Attendance records for major-league baseball games before World War II are sketchy. If you look at any team's day-by-day schedule at baseball-reference.com for games in that era, you'll see that many of the entries under "attendance" are either blank or list an even thousand number, likely an estimate.
This doesn't mean the numbers don't exist -- the teams reported very specific overall attendance figures for full seasons. In 1934, the Cubs drew 707,525, which was actually up from the previous year (and second in the National League), though well off the 1929 record of 1,485,166. This was likely due to two primary factors: not winning the pennant for a couple of years, and the Depression, which would take up much of the 1930s.
Sunday, July 8, was different, at least for Cubs attendance. Not only was a specific number reported in the boxscore and newspaper articles, but it was one of the largest of its time: 47,138. The site ballparks.com says the official capacity of Wrigley Field was 40,000 between 1928 and 1937, so on this day, on which a doubleheader was played, Wrigley was stuffed more than 7,000 beyond its listed seating capacity.
This sort of thing used to go on well into the 1970s; overflow crowds and standing room were allowed in nearly every area of the ballpark. I can remember days in the late 1970s where people were permitted to sit in the aisle in the bleachers, likely several hundred over the "official" bleacher capacity (3,300 in those days).
The Chicago Fire Department put a stop to this practice around 1980; to this day you can find the limits of Wrigley's capacity in all its areas (lower deck, upper deck, bleachers) posted in CFD signs that are located near the Fan Services window near home plate. Next time you're at the ballpark, go check them out. (If you add up all the figures on the signs they come to about 10,000 over the actual capacity, likely due to double-counting one of the areas.)
Edward Burns (listed, in a typo, as "Edwards Burns" in the byline to his story) had the July 8, 1934 recap in the Tribune:
The Pittsburgh Pirates made the Cubs look like raw bushers before 47,138 folks at Wrigley field yesterday in the first game of a double header, which the Pittsburghers won, 11 to 4, in a most distressing way. And the high spirited Chicagoans came right back in the second game and taught the fresh Pirates a lesson by making eight runs in the first inning and then carrying on to an ultimate 12 to 3 victory.
I just love the writing from this era. "In a most distressing way." Calling people "fresh"; that usage of that word has long been forgotten by most, but one definition, listed as "informal", is "presumptuous or disrespectful; forward". I remember my grandparents using the word that way ("Don't be fresh!") but it's fallen out of use.
The Cubs were just two games out of first place after this doubleheader split, but managed just a 40-35 record the rest of the way, and the Cardinals ran away with the pennant.