Further extrapolations differ from Newton Cotes formulas. When Townshend quit the West Indies he discharged Jervis into the under Admiral Thomas Cotes. Roger Cotes computed the derivative of sine in his "Harmonia Mensurarum" (1722). He lives at Keal Cotes in Lincolnshire. Duncan moved from journalism to writing fiction after her marriage to Cotes. Lady Cotes took Cullwick to London. However, through the vigorous passion displayed by Cotes, Newton's scientific hunger was once again reignited. For example, Coates in Cambridgeshire or Cotes in Leicestershire. During the printing of this edition a correspondence went on continuously between Newton and Cotes. The shapes of the orbits of an inverse cube law are known as Cotes spirals. Cotes was born in Burbage, Leicestershire. Cotes formulas, of which the rectangle rule and the trapezoidal rule are examples.