Anonymously written. Found in *Memorabilia Mathematica or the Philomath's Quotation-Book*, Robert Edouard Moritz, 1914, pp.
320-322. Republished as *On Mathematics and Mathematicians*, Dover 19.

## Verse #1A moving form or rigid mass, Under whate'er conditions Along successive screws must pass Between each two positions, It turns around and slides along: This is the burden of my song. |
## Verse #2The pitch of screw, if multiplied By angle or rotation, Will give the distance it must glide In motion of translation. Inf'nite pitch means pure translation, And zero pitch means pure rotation. |
## Verse #3Two motions on two given screws, With amplitudes at pleasure, Into a third screw-motion fuse, Whose amplitude we measure By parallelogram construction (A very obvious deduction). |

## Verse #4Its axis cuts the nodal line Which to both screws is normal, And generates a form divine, Whose name, in language formal Is "surface-ruled of third degree." Cylindroid is the name for me. |
## Verse #5Rotation round a given line Is like a force along. If to say couple you decline, You're clearly in the wrong; 'tis obvious, upon reflection A line is not a mere direction. |
## Verse #6So couples with translations too In all respects agree; And thus there centres in the screw A wondrous harmony Of Kinematics, and of Statics, The sweetest thing in mathematics. |

## Verse #7The forces on one given screw, With motion on a second, In ge-ne-ral some work will do, Whose magnitude is reckoned By angle, force, and what we call The coefficient virtual. |
## Verse #8Rotation now to force convert, And force into rotation; Unchanged the work (we can assert) In spite of transformation. And if two screws no work can claim, Reciprocal will be their name. |
## Verse #9Five numbers will a screw define, A screwing motion six; For four will give the axial line, One more the pitch will fix; And hence we always can contrive One screw reciprocal to five. |

## Verse #10Screws-two, three four or five, combined (No question here of six), Yield other screws which are confined Within one screw complex. Thus we obtain the clearest notion Of freedom and constraint of motion. |
## Verse #11In complex III, three several screws At every point you find, Or if you one direction choose, One screw is to your mind; And complexes of order III Their own reciprocals may be. |
## Verse #12In IV, wherever you arrive, You find of screws a cone, On every line of complex V. There is precisely one; At each point of this complex rich, A plane of screws have given pitch. |

## Verse #13But time would fail me to discourse Of Order and Degree; Of Impulse, Energy and Force, And Reciprocity All these and more, for motions small, Have been discussed by Dr. Ball. |