GOLD IN SCIENCE AND IN INDUSTEY. 227 



of view of the physical i:hemist we are here in presence of sohitions of 

 a very remarkable order of dilution. A solution containing 1 gram 

 per cubic meter is in round numbers N/200,000, and the weaker solu- 

 tion containing • 1 gram is N/2,000,000. It is convenient to remember 

 that the latter contains a little more than 1^ grains per ton. In exper- 

 iments on the properties of dilute solutions the extreme point of dilu- 

 tion was reached by Kohlrausch, who employed solutions containing 

 1/100,000 of a gram molecule of solute per liter for his conductivity 

 experiments. These solutions were therefore twice as strong as the 

 gold solution with 1 gram per cubic meter and 20 times as strong as 

 the more dilute solution. This fact must be my excuse for placing 

 before you the results of a few simple calculations as to the molecular 

 distribution in these solutions, which have certainly given me an 

 entirely new view of what constitutes a really dilute solution from the 

 molecular point of view. 



In estimating the number of molecules in a given volume of solution 

 the method adopted is to divide the space into minute cubical cells, 

 each of which can exactly contain a sphere of the diameter of the 

 molecule. In this way a form of piling for the molecules is assumed 

 which, though not the closest possible, may qiute probably represent 

 the piling of water molecules. Taking the molecular diameter as 

 0*2X10~'"' millimeters — a figure which is possibly too small for the 

 water molecules and too large for the gold — it is found that a cubic 

 millimeter of solution contains 125 X 10^^ molecules, or 125 quadril- 

 lions. The head of an ordinary pin, if it were spherical, would have 

 a volume of about 1 cubic millimeter. 



If these water molecules could be arranged in a single row, each 

 molecule just touching its two nearest neighbors, the length of the 

 row would be 25,000,000 kilometers. A thread of these fairy beads, 

 which contained the molecules of one very small drop of a volume of 

 G cubic millimeters, would reach from the earth to the sun, a distance 

 of about 150,000,000 kilometers. 



In a solution containing 1.^ grains of gold per ton, or 1 decigram 

 per cubic meter, the ratio of gold molecules to water molecules is as 

 1 : 1 5 );^> ,000,000. Each cubic millimeter of the solution, therefore, con- 

 tains 0,500,000,000 gold molecules. If these are uniformly distriV)uted 

 throughout the solution each will be about 400 micromillimeters, or 

 1 00,000 of an inch, from its nearest neighbors. This is not really 

 very wide spacing, for the point of the finest sewing needle would 

 cover about 1,500 gold molecules. 



If a cubic meter of solution could be spread out in a sheet one 

 molecule in thickness it would cover an area of 1,680 square miles, 

 and nowhere in this area would it be possible to put down the jioint of 

 tlie needle without touching some hundreds of gold molecules simid- 

 taneously. 



