All data on the historic daily quotes of the Dow Jones Averages come from a publication, published in several issues by the Dow Jones Company. The latest issue is The Dow Jones Averages, 1885-1995, Phyllis S. Pierce (ed.) Chicago: Irwin Professional Pub., c1996. There are four indexes published in this book that have been used to create this series. Each series was "spliced" to the next by the value of the two consecutive indexes on a common day.
The DJIA is regarded as a consistent index from the present back to December 12, 1914. During that time, when the number of stocks was increased or there was a split or stocks were replaced, the average was adjusted.
To compute the index from July 30, 1914 back to October 7, 1896, the values of the first DJIA of 12 stocks are multiplied by (54.62/74.56), the ratio of the second index of 20 to first index of 12 on December 12, 1914.
The numbers from September 23, 1889 to October 7, 1896 are from a list called The 20-Stock Average that is published in The Dow Jones Averages, 1885-1995, with a sub title, "20 Mixed Stocks. . . 18 Railroads and 2 Industrials." The publication does not say where this index comes from, however, it is moves very closely with the published DJA of 12 stocks.
To carry the index back during this period, the values of this 20-stock average is multiplied by .5825. This is (54.62 /74.56) from above times .795, the ratio of DJIA to the value of the mixed index on December 31, 1896.
Finally to carry the index back to 1885, DJA of 12 stocks is multiplied by a factor of 0.45775, because this average is 78.58% larger than the 20 stock average on September 23, 1889.
Jack Wilson, Professor of Finance at the North Carolina State University, kindly supplied all of the data to us.