CONTENTS. Vll 



Chapter IX Continued. 



Page 



171. Divergence of a Vector in Space, 116 



172. Curl of a Two-Dimensional Vector, 119 



173. Curl of a Vector in Space, 121 



174. Complex Differential Operations 122 



175. Pure Time-Differentiations and Time- Integrations of Scalar Fields, ... 124 



176. Pure Time-Differentiations and Time-Integrations of Vector-Fields, ... 126 



177. Complex Time and Space Differentiation, 128 



Chapter X. The Forced Vertical Motion at the Bounding Surfaces. 



178. Hypsometric and Bathymetric Maps, 131 



179. Charts of Idealized Topography, 132 



180. The Motion in the Lowest Surface of Flow, 134 



181. Charts of Vertical Velocity at the Ground, 134 



182. Ascendant-Charts, 135 



183. ChangeofVelocityintoSpecificMomentum. Charts of Density at the Ground, 136 



184. Direct Method of Determining Vertical Specific Momentum from Horizontal 



Velocity at the Ground, 138 



Chapter XI. Vertical Motion in Free Space Complete Kinematic Diagnosis. 



185. Free Vertical Motion, .... 139 



186. Diagnostic Use of the Solenoidal Condition, 139 



187. Change of Variables, 142 



188. Example: Cyclonic Center, United States of America, November 28, 1905, 145 



189. Complete Kinematic Diagnosis 154 



Chapter XII. Kinematic Prognosis. 



190. Determination of Displacements from Given Velocities 157 



191. Synoptical Representation of Horizontal Displacements 157 



192. Different Forms of the Equation of Continuity, 158 



193. Equation of Continuity as a Prognostic Equation, 159 



Chapter XIII. Reversal of the Problem of Kinematic Prognosis. Kine- 

 matic Determination of Acceleration. 



194. On the Reversed Problems 163 



195. Determination of Displacements in the Second Approximation, .... 163 



196. Discontinuous Method for Constructing Charts of Acceleration 165 



197. Continuous Method for Constructing Charts of Acceleration, .... 166 



198. Special Remarks 167 



199. Return to the Problem of Prognosis, 168 



Chapter XIV. Examples of Atmospheric Motions. 



200. Indian Southwest Monsoon in July, 169 



201. North America, 1905, November 28, 8 a. m. 170 



202. Practical Applications of the Charts of Motion 172 



203. Charts of Acceleration, 173 



204. Main Example of Kinematic Diagnosis, Europe, 1907, July 25, 7 a. m., 



Greenwich 174 



