1879.] 



the Measurement of a Body under Strain. 



161 



and the decrement of the distance between \ and & 2 or k — h' is 



2er cos 6 



hence - — -=— — ±=^. 



lb —h K 2 



The limit to the smallness of curvature which can be employed to 

 measure /t by this method depends on the smallness of the interval 

 which can be satisfactorily measured by the microscope and micro- 

 meter screw. In my experiments h'—h varied from '015 to "03 inch, 

 e being about 3 inches and r nearly '5 inch. These values would 

 make vary from 200 inches upwards. The dimensions of the bars 

 employed were about 8 x 1 x "25 inches, so that the third proportional 

 to the thickness, breadth (viz., 4 inches), fulfils the condition of being 

 small compared to R. In fact, I found that much larger curvatures 

 might be - employed without sensibly altering the values obtained 

 for f.i. 



My method admits of the determination of fi for substances which 

 are not isotropic. Some examples of this are given in the table 

 below in the case of the woods box, beech, and deal ; /n p , are the 

 values of ix parallel and perpendicular to the radial plane of the tree, 

 i.e., the plane which contains the medullary fibres ; fi T is the value in 

 the plane cutting the axis of the tree at right angles. 



It will be noticed that in all three cases fx^ is greater than /a p . 



Beech-wood seems even to grow rather less dense in a radial direc- 

 tion under longitudinal pressure, but this is the only instance in 

 which I found a value for /m greater than '5. 



Values of p, for various Substances. 



Substance. 



H- 









Steel 



•253 











•325 











•348 











•375 











•180 











•230 











•389 











•50 











•50 









Paraffin 



■50 











•181 











•2 









Cork 



•00 













•42 



•406 









•53 



•408 









•486 



•372 



•227 



