The first step in the double-murder trial of former city supervisor Dan White was completed today with the selection of four alternate jurors to join the twelve seated Friday.

The rapid empaneling of the jury surprised most courtroom observers. The trial is to begin Tuesday.

White is charged with two counts of first-degree murder in the Nov. 27 City Hall slayings of Mayor George Moscone and Supervisor Harvey Milk.

White resigned from the Board of Supervisors Nov. 10 saying he could not support his wife and baby on his $9,600 supervisor's salary. But he later requested reinstatement.

Moscone initally accepted White's request, but legal objections by the city attorney and growing opposition to White within his district apparently persuaded Moscone to appoint someone else. Moscone and Milk were killed moments before the mayor was to announce White's successor.

The 32-year-old White, a former police officer and firefighter, was charged under the "special circumstances" provision of a new state law that provides for the death penalty in cases where a public official has been killed or where a multiple death is involved.

Superior Court Judge Walter Calcagno has indicated that the jury must first decide whether White is innocent or guilty of the charges, and then-if guilty-will have to determine whether the crime involved special circumstances.

White's attorney, Douglas Schmidt, said he would attack the constitutionality of the "special circumstances" provision in motions to be presented Tuesday.