Oct. 1926 SLEPIAN: T E M P E R A T U R E OF A CONTACT 933

Letting к be the heat conductivity of the material and Ф the temperature a t any point, the heat flowing into the shell from the inner surface will be per sec ,

/ ξ Γ \ — к Χ 2 π r 2 ^ - ^ σ J calories/sec. (6)

The heat flowing out of the shell from the outer surface will be

/ ОТ \ -κ2ςγ(γ + ΰγσ( — \ (7)

In the steady state, (5) = (7) — (6), hence

/ ò T \ / òT \ к2жг2[ - r — ) -к2т (r + dr)2l - γ — I

V òr / r = r \ ò r / r + d r

a2

= 0.375 E2 — — d r

Hence, dividing by d r and passing to limit,

- 2жк ò 7 ò Ф \ E2 a2

( r 2 " ò 7 / = 2 7 r X 0 - 0 5 9

(8)

(9) òr \ òr / ρ fl

Integrating with the boundary condition Ф = 0 and

ÒT òr = 0 when r = ρ ξ ,

Letting r = α,

Ф =

Ф =

Е2

33f5 к ρ r 2

E 2

33.5 к ρ

(10)

(11)

RELATIVITY IN OBLIQUE COORDINATES

During the past three years Professor Vladimir Karapetoff has given talks on "Straight-Line Rela­tivity in Oblique Coordinates" before several Institute Sections, as well as a t some conventions of other socie­ties, and has demonstrated his "blue and red" mechani­cal model of Einstein's fundamental relations. Insti­tute members and readers of the JOURNAL will be inter­ested to know that an article by Professor Karapetoff, containing a detailed elementary theory of restricted relativity in his oblique coordinates and a description of the model, has appeared in the August issue of the Journal of the Optical Society of America. Professor F . K. Richtmyer, Cornell University, Ithaca, N . Y., is the feusiness Manager of the Journal; the price of single issues, as long as they last, is 60 cents.

ELECTRICITY TO KEEP TRAINS SAFE

Making 7770 miles of railway in the United States safe against train collisions is no trivial task The accomplishment, as announced by the Interstate Commerce Commission July 28, marks the progress of the first quarter century of automatic train control in this country. This announcement registers the fact that after many years of heartbreaking experiment with all sorts of strange devices for stopping trains from running into danger, electricity has proved the only agency whereby this can do it. Hence the Com­mission has now given approval for train control schemes protecting 7770 track miles. How fast the Commission may order the rest of the country's mileage under automatic train control remains to be seen.

Most of the automatic control and stop devices in service consist of a magnet, about rail high, beside the track at the point where it enters each signal block. Suspended from each locomotive is another type of magnet. When they pass, a flash of electric current opens a relay which actuates an air mechanism in the engineer's cab so as to set the brakes at once and bring the train to a stop.

I t is provided tha t the engineer can forestall this brake setting by touching a button or small lever as his engine passes over each of the track magnets. He must, therefore, be alert a t all times or his train will be taken out of his hands and brought to a standstill whether or not there is immediate danger ahead. This is electricity's guarantee tha t train operation in the future will be safer.

In 1914 the first permanent installation of a device to stop trains automatically was made on the Chicago & Eastern Illinois which runs south out of Chicago. Since then a vast amount of study and test has produced four or five general types which are now in use. Some exercise only intermittent control over trains operating only at given points. Others are continuous. Some merely apply brakes once, so as to bring a train to a stop with what is known as a "service" or ordinary application of air. Others begin by slowing down a train a t one point, setting the brakes up tighter if the train passes another point and finally clamping down the shoes for an "emergency" stop.

Nearly all of them operate in connection with the block signal system. Since electric block signals, after long years of use, have proved that they fail only once in 40 million operations, the attached train control device is not going to suffer much instability by reason of signal system failure. But none of the devices that have been approved are considered beyond the possi­bility of improvement. Thus the 7770 miles of track and the 3700 engines equipped with the new appliances are considered a vast experimental laboratory to pre­vent many wrecks and save many lives while loading up to a closer approach to perfection in automatic train control.