Politically and economically the kelpers seem equally apathetic. They mostly toil as shepherds, living in a feudal 19th-century English country society on large farms owned by companies back in England.

They say Leonard Minto tried to slit his throat after slitting that of his wife. Their 14-year-old son heard the screams. Mr. Minto is now in Toddy McMillan's jail, charged with murder. Just nine months earlier a Chilean hand pulled his shepherd knife and killed a British worker in a drunken brawl.

They were the first killings in at least 40 years and it is hard on Toddy. He is only an acting police chief, his heart is not so strong these days and he is past the age of retirement. But the island officials have not found anyone qualified to replace him yet. They are recruiting in England.

Mrs. Minto's death was probably to have been expected. She and her husband were separated and she was living with another man. Indeed, there are so many instances of this sort, it would seem that jealousy would lead to more violence. The Problem: Too Few Women

At the root of the problem is a simple statistic: for every three men between the ages of 30 and 64, there are two women. It is even worse in the outlying areas. In a census of West Falkland Island eight years ago, there was one single woman over the age of 19 and there were 51 single men.

There is little reason to believe that the situation has changed. More men come from Britain for the work available here. More women go to Britain for the life style there, often as the bride of one of the 40 marines stationed here on one-year tours. This galls the local men.

''Women here are like hen's teeth -bloody rare,'' said Peter Clement, a 31-year-old sheep shearer. It is one of the reasons that Mr. Clement and many of his friends leave each year, joining a small band of wanderers who follow the sheep-shearing season around the world. It has taken him to New Zealand, Australia, Norway and even the United States - as an illegal alien -but he always comes back.