Here's a quote from the Model T forum. He says the engine was a Dodge fast 4. He included the same picture you have.
"My grandfather owned this sprint car. It sat, complete, in a scrap yard until the mid 80's. By the time I found that out, and went to get it, the scrap yard was long gone. Now, I want to build it. All I have is this picture and know that it was a T chassis with a supercharged Dodge Fast Four engine. It was completed in 1927 and, according to old newspapers, won several races around Texas. I'm not yet a T head and know zero about T's at this point so, I turn to the experts. What can be learned from this picture and where do I start?"