] 32 Royal Society : — 



The amount of resistance offered by the diagonal fibres is shown 

 as follows : — 



abed represents a portion of a beam strained by transverse 

 forces into the circular curve a e. 

 Two resistances arise. 



1. That due to the extension and compression of the longitudinal 

 fibres produced by the rotation of b d about the neutral axis, which 

 is the resistance considered in the theory of Leibnitz. 



2. That due to the extension and compression of the diagonal 

 fibres, caused by the deformation of the square abed into the figure 

 a hoc, which is the resistance of flexure. 



It is then shown that, in a solid rectangular beam, the second 

 resistance is equal to the first, and that both resistances act indepen- 

 dently, and consequently that the true theoretic resistance of a solid 

 rectangular beam is exactly twice that arrived at by the theory of 

 Leibnitz, 



The strength so computed is in general accordance with the results 

 of experiments in cast iron, wrought iron, steel, and other materials, 

 the maximum strength being found in cast iron, which is one- 

 eighth above, and the minimum in glass, which is one-fourth below 

 the calculated strength. 



The author considers this treatment of the subject as arising ne- 

 cessarily out of Dr. Hook's law "ut tensio sic vis," and that it is 

 in effect completing the application of those principles which were 

 only partially applied by Leibnitz. 



The paper concludes with some practical illustrations (accompa- 

 nied by photographs) of the effect of diagonal action. 



The appendix contains the results of experiments on the tensile, 

 compressive, and transverse resistances of steel. 



" On Deep-sea Thermometers." By Staff-Commander John E. 

 Davis, R.N. 



The results of thermometric observations at great depths in the 

 ocean not being of a satisfactory nature, the attention of the Hy- 

 drographer of the Navy was directed to the defects in the construc- 

 tion of the Six's self-registering thermometers then in use, and also 

 to the want of knowledge of the effects of compression on the bulb ; 



