The 1879 and 1880 entries follow.
There is no Elias Apgar in the 1880 Chicago City Directory on Fold3.com. This may explain his absence in the 1880 Federal census. Amos, George, and Philip Apgar are listed in 1880 as shown below.
City directories are useful, but I'm not certain how helpful they will be for me in this problem. I'm looking to see if Elias Apgar adopted William Frame some time after Apgar married in 1874 and before he died in 1894. I'm not certain directories will provide much assistance and I'm hesitant to spend the time on it at this point. Suggestions or ideas are welcomed.