160 Miscellaneous Intelligence. 



If it were wished to divide the line AB, fig. 3, into five equal 

 parts, 



the proportion m : / :: (p + 1) '. (p — I) would become m : Z :: 6 

 : 4, or m : / :: 3 : 2 ; hence three parts may be laid down in AC, 

 and a line drawn from F to the extremity of the second part will 

 divide BA in G, giving BG = to the fifth part of AB. 



The metliod above detailed, of dividing a line into any number 

 of equal parts, appears to me to have some advantages over those 

 generally given, inasmuch as it is more expeditious, and does not 

 require the construction of parallel lines, which may easily intro- 

 duce graphical errors. — Bib. Univ. xxvi. 3. 



Art. XIII.— miscellaneous INTELLIGENCE. 



Mechanical Science. 



1. On the Action of Iron in Motion on Tempered Steel, by MM. 

 Darier and Colladon. — The manner in which steel is cut by soft 

 iron, as acertained by Mr. Barnes, has been pointed out, p. 155 of 

 our last Volume ; and since then the eftect has been attributed to 

 the softening of the steel at the point of contact by the heat result- 

 ing from the friction. The following experiments and results in 

 relation to this subject are extracted from a memoire published in 

 the Bib. Univ. xxv. p. 283. 



The authors of the paper were led to doubt of the sufficiency of 

 the reason above given, by finding on an examination of the iron 

 plate made use of to cut some steel, that its edge was set with 

 small particles of steel, which seen through a lens did not appear as 

 if untempered, and which, when tried witli a file, were found as hard 

 as the best tempered steel. Suspecting, therefore, some other cause 

 for the effect, tliey first endeavoured to ascertain what degree of 

 motion was sufficient, simply to compensate for the power which in 

 ordinary circumstances steel has of cutting iron, and above which 

 iron on the contrary becomes possessed of the power of cutting 

 steel. 



The steel employed consisted of gravers, very carefully tempered. 

 The soft iron plate used was 7 inches 5 lines in diameter, and 

 very carefully centred and mounted, so that any required degree 



