336 



SCIENCE. 



[N. S. Vol. XVI. No. 400. 



The cases in which this more exact pro- 

 cedure is most necessary are to be found 

 chiefly among problems in thin plates, rods, 

 trusses with very light webbing, arches and 

 suspension bridges. 



A simple case is the post under com- 

 bined axial and transverse load. Standard 

 posts may have bending moments and de- 

 flections a third to a half greater than they 

 would were they simple beams. And this 

 is equally true whether the end pressure be 

 due to loads or to a stressed tie (primary 

 stress) . 



The posts under combined axial and 

 transverse loads are comparable to the 

 parabolic arch ring under uniform load 

 and bent by a concentrated load. 



They are sufficiently slender to have 

 materially increased stresses and deflections 

 in consequence of their distortion. 



Frameworks with sufficiently light web- 

 bing may have very different stresses and 

 deflections from those determined by the 

 usual methods. This is particularlj^ the 

 case with heavy bowstring trusses. 



But the greatest divergencies in practice 

 resulting from the application of the more 

 exact analysis which takes account of small 

 changes in form, are found in connection 

 with suspension bridges. There the funda- 

 mental proposition of the usual analysis, 

 that single loads on the stiffening truss 

 cause a uniform increase in the suspender 

 stresses, is sensibly in error and leads to 

 many most incorrect conclusions. 



To sum up, even small changes in the 

 form of some structure have most appreci- 

 able consequences, and stresses existing at 

 the time of the application of a load may 

 most seriously modify its effects. These 

 truths require more general consideration. 



The Ratio of Direct to Transverse Change 

 of Dimension under Longitudinal Stress 

 (Poisson's Ratio) : Professor Thom-\s 

 Gray. 



This paper consisted mainly of a descrip- 

 tion of the apparatus and methods of meas- 

 urement employed in the determination of 

 Poisson "s ratio for metal bars. 



The specimens used were round bars 

 varying in thickness between one and a 

 quarter and two inches. The stress, either 

 tension or compression, was applied and 

 measured by means of a Rhiele testing ma- 

 chine capable of applying a total load of 

 100,000 pounds. The lengths under test 

 were usually either ten inches or sixteen 

 inches, and the elongation or compression 

 was measured by means of the author's au- 

 tographic attachment to the machine {T. 

 A. S. M. E., Vol. XIIL, 1892). The auto- 

 graphic record was omitted, the change of 

 length as indicated by the magnifying 

 levers being read, for particular loads, from 

 a scale. The transverse change of dimen- 

 sion, which is much the more difficult to 

 measure with accuracy, was obtained by 

 means of a special calipering device con- 

 trived by the author of the paper and con- 

 structed in the Rose Polytechnic shops. 

 This apparatus was carried by the speci- 

 men at the middle of the test length, in such 

 a way that the points of contact of the cali- 

 per levers were at opposite extremities of a 

 diameter and remained constant. The mag- 

 nifying power was adjustable and could be 

 made such that a change of diameter of less 

 than one millionth of an inch gave a posi- 

 tive indication. The total change of dimen- 

 sions which can be obtained, within elastic 

 limits, is very small even for steel, being only 

 about one three thousandth of an inch on a 

 diameter of one inch. 



It has been customary to infer the value 

 of this ratio for separate determination of 

 the Young's and the rigidity modulus of 

 elasticity on the assumption that the materi- 

 al is nearly enough isotropic. One of the 

 ob.jects of this direct measurement was to 

 test the reliability of this method of infer- 

 ence. If E be Younsr's modulus in the 



