By Kate Holton and Michael Holden LONDON (Reuters) -Princes William and Harry stood vigil at either end of the coffin of their grandmother Queen Elizabeth on Saturday, heads bowed as a line of mourners streamed past the late monarch’s lying-in-state. The two sons of King Charles, attired in military uniforms, stood in silence at a 15-minute vigil in the vast Westminster Hall where the coffin has been lying since Wednesday, draped in the Royal Standard and with the bejewelled Imperial State Crown on top. William and Harry were joined by their six cousins, including Princess Beatrice and Eugenie…