190 DS. EVEEETT ON THE EIGIDITT OF GLASS. 



For finding M, w, k, and s the formulae are 



r denoting the radius of the rod =-39321. Hence we find 



M=614,330,000, 

 n =244,170,000, 

 k =423,010,000; 



and since log/- logiJ=7-06195-6-96228=-09967= log 1-258, we have 



(r=-258. 



As regards the accuracy of these results, I think a fair estimate of the probable error 

 of M and n is about ^ per cent, for each ; hence it is found by the proper investigation 

 that the probable errors of k and o- are each about 4 per cent. 



The rod was of flint glass, and was from the works of James Coupee and Sons, 

 Glasgow. 



It is intended shortly to continue our experiments, with some modifications in the 

 apparatus, and to determine the values of the constants M, n, k, and c for a variety of 

 substances. 



Experiments for determining the value of a for steel and brass have been described 

 by KmcHHOFF||. 



The method of observation described in the present paper possesses the following 

 advantages over that of Kirchhofp : — 



1. The portion of the glass rod whose flexure and torsion are observed is sufficiently 

 distant from the places where external forces are applied to be free from the irregu- 

 larities which exist in their neighbourhood. 



In Kirchhoff's experiments the rod was subjected to external forces applied at three 

 places in its length (being held in the middle and weighed at the ends), and the flexure 

 and torsion observed were those of the whole rod. 



2. Both the bending and twisting couple are uniform through the whole length. 



In Kirchhoff's experiments the bending couple is greatest at the middle of the rod 

 and diminishes to zero at the ends, whereas the twisting couple is uniform through the 

 whole length. If, then, the middle of the rod be more or less stiff" than the ends, the 

 comparison between flexure and torsion is fallacious. 



* The flexural rigidity of a cylindrical rod is equal to Toting's Modulus multiplied by the moment of inertia 

 of a circular section about a diameter. — § 715, Thomson and Tait's ' Natural Philosophy.' 



t The torsional rigidity of a cylindrical rod is equal to the absolute rigidity multiplied by the moment of 

 inertia of a circular section about the centre. — § 701, ihid. 



% Easily derived from § 684, ihid. § 694, ibid. 



II Poggendoeff's ' Annalen' for 1859, vol. cviii. page 369 ; see also Philosophical Magazine, January 1862, 

 page 28. 



