A new method is described for measuring the surface impedance of metals at low temperatures and at radio-frequencies. Using this method, the surface impedance of normal tin and the penetration depth λ in superconducting tin have been studied at about 9 Mc/s frequency as a function of impurity content. The measured surface impedances agree well with the values expected, and the penetration depths increase with impurity content, in confirmation of Pippard's observations (14) at 9400 Mc/s. The variation of λ with reduced temperature t is well represented by the equation λ/λ0 = (1 − t4)−½, in impure as well as in pure tin. The absolute value of λ found for pure tin is about 4 × 10−6 cm., significantly lower than the values previously found.

In the expression of Taylor's theorem

there are three well-known forms of the remainder R(n, a, b). The first is the Schlömilch form

The following theorem was stated and proved by Krull(l). We give a new and simple proof.

Theorem. Let K be afield with valuation υ, value group Γ and residue class field R.