During the construction of the Quebec Bridge in $1907,$ the bridge's designer, Theodore Cooper, received word that the suspended span being built out from the bridge's cantilever was deflecting downward by a fraction of an inch ($2.54$ centimeters). Before he could telegraph to freeze the project, the whole cantilever arm broke off and plunged, along with seven dozen workers, into the St. Lawrence River. It was the worst bridge construction disaster in history. As a direct result of the inquiry that followed, the engineering "rules of thumb" by which thousands of bridges had been built around the world went down with the Quebec Bridge. Twentieth-century bridge engineers would thereafter depend on far more rigorous applications of mathematical analysis. Which one of the following statements can be properly inferred from the passage?
- Prior to $1907$ the mathematical analysis incorporated in engineering rules of thumb was insufficient to completely assure the safety of bridges under construction.
- Cooper's absence from the Quebec Bridge construction site resulted in the breaking off of the cantilever.
- Nineteenth-century bridge engineers relied on their rules of thumb because analytical methods were inadequate to solve their design problems.
- Only a more rigorous application of mathematical analysis to the design of the Quebec Bridge could have prevented its collapse.