582 Professor Ernest G. Coker [Feb. 18, 



than the calculated values, and, if the correction is made, there is 

 a very good agreement, as the table shows. In more complicated 

 cases the stresses are less amenable to calculation, as in cylinders 

 provided with ribs for aeroplane engines, or tubes constructed in 

 sectors bolted together, as in underground railways, but it would not 

 be difficult to determine experimentally the stresses produced under 

 working conditions, although not in so simple a manner. 



So far our measurements have only utilized a property which 

 enables us to measure the difference of the principal stresses at 

 a point in a plate subjected to plane stress, but by far the greater 

 number of problems require a knowledge of the magnitudes of each 

 stress separately, as well as their directions, and it is to these deter- 

 minations which we must now address ourselves. First, as to the 

 determination of the magnitude of the principal stresses : — 



Principal Stresses. 



A measure of the sum of the principal stresses at a point can he 

 obtained, as Mesnager suggested, if advantage be taken of the fact 

 that the stress causes a change in the thickness of a plate of 

 material proportional to the sum (p - q) of the principal stresses in 

 its own plane. If, for example, both stresses are tensions, there 

 will be a lateral contraction of {p + q)/jn^, where E is the modulus 

 of direct elasticity, and m is Poisson's ratio. Both these latter 

 quantities can be determined, and the sum of the stresses can be 

 measured, if an extensometer is used of sufficient accuracy to 

 measure the lateral contraction. The values of the physical quantities 

 E and m differ very much for different materials, but for the artificial 

 transparent material used here they are much smaller than for a metal, 

 and the difficulty of this kind of measurement is therefore much 

 lessened. A fair valve of E for xylonite is 300,000 in pound and 

 inch units, while m has a value of about 2-5, so that for each 

 1000 ]b. of stress intensity, the corresponding lateral contraction for 

 plates of the usual thickness of J inch is 3 qVu of an inch. To measure 

 such a quantity to an accuracy of within 1 or 2 per cent it is advisable 

 to use an instrument capable of indicating a change of at least one- 

 hundredth of this quantity ; such changes have been measured 

 with fair accuracy by using a lateral extensometer capable of detect- 

 ing a change of about half-a-millionth of an inch. An instrument of 

 this kind has been employed by Mr. Scoble and myself in several in- 

 vestigations, and an elevation of one form of this apparatus is shown 

 in Fig. 5 attached to a specimen A. 



In this arrangement, a frame B carries a calibrating screw C, the 

 point of which bears against the plate of transparent material, and is 

 immediately opposite to a second piece D, the inner end of which is 

 lightly pressed against the plate by a spring E, while the outer end 



