Round Trip

chandler perpetual motion

Eric Chandler offered this perpetual-motion scheme for Edward Barbeau’s “Fallacies, Flaws and Flimflam” column in the College Mathematical Journal. Points A and B are at the same height, and C is halfway between them. The ramp AC is a segment of a cycloid, a curve designed to produce the fastest descent under gravity.

A ball released at A rolls down the ramp AC to C covering a greater distance in a shorter time than it would have had it rolled down BC to C. The relation Velocity = Distance/Time thus implies that the ball arrives at C with greater velocity than it would have had it rolled down BC. This added velocity enables the ball to roll from C up to and past B to a point D a little farther along. It then returns to A along the inclined ramp DA to repeat the cycle endlessly.

Where is the error?

| Science & Math

Feathered Fighters

Early in World War I, parrots were placed in the Eiffel Tower to detect the approach of aircraft, which they could hear 20 minutes before they became audible to human ears. Unfortunately, they proved unable to distinguish between German and French planes.

The British navy also briefly tried to train seagulls to perch on enemy periscopes, in hopes they might defecate opportunely and blind the Germans. “For a short while,” writes historian Colin Simpson, “a remote corner of Poole harbor in Dorset was littered with dummy periscopes and hopefully incontinent sea gulls.” Churchill canceled the program.

| History

Math Notes

99999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999989999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999 is prime.

| Science & Math

Mountain Hazard

http://books.google.com/books?id=6_0OAAAAYAAJ&printsec=frontcover#v=onepage&q&f=false

Although in our days the carrying off of Ganymede is not re-enacted, yet the inhabitants of mountainous countries have some ground for accusing the eagles of bearing off their children. A well known fact of this kind took place in the Valais in 1838. A little girl, five years old, called Marie Delex, was playing with one of her companions on a mossy slope of the mountain, when all at once an eagle swooped down upon her and carried her away in spite of the cries and presence of her young friend. Some peasants, hearing the screams, hastened to the spot, but sought in vain for the child, for they found nothing but one of her shoes on the edge of the precipice. The child, however, was not carried to the eagle’s nest, where only two eaglets were seen, surrounded by heaps of goat and sheep bones. It was not till two months after this that a shepherd discovered the corpse of Marie Delex, frightfully mutilated, upon a rock half a league from where she had been borne off.

— Henry Davenport Northrop, Earth, Sea and Sky, 1887

| Oddities

Wanderlust

In 1886, French gas fitter Jean-Albert Dadas was admitted to a Bordeaux hospital suffering from exhaustion. Normally he led a quiet life, he told a medical student, but occasionally he would be overcome by anxiety and headaches and then find himself in a distant city, apparently having traveled there on foot. If the local police didn’t arrest him for vagrancy he would report to the French consul, who would arrange for his travel back home.

Dadas was 26 when he arrived at the hospital, but the attacks had begun when he was 12. He’d been working as a manufacturer’s apprentice when he simply disappeared, and his brother found him in a neighboring town helping an umbrella salesman. Since then, the medical student wrote, Dadas had regularly deserted “family, work and daily life to walk as fast as he could, straight ahead, sometimes doing 70 kilometers a day.” Some journeys had taken him as far as Algeria and Moscow.

Dadas’ condition was diagnosed as dromomania or “pathological tourism.” Though they’re rarely seen today, such fugue states saw a curious vogue in France in the 1890s — and produced one memorable case in Pennsylvania.

