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 1 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, is, 

 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 express 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 &quot;principal screws of inertia&quot;? Pray for once sacrifice this 



