His example was with the differences between men and women. Scientists thought that men were superior in terms of their brains. When it was found that male brains weighed more than female brains, this was considered their proof. When the argument turned around that elephant brains weigh more than human brains (in other words, so what?), they then argued that it was the ratio of brain weight to body weight . . . except this favored women. And so came more rationalizations, etc.
Society has a much different temperament these days (Russell wrote this particular essay in 1932), but here's the money quote:
But the alliance between politicians and pseudo-scientists is so strong that it will take a long time before such facts become commonly known. The general public cannot tell which among scientists is to be trusted and will therefore be wise to be very sceptical whenever they hear a man of science giving a confident opinion about a matter on which he has strong prejudices. Men of science are not supermen and are as liable to error as the rest of us.It's a bit of general advice worth bearing in mind; that PhD next to your name doesn't shield you from uncritical thinking. I included the first sentence along with the quote because, whatever the issues where that he was writing about then, I'd say the relationship between scientific advocacy groups and politicians of any persuasion has become ever more complicated.
Think global warming. You have scientists on both sides of that divide spouting different facts and announcing either the salvation or doom of mankind. The truth of the matter may not emerge until this topic leaves the realm of politics.