As a side note to the above equations, there are several variations to the AC3 transformation equation, which are primarily based on carbon content of the steel. These equations can be found in the Physical Metallurgy Handbook by Anhil Sinha. In his book, which is an excellent resource book for metallurgists, he lists the various AC3 transformation equations for the applicable grade of steel.
So, it is not unusual to see a variation in AC3 transformation temperature between several equations because you need to select the correct equation for the grade of steel.