Nature's Operations tohieh Man is competent to Study. 461 



3. That the mean spacing of the chemical atoms of 

 which solids and liquids consist lies somewhere in the 

 neighbourhood of a tenth- metret. This, like the last, was 

 an estimate. 



4. That the number of molecules in a cubic centimetre 

 of gas at standard temperature and pressure is somewhere 

 in the neighbourhood of a uno-twentyone. This follows 

 as a corollary from (2). 



5. That the number of chemical atoms in a cubic 

 centimetre of a solid or liquid is a number of the same 

 order as a uno-twentyfour. This follows from (3). 



6. That the masses of the chemical atoms probably lie 

 between the twentysecondet and the twentyfifthet of a 

 gramme. This follows from (4), and from the known 

 densities of solids and liquids. 



The tenth-metret, the smallest of the above measures, is the 

 ten-thousand-millionth part of a metre. It is about the two- 

 thousandth part of the smallest interval which the best micro- 

 scope can detect when most carefully handled. 



Another branch of physical inquiry has introduced us into 

 the same region of magnitudes, and has even carried us farther. 

 The wave-lengths of visible light range from 38 to 76 eighth- 

 metrets, and can, by methods which will be described farther 

 on, be measured with such marvellous precision that it is 

 possible to detect differences of wave-length which amount to 

 a very small fraction of a tenth-metret. 



Nature's Operations on a Large Scale. 



When we turn our attention to Nature's operations on the 

 large scale we find that the greatest lengths we can as yet 



ance with this convention, 3 ninth-metrets, 2 ninth-metrets, 1 ninth-nietret, 

 \ ninth-metret, and § ninth-nietret are all quantities " of the same order 

 as " a ninth-metret. Any of these lengths is better represented by a ninth- 

 metret than it would be by either a tenth-metret or an eigbth-metret. 



When we deduce the number of molecules in a gas from the spacing 

 of the molecules we have to deal with the cube of an already estimated 

 number, and accordingly the range implied by the phrase " of the same 

 order as " becomes widened. It now ranges from V 1000 times the 

 assigned value (in this case a uno-eighteen per cubic millim.) to 1/ sf 1000 

 times this value : so that it includes 30, -0, 10 times, and 1/10, 1/20, and 

 1/30 of a uno-eighteen. Any of these numbers is much better repre- 

 sented by a imo-eighteen than it would be by a uno-tifteen, the number 

 which is a thousand times smaller, or by a uno-twentyone, the number 

 which is a thousand times larger. The knowledge thus reached as to the 

 number of molecules that are present may seem very indefinite ; but it is 

 far from being valueless. 



