After the longest internal investigation in Senate history, the Senate Select Committee on Ethics finally will get to question Sen. Herman E. Talmadge (D-Ga.) publicly today about allegations of his financial misconduct.

Talmadge, a 23-year Senate veteran, is appearing reluctantly under oath before the six-member panel. Attorneys for the Georgia senator sought unsuccessfully last month to have the five charges brought against him by the committe's special counsel, Carl Eardley, dropped for lack of evidence.

The charges center on allegations by Talmadge's former chief aide, Daniel Minchew. Minchew told the committee he set up a secret bank account here in 1973 with Talmadge's approval. More than $39,000 in improper Senate payments and in campaign contributions were funneled through the account, and Minchew testified that Talmadge got some of the money.

Talmadge repeatedly has denied Minchew's charge. In his opening statement to the committee April 30, when he was not under oath, Talmadge told the ethics panel that Minchew was "a proven liar, cheat and embezzler."

Committee members have said they also want to question Talmadge about an alleged cache of $100 bills that Talmadge's former wife, Betty, said he kept hidden in an overcoat in their apartment here for years. Testifying last month, Betty Talmadge said the cache sometimes totaled $45,000 and had existed since the 1940s, when Talmadge was governor of Georgia.

In testimony yesterday, Talmadge's press secretary, Gordon Roberts, and Rep. Ronald (Bo) Ginn (D-Ga.), another former Talmadge staff member, told the panel they never saw Talmadge with $100 bills.

Roberts, who has been Talmadge's press secretary for 17 years, said that during conversations in 1974 and 1976, Betty Talmadge told him that if her husband tried to divorce her, "she would get him if it was the last thing she ever did." The couple was divorced in 1977.

Asked whether she might have lied about the secret cache to harm her former husband, Roberts answered, "It is my judgment she would be capable of that." But he said he had no recollection of any other possible lies by the senator's former wife.

According to Betty Talmadge's testimony, she kept 77 of the $100 bills when she found them in 1974 and turned them over to the committee this year along with the envelope she said contained the money. The name of Maryland attorney Harry P. Anestos, a Talmadge supporter, was scrawled on the envelope.

Anestos testified last month that he never gave any envelope to Talmadge and did not give the senator any cash after 1973.

Talmadge's attorneys have challenged Mrs. Talmadge's assertion that she found the money in 1974 in an envelope with Anestos' name on it.

Called back to testify yesterday, Anestos said he did visit Talmadge's former chief aide, T. Rogers Wade, in November 1974 and gave him printed material about a speech he wanted Talmadge to make to a Greek organization. Anestos said he did not give Wade any cash then.

Under cross-examination by committee counsel Douglas McCullough, however, Anestos acknowledged that he took $250 out of his bank account on the day of the visit and later got a letter from Talmadge thanking him for his "support." Anestos said his 1973 contribution to the senator had been for $250.

In other testimony, Talmadge's daughter-in-law, Lyniece Talmadge, disputed a claim by Minchew that he gave money from the secret account to her late husband, Robert Talmadge. CAPTION: Picture, Talmadge holds grandaughter Libby before the start of yesterday's hearing. By James K. W. Atherton - The Washington Post