NATURAL PHILOSOPHY. 143 



quires as much more to be put in before the original state is restored. So 

 soon as the law of matter is as clearly known as the law of the basket, there 

 is an end of looking for the perpetual motion. 



That people do try after a perpetual motion to this day is certain. A 

 good many years ago a perpetual motion company was in contemplation ; 

 and the promoters did me the unsolicited honor of putting my name on the 

 list of directors. Fortunately the intention came round to me before the list 

 was circulated ; and a word to the editor of a periodical produced an article 

 which, I believe, destroyed the concern. The plan was to put a drum or 

 broad wheel with one verticle half in mercury and the other in vacuum. 

 This instrument, the most unlucky drum since Parolles, feeling the balance 

 of its two halves very unsatisfactory, was to go round and round in search 

 of an easy position, forever and ever, working away all the time, I mean 

 all the eternity, at lace-making, or water-pumping, or any other useful 

 employment. People were told that if they would sell their steam engines 

 for old iron, they might buy new machines with the money, which would 

 work as long as they held together without costing a farthing for fuel. Cer- 

 tainly, had the scheme been proposed to me, I should have declined to join 

 until I had derived assurance from seeing the donkey who originated it 

 turned into a head-ovcr-heels perpetual motion by tying a heavy weight to 

 his tail and an exhausted receiver to his nose. 



3. Quadrature of the circle. The arithmetical quadrature involves the de- 

 termination of the circumference by a definite arithmetical multiplier, which 

 shall be perfectly accurate. Lambert proved that the multiplier must be an 

 interminable decimal fraction ; and the proof may be found in Legendre's 

 geometry, and in Brewster's translation of that work. The arithmeticians 

 have given plenty of approximate multipliers. The last one, and the most 

 accurate of all, was published a few years ago by Mr. W. Shanks, of 

 Houghton-le-Spring, a calculator to whom multiplication is no A-cxation, 

 etc. He published the requisite multiplier (which mathematicians denote by 

 IT) to six hundred and seven decimal places, of which 441 were verified by 

 Dr. Rutherford. To give an idea of the power of this multiplier, we must 

 try to master such a supposition as the following. 



There are living things on our globe so small that, if due proportion were 

 observed, the corpuscles of their blood would be no more than a millionth 

 of an inch in diameter. Suppose another globe like ours, but so much 

 l.irgcr that our great globe itself, is but fit to be a corpuscle in the blood of 

 one of its animalcules; and call this the first globe abovcus. Let there be 

 another globe so large that this first globe above us is but a corpuscle in the 

 animalcule of that globe ; and call this the second globe above us. Go on 

 in this way till we come to the twentieth globe above us. Next, let the 

 minute corpuscle on our globe be another globe like ours, with everything in 

 proportion ; and call this the first globe below us. Take a blood-corpuscle 

 from the animalcule of that globe, and make it the second globe below us ; 

 and so on, down to the twentieth globe below us. Then if the inhabitants 

 of the twentieth globe above us were to calculate the circumference of their 

 globe from its diameter by the G07 decimals, their error of length could not 



