344 SECTIONAL TRANSACTIONS.— B. 



a colorimetric method may be used. Halogens yield halogen acids, which are 

 titrated by the method of Volhard. The nitrogen of organic compounds givea 

 ammonia, which is also estimated volumetrically. Oxygen is changed into water 

 that is weighed after absorption in calcium-chloride. Arsenic and mercury are 

 both set free and weighed in metallic state. 



7. Mr. J. J. Manley. — The Union of Mercury and Helium. 



8. Dr. G. Martin. — The Chemistry of Fine Grinding and Fine Powders. 



The subject of fine grinding and fine powders has attracted an increasing amount 

 of research work during the last few years. Fine powders behave in many respects 

 like fluids, and possess many curious properties, especially when colloidal dimensions 

 are approached. The mathematical laws regulating their production have only been 

 ascertained between 1923 and 1925 by researches carried out by the author and his 

 assistants. The powders were produced in an 18-in. by 18-in. experimental tube- 

 mill, using quartz sand and 1-in. steel balls. The powders were subsequently 

 elutriated in a stream of air of definite and measured speeds, and the weight, number, 

 and surface of the particles composing them were ascertained. 



The following laws were found to hold rigorously : — 



Law 1. The surface produced is accurately proportional to the work done. Double the 

 work and the surface produced is doubled, treble the work and the surface produced 

 is trebled. 



The cause of this is the constant nature of molecular attraction. In a liquid the work 

 done in extending a film is also proportional to the surface, because here also the 

 surface tension is a constant force. 

 Mathematically expressed, 



W=B(S.,-Si), 



where W is the work done. Si the original surface of the powder, and S2 the final 

 surface. B is a constant peculiar to the material ground and also depending upon 

 the efiiciency of the mill. 



The heat of volatilisation of a substance is obviously equal to the work done in 

 grinding down to molecular dimensions. Substances difficult to volatilise (i.e. with 

 a high heat of volatilisation) in general are difficult to grind (compare ice and the 

 diamond). From such considerations and recent determinations of molecular 

 dimensions the absolute efficiency of a tube-mill may be calculated as being only about 

 ]/15th per cent. ; so that great improvements in grinding machinery are theoretically 

 possible. 



Law 2. The number N of particles produced increases with decreasing diameter X 

 according to the compound-interest law. 



In symbols, N=ae"''', 



where N is the number of particles, x is the diameter, a and 6 are constants, and 

 e is the Napierian base of logarithms. 



Consequently, plotting the logarithm of the number against the diameter gives 

 a straight line. 



Also the weight W of any grade of particles can be ascertained, because plotting 

 Log W/X-' against X (where W is the weight of the grade and X the average diameter 

 of particles forming the grade) likewise gives a straight line. 



Law 3. The average shape of the particles produced in crushing remains the same 

 whether they are large or small. 



If S be the statistical surface of the particles of any diameter X, which compose 

 a homogeneous grade, then 



S/X2=constant A, or S=AX'2 



For quartz sand experiment showed that A equals 2 nearly. 



