T' 



Incidentally, it may be noted that the notation is more 

 concise. This, however, is merely an accidental jioint, 

 the main thing being that the C. D. S. system is " ethi- 

 cally '' more correct, and that it does not distort ideas so 

 much in the handling as the C. G. S. system does. 



Jt will be found convenient to denote the different 

 quantities by means of subscript letters. Thus, Rg , 

 Km, Res, Rem> Rh represent gravitational, magnetic, 

 electrostatic, electromagnetic, and heat resistances. So, 

 also, Wj; represents gravitational work, i.e., l/2mir, Wem 

 represents electrical work, or C'R, W^ represents heat 

 energy, being really only a particular case of W,, , in 

 which the algebraic sum of the vectors representing the 

 velocities is zero, and W^ represents magnetic work, or 

 B X M.M.F. One or two remarks may be made in regai-d 

 to these formulae. There has been some doubt in regard 

 to the correct dimensional formula for temperature. This 

 has been caused by the incorrect assumption that k, the 

 specific heat of a body, is a number. That this is not the 

 case follows from the law of Dulong and Petit. Accord- 

 ing to this, the atomic heat of all the elements is the 

 same. Therefore, the heat required to raise a cubic cen- 

 timetre of any substance one degree C, i. ''., its specific 

 heat, is equal to the heat required to raise the tempera- 

 ture of a single atom the same amount x the number of 

 atoms in the cube. This last is a number, and the former 

 dejjends upon the kinetic energy of the atom. As the 

 dimensional formula for kinetic energj' is the same as that 

 for work, i. e., LF. (in the C. D. S. system), the formula 

 for temjierature must equal FL-^FL., i. e., unit}-. 



We obtain the same result by considering the fact that 

 Quantity of Heat x Heat Potential must equal Work, i. e., 

 LF X beat potential=Lr. A current of Heat, then, is a cur- 



