is commonly termed a '^Vacuum.^^ 113 



visible on any scale, and the number of molecules of re- 

 sidual gas contained even in a cubic centimetre of space may 

 be reckoned by billions. In the case of what would be re- 

 garded as an ordinary " good vacuum," such as that used in 

 Geissler's vacuum-tubes for electric discharges (say, 0*7 of a 

 millimetre of mercury, or a rarefaction of one thousandth), 

 the distance shifted through by the molecules under the 

 action of the pump in the act of rarefying would be only 

 about ^^ of an inch, and the number of molecules in a 

 cubic centimetre of the residual gas 19 thousand million mil- 

 lions (a cubic centimetre being about one fourteenth of a cubic 

 inch). 



5. It may perhaps be of interest to consider what effect the 

 rarefaction has upon the mean path of the molecules of gas, 

 the mean path being the mean or average distance moved 

 through by a molecule before coming into collision with ano- 

 ther molecule. The mean path of the molecules of several 

 well-known gases has been calculated by Professor Maxwell 

 from some carefully executed diffusion-experiments by M. 

 Loschmidt. The mean path of a molecule of hydrogen at 

 normal density is given at '0000965 of a millimetre, or 

 about „r,}r,nn ^f ^^ inch. Loschmidt has deduced the fol- 

 lowing proportion : — ''As the volume of a gas is to the combined 

 volume of all the molecules contained in it, so is the mean path 

 of a molecule to one eighth of the diameter of a molecule^ The 

 mean path of a molecule therefore increases directly as the 

 number of molecules in the unit volume of the gas is dimi- 

 nished. The mean path accordingly increases directly as the 

 number of times the gas is rarefied. The value of the mean 

 path therefore augments, on rarefying, at a disproportion- 

 ately greater rate than that of the mean distance of the mole- 

 cules of gas. 



6. It appears to have been assumed in certain radiometric 

 experiments that the mean path of the molecules of the resi- 

 dual gas is comparable to the diameter of the bulb of the radio- 

 meter itself. In a paper by Mr. Crookes which appeared in 

 the ' Philosophical Magazine ' for June last, is the following 

 passage : — " But when the exhaustion is carried to so high a 

 point that the molecules are sufficiently few, and the mean 

 length of path between their successive collisions is com- 

 parable with the dimensions of the vessel." This is also 

 assumed in a paper by M. Finkener in PoggendorfFs An- 

 nalen on the subject of the radiometer, where the assump- 

 tion is made that the gas is rarefied so far that the mean 

 length of path of the molecules is very great compared with 



Fhil, Mag. S. 5. Vol. 4. No. 23. Aug. 1877. I 



