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of the imperfections incident to every work the latter can place in his hands. He must, therefore, endeavour so to combine his observations, so to choose his opportunities, and so to familiarize himself with all the causes which may produce instrumental derangement, and with all the peculiarities of structure and material of each instrument he possesses, as not to allow himself to be misled by their errors, but to extract from their indications, as far as possible, all that is true, and reject all that is erroneous. It is in this that the art of the practical astronomer consists, — an art of itself of a curious and intricate nature, and of which we can here only notice some of the leading and general features.
(132.) The great aim of the practical astronomer being numerical correctness in the results of instrumental measurement, his constant care and vigilance must be directed to the detection and compensation of errors, either by annihilating, or by taking account of, and allowing for them. Now, if we examine the sources from which errors may arise in any instrumental determination, we shall find them chiefly reducible to three principal heads: —
(133.) 1st, External or incidental causes of error; comprehending such as depend on external, uncontrollable circumstances: such as, fluctuations of weather, which disturb the amount of refraction from its tabulated value, and, being reducible to no fixed law, induce uncertainty to the extent of their own possible magnitude; such as, by varying the temperature of the air, vary also the form and position of the instruments used, by altering the relative magnitudes and the tension of their parts ; and others of the like nature.
(134.) 2dly, Errors of observation: such as arise, for example, from inexpertness, defective vision, slowness in seizing the exact instant of occurrence of a phenomenon, or precipitancy in anticipating it, &c.; from atmospheric indistinctness; insufficient optical power in the instrument, and the like. Under this head may also be classed all errors arising from momentary instrumental derangement, — slips in clamping, looseness of screws, &c
(135.) 3dly, The third, and by far the most numerous clou of errors to which astronomical measurements are liable, arise from causes which may be deemed instrumental, and which may be subdivided into two principal classes. The first comprehends those which arise from an instrument not being what it professes to be, which is error of workmanship. Thus, if a pivot or axis, instead of being, as it ought, exactly cylindrical, be slightly flattened, or elliptical, — if it be not exactly (as it is intended it should) concentric with the circle it carries; — if this circle (so called) be in reality not exactly circular, or not in one plane ; — if its divisions, intended to be precisely equidistant, should be placed in reality at unequal intervals, — and a hundred other things of the same sort. These are not mere speculative sources of error, but practical annoyances, which every observer has to contend with.
(136.) The other subdivision of instrumental errors comprehends such as arise from an instrument not being placed in the position it ought to have; and from those of its parts, which are made purposely moveable, not being properly disposed inter se. These are errors of adjustment. Some are unavoidable, as they arise from a general unsteadiness of the soil or building in which the instruments are placed; which, though too minute to be noticed in any other way, become appretiable in delicate astronomical observations: others, again, are consequences of imperfect workmanship, as where an instrument once well adjusted will not remain so, but keeps deviating and shifting. But the most important of this class of errors arise from the non-existence of natural indications, other than those afforded by astronomical observations themselves, whether an instrument has or has not the exact position, with respect to the horizon and its cardinal points, the axis of the earth, or to other principal astronomical lines and circles, which it ought to have to fulfil properly its objects.
(137.) Now, with respect to the first two classes of error, it must be observed, that, in so far as they cannot be reduced to known laws, and thereby become subjects of calculation and due allowance, they actually vitiate, to their full extent, the results of any observations in which they subsist Being, however, in their nature casual and accidental, their effects necessarily lie sometimes one way, sometimes the other; sometimes diminishing, sometimes tending to increase the results. Hence, by greatly multiplying observations, under varied circumstances, by avoiding unfavourable, and taking advantage of favourable circumstances of weather, or otherwise using opportunity to advantage — and finally, by taking the mean or average of the results obtained, this class of errors may be so far subdued, by setting them to destroy one another, as no longer sensibly to vitiate any theoretical or practical conclusion. This is the great and indeed only resource against such errors, not merely to the astronomer, but to the investigator of numerical results in every department of physical research.
