WHAT PASSAGE OF THE TORAH WAS READ THE WEEK OF JULY 3, 1955?

Dear Shulkin, 

The 3rd of July 1955 was a sunday. 

On the saturday before, the 2nd of July, Hukath and Balak were read. 

On the saturday afterwards (which the important one for this answer),
July 9th 1955, Pinhas was read. Pinhas is the "Parasha" of Bemidbar
(Numbers) 25.10 - 30.1 .

Here are several sites with information on this passage (Parasha): 

Jewish Agency for Israel 
<http://www.jafi.org.il/education/torani/NEHAMA/pinchas.html> 

A Reconstructionist Dvar Torah
Pinhas I  
<http://www.jrf.org/recondt/pinchas-2000-cohen.html> 
Pinhas II 
<http://www.jrf.org/recondt/pinchas_hirsh.html> 

Torat haTeva 
<http://www.torathateva.org/torah_archives/Pinhas5762.html> 
 
I hope this answers your question. Please contact me if you need any
further clarification on this answer before you rate it.

Search strategy: regarding the commentaries on the passage, I just
searched [parashat pinhas] ; regarding the conversion, to find what
was the weekly Parasha on that week, I used the Jewish Calendar
Calculation   by Tichnut.de

Jewish Calendar Calculation   
<http://www.tichnut.de/onlinekalender/kalender.html>  - very neat!

Just perfectly done.