1002 



SCIENCE. 



[N. S. Vol. XII. No. 313. 



will be seeu even when the scope of the investi- 

 gations is limited to conservative forces and in- 

 finitely small displacements, for the form of 

 the body does not enter the discussions. 



To give an analysis of the book or of Ball's 

 method would be presumption, as Ball did this 

 himself in his inimitable address before the 

 British Association at the Manchester Meeting 

 in 1887, reprinted in Nature of the same year, 

 as many of the readers of Science will remem- 

 ber. Though the address is fourteen quarto 

 pages long, it preserves its exquisite flavor 

 throughout. Ball begins thus: "There was 

 once a rigid body which lay peacefully at rest. 

 A committee of natural philosophers was ap- 

 pointed to make an experimental and rational 

 inquiry into the dynamics of that body. The 

 committee received special instructions. They 

 were to find out why the bodj' remained at 

 rest, notwithstanding that certain forces were 

 in action. They were to apply impulsive 

 forces and observe bow the body would begin 

 to move. They were also to investigate the 

 small oscillations. These being settled, they 

 were then to — but here the chairman inter- 

 posed ; he considered that for the present, at 

 least, there was sufficient work in prospect. 

 He pointed out how the questions already pro- 

 posed just completed a natural group. ' Let it 

 suffice for us,' he said, 'to experiment upon 

 the dynamics of this body so long as it remains 

 in or near to the position it now occupies. "\Ye 

 may leave to some more ambitious committee 

 the task of following the body in all conceivable 

 gyrations through the universe.' " 



"The committee was judiciously chosen. 

 Mr. Auharmonic undertook the geometry. 

 He was found to be of the utmost value in 

 the more delicate parts of the work, though 

 his colleagues thought him rather prosy at 

 times. He was much aided by his two friends, 

 Mr. One-to-one, who had charge of the homo- 

 graphic department, and Mr. Helix, whose 

 labors will be seen to be of much importance. 

 As a most respectable, if rather old fashioned 

 member, Mr. Cartesian was added to the com- 

 mittee, but his antiquated tactics were quite 

 outmanceuvered by those of Helix and One-to- 

 one. I need only mention two more names. 

 Mr. Commonsense was, of course, present as an 



ex officio member, and valuable service was ren- 

 dered even by Mr. Querulous, who objected at 

 first to serve on the committee at all. He said 

 that the inquiry was all nonsense, because 

 everybody knew as much as they wished to 

 know about the dynamics of a rigid 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 ap- 

 pear that a remarkable result of the labors of 

 the committee was the conversion of Mr. 

 Querulous himself. 



"The committee assembled in the presence 

 of the rigid body to commence their memorable 

 labors. 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 bewil- 

 dering nature of the constraints by which the 

 movements of the body were hampered. 

 They had been accustomed to nice mechanical 

 problems, in which a smooth body lay on a 

 smooth table, * * * in fact the chairman 

 truly appreciated the situation when he said 

 the conslraints were of a perfectly general type. ' ' 

 Later in the proceedings Mr. Querulous is 

 heard from. "'How could you,' he said, 

 ' make any geometrical theory of the mobility 

 of the body without knowing all about the 

 constraints ? And yet you are attempting to 

 do so with perfectly general constraints of 

 which you know nothing.' " The committee 

 having got to work assigned certain duties, 

 whereupon that ' most respectable if rather old 

 fashioned member,' gives an account of him- 

 self: "Mr. Cartesian having a reputation for 

 such work, was requested to undertake the 

 inquiry and 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 par- 

 allel 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." 



