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From: Mark Borgerson on 6 Feb 2010 11:47 In article <3e75d4db-b585-42d3-af46-993ed471e136 @k19g2000yqc.googlegroups.com>, k_over_hbarc(a)yahoo.com says... > On Feb 4, 9:22 pm, Michael Press <rub...(a)pacbell.net> wrote: > > > The USA gallon aka Queen Anne gallon aka wine gallon > > started life as a cylinder 7 inch in diameter by 6 inch high. > > So why is it exactly 231 inch^3? > > Take the approximation pi = 22/7 and you'll get it! Of course, the > only gallon that ought to be used anymore is the imperial, ~277.42 > cubic inches. > > > A mile is a thousand double paces. > > One can still pace out long distances, like the Romans did, and 1,000 > paces = 1 mile is pretty close. > You must be counting two steps per pace, then. The most common definition of a pace is 30 inches, so it takes about 2000 of them per mile. The old Roman pace was two steps or five Roman feet: 58.1 inches. 1000 of those gets you 0.92 miles. If ~8% error is OK with you, I guess you can call that a mile. Mark Borgerson
From: Mark Borgerson on 6 Feb 2010 12:01 In article <45382ab0-761a-4593-b9bb- 67b58e8f7bbc(a)d37g2000yqa.googlegroups.com>, k_over_hbarc(a)yahoo.com says... > On Feb 4, 9:20 pm, Mark Borgerson <mborger...(a)comcast.net> wrote: > > > > Well, yes, technically. But if you used a weight measured with a scale > > > (any type) the correction does come into account. > > > > That's not necessarily true either. If you are weighing iron > > cannonballs on a balance scale using iron weights, no correction > > is necessary. The same holds true on a balance scale whenever > > the item and weights are of equal density. If the weights are > > properly calibrated for their mass in vacuo, you will get > > the proper in-vacuo weight of the cannonball. > > Yes, but balances are almost obsolete. When measuring force as modern > scales do, the full correction is needed. That depends on what you call a modern scale. If it's a spring or electronic scale, you need the correction. If it's a lever-arm balance scale, you don't need the full correction, but a correction based on the relative densities of the movable or additional weights and the ratio of the lever arm. I still see a lot of those lever-arm balances on loading docks and other places where weights in the hundreds of pounds are measured. > > > > > > Of > > > > > course it changes with temperature as well; it's rather fortunate that > > > > > water has a much lower thermal expansion than any other liquid at > > > > > normal temperatures. > > > > Except for mercury, of course. Mercury has a coefficient of thermal > > expansion of 18e-5, while water is 21e-5. Given that low coefficient > > I suppose that mercury was used in thermometers, not because it > > was the best expansion medium, but because of low vapor pressures > > and high visibility. > > More so, actually, because the expansion of mercury (like most metals) > is very uniform with temperature, so that thermometers could be > divided on a linear scale and be fairly accurate. Also the very wide > temperature range - mercury freezes only at -38 F, and does not > decompose at the highest temperatures. Finally the thermal expansion > of mercury is much lower than that of organic liquids, and the stem > correction is proportional to it. Good point. I'd forgotten all about the immersion marks on the old chemistry class thermometers that made the stem correction valid. > > The thermal expansion of water, on the other hand, goes from -5e-5 at > freezing to 44e-5 at boiling (per degree F). > > > > > (unless, of course, you go below 32F! ;-) > > > > > No. That's negative thermal expansion! > > > > Not really---ice has a coefficient of thermal expansion quite different > > from the volume change with the phase change. > > When you cool water to make ice, it expands. That's the reverse of > normal, and so can be called negative, I would say. > > Yes, ice itself has a positive expansion. > Mark Borgerson
