John Carmichael wrote : >>In proofreading the new fifth edition of my "Sundial Owner's Manual", when >>discussing sundials, I think that I mistakenly used the words, "precise" and >>"accurate", interchangeably, as if they meant the same thing.
This is a confusing area. I am not a metrologist, though I am involved in measurement. I would suggest that accuracy is a more generally useful term. The "small divisions" concept is perhaps more often related to resolution than accuracy. A (clockwork) stopwatch has a typical resolution of 1/5 or 1/10 second (some are faster) and can discriminate between values on this basis. However its accuracy - and the accuracy of a measurement made with it - can be independent of its resolution as it might gain say 1 minute per hour or 1.6%. The two errors will respectively dominate at short or long interval measurements. But with a sundial, which is analogue, the observer will interpolate between values and the more divisions are present the less chance of introducing errors by poor interpolation. Another concept is reproducibility - which with a stopwatch might depend on the person pressing the button as much as on the constancy of the mechanism. If you measure something twice (difficult with time!) do you get the same value? For a sundial, would several simultaneous observers agree on its reading (perhaps this is a red herring)? In my own instinctive view of these things: A noon mark may be precise - giving the time of noon to a few seconds (e.g. St Sulpice) accurate - agreeing with the general definition of local noon imprecise - fuzzy shadow or solar image inaccurate - wrongly aligned However it is definitely no good at all for telling the time at 4 p.m.! It is not necessary to have a lot of fine divisions to be precise - dictionary definitions are not always helpful! However the divisions that do exist have to be good ones. A length end standard (slip gauge) is very precise indeed - and, one hopes, also accurate - but has no divisions at all. Even more so is the prototype kilogramme - a lump of metal near Paris which defines the unit for the rest of the world and is therefore accurate by agreement. Similarly a capacity measure such as a volumetric flask (or pint glass) can be precise as well as accurate but is not subdivided. If the length standard were significantly short of its nominal value then using it would make for a precise but inaccurate measurement. So a dial whose gnomon is well shaped and throws the best possible shadow onto an hour line - agreeing with the line all the way along it - may be precise, even if it has only hour lines. If it is wrongly set up it would however be inaccurate. If it were badly delineated it would certainly be inaccurate but might I think still be precise - this is the difficult case to argue. A heliochronometer that is well made should be precise. However if incorrectly set up it would be inaccurate; you would get an excellent measure, to the minute, of the wrong thing! Finally, you can make an accurate measurement using an inaccurate instrument of known (and reproducible) error at the measurement point. Combining the instrument and knowledge of its error produces a better, imaginary, instrument. In one sense, applying the equation of time to a good sundial (which even if it is at least precise normally provides an only inaccurate measure of mean time) is doing just this to get an accurate measure of mean time. Sorry this has got rather long. I don't know whether this is helpful or the reverse ... let alone accurate or precise ;-) Regards Andrew James
