The Foundation

That's what physics is...the foundation of science. It's at the bottom of every material and energetic process in the universe from the exotic heart of a supermassive black hole, to your car's engine, to your own metabolism. So, physics is important.

I still plan to shift my focus to chemistry and geology next year. I'm really looking forward to exploring the spectacular geology in my area. But I don't want to drop physics and astronomy, so I will continue working on the physics and astronomy LabBooks.

It will be awhile before I've finished the introductory section of the Astronomy LabBook but I've completed the first two brief, introductory sheets of the Physics LabBook and an indepth exploration of measurement, precision, points, graphing, and geometry with lots of hands on excursions. You can find it here:

Physics LabBook

The first few sheets will be concerned with the fundamental measurements and methods that physicists use to explore the world. I make sure to bring it home to do it yourself projects and survival techniques.

Like the other LabBooks, this one is a LibreOffice spreadsheet, so download and install the free LibreOffice suite before trying to view it.

Physics: The Fundamental Science

I'm not a physicist, but I will be impersonating one on this blog for the next year or two  Actually, I love science demonstrations and have since I was a kid with my science kits.

Why is physics fundamental and in what way?

Well let's think about the prairie dogs out in the Bear Creek Greenway. They would be (and are currently) of interest to biologists. But, being animals, they have to eat to survive and they get most of their energy from carbohydrates, much like humans. The processes they use to extract that energy has to do with the interactions between molecules and atoms. Now, we're in the realm of chemistry, but the interactions between chemical substances care governed by charges, so, now we're solidly in the realm of physics.

The furry little things move around (a lot!) and their bones and muscles work by the same principles as any other machines - again, physics.

The Table Mountains in Golden are geologically interesting remnants of ancient volcanoes. They have deposits of basalt to prove it. Basalt is like granite but hardened so quickly that  large crystals could not form. The way substances change phase are physical phenomenon, and the processes that uncovered those ancient volcanoes are also physical forces.

The point is that all the sciences, at some level become the purview of physics. The ways we measure things are governed by physical processes. If you pour a liquid into a graduated cylinder, you will see that the surface is curved and accurate measurement requires that you take that curvature into consideration. The forces that curve the surface of the liquid are physical. The smartphone I use to measure things on the trail and make photographs relies on electronics to function.

Physics is at the bottom of all the sciences.

There are several "flavors" of physics that have developed over the years. The more intuitive, everyday version is Newtonian mechanics. Most folks have a pretty good grasp of the regular push and pull of things although some of the details may be surprising, but Newton died with a serious question on his mind. He knew how gravity worked, but he didn't know what it was, and his idea that light was particles was not completely right. By the time James Clerk Maxwell came along, it was well established that light had a wave nature and he gathered all the parts of electromagnetic theory together. 

A lot of people think that Einstein's theories of relativity replaced classical physics, the combined physics of Newton and Maxwell, but again, that's not quite true, in fact, Einstein started with the proposition that classical physics had to be true for every observer in every (inertial) frame of reference. From this seemingly innocent proposition, things began to get weird. As an object gets faster, both its size and time contracts (time runs differently for objects moving at different speeds), and the speed of light in a vacuum is the upper limit of speed in our Universe. But the theories of relativity have been soundly verified.

During Einstein's life, physicists came to the surprising conclusion that in the subatomic world, things did not move smoothly but in discrete steps, things could jump from one place to another without existing anywhere between, and we could not simultaneously know the position and velocity of an electron. Some things are, in fact, indeterminate.  The atomic world was weirder than we had ever imagined. Quantum physics shocked everyone, including Einstein.

So what does the future hold? It seems to be deeper down the rabbit hole. The future of physics is sure to be an adventure.

But, for awhile, let's go back to the comfortable world of Newton and explore how our everyday physics works and, yes, it still works.

