1866.] Mr. Everett on the Rigidity of a Glass Rod, ^c. 19 



dicates. Similar estimations made at considerable intervals of time might 

 show whether the brightness of these bodies is undergoing increase, dimi- 

 nution, or a periodic variation. 



The paper concludes with some observations on the measures of the 

 diameters of some of the planetary nebulae. A very careful set of mea- 

 sures of 4232, 5 2, by the Rev. W. K. Dawes, F.R.S., is given, which 

 makes the equatorial diameter = 15"' 9. Also measures by the author of 

 1414, 73 H. IV. which give its diameter in R. A.=30"-8. 



February 22, 1866. 



J. P. GASSIOT, Esq., Vice-President, in the Chair. 

 The following communications were read : — ■ 

 I. '^Account of Experiments on the Flexural and Torsional Rigidity 

 of a Glass Rod, leading to the Determination of the Rigidity of 

 Glass." By Joseph D. Everett, D.C.L., Assistant to the 

 Professor of Mathematics in the University of Glasgow. Com- 

 municated by Professor W^illiam Thomson, F.R.S. Received 

 February 1, 1866. 



(xlbstract.) 



In these experiments a cylindrical rod of glass is subjected to a bending 

 couple of known moment, applied near its ends. The amount of bending 

 produced in the central portion of the rod is measured by means of two 

 mirrors, rigidly attached to the rod at distances of several diameters from 

 each end, which form by reflexion upon a screen two images of a fine wire 

 placed in front of a lamp -flame. The separation or approach of these 

 two images, which takes place on applying the bending couple, serves to 

 determine the amount of flexure. 



In like manner, when a twisting couple is applied, the separation or 

 approach of the images serves to determine the amount of torsion. 



The flexural and torsional rigidities, / and which are thus found by ex- 

 periment, lead to the determination of Young's Modulus of Elasticity, M 

 (or the resistance to longitudinal extension), and the absolute rigidity, n (or 

 resistance to shearing) ; M being equal to / divided by the moment of 

 inertia of a circular section of the rod about a diameter, and n being 

 equal to t divided by the moment of inertia of a circular section about the 

 centre. The resistance to compression," ky is then determined by 

 the formula 



3k M n 



and the " ratio of the lateral contraction to longitudinal extension," o-, by 

 the formula 



M , 



