The early hydration of tri-calcium silicate $(C_3S)$ with different cooling conditions was studied by varing water/solid ratio and atmosphere. The cooling condition and water/solid ratio affected to the second peak of heat liberation but it had no correlation to the induction period. The $Ca^{2+}$ concentration in the aqueous solution was maximized at the starting point of the second peak of heat liberation but in the $CO_2$ exsistence the $Ca^{2+}$ concentration was low and $SiO_2$ con-centration was increased. The hydration rate of $C_3S$ was so accelerated that the induction period could not appear in the $CO_2$ exsistence.