284 Mr. S. U. Pickering on the Hypothetical 



compressive stresses are : — 



at the ends, /= F ( -~ + -r J ; 



F fWZ U 



at the middle, /= -r- + ^~- ^ — ^ 



FA 



Zcos/^/J 



The problem to find for a given strut and given maximum 

 stress / the value of h which will cause F to be a maximum 

 is easily worked out if a numerical example be taken. 



It is obvious from this and from other examples that may 

 be taken, that whether a strut is loaded laterally or is imper- 

 fectly straight or has other faults which would cause it to 

 break with a load F smaller than U and /A, it is always possible 

 to adjust the loading so that F may be increased. Thus if a 

 strut is being tested and if for small loads we find that it 

 deflects, the load ought to be readjusted in such a way that 

 its application produces the minimum deflexion ; and now if 

 the load is increased we shall find that the strut breaks with 

 a much greater load than if we had not adjusted the method 

 of its application. This adjustment of the method of loading 

 ought to be applied also in the building of structures. 



It will be seen that I have merely touched on a few of the 

 many very interesting problems on structures to which the 

 general treatment (3) to (30) may be applied. The lateral 

 load required to prevent a straight strut from bending and to 

 cause its breaking-thrust to be /A is evidently small. We 

 can assume, however, an initial want of straightness or an 

 accidental deflexion, and so find how very slight need be the 

 diagonal bracing in the large struts used in bridge-building. 



I have to thank Messrs. Field and Clinton, of the Finsbury 

 College, for checking the mathematical work in this paper. 



XXVIII. The Hypothetical Tetrachloride of Manganese. 

 By Spencer Umfeeville Pickeeing, F.R.S* 



IN a paper read before the Chemical Society in April, 1890, 

 Mr. H. M. Vernon adduced some evidence which appa- 

 rently he considered to be adverse to my conclusion that the 

 higher chloride of manganese was Mn 2 Cl 6 , and not MnCl 4 ; 

 and at the same time he attempted to demolish the evidence 

 on which my original conclusions were based, although he did 

 not in any way question the validity of the objections which 



* Communicated by the Author. 



