William taught Caroline physics and math so she could do the calculations and proofread the papers he sent to other astronomers and to the Royal Academy. He called the math problems he designed for her “little lessons for Lina.” By 1780, Caroline spoke two languages and knew astronomy and mathematics. Despite her mother’s efforts to the contrary, she was better educated than most women in Europe.

   A critical member of the Herschel team, Carolyn recorded observations and calculated star locations and movements. She compiled all the information into usable tables. She also reorganized the leading star catalog, listing stars by specific zones, based on degrees from the poles, rather than by constellation. In two catalogs, The Index to the Catalogue of 860 Stars Observed by Flamsteed but Not Included in the British Catalogue, and Index to Every Observation of Every Star in the British Catalogue, Caroline resolved many discrepancies found in earlier publications. She expanded the number of stars included in the catalogs. Then she designed an index that made the catalogs far more useful than they had been.

   Using the enormous telescopes the Herschels built, astronomers suddenly found themselves looking at things they couldn’t identify. Some objects appeared as fuzzy blobs. They called these blobs nebulae, from the word “nebulous,” meaning undefined. These nebulae weren’t stars or planets. And their discovery puzzled astronomers everywhere. Caroline’s catalog of 2,600 nebulae ignited a world-wide debate about their identity. The debate advanced astronomy rapidly.

   Astronomers were not the only people who wanted the new telescopes. Even George III, the King of England, had to have one. An enthusiastic amateur astronomer himself, King George gave William a small salary as a reward for discovering Uranus. Then the king asked the Herschels to move closer to the castle so they would be handy when he wanted astronomy lessons. The salary let the Herschels give up professional music. They left Bath and turned to full-time astronomy.