Dedicated to Prof. Dr. E. Wicke on the occasion of his 80th birthdayThe static electric polarizabilities a of silicon clusters with up to 60 atoms have been measured employing a mass selective molecular beam deflection method. The polarizability per atom aN = ol/N of the Sijy-clusters has been investigated for Siu and the size ranges N = 14-28, 22-34, 28-44, 34-50, 41 -58, and 42-68. The results show that the polarizability per atom decreases from N = 11 until a minimum at N « 28 is reached. The polarizability per atom increases for N > 28, passes through a maximum at N « 36 and finally converges between N « 50-70 against the value a.N = 1.9 A3. If the model of a homogeneous dielectric sphere is applied to the larger clusters one calculates that the value a.N = 1.9 Ä3 corresponds to a dielectric constant of e = 3.2. This value is significantly smaller than the dielectric constant of bulk silicon eb = 11.8.The present paper focuses on the maximum in the polarizability at N » 36. This effect is discussed with special emphasis to recent Car-Parinello calculations which have predicted cage-like silicon structures that enclose a core of several highly coordinated atoms. This structure suggests an im proved dielectric sphere model where the core is represented by a smaller sphere with its own dielectric constant ec. It is shown within this model that the observed maximum in polarizability is due to a significant enhancement of the core dielectric constant to a value of ec « 50. This enhance ment is related by means of a simple model to the effect that silicon becomes metallic under high pressure.