the forces exerted and the work done in machines; the means of measuring those quantities by indicators and dynamometers, of determining and balancing the reactions of moving masses in machines, and of regulating work and speed; and the efficiency, or proportion in which the useful work is less than the total work, in the different sorts of moving pieces, and in their various combinations.

Considering that a convenient single word is wanted to denote the proportion in which the total work in a machine is greater than the useful work, I have ventured to propose the word COUNTEREFFICIENCY for that purpose.

Under the head of the Materials, Strength, and Construction of Machinery are considered, first, the properties of various materials, as affecting their treatment and use in the construction of machines; secondly, the general principles of the strength of materials; thirdly, the special application of those principles to questions relating to the strength and the construction of various parts of machines; and fourthly, the principles of the action of cutting tools.

Great care has been taken to ascertain the values of the factor of safety and of the working stress in successful examples of actual machinery; and some of the problems respecting the strength of special parts of machines have not been published previously except in scientific journals and in lectures.

Authorities for facts and information are cited where it is necessary to do so. The following works are so frequently referred to, that it may be desirable to mention them here specially :WILLIS On Mechanism, first edition, 1841; second edition, 1870. FAIRBAIRN On Millwork.

HOLTZAPFFEL On Mechanical Manipulation.

:

BUCHANAN On Millwork; edited by TREDGOLD and G. RENNIE, with an Essay on Tools by NASMYTH.

W. J. M. R.

The Seventh Edition has been revised, and additional matter relating to recent improvements added to Appendix.

GLASGOW, May, 1893.

W. J. M.

CHAPTER I.-ELEMENTARY RULES IN DescriptiVE GEOMETRY.

SECTION I. General Explanations: 22A. Given, the Projections of a

CHAPTER II.-OF THE MOTIONS OF PRIMARY MOVING PIECES IN MACHINES.

CHAPTER III.—OF THE MOTIONS OF SECONDARY MOVING PIECES.

CHAPTER IV.-OF ELEMENTARY COMBINATIONS IN MECHANISM.

SECTION I.-Definitions, General Prin-

ciples, and Classification.

89. Elementary Combinations De-

fined.

90. Line of Connection,

91. Comparative Motions of Con-

nected Points and Pieces,

92. Adjustments of Speed,

93. Train of Mechanism,

77

77

78

80

80

94. Elementary Combinations Classed, 8C

SECTION II.-Of Rolling Contact and

Pitch Surfaces.

95. Pitch Surfaces,

119. Diametral and Radial Pitch, 111

120. Relative Positions of Parallel

Axes in Wheelwork,

121. Laying-off Pitch, and Sub-

division of Pitch-lines,

113

113

SECTION IV.-Sliding Contact; Teeth,

Screw-Gearing, and Cams.

122. General Principle of Sliding

Contact,

114

115

123. Teeth of Wheels and Racks;

General Principle,

124. Teeth-Definition of their Parts, 115

125. Customary Dimensions of Teeth, 116

126. Teeth for Inside Gearing,.

127. Common Velocity and Relative

Velocity of Teeth-Approach

. 117

and Recess-Path of Contact, 117

128. Arc of Contact,

96. Toothless Wheels,

Rollers,

Toothless Racks,

97. Ideal Pitch Surfaces,

82

98. Pitch Line,

82

119

82

100. Wheels with Parallel Axes,

83

129. Obliquity of Action,.

101. Wheel and Rack,

130. Teeth of Spur-Wheels and

84

102. Circular Wheels in General,

Racks,

120

84

103. Circular Spur Wheels,

131. Involute Teeth for Circular

85

104. Circular Wheel and Straight

Rack,

132. Involute Teeth for Racks,

125

85

105. Circular Bevel Wheels,

133. Peculiar Properties of Involute

86

106. Circular Skew Bevel Wheels,

Teeth,

125

87

107, Non-Circular Wheels in General,

92

134. Teeth for a given Path of

108. Elliptic Wheels,

95

109. Lobed Wheels,

97

110. Logarithmic Spiral Sectors or

Rolling Cams,

111, Frictional Gearing,

SECTION III.-Of the Pitch and Number

of the Teeth of Wheels.

112. Relation between Teeth and

Pitch Surfaces-Nature of the

Subject,

113. Pitch Defined,.

114. General Principles,

115. Frequency of Contact-Hunt-

135. Teeth Traced by Rolling Curves, 129

136. Epicycloidal Teeth in General,. 130

137. Tracing Epicycloidal Teeth by

Templets,

138. Straight Flanked Epicycloidal

Teeth,

139. Epicycloidal Teeth Traced by an

Uniform Describing Circle,

140. Approximate Drawing of Epi-

cycloidal Teeth,

141. Teeth Gearing with Round

Staves-Trundles, Pin-Wheels,

103

103

104

and Pin-Racks,

142. Intermittent Gearing,

. 104

ing-Cog,

116. Smallest Pinion,

118. Train of Wheelwork,

143. Teeth of Non-Circular Wheels,

144. Teeth of Bevel-Wheels,

145. Teeth of Skew-Bevel Wheels-

General Conditions,

131

133

134

134

137

139

141

143

116