Students of mathematics are familiar with the Jacobi matrix. This is usually dealt with in the second semester of the analysis lectures. The name Jacobi honors  Carl Gustav Jacob Jacobi, who did actually think about the Jacobi matrix. His brother, Moritz von Jacobi was perhaps a more practical man. We have Jacobi's law, which was discovered by Moritz and which is concerned with electricity. In 1838, Moritz von Jacobi motored 7 1/2 kilometers along the Neva river in St. Petersberg in a 28 foot electrical paddle-wheel boat at the speed of 2 1/2 km/hr, using a 220 watt motor. A year later, he had constructed an improved motor delivering a power of 700 watts, which is nearly one horse-power. His battery was constructed using zinc and platinum - a rather expensive mixture!
    So here we are almost 175 years later, and the whole world is now excited about the prospect of having electrical cars in the future.

(This public domain image of Thomas Edison, proudly presenting his electrical car in the year 1913, can be found in the Wikepedia.)

Indeed, our neighbor, who was a professor of electricity, was also enthusiastic about getting an electrical car after his retirement. A very expensive proposition! He bought one about 10 years ago and drove it for a year or two before finally giving up, realizing that even a life's worth of enthusiasm for electricity is not sufficient to make electrical cars into a practical proposition.
    Making electrical motors is a simple, almost primitive business. Low tech. When we first moved into our house with its large garden and much grass to mow, I got an electrical lawn mower. I hate those noisy, smelly gasoline mowers which some of the other neighbors have. When they start mowing their lawns, I put in my ear plugs to dampen down the irritation. Then I think of the smell they are producing, the poisonous gases. And what a problem gasoline motors in lawn mowers give to their owners! How many people have gotten their backs out of joint pulling away at the starting chord? Then if the mixture isn't quite right, you have to fiddle with the screws on the carburettor, hopefully getting the motor to settle down to a loud, but steady, racket. You have to take it in to be serviced every year. No! I wanted nothing to do with such problems and so I just got a simple electrical lawn mower. After 20 years it is still working perfectly; no loud noise, no stink. It has never been serviced. As good as new!
    Electrical lawn mowers are vastly superior to gasoline lawn mowers owing to the fact that you can simply plug them in to an external electrical plug on the house with a long electrical cable. The distance from the electrical plug to the most distant bit of lawn in our garden is about 30 meters or so. This can be dealt with using a standard electrical garden cable, obtainable at any hardware shop.
    The problem with electrical cars though, is that they are expected to drive more than 30 meters away from the outside electrical plug on the owner's house to more distant destinations. Even kilometers away. Even thousands of kilometers away! At least that is what we are used to doing with modern cars using the principle of internal combustion, thus making us independent of the power plug in the house.
    A solution to this problem is offered by the technique of carrying a battery around with you in the car. The solution found by Moritz von Jacobi involved the use of that very fine metal, platinum. I see that despite the fact that the price of gold has ballooned up in recent times to over $1,000 an ounce, still, platinum remains even more expensive. Googling the price of platinum just now, I have discovered that it costs $1,337 an ounce. Thus, while it may have provided Moritz von Jacobi with a wonderfully elegant battery with which to progress gracefully along the Neva past all those magnificent palaces of the old Russian aristocracy, still, for the common man, it remains too expensive, even today.
    The common people have been making do with lead for the last 175 years. Now it is true that a lead battery is satisfactorily robust. Nevertheless, it is heavy - as heavy as lead! And the amount of electrical energy which can be stored in a 10 or 20 kg. lead battery, while being more than enough to run the lights, radio and the starter motor of a car, is insufficient to actually drive very far. Thus a lead battery car, such as that of Thomas Edison, becomes extremely heavy if it is expected to be driven more than just a few miles between recharges. To cut down on weight, people try to make the structures of these cars as light as possible. So you end up with a flimsy car, loaded down with a ton of lead. A seemingly absurd, inefficient and dangerous proposition! Even worse, the lead battery only lasts a couple of years, after which it must be replaced at great expense. Furthermore, lead, a heavy metal, is considered to be dangerously poisonous if the battery corrodes and becomes leaky.
    But no! Lead batteries are now passé. For example the battery in this laptop computer which I have had for the last 4 or 5 years runs on lithium ions. The most common isotope of lithium has an atomic weight of 7, so it stands at the other (lighter) end of the periodic table when compared with lead. It is also a metal, yet so light that its density is only about half that of water, so that it would float. On the other hand, it would not be a particularly good idea to try floating a slab of lithium on water since this would probably lead to an unpleasant explosion. The lithium atoms will violently grab the oxygen atoms from the water molecules, releasing the hydrogen from the water which, presumably, would then further explode when reacting with the free oxygen in the air. Indeed, one sometimes reads in the papers of exploding laptop batteries, or of exploding mobile telephones. Lithium is, in fact, so explosive that it has been used for making incendiary bombs for military use! If, heaven forbid! you are so careless as to short-circuit a lithium ion battery, then you get a very dangerous and intense fire which is practically impossible to put out.
    Thus - it is emphasized - you are not allowed to use a no-name replacement battery in your laptop. Instead, in order to avoid explosions, you must install a certified, authentic replacement. The Internet is filled with offers of cheap alternative batteries for my laptop, yet even they cost about €50. The official replacement battery costs more than €100.
    Although lithium is light, when I take the battery out and hold it in my hand, it seems to me to be still quite heavy. It's almost as heavy as if it were a lead battery. Perhaps all that weight comes from the layers of material forming the casing, keeping all that explosive lithium isolated from the outside world. Putting it on the kitchen scales, I see that it weighs 414 grams, or about one pound. For that, it has a capacity of 4300mAh at 14.8 volts, which, in more conventional terms means that it stores about 0.064 kilowatt hours of energy. A tiny fraction of the energy which Moritz von Jacobi's platinum battery was able to store back in 1838. Thinking about it, I see that you would need perhaps 100 pounds of these lithium ion batteries in order to run Moritz's paddle-wheel boat with the one horsepower motor for a couple of hours along the Neva river, taking you a few kilometers.
    Unfortunately though, the lithium ion battery in my laptop - having reached the advanced age of 4 or 5 years - is gradually giving up the ghost. Whereas when new it was able to power the computer for 3 or 4 hours, now its feeble remaining power is only capable of keeping things alive for at most an hour. The capacity must have dropped to only 0.02 kilowatt hours, or even less! Probably most people would say that the best thing to do would be to just chuck things in the garbage and get a new laptop, since this one is so much behind the times anyway. But it says in small, but capital letters on the battery that rather than chucking it into the garbage, one should "DISPOSE OF PROPERLY". So maybe it is not only expensive and explosive, but poisonous as well.
    Translating all of this into the problem of running a car on batteries, rather than a mere laptop, I begin to understand the seemingly absurd problems which the automobile industry now faces. I can ignore the fact that the battery in this laptop has become old and weak; after all, it runs just as well plugged into the power in the wall. But you can't do that with an electrical car. If it costs €100 to replace the one pound battery in this laptop, then (using a rather unfair calculation) it would cost €100,000 to replace the thousand pound battery every two or three years in an electrical car! Even if I had so much money, I wouldn't waste it on that.

