In a small commonplace book, bearing on the seventh page the date of January 1663/1664, there are several articles on angular sections, and the squaring of curves and " crooked lines that may be squared," several calculations about musical notes, geometrical propositions from Francis Vieta and Frans van Schooten, annotations out of Wallis's Arithmetic of Infinities, together with observations on refraction, on the grinding of " spherical optic glasses," on the errors of lenses and the method of rectifying them, and on the extraction of all kinds of roots, particularly those " in affected powers."

With this conception of the infinite as absolutely unconditioned should be compared what may be described roughly as lesser infinities which can be philosophically conceived and mathematically demonstrated.

In reality, these infinities can never be realized because of the intervention of physical forces, which prevent further smaller wiggles being made.

This was followed by a long series of popular treatises in rapid succession, amongst the more important of which are Light Science for Leisure Hours and The Sun (1871); The Orbs around Us and Essays on Astronomy (1872); The Expanse of Heaven, The Moon and The Borderland of Science (1873); The Universe and the Coming Transits and Transits of Venus (1874);(1874); Our Place among Infinities (1875); Myths and Marvels of Astronomy (1877); The Universe of Stars (1878); Flowers of the Sky (1879); The Peotry of Astronomy (1880); Easy Star Lessons and Familiar Science Studies (1882); Mysteries of Time and Space and The Great Pyramid (1883); The Universe of Suns (1884); The Seasons (1885); Other Suns than Ours and Half-Hours with the Stars (1887).