652 THE POPULAR SCIENCE MONTHLY, 



SUX-IvIXKS. 



Bt T. O'COXOE SL0A2s'E, Pn. D. 



IN a recent journal of this city an article descriptive of a railroad 

 accident appeared, under the heading, " Derailed by a Sun-Kink." 

 The title doubtless puzzled many readers. The terra indicates that 

 the rails were thrown out of line by expansion, due to the heat of the 

 sun. Few accidents are attributed to this cause, though it may be re- 

 sponsible for more than are supposed. It will be interesting to deter- 

 mine a few maxima of distortion that can be thus produced. 



The expansion of metals under the influence of heat is very slight. 

 A mile of iron rails, for an elevation of temperature of 100° Fahr., only 

 expands two feet eight and one half inches. This is so little as to be 

 readily taken up by the one hundred and seventy-six joints that exist 

 in that length of rails. If the rails were laid in very cold weather, in 

 solid contact with each other, then, on a warm, sunny day, a consider- 

 able disalignment could be produced. To find the maximum for the 

 mile of rails, we must suppose that the line breaks in the middle, and 

 bulges out like a flattened letter V. In this condition of things, the 

 broken line of rail, with the original line for base, would form an equi- 

 lateral triangle. The altitude of the triangle may be calculated by the 

 familiar rule of the reverse of the hypotenuse. It will be found equal 

 to nearly ninety feet. The result, though deduced by the simplest of 

 calculations, is an astonishing one. It is enough to account for any 

 number of " sun-kinks." The books are very prolific of instances of 

 expansion by heat, and always speak of the expansion of rails. They 

 do not, however, allude to the geometrical element of danger ; they 

 concern themselves only with the physical one. 



It is obvious that a mile of rails would never expand in this way. 

 Disturbances of alignment would be confined to smaller sections. The 

 calculation shows a maximum that would never be attained. The con- 

 ditions might be fulfilled by four rails. For the given elevation of 

 temperature they would expand about eight tenths of an inch, with a 

 lateral displacement of over two feet. For an expansion through 50° 

 Fahr., the displacement would be eighteen inches. 



Two rails would act in accordance with the supposition most read- 

 ily. Their total expansion, for 100° Fahr., is four tenths of an inch, 

 and the bulge due to such expansion would be twelve inches. For 

 half the number of deorrees it would be nine inches. This shows how 

 very small a rise of temperature might produce a spreading suflicient 

 to throw a train from the track. The smaller figures are as impressive 

 as the ninety feet, when it is recollected that four inches displacement 

 of the rails might produce a catastrophe. 



The distortion might be confined to a single rail ; and, from what 



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