From: Mark Borgerson on 6 Feb 2010 12:13 In article <-MmdnZ5_XuM7kPDWnZ2dnUVZ8r-dnZ2d(a)bt.com>, platinum198 @pants.btinternet.com says... > Mark Borgerson wrote: > > In article <xeqdndkzMMsZXPbWnZ2dnUVZ8t6dnZ2d(a)bt.com>, platinum198 > > @pants.btinternet.com says... > >> Mark Borgerson wrote: > >>> In article <gerry-4EAAE0.12594505022010(a)news.eternal-september.org>, > >>> gerry(a)maths.mq.edi.ai.i2u4email says... > >>>> In article <f7jmm5trftkja8ikb1r2lcu6gmthcptdpg(a)4ax.com>, > >>>> Antares 531 <gordonlrDELETE(a)swbell.net> wrote: > >>>> > >>>>> On Fri, 05 Feb 2010 09:09:55 +1100, Gerry Myerson > >>>>> <gerry(a)maths.mq.edi.ai.i2u4email> wrote: > >>>>> > >>>>>> In article <hkeig101lnd(a)news3.newsguy.com>, jmfbahciv > >>>>>> <jmfbahciv(a)aol> wrote: > >>>>>> > >>>>>>> I grew up in the US and cannot think in metric terms so I > >>>>>>> always have to do a conversion to make guesstimates. > >>>>>>> For some strange reason, kilometers seem to take "longer" > >>>>>>> to drive than miles when I drove from Buffalo to Port > >>>>>>> Huron, Michigan. :-) > >>>>>> > >>>>>> Probably because of those metric Canadian hours, what with > >>>>>> each one being 100 minutes long. > >>>>>> > >>>>> When are they likely to change over to a metric week of 10 days? > >>>> > >>>> I believe that idea was tried and found wanting in the earliest > >>>> days of the metric system in Revolutionary France. > >>> > >>> Those pesky days, months and years---are, unfortunately, tied > >>> to the orbital and rotational periods of the Earth and Moon. Those > >>> intervals have, so far, not been easy to change! ;-) > >>> > >>> Lots of science fiction novels have proposed clocks and calendars > >>> with more decimal-like intervals. At some point, though, they > >>> have to define a small integral unit of time or distance. > >>> > >>> The meter started out as one ten-millionth of the circumference of > >>> the earth along a meridian passing through Paris. Just as logical > >>> as measuring Longitude from Greenwich, I suppose. ;-) > >> > >> Not the full circumference, but the length of the 90-degree arc from > >> pole to equator. > > > > Thanks. I missed that factor of four. Nominal 40,000 km > > circumference divided by 4 = 10,000km = 1x10^7 m. > >> > >> The decision to base longitude from the Greenwich meridian was at > >> least reached by an international agreement after long negotiations, > >> and was done to reduce navigational confusion and the cost of > >> carrying multiple copies of charts around in every ship. At the > >> time the (serious) choice was between Washington (US Naval > >> Observatory meridian), Greenwich Observatory meridian, and Paris > >> Observatory meridian. > > > > The British government also put up the prize that resulted in the > > Harrison clocks----which made determination of longitude practical. > > That was a shameful episode, recounted in "Longitude" by Dava Sobell. > I agree. The prize judges did all they could to deny him the prize. It took an intervention by the King to get him a partial award. While reading up on Harrison, I also discovered that he invented the bimetallic strip thermometer. When I visited England about 5 years ago a visit to the National Maritime Museum at Greenwich was a highlight of the trip. I got to see several restored Harrison clocks in operation. Not only that, but it was some sort of education weekend and all the museums had free admission. That saved me quite a number of pre-decimalization pounds---which I applied to the purchase of pints of porter! Mark Borgerson
From: Andrew Usher on 6 Feb 2010 16:48 On Feb 6, 7:05 am, jmfbahciv <jmfbahciv(a)aol> wrote: > If you have a business which wants to sell widgets to > people in countries who use metric, you should manufacture > your products using screws and bolts and things which > are metric. Not necessarily. The user of a machine usually doesn't care what units it's built to internally, only what it does. This point is made in that great book I referenced: "The metric fallacy". Andrew Usher
From: Andrew Usher on 6 Feb 2010 16:50
On Feb 6, 7:10 am, jmfbahciv <jmfbahciv(a)aol> wrote: > >> A mile is a thousand double paces. > > > One can still pace out long distances, like the Romans did, and 1,000 > > paces = 1 mile is pretty close. > > What do you do? Hop? A pace is properly the distance between two successive steps of the same foot, i.e. a double step. Andrew Usher |