vi CONTENTS. 



Chapter V Continued. Pag 



128. Simplest Singularities in the Field of the Lines of Flow, 47 



129. Complexes of Singular Points, 50 



130. Complex Phenomena in Connection with Lines of Convergence and of 



Divergence, 5 1 



131. Influence of Wave-Motions on the Aspect of the Lines of Flow, .... 54 



132. Practical Rules for the Direct Drawing of the Lines of Flow and the Curves 



of Equal Intensity 55 



Chapter VI. Supplementary Rules to Assist in the Drawing of the Lines 

 of Flow and of the Curves of Equal Intensity. 



133. Remarks on the Digression 57 



134. Relation of the Kinematic Singularities to Dynamic and Thermodynamic 



Phenomena, . . 57 



135. Consequences of the Stability of Atmospheric or Hydrospheric Equilibrium, 58 



136. Consequences of Kinetic Instability, Discontinuous Motions, and Eddies, . 59 



137. Cold Wave, Warm Wave, 60 



138. Lines of Convergence at the Sea's Surface, 60 



139. Dynamic Diagnosis of Motion in the Free Space, 61 



Chapter VII. Isogonal Curves. 



140. Isogonal Curves, .... 63 



141. Singular Points in the Field of a Multiple-Valued Scalar, 63 



142. Further Remarks on the Field of Isogonal Curves and their Relation to the 



Vector-Field, 65 



143. Sandstrom's Integration-Machines, 66 



144. Equivalence of Isogons and Vector-Lines for the Representation of Vector- 



Fields, 68 



Chapter VIII. Graphical Algebra. 



145. Graphical Mathematics, 69 



146. Drawing-Board 69 



147. Graphical Algebra with One Variable, 70 



148. Graphical Algebra with Two Variables, 72 



149. Addition of Scalar Fields, 73 



150. Multiplication of Scalar Fields, 74 



151. Division of Scalar Fields, 76 



152. Case of Three or More Variables 77 



153. Vector-Algebra, ... 78 



154. Consistent Use of Rectangular Components in Graphical Vector- Algebra, . 81 



155. Use of Angles to Represent the Directions of Vectors 83 



156. Projections of a Vector ; Scalar Product and Vector-Product 85 



157. Addition of Vectors which are Normal to Each Other, 86 



158. Addition of Any Vectors 89 



159. Easily Accessible Data Regarding the Field of the Vector-Sum, .... 91 



160. Graphical Tables for Vector-Addition, 93 



161. Complete Resultantometer, 96 



Chapter IX. Graphical Differentiation and Integration. 



162. Different Forms of the Problems, 99 



163. Directional Differentiation and Integration 99 



164. Linear Differentiation and Integration, 100 



165. Application to Two-Dimensional Scalar Fields, 103 



166. Other Forms of the Problem of Linear Differentiation and Integration, . . 105 



167. Curves of Equal Intensity and Curves of Equal Transport, 107 



168. Differentiations of Higher Order. Curvature and Divergence of a System 



of Curves, 109 



169. Partial Derivatives; Ascendant and Gradient, 111 



170. Divergence of a Two-Dimensional Vector, 113 



