End Friction with Soft Plates. 
441 
1908-9.] 
ffibove this pressure of fluidity, the whole of the lead is squeezed out long 
before rupture occurs, and the metal has again very little influence upon 
the maximum load carried by the piece. 
The value of the ratio c"/c, though of little use, is not uninteresting: — 
c" sin (3 cos (3 - /x sin 2 (3 
c ~ sin f3" cos f3 " - fj. sin 2 (3" + /x/x" sin f3" cos /3" 4- /x" sin 2 (3" 
cos <£" (1 - sin <f>) Jl+ /x 2 - /x 
~ I — sin (</>-</>") = V(1 +/x 2 )(1+/? 7 2)-(/x-/x' 7 ) 
The numerical values of fj, for stone have been given already on page 437, 
but the coefficient of friction of lead upon stone does not seem to have been 
determined. In order to obtain some idea of the importance of the action 
of the lead, let /u" be taken as 0’5, corresponding with </>" = 27°, roughly. 
For /x = 04, and /x" = 05 ; (3" = 47^°, and c"/c = 052. 
For /x = 065, and fx' = 05 ; (3" = 42°, and c"/c — 046. 
Though no great accuracy is claimed for these results, on account of 
the uncertainty as to the value of fx" they show very clearly the weakening 
effect produced by the lateral flow of the lead ; this effect will be greater 
or less than the above according as the true value of /m" is greater or less 
than 05„ 
A few measurements made upon blocks of cement and of mortar which 
had been crushed between sheets of lead showed that the inclination of the 
sliding surfaces was very little greater than when no lead was interposed. 
The pieces, especially those of cement, failed chiefly by splitting vertically 
into small fragments, as described below ; but a few surfaces of shearing 
were unmistakable. 
As already mentioned, stone specimens crushed between sheets of lead 
or other soft and plastic material do not usually give way by shearing. 
The frictional drag of the moving lead gives rise to a tensile stress in a 
direction normal to the crushing load ; rupture seems to be caused chiefly 
by this tension, and the stone splits into a number of vertical prisms. A 
little consideration shows that the tensile stress is a maximum on two 
vertical planes passing through the axis of the block in directions parallel 
with the vertical faces, and that its value on these planes approximates to 
\fx'c" if the specimen is cubical. Experiments show that the initial cracks 
occur, as a rule, in the middle of the vertical sides of the piece, and that the 
cracks soon extend inwards to the centre (5) . The stone does not give way 
immediately, but continues to break up into smaller and smaller prisms as 
the load is increased, until complete failure occurs. The breaking load 
averages only about one-half of the value obtained without lead, but what 
