"Now, with regard to the first two classes of error, it must be observed, that in so far as they can not be reduced to known laws, and thereby become the subjects of calculation and due allowance, they actually vitiate in their full extent the results of any observations in which they subsist. With regard to errors of adjustment, not only the possibility, but the certainty of their existence in every imaginable form, in all instruments, must be contemplated. Human hands or machines never formed a circle, drew a straight line, or executed a perpendicular, nor ever placed an instrument in perfect adjustment, unless accidentally, and then only during an instant of time."
The bearing of these important and candid admissions of error in astronomical observations upon all kinds of other observations made by mortal eyes, and with instruments framed by human hands, in every department of science, is obvious. No philosophical observation or experiment is absolutely accurate, or can possibly be more than tolerably near the truth. The error of a thousandth part of an inch in an instrument will multiply itself into thousands, and millions of miles, according to the distance of the object, or the profundity of the calculation. Our faith in the absolute infallibility of scientific observers, and consequently in the absolute certainty of science, being thus rudely upheaved from its very foundations by Sir John Herschel's crowbar, we are prepared to learn that scientific men have made errors great and numerous.
To begin at home, with our own little globe, where certainty is much more attainable than among distant stars, we have seen that astronomers of the very highest rank are by no means agreed as to its diameter. Its precise form is equally difficult to determine. Newton showed that an ellipsoid of revolution should differ from a sphere by a compression of 1/230. The mean of a number of varying measurements of arcs, in five different places, would give 1/299. The pendulum measurement differs very considerably from both, and "no two sets of pendulum experiments give the same result."[335] The same liability to error, and uncertainty of the actual truth, attends the other modes of ascertaining this fundamental measurement. A very small error here will vitiate all other astronomical calculations; for the earth's radius, and the radius of its orbit, are the foot-rule and surveyor's chain with which the astronomer measures the heavens. But this last and most used standard is uncertain; and of the nine different estimates, it is certain that eight must be wrong; and probably that all are erroneous. For example, Encke, in 1761, gives the earth's distance from the sun at
| 95,141,830 | ||
| Encke, in 1769, | 95,820,610 | |
| Lacaille, | 76,927,900 | |
| Henderson, | 90,164,110 | |
| Gillies and Gould, | 96,160,000 | |
| Mayer, | 104,097,100 | |
| Le Verrier, | 91,066,350 | |
| Sir John Herschel, | 91,718,000 | |
| Humboldt, | 82,728,000 | [336] |
Here now is the fundamental standard measure of astronomy; and nine first-class astronomers are set to determine its length; but their measurements range all the way from seventy-seven to one hundred and four millions of miles—a difference of nearly one-fourth. Why the old-fashioned finger and thumb measure used before the carpenter's two-foot rule was invented never made such discrepancies; it could always make a foot within an inch more or less; but our scientific measurers, it seems, can not guess within two inches on the foot.
Their smaller measurements are equally inaccurate. Lias says the Aurora Borealis is only two and a half miles high; Hood and Richardson make its height double that, or five miles; Olmsted and Twining run it up to forty-two, one hundred, and one hundred and sixty miles![337] When they are thus inaccurate in the measurement of a phenomenon so near the earth, how can we believe in the infallibility of their measurements of the distances of the stars and the nebulæ in the distant heavens?
The moon is the nearest to us of all the heavenly bodies, and exercises the greatest influence of any, save the sun, upon our crops, ships, health and lives, and consequently has had a larger share of astronomical attention than any other celestial body. But the most conflicting statements are made by astronomers regarding her state and influences. There is no end to the controversy whether the moon influences the weather; though one would think that question, being rather a terrestrial one, could easily be decided. Schwabe says Herschel is wrong in saying that the years of most solar spots were fruitful; but Wolf looks up the Zurich meteorological tables, and confirms Herschel.
In Ferguson's Astronomy, the standard text-book of its day, we are informed that "Some of her mountains (the moon's) by comparing their height with her diameter, are found to be three times higher than the highest hills on earth." They would thus be over fifteen miles high. But Sir Wm. Herschel assures us that "The generality do not exceed half a mile in their general elevation." Transactions of the Royal Society, May 11, 1780. Beer and Madler have measured thirty-nine whose height they assure us exceed Mont Blanc. But M. Gussew, of the Imperial Observatory at Wilna, describes to us, "a mountain mass in the form of a meniscus lens, rising in the middle to a height of seventy-nine English miles."[338] As this makes the moon lopsided, with the heavy side toward the earth, the question of an atmosphere, and of the moon's inhabitability is reopened; and the discussion seems to favor the man in the moon; only he keeps on the other side always, so that we can not see him.
The best astronomers have gravely calculated the most absurd problems—for instance the projection of meteorites from lunar volcanoes; Poisson calculated that they would require an initial velocity of projection of seven thousand nine hundred and ninety-five feet per second; others demanded eight thousand two hundred and eighty-two; Olbers demanded fourteen times as much; but La Place, the great inventor of the nebular theory, after thirty years' study fixed it definitely at seven thousand eight hundred and sixty-two! It appears that the absurdity of the discharging force of a part greater than the attracting force of the whole never occurred to him.[339]
This same La Place supposed, that he could have placed the moon in a much better position for giving light than she now occupies; and that this was the only object of her existence. As this was not done he argued that her waxing and waning light was a proof that she was not located by an Omniscient Creator. He says he would have placed her in the beginning in opposition to the sun, in the plane of the ecliptic, and about four times her present distance from us, with such a motion as would ever maintain that position, thus securing full moon from sunset to sunrise, without possibility of eclipse. But Lionville demonstrates that "if the moon had occupied at the beginning the position assigned her, by the illustrious author of the Mecanique Celeste, she could not have maintained it but a very short time."[340] In short, La Place's hypothetical calculations generally have proved erroneous when applied to any existing facts; and we have no reason to attach more value to his nebular theory calculations.