570 REPORT — 1887. 



lie said that tbe inquiry was all nonsense, because everybody knew as mucli as they 

 wished to know about the dynamics of a rifjid body. The subject was as old as 

 the hills, and had all been settled long ago. He was persuaded, however, to look 

 in occasionally. It will appear that a remarkable result of the labours of the 

 committee was the conversion of Mr. Querulous himself. 



The committee assembled in the presence of the rigid body to commence their 

 memorable labours. There was the body at rest, a huge amorphous mass, with no 

 regularity in its shape — no uniformity in its texture. But what chiefly alarmed 

 the committee was the bewildering nature of the constraints by which the move- 

 ments of the body were hampered. They had been accustomed to nice mechanical 

 problems, in which a smooth body lay on a smooth table, or a wheel rotated on an 

 axle, or a body rotated around a point. In all these cases the constraints were of a 

 simple character, and the possible movements of the body were obvious. But the 

 constraints in the present case were of puzzling complexity. There were cords and 

 links, moving axes, surfaces with which the body lay in contact, and manj' other 

 geometrical constraints. Experience of ordinary problems in mechanics would be 

 of little avail. In fact, the chairman truly appreciated the situation when he 

 said, that the constraints were of a perfecfli/ f/eneral type. 



In the dismay with which this announcement was received Mr. Commousense 

 advanced to the body and tried whether it could move at all. Yes, it was obvious 

 that in some ways the body could be moved. Then said Commonsense, ' Ought 

 we not first to study carefully the nature of the freedom which the body possesses ? 

 Ought we not to make an inventory of everj' distinct movement of which the 

 body is capable ? Until this has been obtained I do not see how we can make 

 any progress in the dynamical part of our business.' 



Mr. Querulous ridiculed this proposal. ' How could you,' he said, ' make any 

 geometrical theory of the mobility of a body without knowing all about the 

 constraints ? And yet you are attempting to do so with perfectly general con- 

 straints of which you know nothing. It must be all waste of time, for though I 

 have read many books on mechanics, 1 never saw anything like it.' 



Here the gentle voice of Mr. Anharmonic was heard. ' Let us try, let ua 

 simply experiment on the mobility of the body, and let us faithfully record what 

 we find.' In justification of this advice Mr. Anharmonic made a remark which 

 was new to most members of the committee ; he asserted that, thoinjh the con- 

 straints may he of endless variety and complexiiy, there can he only a very limited 

 variety in the types of possible mobility. 



It was therefore resolved to make a series of experiments with the simple 

 object of seeing how the body could be moved. Mr. ('artesian, having a 

 reputation for such work, was requested to rmdertake the inquiry and to report 

 to the committee. Cartesian commenced operations in accordance with the well- 

 known traditions of his craft. He erected a cumbrous apparatus which he called 

 his three 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. 

 Cartesian's crude notions. 



We shall subsequenth^ find that the movements of the bodj- are necessarily 

 of an exquisitely simple type, yet sucli 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 can neither move parallel to x, nor toy, nor to s ; neither can I make 



