conclude a general model of the phenomenon.

[**1**]{}. To a good approximation, the experimental observation of decrease in $B$ (or increase in $I$) for $N^i$ to $N^*$ can be explained by using rigid rotor picture for the cluster since this falls in line with the fact that a $^4$He atom interacts more strongly with M than with another $^4$He atom, the structure of the cluster M:He$_N$ for $N=N^i$ to $N=N^*$ can, therefore, be presumed to have a rigid rotor structure for the first few rotational excitations of each cluster. We note that $N^*$ can be different for different M (depending on its physico-chemical nature), while $N^i$ can, in principle, be as small as 1.

[**2**]{}. However, the non-trivial dependence of $B$ on $N$ represented by the observations that B remains nearly unchanged when $N$ changes by one or two $^4$He-atoms beyond $N^*$ and there after it follows cycles of its increase from $N^*+\Delta N$ to $N_1$, $N_2$ to $N_3$, ... and decrease from $N_1$ to $N_2$, $N_3$ to $N_4$, ... . This unexpected observation, naturally indicates its relation with superfluidity of $^4$He-atoms. Consequently, we try to explain it interms of an important aspect of superfluid $^4$He exhibited by it ubder 