226 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



with the time, so that the curves of equal variation of temperature 

 may be concentric circles around the center of the cyclone. 



In the general case where the isotherms have at first any situa- 

 tion whatever, the system of wind is mobile, and the trajectory 

 of the barometric minimum depends on the situation of the iso- 

 therms before the motion commences. 



The isotherms at the surface of the earth belong to particles of 

 air that move without vertical velocity. The trajectories of those 

 particles of air that remain always at the surface of the earth assume 

 the form 



x = x Q +f(t) ) 



„ \ (1) 



y - y<> + iV) J 



by taking the axis of X and of Y at the surface of the earth, and 

 designating the time by t. 



Let the equation of the isotherms for the time / = o, be 



F (* To) = (2) 



If we assume that the particles of air maintain their temperature 

 during motion, we determine the equation of the isotherms at any 

 moment by eliminating x and y between equations (i) and (2). 



If, on the contrary, the temperature of a particle of air varies, 

 either because the pressure changes its value or because the surface 

 of the earth causes a heating or a cooling, we shall be obliged to 

 consider its temperature as dependent on the time while the particle 

 is moving. The problem will be very complicated but its solution 

 can be effected approximately by the graphic method by construct- 

 ing the trajectories of the particles of air and thus following up the 

 variations of temperature due to the pressure and to the surface 

 of the earth. 



First example. Let the trajectories be straight lines parallel to 

 a b (fig. 42) and the velocity be constant. Their equations become 



x = x + at; y = y + bt. 



Assume that the isotherms for the initial time, t = o are straight 

 lines parallel to the axis Y; their equations become 



x = f (t) 



Eliminating x we shall have 



x - / (t) + at 



