Computing the Cassels-Tate pairing on the 2-Selmer group of an elliptic curve improves the upper bound for the rank of the elliptic curve from that obtained by 2-descent to that obtained by 4-descent. Cassels described a method for computing this pairing that involves solving conics over the fields of definition of the 2-torsion points of the elliptic curve. More recently, Steve Donnelly found a method that only involves solving a conic over the base field. I will describe an explicit formula that arises as a variant of his method. The formula involves certain (2,2,2)-forms that might be seen as generalising Bhargava's description of Gauss composition (for binary quadratic forms) to binary quartic forms.