Both the single or double roller provide the necessary safety action. However, the safety roller segment of a double roller has a smaller diameter than the perimeter of a single roller. This provides certain mechanical advantages over the single roller escapement.
The mechanical advantage that Jerry talked about deal with the fact that a double roller results in less contact between the dart and the roller.
In order for a balance to oscillate at a constant rate, it must never be touched. The lever escapement is better than many others because most of the time the balance is free of contact. Of course, it has to contact the pallet in order to unlock the escape wheel and then to receive energy to keep it swinging. It is also touched by the guard pin or dart when the watch receives a shock. The guard pin touching the roller preventing the balance from going "out of action", sometimes improperly called "overbanking". Out of action is allowing the roller jewel to get on the wrong side of the pallet horns and locking the mechanism. The smaller safety roller does this job with less friction and interference on the balance motion. The reason is that the guard pin touches the smaller roller at a more obtuse angle.
Hamilton put a double roller on the 940, their best selling railroad watch of the time, in 1906. The 946, their 23 jewel model, was orginally produced with a double roller in 1904, but they did not sell any until 1906. The 21 jewel 942 had a double roller in 1900. This was a higher priced 940, but only 5913 were ever made. Eventually a double roller was required of railroad watches, but I can't remember when that became common with time inspection.
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