Abstran We study the dilution of the spin-1/2 transverse Ising Model by means oic an effective fleld type treatment based on an extension of Callen's relation (Phys. Lett. 4, 161 (1963)) to the present model. The thermodynanics of the diluted model is obtained and the resultsareshown to be an improvement over the standard mean field treatment. Wealsocompare the results w ith the Monte Carlo calculation for the spin-oo transverse Ising Model. The transverse Ising model has been used tp describe phase transitionc in ferroelectrics, ferromagnets and cooperative Jahn-Teller systems with an applied external magnetic field. This model hamiltonian was f i rst proposed by de ~ennes' to represent the basic features of hydrogen-boncled ferroelectrics of the KH2P04 family. In these systems the Ising term corresponds to the interaction between the protons at different lattice sites and the transverse field accounts for the possibility of the protons occupy one of the two minima of a doublepotential well in a given site. The mdel can also be applied to study rare - earth compounds with s inglet c rystal field ground states, as has been done by Wang and cooper2. In these systems there is a competition between the exchange interactlon represented by the Ising term and the crystal field represented by the transverse field. There will be magnetic ordering if the ratio between these two terms exceeds a certain value. Cooperative Jahn-Teller systems with an applied external magnetic field is another example where this model hami I tonian works we11 3. Here the phase transition is driven by the interaction between localized orbital electronic states and the crystal lattice. Even at low temperatures sufficiently high applied external magnetic field can retrieve the high temperature phase. We refer to a paper by Stinchcombe 4 which gives a