Chicago City Directories for Elias Apgar

I've been doing some preliminary city directory work on Elias Apgar--who I'm trying to find in the 1880 census and who I think may be the adopted father of William Frame Apgar, who was born in Chicago in 1888. So far, I've just got the entries for 1879 and 1880. I'm not certain if I'm going to trace Elias in every directory--my goal is to try and learn if he really adopted William Frame.

The 1879 and 1880 entries follow.

1879 Chicago City Directory--Apgar entries from Fold3.com

Elias Apgar is listed as a moulder with a house at 325 Illinois.

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.