The New York Times will stop charging for access to parts of its Web site, effective at midnight Tuesday night, reflecting a growing view in the industry that subscription fees cannot outweigh the potential ad revenue from increased traffic on a free site. The move comes two years to the day after The Times began the subscription program, TimesSelect, which has charged $49.95 a year, or $7.95 a month, for online access to the work of its columnists and to the newspapers archives. TimesSelect has been free to print subscribers to The Times and to some students and educators. In addition to opening the entire site to all readers, The Times will also make available its archives from 1987 to the present without charge, as well as those from 1851 to 1922, which are in the public domain. There will be charges for some material from the period 1923 to 1986, and some will be free. The Times said the project had met expectations, drawing 227,000 paying subscribers out of 787,000 over all and generating about $10 million a year in revenue.