A Treatise on the Theory of Screws

APPENDIX II. 505 than six) of double screws common to these two systems. As the double points in the homography of point systems are fruitful in geometry, so the double screws in the homography of screw systems are fruitful in Dynamics.’ A question for experimental inquiry could now be distinctly stated. Does a double screw possess the property that an impulsive wrench delivered thereon will make the body commence to move by twisting about the same screw ? This was immediately tested. Mr Anharmonic, guided by the indications of homography, soon pointed out the few double screws. One of these was chosen, a vigorous impulsive wrench was imparted thereon. The observations were conducted as before, the anticipated result was triumphantly verified, for the body commenced to twist about the identical screw on which the wrench was imparted. The other double screws were similarly tried, and with a like result. In each case the instantaneous screw was identical both in pitch and in position with the impulsive screw. ‘ But surely,’ said Mr Querulous, ‘ there is nothing wonderful in this. Who is surprised to learn that the body twists about the same screw as that on which the wrench was administered 1 I am sure I could find many such screws. Indeed, the real wonder is not that the impulsive screw and the instantaneous screw are ever the same, but that they should ever be different.’ And Mr Querulous proceeded to illustrate his views by experiments on the rigid body. He gave the body all sorts of impulses, but in spite of all his endeavours the body invariably commenced to twist about some screw which was not the impulsive screw. ‘ You may try till Doomsday,’ said Mr Anharmonic, ‘you will never find any besides the few I have indicated.’ It was thought convenient to assign a name to these remarkable screws, and they were accordingly designated the principal screws of inertia. There are for example six principal screws of inertia when the body is perfectly free, and two when the body is free to twist about the screws of a cylindroid. The committee regarded the discovery of the principal screws of inertia as the most remarkable result they had yet obtained. Mr Cartesian was very unhappy. The generality of the subject was too great for his comprehension. He had an invincible attachment to the x, y, z, which he regarded as the ne plus ultra of dynamics. ‘ Why will you burden the science,’ he sighs, ‘with all these additional names ? Can you not expx’ess what you want without talking about cylindroids, and twists, and wrenches, and impulsive screws, and instantaneous screws, and all the rest of it?’ ‘No,’ said Mr One-to- One, ‘ there can be no simpler way of stating the results than that natural method we have followed. You would not object to the language if your ideas of natural phenomena had been sufficiently capacious. We are dealing with questions of perfect generality, and it would involve a sacrifice of generality were we to speak of the movement of a body except as a twist, or of a system of forces except as a wrench.’ ‘ But,’ said Mr Commonsense, ‘ can you not as a concession to our ignorance tell us something in ordinary language which will give an idea of what you mean when you talk of your “principal screws of inertia”? Pray for once sacrifice this