component in the expansion of $V(Q_1, Q_2, ... ... Q_S)$. Although, it is difficult to argue in favour of increase or decrease in the value of potential constant of the chosen vibration, yet, however, a simple logic indicates that $\nu$ should increase for first few $^4$He atoms which occupy position in the closest vicinity of M since He-atoms are saturated with the electron charge density for which they would give away a small fraction of their own electron density to M which should strengthen the forces that govern its different modes of vibration and this is corroborated by experimental observation. Although, with $^4$He atoms occupying second or third, ... positions counting from M (at zero-th position), it is difficult to argue whether $\nu$ would increase or decrease with $N$, however, it is clear the effect on $\nu$ should decrease with each added atom and this expectation agrees with decrease in slope of $\Delta\nu$ [*vs*]{} $N$ observed experimentally. In what follows from these points, the change in $\Delta\nu$ with $N$ has nothing to do with microscopic superfluidity of the $^4$He atoms in the cluster. Hence, in this paper, we simply concentrate to find the origin of (A), (B) and (C) and 