Tenochtitlan on Lake Texcoco

Modern Mexico City: a super metropolis of nine million people, was once a series of lakes. The Aztec capital, Tenochtitlan, was located there on a network of artificial islands. In those lakes, in countless numbers, swam the axolotl, Ambystoma mexicanum, a wholly aquatic salamander. According to Aztec mythology, the underworld god Xolotl transformed himself into an axolotl to escape being murdered. In a world composed of diverse, and at times weird, animals axolotls stand out as being very strange. The axolotl has a link to the underworld and a legend of divinity.

Axolotls are neotenic. Set apart from most amphibians, the axolotl never transforms into a terrestrial organism. It maintains gills (clearly visible as six long tree-like appendages at the back of their head) and a tail for swimming throughout their entire lifespan. They resemble a tadpole that is in the middle of it’s transformation into a frog, when it has grown arms and legs but has not “lost” its tail yet. Although it seems as though the axolotl should be stunted by its inability to achieve metamorphosis, the fact is that the axolotl achieves far more growth and life expectancy compared to the tiger salamander (a non-neotenic salamander of which the axolotl is genetically close to). Adult axolotls range from nine to twelve inches in length and can live for up to twenty five years; although a lifespan of ten to fifteen years is typical. They are freshwater carnivores hunting worms, minnows, and aquatic insects via smell.

Xolotl was the god of misfortune, and bad luck is currently dogging the wild axolotl. The lakes of the Mexican basin have been one of the most populated areas of the western hemisphere since the fourteenth century. Axolotl tacos were a favorite meal of the inhabitants for centuries and the creature was overfished up until the twentieth century…when the lakes were drained to prevent flooding. Now the lakes largely exist in huge pipes deep below the city and as a series of polluted channels and small reservoirs. Not only are these remaining canals choked with pollution, but super competitive non-native fish have been introduced, most prominently the African tilapia and the Asian carp.

Axolotls are nearly extinct in the wild, and it is uncertain whether they will survive there much longer. The animals have, however found a dark refuge which ensures their continuing existence. As a result of their neoteny, axolotls have extraordinary abilities to heal themselves. Not only can they completely regrow lost arms and legs back to full size and function, they can also regenerate damaged vital organs – including portions of their brains. Axolotls do not heal by scarring, but seem to use some more fundamental ability to regenerate. Of course these remarkable abilities can not help axolotls when they are cooked into a burrito or devoured whole by a carp, but their unusual healing has brought them to the attention of biologists and medical scientists (as has their longevity in comparison with similar salamanders).

Axolotls have joined fruit flies, mice, zebrafish, and rhesus monkeys as a model animal for the laboratory. The salamanders may individually be vivisected, dissected, and subjected to crazy organ transplants or chemical manipulations, but overall they have found an ecosystem to thrive in. Their population numbers have been growing and axolotls will not be extinct until life science is. Indeed if the field of regenerative medicine begins to flourish, all of humankind might have reason to revere the axolotl far more than the Aztecs esteemed Xolotl.

The Swiss Screw Thread

In 1876 the Société des Arts de Genève formed a committee to standardize small screw threads for instruments, clocks and watches, Geneva being a center of the watch industry. The committee consisted principally of persons actually active in horological manufacturing. They began by forming an extensive collection of screws and documents related to screws, and then placed these materials in the hands of Professor Marc Thury. In 1877 the Society convened a conference in Geneva to agree upon a thread series.

The goal was to create a thread series that, while it differed as little as possible from current practice, was based on a simple, mathematical regularity. This Thury achieved. 

A screw diameter of 6 millimeters was chosen as size 0 and assigned a pitch of 1 mm. The 6 mm diameter was selected because that was roughly the diameter of currently-used screws that had a pitch of 1 mm. 

From size zero, progressively higher numbers identified progressively smaller screws, ending with number 25, the smallest. Sizes of screws larger than 6mm were negative numbers, beginning with minus 1 and ending at minus 20, the largest size. Thus in both cases, the bigger the number, the smaller the screw.

Pitch

The pitches of adjacent sizes differed by a factor of 0.9, which was determined empirically. One consideration in choosing this factor was that it was felt that the sizes in existing thread series were so close together that it was difficult for workers to distinguish sizes by eye; fewer, not more, sizes were desired.

Pitches of screws smaller than 6 mm were successive powers of 0.9, rounded off to 2 or 3 significant places. For example, the pitch of size 1 = 0.9¹; the pitch of size 2is 0.9² = 0.81; the pitch of size 3 is 0.9³ = 0.729, and so on.

Pitches of screws larger than 6 mm were determined by dividing the pitch of the previous size by 0.9 and rounding off to 2 or 3 significant places. For example, size −1 has a pitch of = 1 mm/0.9 = 1.1111… mm = 1.11 mm.

Diameter

The diameter (D) of the screw can be calculated from the pitch (P) by the formula

D = 6P^6/5

So, for example, a #1 screw, with a pitch of 0.9 mm, would have a diameter of 6 × 0.9^6/5 = 6 × 0.9 to the 1.2 power = 6 × 0.881233526… = 5.287401156…, which, again, is rounded off, here to 5.29 using the rule that the second figure is increased by 1 when the third figure is 5 or more.

Thread form

Two different thread forms were defined. The first was used for the screws 6 mm in diameter and smaller. The depth of the thread was 3/5 the pitch. Crests were rounded with a radius equal to 1/6 of the pitch. Roots were rounded with a radius equal to 1/5 of the pitch. Given these requirements, the thread angle will be about 47.5°. When these small screws are threaded in a screw-plate, the circular arcs are compressed into parabolic curves, a desireable profile.

The second thread form was for the larger screws, and intended to be cut on a lathe. The form is an isoceles triangle whose base and height are equal to the pitch. The thread depth is ¾ of the pitch; roots and crests are rounded with a radius of 0.1011 times the pitch. As a result, the thread angle is 53° 8′. Thury credits “M. Steinlen of Mulhouse” for this thread form.

Relief threads

In repairing watches and clocks one sometimes encounters tapped holes that have become enlarged. In this situation a special class of screws with “relief threads” may be used. Such a screw has a diameter half-way between the diameter of the standard screw whose pitch it shares, and the diameter of the next larger standard screw.

Marc Thury.
Systèmatique des vis horologères.
Geneva, 1878.