February 24, 19 16] 



NATURE 



719 



dark field, showing that the stress effect of one 

 neutralises that of the other. The same dark field 

 is produced if an equally stressed compression member 

 is placed with the direction of stress parallel to that 

 of the tension member, and we may readily verify 

 in all cases that tension and compression stresses in 

 the same direction add their effects, while stresses in 

 directions, at right anjjfles subtract them. 



The latter result is of chief importance, since the" 

 stress at any point of a plate can always be represented 

 by the stresses /> and q at right angles, and their 

 optical effect is therefore proix)rtional, p — q. The 

 value of the stress difference may therefore be deter- 

 mined by matching the optical effect produced at the 

 given point with that produced on a simple tension 

 or compression member. The eye is, however, not a 

 very trustworthy instrument, especially after the 

 fatigue of a few minutes' exposure to a brilliant 

 light ; and it is better still to reduce the optical effect 

 to' zero bv a simple tension or compression member 

 set along one of the directions of principal stress, and 

 stressed until a dark field is produced. 



The laws which the optical effects obey may be at 

 once utilised for a variety of cases of practical interest. 



obtained, whii»' the dotted curve represents the results- 

 of. calculation. 



In an experiment carried out on a ring in which 

 the inner radius, r, = o-7i in., and the outer radius, 

 rj=i-43 '"•» '* pressure of 900 lb. per sq. in. was- 

 applied to the interior of the ring, and the experi- 

 mental values compared with those obtained by cal- 

 culation. The following results were obtained : — 



Table I. 



Radius 

 r inches 



071 

 0-85 

 I 00 



1-30 



1-43 



(/ - q) ill lb. per sq. incli 

 Expenmenial value 



Observed 



2100 



1560 



1 185 



870 



670 



Corrected for 



cup leather 



2185 



1625 



1230 



700 



Calculated 

 value 



2400 

 1660 



1205 

 910 



The results shovi- a fair agreement with the theory, 

 which is reallv closer than the numbers indicate, owin;: 



Thick Cylinder. 



An example is furnished by piping for transmitting 

 fluids under pressure. The action of water, or other 

 fluid, in a pipe, can be imitated by applying a 

 uniformly distributed pressure to the interior of a 

 ring, such as is now shown, where the application of 

 a uniformly applied pressure produces a stress distri- 

 bution in the circular ring of a perfectly symmetrical 

 character. The arrangement of the colour bands shows 

 that there is a very large stress at the interior surface, 

 diminishing rapidly at first, and afterwards more 

 gradually as the outer surface of the pipe is approached. 

 In this case there is known to be a radial compression 

 stress accompanied by a circumferential tension stress, 

 and the optical effects produced at any point are pro- 

 portional to the algebraic difference of their intensities 

 — in this case their numerical sum. 



In a thick cylinder of these proportions the radial 

 stress is not large, and its intensity can be determined 

 independently, but the combined effects of both stresses 

 have been measured here, and are plotted in Fig. i, 

 in which the firm line gives the experimental values 



NO. 2417, VOL. 96] 



to the full pressure recorded on the gauge not being 

 effective, as will now be described. 



As is evident, this stress problem requires the appli- 

 cation of a measurable fluid pressure to the cylindrical 

 surface of a ring, in such a way that no essential 

 part is obscured from view, and a simple and effective 

 means has been devised for this purpose by my 

 assistant, Mr. F. H. Withycombe. 



Fig. 2 is a photograph "of the complete apparatus 

 for applying internal and external fluid pressure to 

 rings, and drawings of the essential details are shown 

 in cross section in Fig. 3. 



Fluid pressure of water or other liquid is applied by 

 the action of a small hand-pump P, the piston of 

 which is actuated by a screw to force oil at any desired 

 gauge-pressure into the annular space between two 

 metal discs A, B, bolted together to hold a retaining 

 ring C, shaped like a Bramah cup-leather to prevent 

 leakage of the fluid. This retaining ring projects 

 slightly beyond the periphery of the discs, and carries 

 the transparent ring to be stressed. The cup-leather 

 is \t^,']( ^'^ thin that a pressure of a few pounds jxr 