Classical physics starts with observation and that means measurements. If you've been following my blog, you've seen me measure trail distances and altitude, barometric pressure, weight vs. mass, and temperature vs. heat. The thing is... there's only three fundamental measurements…..three things you can measure directly. For instance, you measure temperature either by measuring the change in length of a substance that changes size when they heat up or cool down, or you can measure voltage differences across a material which changes its resistance in relation to its temperature. Temperature is the average internal energy in a mass and you would have to measure the energy of all the particles in the mass to measure the temperature and, even if you could go that route, the unit of energy is a joule which is the force of one newton acting through a distance of one meter. A newton is the force of one gram accelerated at one meter per second, per second. In other words, temperature and energy are composite measurements, measurements made up of other measurements.

The three fundamental measurements that make up all the others are position, time, and amount (count). That's all. Distance is the difference between two positions and time duration is the difference between two times. I'll be talking about mass later. It's actually an amount, but all three of the fundamental measurements are weirder than you might think.

In the meantime, check out my creations.

I use constructions from construction kits as structures for demonstrations and experiments. I have an Erector set and a Lego set and I order separate parts as I need them. Here are two contraptions I built. 

[Escapement mechanism]

[Gear train]

Every.mechanical clock has one. Clocks are driven by motors, mechanical or electric, which are usually continuous. The old grandfather clock had a weight that slowly unwound a chain on a spool. Later clocks and watches used a wound spring. The problem with both was that they moved smoothly. Clocks have to tock, chopping time up into seconds, minutes, and hours. That is the job of the escapement mechanism. In old clocks, that was usually driven by a pendulum, which can be a very precise time keeper (I'll be looking at pendulums later). Later, escapements used a rebound effect to keep going.

This one uses a swinging weight that slaps a post to interrupt the motion...not very useful for clocks but very visual. The gear train shown above scales down the speed of the unwinding rubber band and transfers the motion to the swinging weight. Watch it go!

[Escapement video]

A company called "Klutz" publishes book-based action kits (project books with kit parts) including Lego compatible construction kits. The escapement mechanism parts and plans were in their Crazy Action Contraptions kit.

I also built a cart out of my Erector set. I'll be using it later when I explore motion in the playground. It has a phone clamp that lets me send my smartphone along for a ride and the Science Journal app can record the trip.

[Phone cart]

The thing about construction kits is that their parts are standardized. All the holes and interlocking dots are the same distance apart. All the parts fit all the other parts. In fact, Lego makes their specifications available to other companies, like Klutz, so there is a wealth of parts out there to do just about whatever you want.

By the way, keep workshop pegboards and circuit plugboards in mind, too. They usually fit into this standardization philosophy. If one system doesn't fit another, a little finagling will usually do the trick. A few holes drilled in some Lego bricks will nicely connect Erector to Lego. (Hint: use washers when using screws in soft plastic parts.) Back a circuit plugboard with Lego bricks using double sided tape and your electronic project integrates into your Lego set.

Check out some construction kits. In addition to science adventures, they make great, creative hobbies. Many regions even have clubs for construction enthusiasts, especially Legos.

I once worked on a pipeline barge as a welder helper. I was in pretty good shape and I stayed that way by exercising regularly. I would do push-ups - standard and inverted (with my feet up on the wall). On land, push-ups are one thing - on the Gulf of Mexico, they're something else. Pushing up as the barge rode down the slope of a wave, I would almost lift off the floor, but if I wasn't ready when the barge was lifted by the next wave, I could find my face in a collision with the floor.

Something was changing as the barge bobbed around in the water. Was it my weight? Was it my mass? Does it make a difference?

I have an assortment of tools for measuring weight and mass. Here's a picture of some of it.

[Tools]

There are some weight (or mass) sets in the center. (I apologize but the vocabulary of weight and mass is incurably tangled.) To the left are some tools to measure weight - I'll call those "scales", although the word is also used for things that measure mass. To the right are tools to measure mass - I'll call those "balances" although that word is also used to refer to weight measuring devices.