(138.) With regard to errors of adjustment and workmanship, 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 erected a perpendicular, nor ever placed an instrument in perfect adjustment, unless accidentally; and then only during an instant of time. This does not prevent, however, that a great approximation to all these desiderata should be attained. But it is the peculiarity of astronomical observation to be the ultimate means of detection of all mechanical defects which elude by their minuteness every other mode of detection. What the eye cannot discern nor the touch perceive, a course of astronomical observations will make distinctly evident. The imperfect products of man's hands are here tested by being brought into comparison under very great magnifying powers (corresponding in effect to a great increase in acuteness of perception) with the perfect workmanship of nature; and there is none which will bear the trial. Now, it may seem like arguing in a vicious circle, to deduce theoretical conclusions and laws from observation, and then to turn round upon the instruments with which those observations were made, accuse them of imperfection, and attempt to detect and rectify their errors by means of the very laws and theories which they have helped us to a knowledge of. A little consideration, however, will suffice to show that such a course of proceeding is perfectly legitimate.
(139.) The steps by which we arrive at the laws of natural phenomena, and especially those which depend for their verification on numerical determinations, are necessarily successive. Gross results and palpable laws are arrived at by rude observation with coarse instruments, or without any instruments at all, and are expressed in language which is not to be considered as absolute, but is to be interpreted with a degree of latitude commensurate to the imperfection of the observations themselves. These results are corrected and refined by nicer scrutiny, and with more delicate means. The first rude expressions of the laws which embody them are perceived to be inexact. The language used in their expression is corrected, its terms more rigidly defined, or fresh terms introduced, until the new state of language and terminology is brought to fit the improved state of knowledge of facts. In the progress of this scrutiny subordinate laws are brought into view which still further modify both the verbal statement and numerical results of those which first offered themselves to our notice; and when these are traced out and reduced to certainty, others, again, subordinate to them, make their appearance, and become subjects of further inquiry. Now, it invariably happens (and the reason is evident) that the first glimpse we catch of such subordinate laws — the first form in which they are dimly shadowed out to our minds — is that of errors. We perceive a discordance between what we expect, and what we find. The first occurrence of such a discordance we attribute to accident. It happens again and again; and we begin to suspect our instruments. We then inquire, to what amount of error their determinations can, by possibility, be liable. If their limit of possible error exceed the observed deviation, we at once condemn the instrument, and set about improving its construction or adjustments. Still the same deviations occur, and, "bo far from being palliated, arc more marked and better defined than before. We are now sure that we are on the traces of a law of nature, and we pursue it till we have reduced it to a definite statement, and verified it by repeated observation, under every variety of circumstances.
(140.) Now, in the course of this inquiry, it will not fail to happen that other discordances will strike us. Taught by experience, we suspect the existence of some natural law, before unknown; we tabulate (i. e. draw out in order) the results of our observations ; and we perceive, in this synoptic statement of them, distinct indications of a regular progression. Again we improve or vary our instruments, and we now lose sight of this supposed new law of nature altogether, or find it replaced by some other, of a totally different character. Thus we are led to suspect an instrumental cause for what we have noticed. We examine, therefore, the theory of our instrument; we suppose defects in its structure, and, by the aid of geometry, we trace their influence in introducing actual errors into its indications. These errors have their laws, which, so long as we have no knowledge of causes to guide us, may be confounded with laws of nature, as they are mixed up with them in their effects. They are not fortuitous, like errors of observation, but, as they arise from sources inherent in the instrument, and unchangeable while it and its adjustments remain unchanged, they are reducible to fixed and ascertainable forms; each particular defect, whether of structure or adjustment, producing its own appropriate form of error. When these are thoroughly investigated, we recognize among them one which coincides in its nature and progression with that of our observed discordances. The mystery is at once solved. We have detected, by direct observation, an instrumental defect.
(141.) It is, therefore, a chief requisite for the practical astronomer to make himself completely familiar with the theory of his instruments. By this alone is he enabled at once to decide what effect on his observations any given imperfection of structure or adjustment will produce in any given circumstances under which an observation can be made. Thio alone also can place him in a condition to derive available and practical means of destroying and eliminating altogether