460 Dr. Gr. Johnstone Stoney : Survey of that part of 



length of the free path is about sixty times what the average 

 spacing of the molecules is at any one instant of time. By 

 combining Clausius's estimate with Maxwell's determination, 

 the present writer was able, in 1860, to infer that the average 

 spacing of the molecules of a gas at the temperatures and 

 pressures which prevail in our houses is about a ninth-metret, 

 and that accordingly there are about a uno-eighteen of mole- 

 cules (1 followed by eighteen ciphers) in each cubic millimetre 

 of the gas. This estimate was communicated to the Royal 

 Society in May 1867, and will be found in the Phil. Mag. for 

 August 1868, p. 141. Further, it is known to chemists that 

 there are two chemical atoms in each molecule of many gases. 

 From this, and from the known degree in which vapours 

 contract when they are condensed into the liquid or solid state, 

 we may infer that the average spacing of chemical atoms in 

 solids and liquids lies somewhere in the neighbourhood of the 

 tenth-metret(0'000,000,000,l of a metre), and that accordingly 

 there are something like a uno-twentyone of chemical atoms 

 in each cubic millimetre of solids and liquids — not exactly that 

 number, but somewhere near it. He thus arrived at an estimate 

 — an estimate, not a determination — as to the number of mole- 

 cules in a gas, and as to the number of chemical atoms in solids 

 and liquids. Such knowledge is imperfect, but is much better 

 than knowing nothing about the scale on which Nature is 

 working in this branch of her operations. 



The general results of the information acquired in 1860 

 were : — 



1. That the mean length of the free paths of the mole- 

 cules of air at a barometric pressure of 760 millimetres 

 and at a temperature of 17° 0. is about six eighth-metrets. 

 This was a determination. 



2. That the mean spacing of the molecules in a gas at 

 the same temperature and pressure is of the same order 

 as * a ninth-metret. This was an estimate. 



* In Molecular Physics, where our estimates, and even our determina- 

 tions, iuevitahly fall far short of attaining- exactness, it is very convenient 

 to be able to describe the result as being " of the same order as " some 

 specified magnitude. 



To give definiteness to this expression, imagine units where there are 

 ciphers in fig. 1. They are a geometrical series, each unit having a value 

 ten times that of the unit to its right. Next form the corresponding series 

 with V 10 as its factor. This will interpolate a new term between every 

 two consecutive terms of the former series. Thus, on either side of the 

 unit so situated in our table as to represent a ninth-metret, will be terms 

 one of which will have the value v^lO ninth-metrets, and the other 

 l/ V 10 of a ninth-metret. Now, any quantity between these two limits 

 may be spoken of as " of the same order as a ninth-mefcret." In accord- 