You might say I have a problem, here. Let's look at the three groups separately.

[Weights]

There are standards of both weight and mass and I have lots of little pieces of metal and other materials that have been created to conform to those standards. For instance, the open black box in the center contains very precise (I had to buy it for lab work when I was in pharmacy school) pieces of metal with gram masses and ounce weights.

The cubes below it are called "density samples" because, despite the fact that they're the same size, they have very different masses. Density is defined as mass per unit volume.

There's also a stack of brass masses on a hook that are just right for hanging.

[Scales]

You've likely seen many scales. The things you use to measure the weight of produce at a grocery store are scales. You also weigh yourself on scales - bathroom scales.

Usually, a scale measures how hard an object pulls on a spring (like the set of spring scales on the lower right, or the Jolly Balance (which is actually a scale), the yellow plastic thing in the upper right corner - it also measures density. Alternately, a scale might measure how hard an object pushes down on an electronic component, like the digital bathroom scales in the picture.

[Balances]

On the other hand, a balance literally balances two objects. If they balance evenly, they are pulling down with equal force. Many science kits include inexpensive balances.

The blue velvet lined box in the picture contains a brass assayer's balance like the ones used long ago to "weigh" gold nuggets. There is also a pocket postal scale (which is actually a balance) and a tiny, three beam balance. It works like the "scales" your doctor uses to weigh you. In that case, the doctor balances you against the slider weights on the bars that are about eye height in front of you. A system of levers magnify the weights of the sliders and the machine calculates your weight when you're balanced. 

Scales measure weight and balances measure mass.

I carried some equipment to the Ross-University Hills branch of the Denver Public Library and rode their elevator to see what would happen when I measured the weight and mass of objects.

[Riding an elevator with a scale]

First, I used a portable electronic scale to weigh a mass. Yeah, I know it's a 20 gram mass that the scale says is 30 grams - I didn't zero the scale, but you can tell that the indicated weight (actually weight translated into grams - more about that below) changes as the elevator goes up and then returns to the first floor.

[Riding an elevator with a balance]

On the other hand, the balance stays balanced. You can tell because the vertical point stays vertical. Why did the weight change but the mass did not?

Mass is simply the amount of matter in an object and that doesn't change as long as the object is intact. The mass of an object is measured by comparing it to another object of known mass.

Weight is actually the force that an object directs straight down vertically. Newton's second law of mechanics, and the one most central to everything, defined force as mass times acceleration, so I need to go over a few technicalities.

When a thing changes position, it moves at a particular speed. In a car, speed is usually measured by a speedometer in miles per hour (at least in America. Everywhere else, it's kilometers per hour.) Speed is measured in distance per time, or distance divided by time.

Physicist do not usually work with speed. They prefer to work with velocity. Velocity is speed in a specified direction. It's called a vector quantity because you have to give more than one measure to fully specify it.

When you're driving a car, you don't maintain a constant speed. Acceleration is how fast you're speeding up or slowing down. Acceleration is measured as speed per time. That means it is measured as the distance traveled per unit time per unit time, or distance per unit time squared. In physics, the most common measure is meters per second squared.

Now we come to force. When I say that force is mass times acceleration, think in terms of pushing an object so that it speeds up faster and faster at a constant rate. Force makes things go faster or slows them down. A common measure of force is the newton which is the amount of push required to accelerate a one kilogram object one meter per second squared.

And weight, being a force, is often measured in newtons (notice that, when "Newton" is a name, it's capitalized, but when it's a unit of force, it's written in lower case.). Weight is mass times acceleration. What acceleration? The acceleration of gravity. That's why the weight of a body can change. The acceleration that gravity imposed on a body in freefall is 9.764 meters per seconds squared...at sea level on the Earth and, although it is different at different places on the Earth's surface, the variance is usually too small to worry about. (Geologists actually do worry about it because large deposits of metal ore will present a slightly different gravitational pull than other rocks and they use of a very sensitive instrument called. "gravitometer" to measure the pull.) As you move out away from the Earth, though, it's pull becomes weaker and your weight also decreases.

