A huge question that pops into my head when reading and discussing about how intelligence can be inherited is whether there is, or at least in Galton's mind, a gene for intelligence. If one's mental abilities can be passed from parent to child, this must be from genes (nature). However, wouldn't a large factor be the environment the individual is raised and lives in (nurture)? Bramwell does not mention much in either his study or Galton's factoring out the way the individual was raised, however based on the careers of the people studied (High Court Judges, Mathematicians, Scientists, Politicians, etc.), I can assume that these families make a decent amount of money and can afford to bring up their children with a good education and other luxuries that would lead to them being more intelligent. Intelligence was not measured by IQ in these studies, so whatever measure they were taking for intelligence could have well been affected by nurture.
The study also in the end concludes that the number of eminent sons from eminent men is greatly decreasing, and blames it on the fact that they just are not having enough sons. In a sense this is a no-brainer, as you can't measure anything if it does not exist. However it also makes sense because the more children one has, the higher the chance of having an eminent son is. This goes back to Bramwell's comparison to flipping a coin. So it seems to me that there is not too much hard evidence in these studies, and that intelligence in the end is based on chance, leading me to believe that intelligence is not in fact inherited.
In the end of the article, a question is posed to the reader: "Has anyone ever heard of even one eminent man both of whose parents were mentally deficient"? This suggests that having eminent parents does raise the odds of a child being eminent or intelligent, but does not in any way support that it is inherited or just gives the child an advantage in being raised to be intelligent.