In case you’ve been wondering what the largest number you can represent with three digits, the answer was provided ninety years ago this month, in the April 1926 issue of Science and Invention magazine.  That number is:

According to the magazine, this is equal to a is a 369,693,100 digit number, the first digit of which is 4, the last of which is 9.  In other words, rounded, it is 4 x 10^369,693,099.

According to the magazine, the number was calculated by one M. Laisant of the Ecole Polytechnique in Paris.  However, it’s unlikely that M. Laisant wrote down the answer, since, it would take 28 years to write down the number, as depicted by the presumably hypothetical gentleman shown in the illustration.  If written with the digits spaced a sixth of an inch apart, the number would stretch about 919 miles.  (The 919 mile figure is given by the magazine, although it seems to me that the answer ought to be 972 miles, since 387,420,489/6/12/5280 = 972.)

It should be noted that the order of operations makes a huge difference in the outcome.  To put it another way, the associate property of addition or multiplication does not apply to exponents.

(9^9)^9 is a very modest 78 digit number, 1.9662705 x 10^77, since it is merely 387,420,489 multiplied by itself nine times.  9^(9^9), on the other hand, is 9 multiplied by itself 387,420,489 times, which results in 4 x 10^369,693,099.

We can do a quick plausibility check of the magazine’s answer by noting that 9^(9^9) < 10^(10^10),  Ten to the tenth power is one followed by ten zeroes, 10,000,000,000.  Ten to the power of 10,000,000,000 is one followed by 10,000,000,000 zeroes, a ten billion and one digit number.  The answer given by the magazine, a mere 369,693,100 digit number, is indeed smaller.  The quick jump from 369 million to 10 billion digits isn’t surprising when you consider the following:

1^1^1 = 1

2^2^2 = 16

3^3^3 =  7,625,597,484,987

Unfortunately, Google calculator fails us, since it reports merely that the answer is “infinity.”  But on the other hand, that’s probably close enough.  Since there are only about 10^80 atoms in the observable universe, a number much larger than that probably has little practical use.

The M. Laisant identified in the article is apparently Charles-Ange Laisant, who wrote more about the problem in Thresholds of Science: Mathematics, published in 1914.

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Sixty years ago this month, the March 1956 issue of Radio-Electronics published the plans for this solar powered radio, probably the first instance of a project using a photovoltaic cell for power.

The actual radio receiver was a simple crystal set, using a germanium diode, with a single CK-721 transistor serving as the audio amplifier.  The basic circuit was about the same as the Boys’ Life CONELRAD receiver shown here previously, which appeared the same year.

The power came from a type B-15 self-generating selenium photocell, manufactured by International Rectifier. The cell didn’t put out the required 1.5 volts, so it was necessary to cut it into four pieces with a hacksaw, and then wire the resulting four smaller cells in series.

For times when the sun wasn’t shining, the plans also called for a mercury cell, which could be switched in in place of the solar cell.

A much smaller version of the selenium solar cell can be seen in this Popular Mechanics advertisement for $1.

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Images from another winter storm. NOAA photo.

Seventy-five years ago today, March 25-26, 1941, central and northern Maine were hit with a severe storm that did considerable damage to telephone and telegraph lines. Strong winds and heavy wet snow took down many lines, and most of the northern part of the state was cut off from any wire communications.

The telegraph companies contacted W1BAV who established communications with Presque Isle and relayed instructions to the service men there. By night, lines were reestablished to many parts of the state.

Between 7:30 and 9:30 PM on the night of the 26th, hams had most of the state hooked up and standing by. By 9:30, the telegraph companies had established enough service so that they were able to advise the hams that they could stand down.

These details were recounted by Maine Section Communication Manager H.W. Castner, W1IIE, in the July 1941 issue of QST.

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Fifty years ago, the February-March 1966 issue of Radio TV Experimenter magazine published a review of the Eico 753. This was a bare-bones SSB and CW (with AM tossed in as an  afterthought) transceiver for 80, 40, and 20 meters. I happen to own one of these monsters, and it’s actually a nice radio for what it is. I’ve worked DX with it, and I even took it with me on a mini-DXpedition to YV-land. I worked a few stateside stations from there, and even worked Europe on 40 phone.

