532 Scientific Proceedings, Royal Dublin Society. 



of such coarse waves as the waves of light) is about half the wave- 

 length of the light admitted to our microscope, that is, it is the 

 ordinate of our standard gauge at some point between two and 

 three metres from its apex. All smaller magnitudes are ultra- 

 visible. 



Y.— The Larger Ultra-visible Magnitudes. 



1 . Ponderable matter is in the gaseous state when its molecules 

 are so little crowded that they have room to dart to a certain 

 distance along a free path, in the intervals between their encounters 

 with one another ; and information as to the average length of 

 these little journeys can be deduced from experiments on the 

 viscosity of gases. If the gas is a tolerably " perfect " one, at the 

 ordinary temperature, and exposed to the pressure of one atmo- 

 sphere, the average length of the " free path " of the molecules is 

 small. In fact the observed amount of the viscosity assigns to it 

 in air a length equal to the ordinate of our gauge at a distance of 

 something like three quarters of a metre (30 inches) from its apex ; 

 and although the mean length of the free path differs from one 

 gas to another, it is in all a magnitude of this order. ^ Note that 

 this is a good deal smaller than what we have found to be the 

 " minimum visibile." 



Within the receiver of an air-pump the free path becomes 

 longer, until at the excessive attenuations that Mr. Crookes obtains 

 by working his compound Sprengel pump for a long time, its 

 average length may even reach to several centimetres, which would 

 be the ordinate of our gauge at a distance from its apex of some 

 hundreds of miles. Ponderable matter is then in what Mr. Crookes 

 calls the radiant state. 



2. The average spacing of the molecules in a gas («. e. their 

 average distance asunder at any one instant of time) may be 

 obtained in various ways,^ e. g. it may be deduced from the last 



1 See Philosophical Magazine iox A-u^st, 1868, p. 138. 



2 Calling the average length of the free path K, the average interval between the 

 molecules tr, and the average ' diameter of a molecule ' 5 ; we can obtain \ from experi- 

 ments on viscosity, we get 5/<r from observing the condensation which the gas undergoes 

 when liquefied, and one other equation between A, a, and 5 would enable us to obtain 

 all three. 



Now it is evident that \ (the average length of the journeys of the molecules) will, 

 cceteris paribus, increase if a (the space between the molecules) is increased, which may 



