076 REPOBT — 1887. 



analogous character suitably enlarged for our present purpose. We have dis- 

 covered that the impulsive screws and the corresponding instantaneous screws form 

 two homographic systems. There will he a certain limited number (never more 

 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 homographv, 

 soon pointed out the few double screws. One of these was chosen, a vi^'orous 

 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 similai-ly 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 'Sir. 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 ? 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 ai-e ever different.' 



And Mr. Querulous proceeded to illustrate his views by experiments on the 

 rigid bodj-. 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 

 the}" were accordingly designated the jmncijxil scretcs 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 

 gi-eat for his comprehension. He had an invincible attachment to the .r, ij, z, 

 which he regarded as the ne ^;/«s ultra of dynamics. ' Why will you burden the 

 science,' he sighs, ' with all these additional names ? Can ynu not express what you 

 want without talking about cjdindroids, 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 sufRciently 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 jou talk of your " principal screws of inertia " ? Pray for once sacrifice 

 this generality you prize so much and put the theory into some extreme shape 

 that ordinary mortals can understand.' 



Mr. Anharmonic would not condescend to comply with this request, so the 

 chairman called upon Mr. One-to-One, who somewhat ungraciously consented. 

 ' I feel,' said he, ' the request to be an irritating one. Extreme cases frequently 

 make bad illustrations of a general theory. That zero multiplied by infinity may 

 be anything is surely not a felicitous exhibition of the perfections of the mul- 

 tiplication table. It is with reluctance that I divest the theory of its flowing 

 geometrical habit, and present it only as a stiff conventional guy from which true 

 grace has departed. 



' Let us suppose that the rigid body, instead of being constrained as heretofore 



