On the Physical Units of Nature. 55 



termined by experiment as 3"10 metre-eights per second, 2'82 

 metre-eights per second, 2'88 metre-eights per second and may be 

 assumed to be not far from 3 metre-eights per second. Accordingly 

 we may put — 



Vi:=3 VIII. metres per second (1). 



Similarly, if we use the value given by Sir John Herschel for 

 the mass of the earth, viz., 5942'XVIII* english tons, which = 

 XXIV. grammes, we find that — 



2 1^ 



To determine Ej, we must first establish a relation between 

 the gaseous molecule of a body, and what in chemistry is called 

 its atom. To do this, let us start with the definition that a 

 chemical atom is the smallest mass of each kind of ponderable 

 matter that has been found to enter or leave a combination. 

 Now from Boyle and Charles's law we know that in all gases 

 there are approximately the same number of molecules per litre, 

 if they be taken at the same temperature and pressure ; from ex- 

 periments on diffusion we know that these molecules are alike in 

 mass ; and from the phenomena of chemistry we know that they 

 are alike in other respects. 



Let, then, a litre of hydrogen and a litre of chlorine be mixed 

 and exploded, and let the resulting hydrochloric acid gas be 

 brought back to the original temperature and pressure. It is 

 then found to measure two litres. Hence, if N be the number of 

 molecules in a litre of gas at that temperature and pressure, we 

 learn by this experiment that N molecules of hydrogen, and N 

 molecules of chlorine produce 2N molecules of hydrochloric acid. 

 Hence, and since the molecules within each gas are alike, each 

 molecule of hydrochloric acid must contain the quantity of hydro- 

 gen represented by a semi-molecule of hydrogen gas, and the 

 quantity of chlorine represented by a semi-molecule of chlorine 

 gas. We are thus introduced to the semi-molecule of each of 

 these gases as a quantity which enters into combination ; and as 

 no other experiments suggest a smaller quantity, the semi- 



* The Koman figures following a number stand for cyphers. Thus 3. VIII signifies 

 3 X 108, and 5942 XVIII stands for eighteen cyphers following 5942. Where no 

 number precedes the Eoman figures, the number 1 is to be understood, so that in XXIV. 

 grammes, the Eoman figures stand for 1 followed by 24 cyphers, in other words for lO^* 

 a number which may conveniently be called the Unit-twenty-four. 



