  The following effects in the nearly forward ("soft") region of the LHC are
proposed to be investigated: 1) At small |t| the fine structure of the cone
(Pomeron) shouldbe scrutinized: a) a break of the cone near $t\approx - 0.1 ~
GeV$^2, due to the two-pion threshold, and required by t-channel unitarity, is
expected, and b) possible small-period oscillations between $t=0$ and the dip
region. 2) In measuring the elastic $pp$ scattering and total $pp$ cross
section at the LHC, the experimentalists are urged to treat the total cross
section $\sigma_t,$ the ratio $\rho$, the forward slope $B$ and the luminosity
${\cal L}$ as free arameters, and to publish model-independent results on
${dN/{dt}}.$ 3) Of extreme interest are the details of the expected diffraction
minimum in the differential cross section. Its position, expected in the
interval $0.4<-t<1$ GeV$^2$ at the level of about $10^{-2} {\rm mb} \cdot$
GeV$^{-2}\div 10^{-1} {\rm mb}\cdot$ GeV$^{-2}$, cannot be predicted
unambiguously, and its depth, i.e. the ratio of $d\sigma/dt$ at the minimum to
that at the subsequent maximum (about $-t=5 $GeV$^2$, which is about 5 is of
great importance. 4) The expected slow-down with increasing $|t|$ of the
shrinkage of the second cone (beyond the dip-bump), together with the
transition from an exponential to a power decrease in $-t$, will be indicative
of the transition from "soft" to "hard" physics. Explicit models are proposed
to help in quantifying this transition. 5) In a number of papers a limiting
behavior, or saturation of the black disc limit (BDL) was predicted. This
controversial phenomenon shows that the BDL may not be the ultimate limit.
