One of the primary empirical evidences, in my view, of the scientific accuracy of the theosophical teachings related by HPB is the treatment of Neptune.
In a footnote on page 102 of volume 1 of the Secret Doctrine, HPB says:
“When we speak of Neptune it is not as an Occultist but as a European. The true Eastern Occultist will maintain that, whereas there are many yet undiscovered planets in our system, Neptune does not belong to it, his apparent connection with our sun and the influence of the latter upon Neptune notwithstanding. This connection is mayavic, imaginary, they say.”
The Titius-Bode Law, known at the time of HPB, explains that the planets of our system are not located at random distances from the sun, but instead follow a precise spacing, based on a sequence of ratios of 0, 1, 2, 4, 8, 16, 32, 64, 128.
After its discovery, this ratio successfully predicted the location of both Uranus and Ceres. In fact, of all the planets in our system only Neptune fails to conform to this precise mathematical spacing. As an example of modern scientific absurdity, when Neptune was discovered to not fit with this spacing, the scientific community discarded any recognition of the Titus-Bode Law and you’ll find very few scientists that even know this ratio exists, despite their study of the planets.
HPB, and the Theosophists, were the only ones to present an alternative, which is basically this: Neptune is an anomaly, not native to our system. So it’s not surprising that it alone doesn’t fit into the spacing ratios.
When Pluto was discovered, scientists used it’s location to entirely dismiss the spacing law, yet if Neptune is not included in the law, then Pluto conforms precisely with the predicted spacing.
It is the Theosophical perspective alone that explains why the Titus-Bode Law holds true, all the way out to Pluto, if only Neptune is skipped, as the non-native planet it is.
Is it not odd that a law that can accurately predict the locations of every planet but one should be discarded because of that one? By sheer statistical probability the law must be seen to be accurate and founded upon some truth; it could not possibly be random and coincidental that the planets are spaced in such a way, and yet this is the position of modern astronomy! Any decent scientist would be inclined to explore why Neptune doesn’t fit, as opposed to why (in their minds) the law doesn’t fit solely because of Neptune.
Here’s a chart displaying the accuracy of the Titus-Bode Law if Neptune is skipped.