Appreciation of Ultra-visible Quantities. 419 



of the molecules will have increased up to being equal to the 

 ordinate of oar gauge at a distance of about a metre from the 

 apex. It is instructive to observe that even this enlarged 

 interval is ultra-visible, and that in this so-called extreme 

 vacuum there remain something like a million millions of mole- 

 cules of the gas in every cubic millimetre of the space within 

 the receiver — i. e. about a thousand in every cubic micron. 



3. The magnitude to be next considered is the diameter of 

 a molecule. By this is to be understood the distance within 

 which the centres of two molecules must come, if they are 

 sensibly to deflect each other's path. This size of the gaseous 

 molecule, as it may be called, is intimately related to the ratio 

 of the last two measures to one another, and may be deduced 

 from that ratio. Or it may be obtained by observing the 

 condensation which a gas or vapour undergoes when passing 

 into the state of a liquid or solid. Estimated in either of 

 these ways, it appears to be usually about the 8th, 10th, or 

 12th of the last measure — that is, it is something like the 

 ordinate of our gauge at a distance of one millimetre from its 

 apex. 



VI. Smaller Magnitudes. 



The diameter of a gaseous molecule, as above defined, is 

 the smallest measurement for which the present gauge is 

 suggested as convenient, as it is also the smallest magnitude 

 of the actual size of which any approximate estimate has been 

 made. But we have, through the spectroscope, indications of 

 important events in nature that are perpetually going on 

 within each gaseous molecule, and probably on a very much 

 smaller scale. For example, an easy calculation will show 

 that the motion within the molecules of sodium to which the 

 principal double line in its spectrum is due* — a motion which 

 is repeated 508,911,000,000,000, i. e. more than five hundred 

 millions of millions of times, every second within each mole- 

 cule — would need to have a velocity several times greater than 

 that of the earth in its orbit (which is a velocity of 30 kilo- 

 metres, 19 miles, per second) if the range of these motions 

 is the whole diameter we have attributed to the molecule. 

 This consideration, though not decisive, is nevertheless quite 

 sufficient foundation on which to base the expectation that, if 

 ever we are able to ascertain the actual range of this motion 

 and others of a like kind, they will turn out to be much 

 smaller than the ordinate of our gauge at a distance of a 

 millimetre from its apex ; so that if ever we discover any 



* See Stoney on Double Lines, Scientific Transactions of the Royal 

 Dublin Society, vol. iv. p. COS. 



