210 THE RANGE OF NATURE'S OPERATIONS. 



of time. By combining Clausius's estimate with MaxwelFs determina- 

 tion, 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 accord- 

 ingly there are about a uno-eighteen of molecules (1 followed by eight- 

 een ciphers) in each cubic millimeter 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 vapors con- 

 tract 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 neighborhood of the tenth-metret (0.0000000001 

 of a meter), and that accordingly there are something like a uno- 

 twenty-one of chemical atoms in each cubic millimeter 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 molecules in a gas, and as to the number of chemical atoms 

 in solids and liquids. Such knowledge is imperfect, but is much bet- 

 ter 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 molecules of air at 

 a barometric pressure of 760 millimeters and at a temperature of 17- C. 

 is about six eighth-metrets. This was a determination. 



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

 perature and pressure is of the same order as ^ a ninth-metret. This 

 was an estimate. 



S. That the mean spacing of the chemical atoms of which solids and 

 liquids consist lies somewhere in the neighborhood of a tenth-metret. 

 This, like the last, was an estimate. 



' In molecular physics, where our estimates, and even our determinations, inevi- 

 tably 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 detiniteness to this expression, imagine imits 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/lO 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 repre.sent a ninth-metret, 

 Willie terms one of which will have the value v/fo nmth-metrets, and. the other 

 l/VlO of a ninth-metret. Now, any quantity between these two limits may be 

 spoken of as "of the same order as a ninth-metret." In accordance with this con- 

 vention, 3 ninth-metrets, 2 ninth-metrets, 1 ninth-metret, * ninth-metret, and J ninth- 

 metret are all quantities ' ' of the same order as " a ninth-metret. Aiiv of these lengths 

 IS better represented by a ninth-metret than it would be bv either a tenth-metret or 

 an eighth-metret . 



When we dedu(;e the number of molecules in a gas from the spacing of the mole- 

 cules we have to deal with the cube of an already estimated number, and accordingly 



