Several features of atmospheric vortices (symmetric tropical cyclones) are examined kinematically by use of the vorticity and circulation theorems. First, generation of a region of negative relative vorticity around a tropical cyclone is derived from the vorticity theorem, and then its necessity is shown from the divergence of integrals of the kinetic energy and the pressure difference. From the data of the Okinawa typhoon of 1924, the existence of this region of negative relative vorticity is verified. Secondly, the circulation theorem is used to examine the effect of latitude on wind. Thirdly, generation of the storm eye is explained from a dynamical point of view. Finally, an application of the vorticity theorem is given.