The moon is smaller than the Earth and, therefore, has less gravitational pull. Acceleration due to it's gravity is only 1.625 meters per second squared on the moon. I weigh 185 pounds on Earth. On the moon, I would only weigh 185 times 1.625/9.774, or 30.8 pounds.

I recorded my phone's accelerometer on the elevator using Google's Science Journal. It looked like this.

[Elevator ride]

Another digression...it can be confusing which direction is which on a phone. Just remember the graphs you drew in algebra. The x axis went left to right, the y axis went up and down and if you were working with three dimensions, the z axis was into and out of the page. It's the same for the phone. Holding the phone flat in front of me, the direction of the elevator's motion was along the z axis. All of the accelerometers produced jagged lines, but look at the scales. The x and y accelerometers showed accelerations around zero and one m/s2. The z accelerometer measured around 9.5 m/s2. That should look familiar - it's the acceleration due to gravity.

When the elevator starts up, weights in the elevator opposes it's motion with an equal but opposite force, (that's Newton's third law). So, add the elevator's acceleration to that due to gravity. Since the accelerometer measures up to twelve m/s2, the elevator must be accelerating at about two and a half meters per second squared until it reached a constant speed, and the tracing smoothed out. At the top, the elevator slows down at about 1.5 meters per second squared and objects lighten up. As the elevator starts back down, objects in it lose weight again, to regain it at the bottom.

That's actually how the phone's accelerometers work. They are tiny (You might have heard of nanotechnology. Cell phone accelerometers are nanotech.) combs that have tiny weights at the end of their times. As the weights accelerate, they move with the acceleration and sensors pick up the motion.

It's not entirely bogus that my electronic scales claim to measure grams (mass). It actually measures weight but, on Earth, weight is mass times a constant 9.764 acceleration due to gravity so the electronics just have to divide the weight by 9.774 to get the mass….but not on the moon.

Riding in a car, notice how you lean as it slows down, speeds up, or turns a corner. That's forces at work. If you have an elevator handy, you might try riding it with a bathroom scales and see how your weight changes and remember...your mass stays the same.

--- Trail temperature vs. air temperature ---

Heat and temperature provide somewhat of a mental challenge to many people. They are different things and it's sorta difficult to wrap one's brain around what they actually are. In addition, they can refer to physically precise qualities, or to sensory experiences. If you say, "Wow! I'm hot!", it means that you feel hot - the opposite of cold. (But don't say, "Ich bin heiss!" in German unless you really mean it - that's something very different.) When a physicist says that something is hot, they have a very precise thing in mind.

Heat is the flow of energy from one place to another. If energy isn't moving, there is no heat. Temperature, on the other hand, is the amount of energy inside an object - it's the total amount of molecular motion in an object.

Heat is measured in units like BTU, calories, joules, or newtons. These are units of work. Work is the amount of energy expended when you move something from point A to point B. Well, everything is moving down to a point that there is no molecular motion at all and, on earth, it is very rare for there to be no motion.

Which brings me to temperature. Temperature is measured in degrees and measuring temperature is a bit more complicated than measuring length. To measure length, you just set a ruler along side the length your measuring and compare the lengths. You can't measure temperature directly. You have to measure the effects it has on things. The classical measurement is the mercury (or, since the demise of mercury thermometers, since mercury has been found to be poisonous, the alcohol) thermometer. Things usually expand when they get hotter (water is weird like that - it expands when it freezes) and you can measure temperature by the amount of expansion. Mercury and alcohol expand predictably when they warm up. Today, we have electronic thermometers that measure temperature by the effect it has on electronic components.

There are three common scales for measuring temperature. In the United States, people are very used to the very weird Fahrenheit scale. Mr. Fahrenheit was interested in things like weather and body temperature, so his scale located things like common air temperatures and normal body temperature on an expanding column of mercury in a glass column. Subsequent researchers modified the scale until normal body temperature today is 98.2 degrees Fahrenheit. Go figure.

