by an atom added to an orbit satisfying $r_2 = 2r_1$, Eqn.(2) gets reduced to a value as low as 1/16 ([*i.e.*]{} $\approx$6.3$\%$) and for the orbit satisfying $r_2 = 3r_1$, the said contribution is as low as 1/81 (or $\approx$1.3$\%$). This speaks of the smallness of the contribution of an added atom to the $I$ of the cluster when it goes to an orbit of higher $r$ and evinces that the said atom has a $+ve$ contribution indicating that $I_{N+1} > I_N$.

In what follows the above stated inferences, we can expect a small increase or almost no change in $I$ for each added atom to the cluster with $N=N^*$. However, it gives no clue for the experimental observations of $I_{N+1} < I_N$ for $N > N^*$. To this effect our critical thinking reveals that the phenomenon is possible only if the added atom reduces the distance of $^4$He atoms (all the $N$ atoms or a few of them) in M:$^4$He$_N$ cluster from the axis of rotation to an extent that contribution to $I$ by the added single atom is over compensated by the decrease in $I_N$. It is also possible if the added atom transforms the structure of 