728 
PROFESSOR 0. REYNOLDS ON CERTAIN DIMENSIONAL 
Art. Page 
42-44. Corresponding results at densities corresponding to the fineness of the plates. Graham’s 
results reconciled . . .. .. . . . . .. . . .. .. .. 767 
45. Verification of Law 1, Art. 9. . .. .. .. ». .. .. .. .. 768 
Section IV.—The radiometer with very small vanes. 
46-48. The apparatus. Fibre of silk .. .. .. .. .. .. .. .. 768 
49-51. Effect of elevating the heater. Bending of the fibre. Spider-line .. . . .. 771 
52. Agreement of the l'esults with the theory .. .. .. .. . . . . .. 772 
Part II.—(Theoretical). 
Section V.—Introduction to the theory. 
53-54. The necessity for a limited surface—no force on an unlimited surface . . . . .. 772 
55-59. Illustration from two opposite batteries „. .. . . . . . . . . . . 774 
60-64. Prefatory description of the mathematical method .. .. .. .. .. 776 
Section VI.—Notation and preliminary steps. 
65-68. Explanation of the symbols o>(Q), A, B, C, D, E, F, G, H .. . . . . .. 779 
69-71. The rates at which mass, momentum, and energy are carried across a plane by any one 
of the groups A, B, C, &c., in a uniform gas .. .. . . .. .. . . 781 
72. Maxwell’s law of distribution of velocities in a uniform gas .. . . . . . • 783 
73. Restriction to gases of uniform texture, such as air or hydrogen . . .. .. 784 
74. Table XX.—Values of «r(Q).784 
Section VII.—Foundations of the theory. The mean range. 
75. The condition of the gas varying from point to point. Line of thought . . . . 786 
76. Sketch of the method by which the fundamental theorems are deduced . . . . 789 
77. The mean component velocities of the molecules which pass through an element . . 790 
78. Limitations and definitions. Condition of the gas. Resultant uniform gas. Inequalities 791 
79. Fundamental assumptions ., .. .. .. .. .. .. . . . . 793 
80. Fundamental theorems (I. and II.). Corollaries.. .. ,. .. .. .. 795 
81. The mean range s .. . . . . .. .. . . .. . . .. • . 799 
82. The mean component values of s. General expressions for c(Q) when the gas is 
continuous .. . . .. .. . . .. .. . . . . ■ . 800 
83-84. c(Q) in the neighbourhood of a solid surface . . .. . . .. .. .. 803 
Section VIII.—Equations of motion. 
85-86. Equations of steady condition. Steady density, momentum, and pressure .. .. 805 
87-88. Conditions of no tangential stress in the gas or on a solid surface . . .. . . 805 
Section IX.—Application to transpiration ancl thermal transpiration through a tube. 
89-91. Equations of steady condition .. .. .. . . .. . . . . .. 806 
92. Transpiration under pressure when s is small compared with c, the distance across 
the tube .. .. .. .. .. .. ., .. .. .. .. 807 
93-94. Relation between s, /i, and other quantities .. .. .. . . . . .. 808 
95. General case of transpiration and thermal transpiration .. .. .. . . .. 810 
96. The value of s 1 —s 3 near a solid surface .. .. .. .. .. .. .. 810 
97-98. The velocity of the gas and the friction at a solid surface . . . , .. .. 811 
99-101. The equations of motion as affected by discontinuity. General form of s\ — s' 2 .. 813 
102. General equation of transpiration .. . . .. .. .. . . .. .. 815 