The rest of the world? Well, I have friends in Canada and I once was exclaiming about the brutal 25 degree temperatures at a camp out in northern Alabama. He wasn't impressed and I was confused until I realized that Canada, like most of the world, uses the Celsius (or centigrade) scale. You see, on the Fahrenheit scale, water freezes at 32 degrees. On the Celsius scale, it freezes at 0 degrees. That's the nice thing about the Celsius scale - water freezes at 0 degrees and it boils at 100 degrees (at sea level atmospheric pressure). Between and beyond, the scale is broken up into intervals of 10, 100, etc.

To convert from Fahrenheit to Celsius, you subtract 32 degrees and multiply by 5/9. To convert from Celsius to Fahrenheit, you multiply by 9/5 and add 32 degrees. Celsius is the metric version of Fahrenheit.

There is another important temperature scale and it's the one used by scientists because it has an absolute bottom. On the Kelvin (or absolute) temperature scale, 0 degrees is where all molecular motion stops. You can't go below zero on this scale (that isn't exactly true because there's still some atomic motion at 0 K, but for our use, let's say 0 K is the absolute bottom.) On the Kelvin scale, water freezes at 273.15 degrees Kelvin. To convert from Kelvin to Celsius, you just add 273.15 degrees.

A good way to grasp the difference between temperature and heat is to see them in action. Sometimes, when your camping out, take a paper cup (not a foam cup!), fill it with water, and set it in the fire. Don't worry, your fire will be safe. The cup will sit there with the water happily boiling away and the only part of the cup that will burn will be the part above the water. Once the water starts boiling, you will still be pumping heat into it (the heat will be increasing in the water) but it will not get any hotter (the temperature will not increase until the water has boiled away).

Actually, if you set a pot of ice on your stove and begin measuring it's temperature as you start heating it up, you will find that the temperature will increase until the ice starts to melt and them the temperature will stick at that point until all the ice is melted, then it will start to rise again until the water starts boiling. Then the temperature will stay around 100 degrees Celsius (or 212 degrees Fahrenheit) until all the water boils away. Then your pot will start getting hotter and you should probably take it off the heat.

Last year, while walking on the Highline Canal in the summer, I noticed that my feet were getting uncomfortably hot, so this year I wondered just how hot the pavement actually gets.

There are three types of material used on the trail - a black paving, a white paving, and crushed granite.

                  [Thermometers: left infrared thermometer, right Sensor portable weather station]

I use two types of thermometer on the trail. Glass thermometers break too easily so I avoid them. I have a weather instrument that I bought from the National Geographic products catalog which has served me well over the years. It's made and sold by the Dakota Watch Company and it's called the Sensor Technology Barometer Thermometer Hygrometer. It's a portable weather station and, as parts of it's duties, it will keep track of air temperatures. (and, yes, it's still available on line for around $40 from various vendors).

I also have an infrared thermometer that came in a child's science kit called ScienceWiz Heat and Temperature. This series of kits are designed by science popularizer Penny Norman Ph.D. and, although they are definitely for young children (the illustrations in the manuals are muy hokey) they are surprisingly deep and always have at least one really cool demonstration - in this case, an IR thermometer.

You see, if something is vibrating, it's giving off radiations. Molecular vibrations will give off radiation in the infrared and visual ranges of light. Small vibrations give off light in the infrared ranges and as a body gets hotter it glows red, then yellow, then blue or white. So you can measure the temperature of a substance by measuring the wavelength of the light it gives off. That's what an infrared thermometer does. It's very portable and easy to use (just one button).

