Scarlet Letter D.J. # 37 - Chapter 19: Part 1.

It was with a feeling which neither of them had ever before experienced, that they sat and watched Pearl’s slow advance. In her was visible the tie that united them. She had been offered to the world, these seven years past, as the living hieroglyphic, in which was revealed the secret they so darkly sought to hide,—all written in this symbol,—all plainly manifest,—had there been a prophet or magician skilled to read the character of flame! And Pearl was the oneness of their being. Be the foregone evil what it might, how could they doubt that their earthly lives and future destinies were conjoined, when they beheld at once the material union, and the spiritual idea, in whom they met, and were to dwell immortally together? Thoughts like these—and perhaps other thoughts, which they did not acknowledge or define—threw an awe about the child, as she came onward. (pg. 180 4th paragraph)
This is when they had the first feeling of family, and when they were watching Peal walk towards the them it was like a dream. Pearl was the reason that they were together now. Her symbol was evident to them, but to the rest of the society it was still mysterious because no one knew who her father was. They continued to compare her features to their own, and Pearl was definitely her father's child.