An elementary treatment of the theory of spinning tops and gyroscopic motion, by Harold Crabtree.
Annotations Tools
INTRODUCTORY CHAPTER 11 Experiment 2. If the wheel is taken out of its bearings at Y, Y', and the framework held in the hands at X, X', a violent attempt tQ tilt it about Y'Y will, unless proper care is taken, result in the wheel wriggling out of the hands altogetherfor the same reason that when properly mounted just now it turned about ZZ'. It is clear that an opposite direction of spin or any attempt to tilt in the opposite direction, produces an opposite direction of turning about ZZ'. Experiment 3. Let us now take the gyroscope when the wheel is not spinning, and its axle XX' is inclined at an angle to the vertical as in Fig. xxIII., the screw at Z not being clamped. If the pedestal ZZ' is held in the hand and slowly swung round, it will be found that XX' turns round about the vertical and points in the same direction as the hand. But let a spin be given to X the wheel, and it will be seen at once that, though the hand revolves round the body, XX' remainiss always pointing in the same direction in which it pointed originally.* This stability of the axle of the X gyroscope may be employed to prove the rotation of the earth. For suppose the spin is maintained during a Z period of several hours by means of electric power, and that the gyroscope is set down in a room with its axle pointing to some particular object in ( the room. After a few hours it will be found that the axle no longer points to that object; showing, not that the axle has changed its position in space, but that the room is in a -- different position in space owing to the rotation of the earth. FIG. XXIII. Thus, if the axis is placed horizontally pointing due east, six hours later it will be pointing south (and upwards), while after another six hours it will be pointing due west (and horizontally). Experiment 4. Now, while the wheel is still spinning, let the turning movement be given to the hand when the screw at Z has been made fast. The gyroscope at once sets itself with the * The friction may not be quite negligible though very nearly so. The frictional couple at Z is probably sufficiently large to turn the frame YY' round when the wheel is not spinning, but totally inadequate when it is spinning. So much as is appreciable tends to turn it about Y'Y, as will be seen later.
-
Scan #1
Page #1
-
Scan #2
Page #2
-
Scan #3
Page #3 - Title Page
-
Scan #4
Page #4
-
Scan #5
Page #5 - Title Page
-
Scan #6
Page #6
-
Scan #7
Page #7
-
Scan #8
Page #8
-
Scan #9
Page VII
-
Scan #10
Page VIII
-
Scan #11
Page IX - Table of Contents
-
Scan #12
Page X - Table of Contents
-
Scan #13
Page XI - Table of Contents
-
Scan #14
Page XII - Table of Contents
-
Scan #15
Page 1
-
Scan #16
Page 2
-
Scan #17
Page 3
-
Scan #18
Page 4
-
Scan #19
Page 5
-
Scan #20
Page 6
-
Scan #21
Page 7
-
Scan #22
Page 8
-
Scan #23
Page 9
-
Scan #24
Page 10
-
Scan #25
Page 11
-
Scan #26
Page 12
-
Scan #27
Page 13
-
Scan #28
Page 14
-
Scan #29
Page 15
-
Scan #30
Page 16
-
Scan #31
Page 17
-
Scan #32
Page 18
-
Scan #33
Page 19
-
Scan #34
Page 20
-
Scan #35
Page 21
-
Scan #36
Page 22
-
Scan #37
Page 23
-
Scan #38
Page 24
-
Scan #39
Page 25
-
Scan #40
Page 26
-
Scan #41
Page 27
-
Scan #42
Page 28
-
Scan #43
Page 29
-
Scan #44
Page 30
-
Scan #45
Page 31
-
Scan #46
Page 32
-
Scan #47
Page 33
-
Scan #48
Page 34
-
Scan #49
Page 35
-
Scan #50
Page 36
-
Scan #51
Page 37
-
Scan #52
Page 38
-
Scan #53
Page 39
-
Scan #54
Page 40
-
