Which month, day and year did Lennie Small die?

In Steinbeck's Of Mice and Men the main characters George and Lennie are migrant farm workers who travel from place to place in California to find agricultural jobs. In Chapter One they have come to a clearing next to the Salinas River and are spending the night before going on to a nearby ranch where they will "buck barley." George talks about getting work passes in the town of Salinas. Even though Steinbeck spends a good deal of time in the beginning of each chapter describing the various settings of the novella, including the clearing near the river, the bunkhouse and the barn, he never explicitly identifies the exact year or season when Lennie dies. Considering, however, that the men were hired to help harvest the ranch's crop of barley it is most certainly at some point in the late summer. According to the USDA, barley in California is planted in the early spring and harvest may begin as early as August 15 and last until October 1. The novella was originally published in 1937 and according to his biographer Jackson Benson, Steinbeck began writing the book in late 1936. The events in the book are certainly contemporary to the Great Depression of the 1930's. Thus, the actual date of Lennie's death was probably a Sunday (day of the week is noted in the beginning of Chapter Five) in September of the year 1935 or 1936. Of course, this is an educated guess and there is no textual evidence to suggest its complete accuracy.