(Thanks, Eleanor.)

| Oddities

Judicial Opinion

In deciding the 1972 case Flood v. Kuhn, which challenged the reserve clause in baseball players’ contracts, Justice Harry Blackmun waxed a bit rhapsodic, listing the players whom he felt deserved immortality:

Then there are the many names, celebrated for one reason or another, that have sparked the diamond and its environs and that have provided tinder for recaptured thrills, for reminiscence and comparisons, and for conversation and anticipation in-season and off-season: Ty Cobb, Babe Ruth, Tris Speaker, Walter Johnson, Henry Chadwick, Eddie Collins, Lou Gehrig, Grover Cleveland Alexander, Rogers Hornsby, Harry Hooper, Goose Goslin, Jackie Robinson, Honus Wagner, Joe McCarthy, John McGraw, Deacon Phillippe, Rube Marquard, Christy Mathewson, Tommy Leach, Big Ed Delahanty, Davy Jones, Germany Schaefer, King Kelly, Big Dan Brouthers, Wahoo Sam Crawford, Wee Willie Keeler, Big Ed Walsh, Jimmy Austin, Fred Snodgrass, Satchel Paige, Hugh Jennings, Fred Merkle, Iron Man McGinnity, Three-Finger Brown, Harry and Stan Coveleski, Connie Mack, Al Bridwell, Red Ruffing, Amos Rusie, Cy Young, Smoky Joe Wood, Chief Meyers, Chief Bender, Bill Klem, Hans Lobert, Johnny Evers, Joe Tinker, Roy Campanella, Miller Huggins, Rube Bressler, Dazzy Vance, Edd Roush, Bill Wambsganss, Clark Griffith, Branch Rickey, Frank Chance, Cap Anson, Nap Lajoie, Sad Sam Jones, Bob O’Farrell, Lefty O’Doul, Bobby Veach, Willie Kamm, Heinie Groh, Lloyd and Paul Waner, Stuffy McInnis, Charles Comiskey, Roger Bresnahan, Bill Dickey, Zack Wheat, George Sisler, Charlie Gehringer, Eppa Rixey, Harry Heilmann, Fred Clarke, Dizzy Dean, Hank Greenberg, Pie Traynor, Rube Waddell, Bill Terry, Carl Hubbell, Old Hoss Radbourne, Moe Berg, Rabbit Maranville, Jimmie Foxx, Lefty Grove. The list seems endless.

Justices Warren Burger and Byron White dissented from Blackmun’s list — but they declined to say whether they felt it was overinclusive, underinclusive, or irrelevant.

| Entertainment

The State of Franklin

In 1784, to help pay off debts after the Revolutionary War, North Carolina offered to give Congress 29 million acres of its territory west of the Appalachians. When the legislature rescinded this offer a few months later, the settlers seceded to establish a new state of their own.

“Franklin” failed of joining the union by two votes in the Continental Congress, but it elected officers, convened a legislature, and wrote a constitution. The economy was based largely in barter — John Wheeler Moore’s 1882 School History of North Carolina quotes the officers’ pay:

His Excellency, the Governor, per annum, one thousand deer skins; His Honor, the Chief Justice, five hundred deer skins, or five hundred raccoon skins; the Treasurer of the State, four hundred and fifty raccoon skins; Clerk of the House of Commons, two hundred raccoon skins; members of Assembly, per diem, three raccoon skins.

Things began to fall apart in 1788, when Franklin’s governor tried to place the defenseless state under Spanish rule. North Carolina arrested him, and the last holdouts turned themselves in. The region now belongs to Tennessee.

| History

“A Revolving Ice Cake”

https://books.google.com/books?id=3YA9AQAAIAAJ&pg=PA85

There is a curious ice formation on the Mianus River, near the village of Bedford, Westchester County, New York. The Mianus at that place is a small stream, averaging about ten feet in width. At a place locally known as the ‘ten foot hole’ the stream widens out into a pool forty or fifty feet wide. In this pool there has formed a cake of ice about twenty five or thirty feet in diameter and perfectly circular in shape. This circular cake of ice is slowly revolving and is surrounded for about two-thirds of its circumference by stationary ice. There is a space of about three inches between the revolving cake and the stationary ice, except at the ‘up stream’ side of the revolving cake, where the water is open and the current quite swift. Each revolution takes about six minutes. I inclose a rough drawing which will give an idea of this curious formation.

— Letter from J.M. Bates to Scientific American, Feb. 9, 1895

| Oddities