"Well," he answered, "I noticed that when you were speaking about the distance of the moon you always said it was about so far away. Why didn't you tell us the exact distance? I'm not a scientific man by any means, but if any one were to ask me the length of a connecting rod on one of my machines I should say '25 inches,' not 'about 25 inches,' for that would not do for a practical man!"
"It's like this, M'Allister," I said. "You measure things with a two-foot rule, which is something you can actually handle, and you know it is made according to a standard measure and must contain exactly 24 inches. If, however, your rule was 241⁄4 inches long, yet still divided into twenty-four equal parts, you could measure work with it just the same, but would know that every measurement was just a little bit out. If you had no possible means of obtaining another rule, you would have to put up with a little inexactitude.
"That is just the position in which astronomers are placed; they have to put up with a measure which they know is not perfectly accurate, yet it is the best which can be secured.
"Their two-foot rule, so to speak, may be the distance from the earth to the sun, or the length of the whole diameter of the earth's orbit, and these cannot be handled like your rule; and although we know the measurements of these are nearly correct, they are not quite so. Yet the distances of the moon, planets, stars, &c., have to be measured by these rules, so it is clear we can only know those distances with a near approximation to accuracy.
"For this reason astronomers are always trying different means of ascertaining the sun's exact distance from the earth in order to obtain a perfectly correct measure; but there are so many difficulties and complications which affect the result, that it will be a long time yet before they succeed in their work.
"You will therefore understand that all these figures as to distances and dimensions of planets and stars are only as near approaches to correctness as is possible to attain in our present circumstances. They must not be regarded as literally exact, although they are usually sufficiently accurate for all general purposes. Astronomers know this and allow for it; but general readers of books, when they find figures which do not agree with others they have seen, are apt to regard them as all being mere guesses, and in this they are doing an injustice to the painstaking labours of generations of astronomers and mathematicians.
"I shall presently be mentioning the heights of mountains, the size of ring-plains, craters, &c., but the same reasoning applies to them; the dimensions given are averages of measurements made by different observers, and, though not quite accurate, are as near the truth as the difficult conditions under which they have to be measured will allow."
"Thank you, Professor," said M'Allister as I concluded. "I'm glad I don't have to work with such rules as those you mention, for measurements a little bit out of correctness would ruin any machine in the world."
"Still, M'Allister," I said, "you would have the advantage over astronomers with your two-foot rule, because you would know that it was a quarter of an inch too long. Their difficulty is that they do not know exactly how much their rule is out of correctness, so cannot obtain absolute accuracy however they may try."