So, when I started from home the air temperature was 74 degrees F. My comfort range is between 40 and 60 degrees so I expected it to become way too hot and I was not disappointed. When I got of the bus and onto the trail at 11:00, the air temperature had risen to 81.7 degrees and, according to the infrared thermometer, the trail was at 115.6 degrees. Surprisingly, the ground around the trail was hotter at 116.7 degrees. Here's a photograph of the pavement at this point and the ground around it.

                                               [Pavement and shoulder at the Iliff trailhead]

Dark substances absorb light and reradiate it as infrared heat. Light substances tend to reflect light.

To give you an idea of what was going on, keep in mind that heat always(!) flows from hotter to cooler regions (you might wonder about air conditioning and refrigeration - heat has to be actively pumped out of an area in those cases and it's not just simply flowing. It takes work!) Body temperature is 98.2 degrees so, as cooler temperatures rise from cooler temperatures toward normal body temperature, heat flows slower and slower out of the body. As it gets hotter than 98.2 (or whatever your body temperature is at the moment), it becomes harder and harder for your body to get rid of the excess heat. One way it does that is through the evaporation of sweat. As a fluid evaporates, it has to take in heat and sweat is in contact with the skin so it sucks heat out of your skin, cooling you off. That's why sweat is dangerous in cold temperatures. Or even in very hot climates like Arizona in the summer. Hypothermia (too much cold) is very dangerous in Arizona when sweat (or pool water) suddenly dries off peoples' skin and draws too much heat out of their bodies.

Outhouses and Porto Potties on the trail can be sweltering in the summer because they convert sunlight to heat and trap the heat. The restroom at the South Quebec Way trailhead was at 91.9 degrees. I didn't stay in there very long.

At 12:23 air temperature was at 98.1 degrees and the trail was at 142.2 degrees. My feet were feeling it.

Remember that shady bench from the last blog? Here it is again.

                                                                [Shady bench]

                                                              [Pavement at bench]

It was 1:05 and the air temperature was at 98.1 degrees. The trail temperature was only 79.3 degrees. Just outside the shade, the air temperature was 98.6 and the trail temperature was 116.7 degrees.

Colorado has dry air and humid, heavy air buffers changes - it resists changes because the air molecules are more closely packed and can't move as easily and they bump into the heavier water molecules. It can be felt!

In Alabama, water is being pumped into the near sea level atmosphere from the Gulf of Mexico and the air is usually much heavier (in terms of atmospheric pressure and water vapor content) than in Colorado. If you step out of the sun on a hot day into the shade, you will get a little relief because your body is no longer converting the direct sunlight into heat, but the air won't be any cooler and the pavement will take a long time to cool off. In Colorado, you get immediate and significant relief because the air can take more heat into itself and things cool off more quickly.

The conclusion to all this is that, from now on I plan to keep my summer hiking short, and, if possible, in the mountains where it's cooler.

Where you live, pay attention to how atmospheric conditions (especially humidity), color of pavement and clothes, air temperature, and how hot you feel relate. When you're swimming, how cold are you when you come out of the water?

--- The Arduino adventure ---

From now on, I'll be doing a lot more technical hikes. I've already done some - the early Bear Creek hikes, where I measured distances and recorded an altitude profile, the smile experiment when I counted how many people smiled back at me when I smiled at them and when I did not smile at them, and the Lookout Mountain hike recording of altitudes, temperatures, and barometric pressures. Beginning with this years explorations of mathematics, I'll be looking at the pure and applied sciences regularly, so I need to make sure that my tools are all in order.

On 1/19/19, I checked the Altitude app (created by Pygdroid and available as an Android app on the Google Play Store) I use to record altitudes and distances to see if I could use it and my camera at the same time. I just wandered around the house with my phone this time and it seemed to work fine but I'll try it later on a walk to the library.

I also checked my Arduino to make sure that it actually works the way I want. I've had it for a couple of years and have not powered it up. I did so today and was happy to see that it works.

I bought my Arduino 101 from SparkFun, a local business that supplies electronic parts, equipment, and kits to hobbyists at great prices. They also offered a plastic carrying case that seemed like a good idea for my adventures. It required a little modifying. The compartments are well divided and I wanted to be able to run wires between them, so I cut some notches into the dividers.

