Below are the weekly Nielsen ratings results for the 1978-79 television season. Viewership wasn't reported by Nielsen until the fall 1988 season, so up until that point the only metric widely available was the household rating (which is what is reported here in this article). To calculate the estimated number of households watching, just multiply each rating by 745,000 as that is what 1 rating point represents.
Full weekly household ratings for every show weren't made available until 1981, so only partial results are available for this season. Only the top 10 results are available for the first seven weeks of the season (from the Raleigh News and Observer), but beginning with the w/e Nov. 5, 1978 there are the top 15 results available (from from The New York Times). Top 20 results are available starting with the w/e Mar. 25, 1979 (from Newsday) and are provided through the end of the season, save for 2 weeks (May 6, 1979 & Sept. 2, 1979) where only the top 15 is available.
Additionally, the second document includes full rankings (without ratings) from The Fort Worth Star-Telegram and these are available for nearly every week of the proper season (not the summer) except for the following weeks: w/e Dec. 17, 1978, Dec. 24, 1978 (top 20 and bottom 10 are provided in the "ratings" document), Dec. 31, 1978, January 14, 1979 (top 20 and bottom 5), and January 21, 1979 (top 20 and bottom 10). The final week of full rankings is the week ending April 15, 1979.
ARCHIVED WEEKS (ratings - all weeks)
ARCHIVED WEEKS (full rankings - thru April 15, 1979)
Source: Nielsen Media Research via Newsday, The New York Times, The Raleigh News & Observer, and The Fort Worth Star-Telegram