Like most of the questions I pose, there are many almost right answers to this question. The first right answer is that one is a slimy creature without a backbone, while the other is like a snail without a shell, but that would delving a little to deeply in Sir Isaacs personal life, matters better left for a court appointed special prosecutor. Another right answer is about 14.6, for those of you who remember your conversion factors between English and metric units. (HUH?) The real right answer is that they are not really comparable, since one is a unit of mass, while the other is a unit of force. Have I finally gone off the deep end, you ask. Believe it or not, there really is a unit of mass called a slug. One slug is the amount of mass that is accelerated at 1 foot per second per second by a force of 1 pound.
So what's the point of this article? I would like to acquaint you, gentle reader, with the wild and crazy world of units, or what we use to measure the physical world around us. There are three basic fundamental units that we are all familiar with, namely the units of mass, length, and time. Yet even these units have more to them than meets the untrained eye.
Let's start with the fundamental unit of length, which in the metric system is the meter. For the metric-phobic among you, a meter is about 10% longer than a yard. (1 meter = 39.370079 inches = 1.0936133 yards) The meter came about by an international agreement back on June 22, 1799, when the worlds leading scientists got together in Paris to make some sense out the crazy mess left us by the English. After lots of measurements, the meter was defined to be one 10 millionth of the distance from the north pole to the equator. A slightly easier way to remember this is that a kilometer (one thousand meters) is one ten-thousandth of this distance, thus the distance from the north pole to the equator is ten thousand kilometers. As a quick aside, knowing this fact can help you estimate large distances with very good accuracy in many cases. How, well if 10K kilometers is one quarter the distance around the Earth, then 40K kilometers must be the (approximate) circumference of the Earth. Now we know that there are 24 hours in a day, and thus 24 times zones as we travel around the Earth. So how far is it from San Francisco to New York? Well, San Francisco is in Pacific Time, and New York is in Eastern Time, so they are 3 hours apart. Thus they are 3/24 = 1/8 of the world apart, or 40K/8 = 5000 kilometers. Not too bad for a crude estimate. Of course this kind of estimating does not work around the poles (north and south, not neighbors of Russia), but fortunately not too many people live there. For a while the meter was defined to be the length of a bar of platinum-iridium alloy in the Archives de la Republique in Paris. This was great for the guys in Paris, who could run over to where the bar was kept whenever they wanted to know exactly how long a meter was, but it didn't work out so great for the physicists in Chicago, or anywhere else in the world for that matter. Also, pretty soon measurements became so precise that defining a meter as a hunk of metal just wasn't accurate enough. After all, the length of the metal depended on the temperature, the humidity, and whether or not the guy touching it was wearing gloves or not. Also it was very difficult to reproduce this hunk of metal with sufficient accuracy that the measurements of the day were requiring. The meter has been redefined several times since then, the most recent being in 1983 when it was defined as the length of the path traveled by light in a vacuum during a time interval of 1/299 792 458 of a second. Pretty wild, eh, but at least any physicist anywhere in the world could now calibrate her equipment great accuracy.
Okay, now that we have length (or should I say width) under our belt, let's take a moment to look at the second. This same body of super scientists decreed that the second would be 1/86 400 of the mean solar day. A problem astronomers discovered is that the mean solar day isn't really all that constant. Oops. Next they changed the definition to be 1/86 400 of the mean solar day on Jan 1, 1900. One problem with this definition is that 1900 comes around once in a lifetime, for those who were alive then, and basically never for the rest of us. Thus it's pretty hard for us to go back and make sure that this second was defined correctly. Also, it didn't take long for time measurements to require much more accuracy than such a definition would allow. It was discovered that certain atoms vibrate with an incredibly regular frequency. Cesium is one such atom, whose internal vibrations vary less than 2 or 3 parts in 10^14, that a 1 with 14 zeros behind it, or about 1 second in 1,400,000 years. Thus in 1967 it was decided to redefine the second to be the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom, and the era of atomic clocks was born. This clock is so fantastically accurate, that it can detect the difference in time that a traveler would experience between flying around the world in a jet and staying home. Yes, the guy in the air actually ages less (his time flows more slowly,) than the guy who stays home, but that is a whole other story.
Finally, let's consider the unit of mass, the gram, which is about what a one-fifth of a teaspoon of water weighs. Now here we have to get careful, because units of weight are often confused with units of mass. A gram is a unit of mass. The problem is that bathroom scales do not measure mass, but they measure weight, which depends on the Earth's gravity. If you weigh 100 kilograms on your bathroom scale, and you go to the moon, you'll discover that all of a sudden the scales says you weigh 20 kilograms. You may have lost some weight on your trip, but I'll bet you still can't squeeze into those bell-bottomed jeans you wore during high school graduation, because you didn't really lose any mass. The mass of an object depends on how much resistance it provides to being accelerated. If you were on the space shuttle, everything would weigh 0, after all that is what weight-less means. Yet it would be much more difficult to move heavy objects, like an astronaut, compared to light objects like a quarter. This intrinsic resistance to changes in motion is the real measure of mass. Not as simple as you thought, right? Originally the kilogram was defined to be the mass of a cubic decimeter (one liter) of water at 4 degrees Centigrade. That is still pretty close to what it is now, though it turned out to be pretty difficult to get exactly one cubic decimeter of anything exact all the time. Now for the shocker, the fundamental unit of mass is a chunk of metal stored in a vault in Sevres, France.
So, let's finally answer the question posed in the title of this piece. What's the difference between a slug and a newton. A slug is a unit of mass. A slug is about 32 pounds or 14.6 kilograms. It is a measure of how difficult it is to accelerate an object. A newton, on the other hand, is a unit of force. At the Earth's surface, gravity exerts a force of 9.8 newtons on a kilogram of mass. Another way of looking at it is if you exert a force of 1 newton on 1 kilogram of mass, it will accelerate at a rate of 1 meter per second per second. Thus if you weigh 100 kilograms, and you jump from a window 5 meters high, the Earth will exert a force of 980 (almost 1000) newtons on your body. Since you weigh 100 kilograms, this will cause you to accelerate at a rate of 9.8 (almost 10) meters per second per second. You will fall for approximately 1 second, and you will be traveling about 10 meters per second (about 22 MPH) when you go splat on the ground.
So there you have it gentle reader. A slug is a slug, and a newton is newton, and never the twain shall meet, unless you're confused, of course. Next time we'll take another look at these units and how they fit into our everyday lives, and perhaps expand our knowledge of measuring the world around us by tackling some units that I'm sure you've heard of, but probably know really know what they are, like the watt, calorie, and kilowatt-hour. May the force of gravity not be with you. Adios.