According to Wikipedia the year 1735 (MDCCXXXV) was a common year (ie one of 365 days)starting on a Saturday of the Gregorian Calendar.
The significant events of the year they list include
April 13 - Japan Emperor Sakuramachi accedes to throne
April 16 - London premiere of Alcina by G F Handel, his first Italian opera for the Royal opera House, Covent Garden
August 4 - New York, New York Weekly Journal writer John Peter Zenger acquitted of seditious libel against the royal governor, on the basis that what he published was true.
October - China, Qianlong Emperor succeeds Yongzheng and begins 60 year reign of Qing dynasty
Poland, War of Polish Succession concludes a preliminary peace (ratified 1738)
Of more interest to me is that this was the year of the conversion of George Whitefield and Hywel Harris and probably Daniel Rowland and that John Wesley began his famous journal (he and Charles were probably converted in 1738) and the Great Awakening was beginning in America.