                                                                 [Arduino case]

Now, I can keep all my Arduino equipment in a case that I can keep in my backpack, or on me.

                                                                    [Arduino rig]

I also bought a plastic cover for the microcomputer. It fits nicely into a smart phone holder that will attach to a camera tripod. I will be making one more alteration of the Arduino case - a bolt in one compartment that I can screw the clip to. That should keep my equipment from moving around in the case while I'm hiking.

                                                               [Arduino and clip]

When I attached the microcomputer to a 9 volt battery, it lit up.

                                                            [Arduino powered up]

and when I opened up my Science Journal app and looked around for the Bluetooth, I found this screen...

                                                         [Arduino on Science Journal]

I am set.

It's sorta frustrating that it wouldn't do you much good for me to go into a lot of depth about using the Arduino 101 since, soon after I bought it, Intel, it's manufacturer, decided that they didn't want to be in the microprocessor business and the Arduino 101, which is set up from the get-go to work with Science Journal, is no longer available.

The good news is that, if you want to play around with a microcomputer on the trail, SparkFun has other Arduino (and other microcomputer) options with Bluetooth.

If you want to check out SparkFun (and I highly recommend them), here is the address of their website...

https://www.sparkfun.com

I then went about testing to make sure that my Arduino would accept external inputs. Here's a photo of my setup.

                                                        [Arduino with photocell]

There are two items on my plugboard. Right on the gutter in the middle is a photocell. Just to the right is a resistor. An electronics hobbyist would immediately recognize this as a voltage divider. Let me explain.

Electricity is very much like a fluid. If you have water running through a hose and you narrow the hose (say, by crimping it), two things happen. First, less water gets through. Second, the pressure at the end of the crimp away from the faucet has less pressure. In other words, pressure is dropped by the crimp.

For electricity, the pressure that drives the electricity is called voltage and it's provided by the source of electricity (battery, generator, etc.). The amount of electricity that flows through the wire over a period of time is called current. The resistor and photocell in this circuit are the crimps. They resist the flow of electricity.

In this circuit, both "crimps" in the line drop a certain amount of pressure. That pressure drop could be measured across either element with a voltmeter. If the two resistors (in a circuit, that's what a crimp is called) have the same value - resistance, the amount the flow of electricity is impeded - then the voltage drop would be the same across each. The voltage would be divided equally between the two. In this circuit, one of the resistors reacts to light. As more light hits the photocell, it resists the flow of electricity more and creates more of a voltage drop. The resulting shared voltage drop across the resistor, then, has to be less. That change can be measured by a voltmeter across either the photocell or the resistor. Here, you can see that I have three wires going to the circuit. The black and green wires run to the Arduino so that it acts as a voltmeter.

The red wire feeds electricity from the Arduino to the circuit through the photocell. The photocell and resistor are connected in series so that all the electricity must run through both to get out through the ground (the black wire). the green wire runs to the voltmeter input to the microprocessor (called an analog input - there are several). So, the Arduino is measuring the voltage drop across the resistor.

The Arduino broadcasts what it measures to my phone via Bluetooth and my Science Journal app records it for me. I waved my finger back and forth across the photocell and this is what Science Journal recorded.

                                                          [Science Journal screenshot]

When I placed my finger over the photocell, the voltage decreased and when light hit the photocell, the voltage increased. The values are "raw" because they show voltage level across the resistance (not in volts). The measurement are not in any standard units but, if I knew the relationship between the values and, say, lumens, I could calculate the actual amount of light, but that wasn't my intention.

So, now, I know that I can take the Arduino on the trail with me to measure things I can't measure otherwise with the internal sensors in my phone or another instrument like my weather meter.

Technical hikes involve measurement. There's a lot that you can do with some really inexpensive equipment and learning to use it is a lot of the fun.