    One consequence of George W. Bush's wars was that along with gold, the price of raw oil ballooned upwards, up to $150 per barrel. And then the atomic power lobby seems to have gotten a semi-religious movement started, whose credo is that it is a sin to use internal combustion engines in cars. Instead, electrical cars must be driven in the future, powered by the electricity generated by their atomic power stations. The proclamations and prophesies of the prophets of this religion have succeeded in implanting such a general feeling of guilt in people that they have become afraid to buy new cars, even though their old ones are wearing out. Thus some of the big companies: General Motors, Chrysler, and so forth, have become bankrupt. In order to "save" them, the government has taken them over, but under the condition that they absolve themselves of their sins. That is, they must now obey the instructions of the powers that be behind atomic power, and produce electrical cars, come what may! The drum-beat of the newspapers, television, and all the rest of the media constantly beat this message into our brains.

    But isn't there a better way to do things? Can't we get away from this whole atomic energy, global warming mantra? In a more rational world, people would realize that a battery, or indeed even gasoline, is nothing more than a way to store energy. So what possibilities are there for storing energy in a way which would be suitable for driving a car? Gasoline is suitable; electricity is not particularly suitable.
    We have the hybrid car, which is supposed to combine the advantages of both. But does it? Or does it combine the dis-advantages of both? The idea is that when applying the brakes, rather than having the kinetic energy of the car simply being dissipated as heat, it is stored in a small battery, then re-used in the electric motors which drive the car. However the real source of energy is a normal internal combustion engine driving a generator which keeps recharging the battery which drives the electric motors.
    All of this may indeed be sensible for people whose driving style involves alternately giving full gas, then hitting the brakes to bring the car to a screeching stop and so terrorizing the rest of the people on the road and giving the passengers in the car a bad case of car-sickness. Indeed, the idea of hybrids would be ideal for racing cars. But for normal people driving in a moderate style, anticipating the traffic ahead, I can't see the sense of hybrids. I try to use the brakes as little as possible, even at a full stop just using them lightly. Only a very tiny fraction of the energy obtained in the motor would be reused after breaking. The price to pay is to have not only a gasoline motor which must be sufficiently powerful to keep up with the traffic for hours on the motorway, but in addition the car must continuously carry around the weight of a battery and electrical motors. I have read that Toyota guarantees the battery for the life of its Prius cars. Judging from the performance of my laptop battery, I wonder how effective the hybrid would be when its battery becomes 5 or more years old?

    So what about hydrogen? It is the lightest of elements. It can be burned in an internal combustion engine, or more efficiently turned into electricity in a fuel cell. Amongst other possibilities, it can be stored under pressure or in a metal hydride. Or perhaps propane, butane, and so forth, could be synthesized from hydrogen and carbon, giving the easily transportable lpg (liquefied petroleum gas). A car would run cleanly for hundreds of miles with a single tank filling. Twenty or thirty years ago, many people said that in the future, the world would gradually become transformed into a hydrogen economy. (This article in the Wikipedia - which is written by anonymous members of the general public clicking themselves in and just writing what they like - is amusing in that it tries at every turn to show the disadvantages of using hydrogen, often stating the obvious in a distorted way.)
    For example it is often pointed out that it is not very sensible to connect windmills or solar cells directly into the electrical power system, since the wind varies and the sun goes down at night. Thus it is necessary to have a conventional generating capacity sufficient to cover the peak of demand. All of this is true, and it shows that the present, highly subventioned, so-called "renewable" energy which people here in Germany are now being forced into for political reasons, is tremendously wasteful. But if we had a hydrogen economy, then at least the variable power produced by windmills could be used to produce hydrogen from water, effectively storing the energy. (Of course hydrogen can also be stored as methane - which is essentially what natural gas is. But this leads to a direct comparison of the conventional method of obtaining natural gas, namely drilling a hole in the ground, with inefficient, polluting, habitat-destroying windmills.)
    The owner of a windmill will obviously prefer to sell his electricity into the power grid if the power companies are required by law to pay the windmill owners three or four times more for the windmill electricity than the cost of producing electricity by conventional means. Thus the leaders of the world are pushing us with united force into a future of impractical, expensive, poisonous electrical batteries, whose manufacture will involve new extremes of environmental pollution.