1879/] 



Mr. F. Gait on on the Geometric Mean. 



365 



Le Bel and Wassermann have found that cold hydrochloric acid has 

 no- action on it, from which it follows that, if normal hexane from 

 mannite yields a hexylene combining with hydrochloric acid in the 

 ^old, it could be only diethylhexylene, which could be easily identified 

 by conversion into ethylpropyl carbinol and oxidising it, when only 

 propionic acid should be formed. 



This was my programme ; the results were, however, quite unex- 

 pected. 



The hexylene obtained by decomposing the hexyl chlorides was left 

 in contact with cold fuming hydrochloric acid for some weeks. The 

 whole of it combined and the hexyl chloride thus formed boiled constantly 

 and ivithout the least decomposition at 124 — 125°. It was converted 

 into the alcohol, which on oxidation yielded only acetic acid and 

 butyric acid, and consequently is methylbutyl carbinol. We have, 

 therefore, the remarkable fact, that two hexanes exist, which must be 

 regarded as normal compounds, and therefore according to our present 

 theory, to be identical. This is, however, not the case. I have 

 already in my first paper pointed out some other differences existing 

 between the two hexanes, but left the question open, whether these 

 are caused by impurities contained in the hexane from petroleum, 

 or whether we have here a case of fine isomerism, for which an 

 explanation has to be found.* I believe the results of my present 

 research speak strongly in favour of the latter view. 



For several reasons I am inclined to believe that petroleum consists 

 chiefly of an inextricable mixture of isomeric and homologous paraffins, 

 in which, however, the normal hydrocarbons preponderate. This 

 would certainly explain why it is so difficult to isolate from it bodies 

 having a constant boiling point, f but not the differences exhibited by 

 the two hexanes. 



A continuation of these researches has already been commenced. 

 My friend Thorpe, who has made the most interesting discovery that 

 the terebinthinate exudation of Tinus Sabiniana contains a large 

 quantity of normal heptane, J has kindly offered me to join him in the 

 chemical investigation of this hydrocarbon. At the same time we shall 

 •compare it with other " normal " heptanes from different sources. 



XII. " The Geometric Mean, in Vital and Social Statistics." 

 By Francis Galton, F.R.S. Received October 21, 1879. 



My purpose is to show that an assumption which lies at the basis of 

 the well-known law of " Frequency of Error " (commonly expressed 



* " Phil. Trans.," vol. clxii, p. 119. 

 t " Journ. Chem. Soc," 1875, p. 306. 

 X "Journ. Chem. Soc," 1879, p. 296. 



