498 THE THEORY OF SCREWS. 



rectangular axes. He then attempted to push the body parallel to one of these 

 axes, but it would not stir. He tried to move the body parallel to each of 

 the other axes, but was again unsuccessful. He then attached the body to one of 

 the axes and tried to effect a rotation around that axis. Again he failed, for the 

 constraints were of too elaborate a type to accommodate themselves to Mr Carte 

 sian s crude notions. 



We shall subsequently find that the movements of the body are necessarily 

 of an exquisitely simple type, yet such was the clumsiness and the artificial 

 character of Mr Cartesian s machinery that he failed to perceive the simplicity. 

 To him it appeared that the body could only move in a highly complex manner ; 

 he saw that it could accept a composite movement consisting of rotations about 

 two or three of his axes and simultaneous translations also parallel to two or 

 three axes. Cartesian was a very skilful calculator, and by a series of experiments 

 even with his unsympathetic apparatus he obtained some knowledge of the 

 subject, sufficient for purposes in which a vivid comprehension of the whole was 

 not required. The inadequacy of Cartesian s geometry was painfully evident when 

 he reported to the committee on the mobility of the rigid body. I find, he said, 

 that the body is unable to move parallel to x, or to y, or to z ; neither can I make 

 it rotate around x, or y, or z; but I could push it an inch parallel to x, pro 

 vided that at the same time I pushed it a foot parallel to y and a yard backwards 

 parallel to z, and that it was also turned a degree around x, half a degree the other 

 way around y, and twenty-three minutes and nineteen seconds around z. 



Is that all? asks the chairman. Oh, no, replied Mr Cartesian, there are 

 other proportions in which the ingredients may be combined so as to produce 

 a possible movement, and he was proceeding to state them when Mr Commonsense 

 interposed. Stop! stop! said he, I can make nothing of all these figures. This 

 jargon about x, y, and z may suffice for your calculations, but it fails to convey to 

 my mind any clear or concise notion of the movements which the body is free to 

 make. 



Many of the committee sympathised with this view of Commonsense, and they 

 came to the conclusion that there was nothing to be extracted from poor old 

 Cartesian and his axes. They felt that there must be some better method, and 

 their hopes of discovering it were raised when they saw Mr Helix volunteer his 

 services and advance to the rigid body. Helix brought with him no cumbrous 

 rectangular axes, but commenced to try the mobility of the body in the simplest 

 manner. He found it lying at rest in a position we may call A. Perceiving that 

 it was in some ways mobile, he gave it a slight displacement to a neighbouring 

 position B. Contrast the procedure of Cartesian with the procedure of Helix. 

 Cartesian tried to force the body to move along certain routes which he had 

 arbitrarily chosen, but which the body had not chosen; in fact the body would not 

 take any one of his routes separately, though it would take all of them together in 

 a most embarrassing manner. But Helix had no preconceived scheme as to the 

 nature of the movements to be expected. He simply found the body in a certain 

 position A, and then he coaxed the body to move, not in this particular way or in 

 that particular way, but any way the body liked to any new position B. 



