Cilley — Theory of Elasticity. 269 



Aet. XXII. — Some Fundamental Propositions in the Theory 

 of Elasticity. A study of primary or self balancing 

 stresses ; by Feank H. Cilley, SB.* 



Looking- at two objects of precisely the same material, size, 

 shape and general appearance, it would at first seem that one 

 would be warranted in regarding them as precisely alike and 

 applying to the one all conclusions which had been found to 

 apply to the other. Yet a little reflection will show that this 

 is by no means necessarily the case, and that, even where there 

 is no hidden difference in structure, there still may exist a dif- 

 ference in internal condition which will have most important 

 consequences. 



Consider, for example, the specially prepared drop of glass 

 with a long slender tail known as a " Prince Rupert drop " or 

 " tear," and a precisely similar appearing drop of the same 

 glass, prepared simply by melting and drawing out a tail fol- 

 lowed by slow cooling. The two drops look just alike, yet 

 we know that there is a very important difference in their con- 

 ditions. For, break off the tail of the Prince Rupert drop and 

 it will explode like a bomb, breaking into innumerable frag- 

 ments, while the other not similarly prepared drop, if treated 

 in the same way, does nothing at all. 



Two lamp chimneys, identical in appearance, are put on two 

 similar lamps. One breaks on the first lighting of the lamp, 

 the other endures indefinitely. 



On a cold winter's day as an electric car passes over a joint 

 in the rails a sharp explosion is heard : the rail has broken at 

 the joint. These joints had been firmly " welded " the previ- 

 ous summer, but the rails had contracted much more than the 

 surrounding soil under the great fall in temperature. 



After a spell of moist weather, windows, which ordinarily 

 would open with ease, stick. The moisture has swelled the 

 wood,---and frame and sash are wedged firmly together. 



Two bicycle wheels look just alike. - They are of the same 

 material and construction. But if the spokes are gently struck 

 we find, not only that no two spokes give forth the same sound 

 but that the spokes of one wheel, on the whole, give forth a 

 much higher sound than those of the other wheel. They have 

 not been equally tightened, and one wheel is more ready to 

 buckle and break than the other. 



* The present article, read before the American Association for the Advancement 

 of Science, Sec. D, New York, June, 1900, is based on an article prepared by the 

 writer in March of 1 897 but never published. The earlier article contained all 

 the essential features of the present article, which is simply otherwise arranged, 

 popularized and less brief and abstract than the original. 



Am. Jour. Sol— Fourth Series, Vol. XI, No. 64 —April. 1901. 

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