The critical index of inter-grain penetration field Hp*was estimated for sintered Bi1.8Pb0.2Sr2Ca2Cu3O yhigh Tcsuperconductor by ac magnetic susceptibilities ac.0´, real part of the linear ac, showed two successive diamagnetic transitions at Tc= 107.8 K and Tc*= 104.6 K for intra- and inter-grain parts, respectively. Below Tc*, 0´´, the imaginary part of the linear ac, appeared and had a positive peak. The temperature and field dependences of 0´´ below Tc*were analysed by the Bean critical state model for the slab geometry on the basis of qualitative agreements of real and imaginary third harmonic components, 2´ and 2´´, respectively. The obtained Hp*well reproduced the results of 0´. The critical index of inter-grain critical current density Jc*was estimated as 2.8 from the relation of Jc*Hp*(1-T/Tc*). The large value of was significant for the present Bi2223 high Tcceramics.