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LINE SINGULARITIES IN COMBINATION 86 



41. Line Source and Sink; Line Vortex Pair 86 



42. Circulating Flow: Cylinders, Vortices, a Wall 91 



43. Line Source and Plane Wall 98 



44. Row of Equal Sources or Vortices; Source Midway between Walls or 



on One Wall; Contracted Channel 100 



45. Alternating Vortices or Sources; Vortex Midway between Walls 107 



46. Row of Equal Line Dipoles on a Transverse Axis; Dipole Midway 

 between Walls, with Parallel Axis; Flow Past Cylinder between 



Walls or through a Grating 108 



47. Row of Equal Line Dipoles on a Longitudinal Axis; Flow 



Past a Grating 112 



48. Alternating Line Dipoles; Dipole Midway between Walls, 



with Perpendicular Axis 114 



49. Line Source, Vortex or Dipole Anywhere between Parallel Walls 115 



50. Two Line Dipoles in Opposition; Dipole and a Wall 116 



51. Line Source and Cylindrical Barrier 117 



52. Line Dipole and Cylindrical Barrier 119 



53. Line Source in Uniform Stream 121 



54. Line Source and Sink in Uniform Stream 124 



55. Vortex Pair in a Uniform Stream 127 



56. Other Combinations Involving Line Sources or Dipoles 129 



57. Sheets of Line Sources or Vortices 130 



58. Source Sheet in a Uniform Stream 131 



59. The Simpler Singularities and Their Transformation 133 



60. Line Singularity in an Angle 134 



TRANSFORMATIONS DEFINED INVERSELY 136 



61. Ellipses and Hyperbolas 136 



