336 DIRECT PROPERTIES OF MOLECULES 122 



The most direct judgment as to the smallness of the 

 atoms is afforded by investigations on the limits to which 

 the divisibility of matter can be pushed. For this purpose 

 strongly-coloured substances have been employed, and these 

 have been diluted by solution until their colour has disap- 

 peared. By experiments of this kind Musschenbroek, 

 A chard, and other older physicists, 1 as also A. W. Hof- 

 mann 2 in later years, have shown that coloured substances 

 can be plainly recognised when diluted to a 100-millionth, 

 or even less, of their strength, from which we may conclude 

 that the smallest quantity that can be weighed can be 

 divided into several hundred million parts. Annaheim 3 

 has calculated in this way that an atom of hydrogen must 

 weigh less than O05 millionth of a milligram [which is 

 6 x 10 15 times our calculated mass]. It is obvious that this 

 method is not suitable for obtaining the outside limit of 

 divisibility, but the experiments are interesting as showing 

 that the numbers calculated in the foregoing paragraphs are 

 really much smaller than the limit attained. 



The same may be said of an experiment by Kirchhoff 

 and Bun sen, 4 by which it was proved that a 3-millionth 

 part of a milligram of sodium chloride is sufficient to colour 

 the flame of a Bunsen burner distinctly yellow. 



In a similar way attempt has been made to push the duc- 

 tility 5 of a substance to the utmost, in order thereby to obtain 

 a limit for the size of the smallest particles. Faraday 6 

 has obtained gold leaves whose thickness he estimates 

 as 100 times less than the length of a wave of light ; since 

 these leaves must contain at least one layer of atoms, it 

 follows that the thickness of an atom of gold is equal to or 

 less than 5 millionths of a millimetre. This limit corre- 



1 The older literature has been put together by Muncke in Gehler's 

 Worterbuch, 1838, ix. p. 709, article ' Theilbarkeit,' and by G. Karsten 

 in the Encyklopadie der Physik, edited by him, 1869, i. pp. 820, 877. 



2 Ber. d. deutsch. chem. Ges. 1870, p. 660. 



3 Ibid. 1876, ix. p. 1151. 



4 Fogg. Ann. 1860, ex. p. 168. 



5 Compare the article ' Dehnbarkeit ' in Gehler's Worterbuch, 1826, ii. 

 p. 504. 



6 Pogg. Ann. 1857, ci. p. 318. 