The review was generally favorable, concluding that “so far, the EICO 753 stacks up as the best ham transceiver buy for 1966.

The radio is affectionately known as the “Seven Drifty Three” for its propensity to drift. The review covers this point:

After a 15 minute warmup the EICO 753’s stability was well within the specified 400 cycles–in fact, we were able to work relatively long contacts with but one or two tuning corrections (done with the receiver offset). We must allow for the other ham’s station having some drift.

In 1966, the radio sold in kit form for $179.95, $299.95 wired. Unless you had a power supply, you would need that as well. The AC supply with speaker sold for $79.95 in kit form, $109.95 wired. Mobile power supplies were available for the same price.

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Ninety years ago, this date’s issue of Radio Digest, February 20, 1926, featured this picture of eighteen year old Fay Wray, who is probably best remembered for her role in the 1933 film King Kong.

Her fame on the cover of this magazine was a result of her being named one of the thriteen WAMPAS Baby Stars for 1926, in a program broadcast by KNX in Los Angeles.  The honor was conferred by the Western Association of Motion Picture Advertisers, which each year honored thirteen young actresses believed to be on the threshold of stardom. Other familiar names in the class of 1926 included Mary Astor and Joan Crawford.

Canadian-born Wray resided in Hollywood, and had appeared in a number of minor roles. After the recognition brought about by the WAMPAS award, she was contracted by Paramount, where she made more than a dozen movies. Her most famous role in King Kong was for RKO.

She died in New York in 2004 at the age of 96. Two days later, the lights of the Empire State Building were extinguished for fifteen minutes in her memory.

There was a time when Americans dressed up for coffee and donuts. The ad here appeared in Life magazine 75 years ago today, February 17, 1941.

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The February 1936 issue of Popular Science shows the plans for this simple portable receiver. “By careful planning and the use of midget parts and space-saving metal tubes, a complete three-tube circut, loudspeaker and all, has been crammed into an ordinary cigar box.” Despite the small size, it could “be built by anyone who boasts a jack knife, a pair of pliers, a screw driver, a soldering iron, and a small drill.”

The circuit consisted of a 6K7 serving as RF amplifier and detector, with a 6C5 serving as audio amplifier to drive a three-inch speaker. A second 6C5 was used as rectifier. A “curtain burner” cord was used to reduce the line voltage to 18 volts in order to light the filaments of the three tubes wired in series.

In testing, the set gave good volume on more than a dozen stations, with a sixty-foot outside antenna.

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Many of the vintage receivers described here require plug-in coils, such as the ones shown in the image at the left. Back in the day, these were readily obtainable in common sizes. And as the February 1941 issue of Popular Mechanics pointed out, “considerable effort can be saved by purchasing ready-wound coils.” However, he magazine also admonished that “the beginner should take the time to wind the coils for at least the first set he builds so that he will understand exactly how they are made,” as the young gentlemen shown at the top of the page are doing.

Today, since pre-manufactured coils are unobtainium, the builder of one of these sets has little choice but to make the coils at home. But as the experimenter 75 years ago learned, the process of making coils is quite simple. This article serves as a good guide for the modern recreator to make the coils. But there is still a slight problem, since the article simply advises purchasing “forms usually made of Bakelite or similar material.” And those coil forms are also unobtanium today.

Fortunately, modern materials come to the rescue, since it’s easy to recreate the forms themselves using readily available PVC tubing, along with the base of a defunct tube. Complete instructions can be found on AA8V’s page.

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Shown here is the radio station at Kern County High School, Bakersfield, California, as depicted in the February, 1916, issue of Popular Mechanics.  The accompanying article notes that the school has a course in wireless telegraphy, with a course in wireless telephony being added.

According to the 1916 call book, the station was licensed as 6GZ, under the control of one A.J. Ludden.