270 Prof. J. Perry on Struts and 



centre of the end), Euler's theory gives the breaking-load as 

 the lesser of the two values 



"-¥ <» 



and / e A. (2) 



The length of strut for which these two answers are the 

 same is 



7 ttJc /E 



if k is the least radius of gyration of the section about a line 

 in the section through its centre of gravity. 



Now we showed that want of homogeneity, inaccuracy of 

 loading, and initial want of straightness in the strut all lead 

 to a smaller load being able to break the strut, and, indeed, 

 that an initial want of straightness (the assumption of an 

 initial deflexion a at the middle) may be taken to represent 

 all three kinds of discrepance. We showed that for such values 

 of I as make the two answers (1) and (2) nearly the same, a 

 very small error a produces very great discrepance — a very 

 great diminution in the real breaking-load from Euler's 

 breakino--load. We showed that when a strut is perfect and 

 perfectly loaded, there is no deflexion until the breaking-load 

 is reached ; and that if a deflexion be artificially produced, 

 the strut will straighten itself again, whereas in the imperfect 

 strut there is a deflexion which increases at first in proportion 

 to the load, and then more rapidly. 



Such deflexions had been observed and carefully tabulated 

 and published by Mr. Hodgkinson and Mr. Edwin Clarke, but 

 hitherto no use had been made of them, and they had been 

 regarded as unaccountable. 



We pointed out that the error a in carefully made and care- 

 fully loaded struts seems roughly to follow a rule, and conse- 

 quently that without making the unwarrantable assumption 

 which has hitherto been used to make Gordon's formula appear 

 to be a rational one, we had a right to look upon Gordon's 

 formula as an empirical formula, which, being of the value (2) 

 for short struts and of the value (1) for long struts, might be 

 taken as right for struts of any length. 



Since the publication of our paper (' The Engineer/ Dec. 

 10th, 1886) I have been in the habit of giving to students 

 problems on struts laterally loaded : as when a strut lies hori- 

 zontally and is loaded with its own weight; or as when a strut 

 like the coupling-rod of a locomotive, or any connecting-rod, 

 is loaded by its own centrifugal force. 



