TRANSACTIONS OF SECTION J. 443 



carried for a long series of years, broken in two minutes when 

 set gently rotating ; also, a bar of fine tough steel so changed 

 in constitution at fracture after a few mouths' rotation as to 

 offer no advautage over a new cast-iron bar of the same section. 

 Sir B. Baker has proved by experimeutiug on fiat bars of steel 

 by repeatedly bending them, that, after subsequent testing in 

 direct tension, and direct crushing, the effect of repeated 

 stresses is more prejudicial in tension than in compression. 



The change which a piece of material undergoes when 

 subjected to repeated stresses is termed " fatigue." It is most 

 marked in the case of stresses alternating between tension and 

 an equal compression, as seen in the fracture of railway-axles. 



The strength of a piece of material when subjected to a 

 gradually-applied load, as in a testing-machine, is termed its 

 " statical strength." When subjected to a load which is 

 entirely removed before being reapplied, the load which will 

 ultimately break the piece is termed its " primitive strength." 

 When subjected to stresses which alternate between tension 

 and an equal compression, the ultimate breaking-stress is 

 termed its " vibrating strength." Approximately, the vibrating 

 strength is to the primitive is to the statical as 1 is to 2 is to 3. 

 The values of these strengths for a variety of materials are 

 recorded in Table VIII. 



Several methods have been proposed which have for their 

 object the representation of the results of the experiments 

 made by Wohler and Bauschinger, and their extension to the 

 various ranges of stress which occur in engineering practice; 

 among wdiich may be noticed Gerber's parabola. If the ranges 

 of stress given in Table VIII. are plotted as ordinates, and the 

 minimum stress as abscissae, the points fall on a parabolic 

 curve, which Professor Unwin expresses thus :— 



Let / max. and / niln. denote the limits of stress, and A, 

 the range of stress ; then — 



^ = f max. + / min. 

 The upper sign is to be taken when the stresses are of like 

 kind, and the lower sign when of opposite kind, as in alter- 

 nating stresses. Let / denote the statical breaking-strength ; 

 then the equation to Gerber's parabola is, — 



(fmin. + f^y + k^ ^ p. 



If the statical strength /is known, and the value oif mm. 

 And f max. for any range of stress at which the bar stands a 

 practically unlimited number of repetitions before breaking,, 

 then k can be determined, and the limits of stress for all con- 

 ditions of loading can be calculated. The parabolas drawn 

 from the above equation, using the results recorded in Table VI., 

 are represented in Plate XIII. 



Soon after Wohler 's results were published. Professor 



