Neile was born at
Bishopsthorpe, the eldest son of
Sir Paul Neile MP for Ripon and Newark. His grandfather was
Richard Neile, the
Archbishop of York. In 1657, he became a student at the
Middle Temple. In the same year he gave his exact rectification of the semicubical parabola and communicated his discovery to
William Brouncker,
Christopher Wren and others connected with
Gresham College. His demonstration was published by Wallis in
De Cycloide (1659). The general formula for rectification by
definite integral was in effect discovered by
Hendrik van Heuraet in 1659. In 1673 Wallis asserted that
Christiaan Huyghens, who was advancing his own claim to have influenced Heuraet, was also slighting the priority of Neile. Neile was elected a fellow of the Royal Society on 7 January 1663 and a member of the council on 11 April 1666. He entered the debate on the theory of
motion, as a critic of the
empiricist stance of other members. His own theory of motion was held up from publication by unfavourable peer review by Wallis, in 1667; a revision was communicated to the society on 29 April 1669. Neile objected to Wren's 1668 work on
collision as lacking discussion of causality: he asked for discussion of the nature of
momentum. His own work was much influenced by ideas drawn from the
De Corpore of
Thomas Hobbes. He made astronomical observations with instruments erected on the roof of his father's residence, the “Hill House” (later called Waltham Place) at
White Waltham in
Berkshire, where he died at the age of 32. A white marble monument in the parish church of White Waltham commemorates him and an inscribed slab in the floor marks his burial-place. He belonged to the
privy council of
King Charles II. ==Notes==