68 i OC. O. BURGE. 
hundred and forty sleepers to the mile will be rather stronger than 
the Cape permanent way with the same bearing surface, and with 
the advantage of having the strength more concentrated in the 
rails as already advocated.* The Cape rails were of iron, whereas 
the present sixty pound rails are of steel, which gives another 
advantage to the road now advocated. 
Now as to ballast, in the sense of increasing bearing surface on 
the formation, The present bearing surface of sleepers in New 
South Wales is twelve thousand square feet per mile, and, if the 
ballast may be taken to spread out at say one and a-half to one 
slope, the six inches depth which is now the standard under the 
nine inch wide sleeper, trebles the bearing on the formation, which 
is approximately therefore thirty-six thousand square feet per 
mile. If we reduce the maximum axle weight by about one half 
of that now imposed on the road, which is the proposal, we may 
reduce the latter item one half, or to eighteen thousand, and this 
divided by one thousand five hundred and forty the proposed 
number of sleepers will give nearly twelve square feet under each 
sleeper or equivalent to three inches depth of ballast. 
* The comparison of forty-five pound raiis with one thousand seven 
hundred and sixty sleepers to the mile, as against sixty pound rails with 
one thousand five huadred and forty sleepers is arrived at in the follow- 
ing way. The weights of these rails are as three to four, and as the 
stiffness of ruils of same material with same distance between supports, 
varies approximitely as square of weight of rail; therefore stiffness of 
forty-five pounds rail : stiffness of sixty pounds rail::9:16. Now, if 
required stiffness be taken as represented by 9, and as the stiffness of any 
rail varies inversely as the cube of the distance between the supports, or 
what is the same thing, directly as the cube of the number of sleepers 
per mile, then, if N be the required equivalent number, 
16 (the stiffness of 60Ib rail with 1760 sleepers) : 9 : : 1760% : N* 
3/9 x 17608 
and N = / 16 = dae 
so that a sixty pound rail with one thousand four hundred and fifty-three 
supports per mile would be as stiff as a forty-five pounds one with one 
thousand seven hundred and sixty; but to preserve same bearing surface 
of sleepers asthe forty-five pound road, with which it is compared, namely 
nine thousand two hundred and forty square feet per mile, we must have 
one thousand five hundred and forty sleepers, so we have a slight excess - 
of stiffness in the sixty pound road proposed. a 
