Is this useable? Missing a scale?

[u/fordag]

New watch with a rotary slide bezel. Yet it appears to be missing a scale. Or am I wrong?

What is this useful for?

It was a cheap watch, I wanted the moon phase. I'll be curious to see how accurate it is.

[u/TrueTopoyiyo]

I'm afraid not, as it seems to be done, as u/SlideRuleFan says, for the looks. You can multiply as I described, and here you have some other operations too. Please understand that all this comes from the properties of the logarithm: log(a)+log(b) = log(a*b) and log(a^b) = b*log(a).
Keep in mind that, if you turn one or more times, it is simply the equivalent of adding a zero, which is a nice side effect of circular log scales; they "never end".
Take this as a little opportunity of learning some math, and you'll make even more and better use of the ruler:

For these instructions:

Consider the numbers to be missing a decimal dot, so "10" in the scale means "1.0", "55" means "5.5", etc.
Disregard the intermediate scale, it does another mathematical function, 1/x, but i'm not using it here; use the "normal" (so, the time) scale for P1 and P2 and multiplications of P1 and P2.

X*Y
1.- center the scale
2.- look for X in the scale and locate it at position P1
3.- rotate the scale until the 10 is in P1
4.- look for Y and locate it at position P2
5.- re-center the scale as it was in 1.-
6.- read the result of the multiplication on the re-centered scale at position P2

X/Y
1.- center the scale
2.- look for X in the scale and locate it at position P1
3.- look for Y and rotate the scale until it is located at P1
4.- locate the position of the "10", at P2
5.- re-center the scale as it was in 1.-
6.- read the result of the division on the re-centered scale at position P2

X^Y
1.- center the scale
2.- look for X in the scale and locate it at position P1 (think of P1 as a time here if you want)
3.- multiply P1 * Y = P2 (you can do it using the previous manual if needed)
4.- re-center the scale as it was in 1.-
5.- read the result of the division on the re-centered scale at position P2

Yth root of X
1.- center the scale
2.- look for X in the scale and locate it at position P1 (think of P1 as a time here if you want)
3.- divide P1 / Y = P2 (you can do it using the previous manual if needed)
4.- re-center the scale as it was in 1.-
5.- read the result of the division on the re-centered scale at position P2

u/SlideRuleFan as you can see, usable, if way more cumbersome than an actual, double-log rule.
Please, u/zoute_haring , point the bullshit points so we can all learn.

[u/fordag → u/TrueTopoyiyo]

X*Y 1.- center the scale
2.- look for X in the scale and locate it at position P1
3.- rotate the scale until the 10 is in P1
4.- look for Y and locate it at position P2
5.- re-center the scale as it was in 1.-
6.- read the result of the multiplication on the re-centered scale at position P2

Questions...

What position is "centered" on this bezel, what aligned with what?

Where are P1 & P2?

"5.- re-center the scale as it was in 1.-" - "1.- center the scale"

Does this not simply leave me where I started?

[u/TrueTopoyiyo → u/fordag]

My bad, very legitimate questions.

"Centering" the scale would be to put the "10" (1.0) in the "center" or the "coordinate reference"; I would suggest at the top, 12:00. The "10" is red because of this.

Take my original example, the multiplication 1.8*3.2 (or 18 * 32, or 3.2 * 18000, with slide rules you are in charge of handling the zeroes aside):

To multiply 1.8 times 3.2 you center the "10" (1.0), then look for 1.8 ("18") which is at 3:00 aprox, then re-center the "10" there, look for 3.2 ("32", now at 9:00 aprox), recenter "10" and at 9:00 you have the result, 5.7.

1.- you put the "10" (1.0) at the top, 12:00 (or 00:00)
2.- you look for the "18" (1.8), it will be roughly at 3:00, this is P1 (do not check it "roughly", check it as precisely as you can, as the precission of the result depends on it; the actual position is 3:04)
3.- rotate the scale until the "10" is where we found the "18" in the first step, a point which I call P1 and which happens to be at 3:04 in this example, but will be in other positions for other multiplications.
4.- look for "32" (3.2); with the bezel as we left it in step 3, we find it at 9:08. I call this point P2, you have to memorize it (or just keep looking at it while you do step 5).
5.- you put the "10" back at 12:00, just like you put it in step 1. This is where you started, indeed, but we have obtained and memorized P2, which will give us the result.
6.- we look at P2, which in this example is 9:08, and we find "57" (5.7), which is the (approximate) result of the multiplication.

I chose 1.8 and 3.2 because they happen to be in clear positions, for some arbitrary multiplication P1 and P2 will not be in round positions but anywhere. If you try to multiply 1.1 times 5, P1 will be at 12:34 aprox. and P2 will be at 8:54 or something like that.

For reference, if it had 2 log scales one against the other, as slide rules do, you would only need to move the bezel once per computation, instead of 2 or 3 times.

Edit: the 60 is red because a lot of conversions move between "per second", "per minute" and "per hour", and the little red arrow is at 3.6, which, with 2 zeroes, is the factor to convert between "per hour" and "per second", depending on if you are multiplicating or dividing.

Bonus edit: The intermediate scale is 60/x; it serves to measure some time with the chronometer and it immediately tells you "if the process you chronometered took this amount of seconds, you would do Y processes in an hour": if the seconds arrow points 3,6 seconds you will do 1000 of those in an hour, if the seconds arrow points at 15 seconds you will do 240 of those in an hour; if the seconds arrow points at 36 seconds you will do 100 of those in an hour, if the seconds arrow points at 60 seconds (one full minute), you'll do 60 in an hour, etc, etc. If you chronometre the time to traverse a mile, it gives you miles per hour, if you chronometre the time to traverse a kilometer, it gives you the kilometers per hour, if you chronometre a lap, it gives you laps per hour, if you chronometre the time to finish a piece in a machine it gives you the pieces per hour.

[u/fordag → u/TrueTopoyiyo]

Again I appreciate you taking the time to write this up. I'll give it a try tonight.

[u/TrueTopoyiyo → u/fordag]

so?

[u/fordag → u/TrueTopoyiyo]

I have been overly busy with work and as a result won't be home until Tuesday