I read it a decade ago from a glass is half empty perspective and found it unconvincing. But, of course, Galton couldn't have been wholly convincing back in 1869: Galton had to dream up most of the conceptual tools (such as twin studies and the correlation coefficient) he needed to prove his insight, which he proceeded to do over the second half of his long and remarkably productive life.
In Hereditary Genius, Galton's basic methodology is to come up with lists of eminent people and determine how many prominent relatives they have. Galton was a great believer in the accuracy of long-term reputation.
Strikingly, he prefers to use other people's lists of eminent men that were created for other purposes so that his biases won't interfere with who makes the list. For example, among statesmen, he is aware of how far men can be propelled by inheritance, luck, and so forth, so he restricts his list to two sources: Prime Ministers (on the ground that you had to have something on the ball to make it all the way to very highest post) and a book written by one of Galton's heroes, Henry Brougham: Sketches of the Statesmen of the time of George III.
Galton cites Brougham, the brilliant Whig politician who largely pushed through the Reform Act of 1832 and the Slavery Abolition Act of 1833, as the exemplar of the man of parts so talented that he would achieve great renown under any circumstances.
Ironically, Brougham is even more overlooked today than Galton. In contrast, Galton's other hero, his own half-cousin Charles Darwin, is now titanically famous. And yet, at least to me, Darwin and Galton, the grandsons of the polymath Erasmus Darwin, appear to be very similar in talents and accomplishments. Darwin, the older of the pair, had the single best idea, but Galton, who was healthier and more energetic, may have had more good ideas (e.g., besides the basic concept of a science of human differences, he invented the concept of regression toward the mean, the basic math of correlation, the weather map, the silent dog whistle, and the system for classifying fingerprints).
Neither Darwin nor Galton radiated an air of being a supreme genius. Both seemed more like enormously curious and resourceful wealthy English amateurs with lots of time on their hands, to the sciences what Lord Peter Wimsey is to fictional crime solving. If Darwin and Galton hadn't been born into a rich family of Whig views and a scientific bent, would they have become so eminent?
The concept of the control group hadn't been dreamed up by 1869 (I don't believe), but Galton cleverly self-analyzes his sample by showing that the likelihood of a relative becoming eminent himself is proportional to the genealogical distance: sons or brothers or fathers of eminent men are more likely to be eminent than nephews, while nephews are more likely to be eminent than cousins or great-nephews.
Galton is aware of the nature-nurture conundrum (he coined the term "nature v. nurture"), so he suggests looking at the careers of favorite nephews of Italian popes. In recent centuries, after the end of the great Renaissance families, the Church became less aristocratic, and popes tended to be the most impressive figure of less distinguished families. How did their favorite nephews do? Not as well as sons do in non-celibate professions, he asserts.
Galton offers other interesting if not wholly convincing arguments for heredity of ability. He wrote in 1869:
Another argument to prove, that the hindrances of English social life, are not effectual in repressing high ability is, that the number of eminent men in England, is as great as in other countries where fewer hindrances exist. Culture is far more widely spread in America, than with us, and the education of their middle and lower classes far more advanced; but, for all that, America most certainly does not beat us in first-class works of literature, philosophy, or art. The higher kind of books, even of the most modern date, read in America, are principally the work of Englishmen. The Americans have an immense amount of the newspaper-article-writer, or of the member-of-congress stamp of ability; but the number of their really eminent authors is more limited even than with us. I argue that, if the hindrances to the rise of genius, were removed from English society as completely as they have been removed from that of America, we should not become materially richer in highly eminent men.
I certainly found that true when forced to study the early classics of American Literature in high school. Before Huckleberry Finn, what from American lit is really worth reading: Bartleby the Scrivener? The Tell-Tale Heart? The best I could say for Thoreau's Walden was that its prose style wasn't quite as soporific as Emerson's Self-Reliance. Most of the early classics appear to be classics mostly out of New Englandish self-regard. New Englanders started most of the colleges, so they got to decide what should be taught in the colleges.
The most prodigious intellectual effort of early American letters, Ben Franklin's 1751 essay Observations Concerning the Increase of Mankind, which, as Malthus admitted in his second edition, foreshadowed him by a half century, is almost unknown today.
Galton's book remains full of great data nerd stuff, such as this digression on an issue that comes up in assessing the talent of military commanders:
There is a singular and curious condition of success in the army and navy, quite independent of ability, that deserves a few words. In order that a young man may fight his way to the top of his profession, he must survive many battles. But it so happens that men of equal ability are not equally likely to escape shot free. Before explaining why, let me remark that the danger of being shot in battle is considerable. No less than seven of the thirty-two commanders mentioned in my appendix, or between one-quarter and one-fifth of them, perished in that way; they are Charles XII., Gustavus Adolphus, Sir Henry Lawrence, Sir John Moore, Nelson, Tromp, and Turenne. (I may add, while talking of these things, though it does not bear on my argument, that four others were murdered, viz. Caesar, Coligny, Philip II. of Macedon, and William the Silent; and that two committed suicide, viz. Lord Clive and Hannibal. In short, 40 per cent. of the whole number died by violent deaths.)
There is a principle of natural selection in an enemy's bullets which bears more heavily against large than against small men. Large men are more likely to be hit. I calculate that the chance of a man being accidentally shot is as the square root of the product of his height multiplied into his weight;¹ that where a man of 16 stone in weight, and 6 feet 2.5 inches high, will escape from chance shots for two years, a man of 8 stone in weight and 5 feet 6 inches high, would escape for three. But the total proportion of the risk run by the large man, is, I believe, considerably greater. He is conspicuous from his size, and is therefore more likely to be recognised and made the object of a special aim. It is also in human nature, that the shooter should pick out the largest man, just as he would pick out the largest bird in a covey, or antelope in a herd.
... This is really an important consideration. Had [Admiral] Nelson [killed at Trafalgar in 1805] been a large man, instead of a mere feather-weight, the probability is that he would not have survived so long.
In short, to have survived is an essential condition to becoming a famed commander; yet persons equally endowed with military gifts—such as the requisite form of high intellectual and moral ability and of constitutional vigour—are by no means equally qualified to escape shot free. The enemy's bullets are least dangerous to the smallest men, and therefore small men are more likely to achieve high fame as commanders than their equally gifted contemporaries whose physical frames are larger.