In 1902, Ayrton published The Electric Arc, a summary of her research and work on the electric arc, with origins in her earlier articles from the Electrician published between 1895 and 1896. With this publication, her contribution to the field of electrical engineering began to be cemented. However, initially at least, Ayrton was not well received by the more prestigious and traditional scientific societies such as the Royal Society. In the aftermath of the publication of The Electric Arc, Ayrton was proposed as a Fellow of the Royal Society by renowned electrical engineer John Perry in 1902. Her application was turned down by the Council of the Royal Society, who decreed that married women were not eligible to be Fellows. However, in 1904, she became the first woman to read a paper before the Royal Society when she was allowed to read her paper "The Origin and Growth of Ripple Marks" and this was later published in the Proceedings of the Royal Society. In 1906, she was awarded the Royal Society's prestigious Hughes Medal "for her experimental investigations on the electric arc, and also on sand ripples." She was the fifth recipient of this prize, awarded annually since 1902, in recognition of an original discovery in the physical sciences, particularly electricity and magnetism or their applications, and as of 2018, one of only two women so honoured, the other being Michele Dougherty in 2008.