Scan #55
Page 41
-
Scan #56
Page 42
-
Scan #57
Page 43
-
Scan #58
Page 44
-
Scan #59
Page 45
-
Scan #60
Page 46
-
Scan #61
Page 47
-
Scan #62
Page 48
-
Scan #63
Page 49
-
Scan #64
Page 50
-
Scan #65
Page 51
-
Scan #66
Page 52
-
Scan #67
Page 53
-
Scan #68
Page 54
-
Scan #69
Page 55
-
Scan #70
Page 56
-
Scan #71
Page 57
-
Scan #72
Page 58
-
Scan #73
Page 59
-
Scan #74
Page 60
-
Scan #75
Page 61
-
Scan #76
Page 62
-
Scan #77
Page 63
-
Scan #78
Page 64
-
Scan #79
Page 65
-
Scan #80
Page 66
-
Scan #81
Page 67
-
Scan #82
Page 68
-
Scan #83
Page 69
-
Scan #84
Page 70
-
Scan #85
Page 71
-
Scan #86
Page 72
-
Scan #87
Page 73
-
Scan #88
Page 74
-
Scan #89
Page 75
-
Scan #90
Page 76
-
Scan #91
Page 77
-
Scan #92
Page 78
-
Scan #93
Page 79
-
Scan #94
Page 80
-
Scan #95
Page 81
-
Scan #96
Page 82
-
Scan #97
Page 83
-
Scan #98
Page 84
-
Scan #99
Page 85
-
Scan #100
Page 86
-
Scan #101
Page 87
-
Scan #102
Page 88
-
Scan #103
Page 89
-
Scan #104
Page 90
-
Scan #105
Page 91
-
Scan #106
Page 92
-
Scan #107
Page 93
-
Scan #108
Page 94
-
Scan #109
Page 95
-
Scan #110
Page 96
-
Scan #111
Page 97
-
Scan #112
Page 98
-
Scan #113
Page 99
-
Scan #114
Page 100
-
Scan #115
Page 101
-
Scan #116
Page 102
-
Scan #117
Page 103
-
Scan #118
Page 104
-
Scan #119
Page 105
-
Scan #120
Page 106
-
Scan #121
Page 107
-
Scan #122
Page 108
-
Scan #123
Page 109
-
Scan #124
Page 110
-
Scan #125
Page 111
-
Scan #126
Page 112
-
Scan #127
Page 113
-
Scan #128
Page 114
-
Scan #129
Page 115
-
Scan #130
Page 116
-
Scan #131
Page 117
-
Scan #132
Page 118
-
Scan #133
Page 119
-
Scan #134
Page 120
-
Scan #135
Page 121
-
Scan #136
Page 122
-
Scan #137
Page 123
-
Scan #138
Page 124
-
Scan #139
Page 125
-
Scan #140
Page 126
-
Scan #141
Page 127
-
Scan #142
Page 128
-
Scan #143
Page 129
-
Scan #144
Page 130
-
Scan #145
Page 131
-
Scan #146
Page 132
-
Scan #147
Page 133
-
Scan #148
Page 134
-
Scan #149
Page 135
-
Scan #150
Page 136
-
Scan #151
Page 137
-
Scan #152
Page 138
-
Scan #153
Page 139
-
Scan #154
Page 140
-
Scan #155
Page I
-
Scan #156
Page #156
-
Scan #157
Page II
-
Scan #158
Page #158
-
Scan #159
Page III
-
Scan #160
Page #160
Actions
About this Item
- Title
- An elementary treatment of the theory of spinning tops and gyroscopic motion, by Harold Crabtree.
- Author
- Crabtree, Harold.
- Canvas
- Page 7
- Publication
- London,: Longmans, Green, and co.,
- 1909.
- Subject terms
- Tops
- Gyroscopes
Technical Details
- Link to this Item
-
https://name.umdl.umich.edu/abr4615.0001.001
- Link to this scan
-
https://quod.lib.umich.edu/u/umhistmath/abr4615.0001.001/25
Rights and Permissions
The University of Michigan Library provides access to these materials for educational and research purposes. These materials are in the public domain in the United States. If you have questions about the collection, please contact Historical Mathematics Digital Collection Help at [email protected]. If you have concerns about the inclusion of an item in this collection, please contact Library Information Technology at [email protected].
DPLA Rights Statement: No Copyright - United States
Related Links
IIIF
- Manifest
-
https://quod.lib.umich.edu/cgi/t/text/api/manifest/umhistmath:abr4615.0001.001
Cite this Item
- Full citation
-
"An elementary treatment of the theory of spinning tops and gyroscopic motion, by Harold Crabtree." In the digital collection University of Michigan Historical Math Collection. https://name.umdl.umich.edu/abr4615.0001.001. University of Michigan Library Digital Collections. Accessed April 30, 2025.