II 



OBSERVATION AND KXI'KRIMRNT. 



OBSERVATORIES, ASTRONOMICAL. 



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neous from the imperfection* at our MOM*. Whrn a ant innot U 

 observed, it U MOD MM, for instance, whether H has or has not 

 wing*, and the question one* settled it Anally settled. But when, say 

 the specific gravity of a gaseous substance, U a kiven pressure and 

 temperature, i* wuanrnl, it i iaipoouble to consider the question at 

 settled at any Urn*. Say that, under given circumstances, the specific 

 gravity U anertod to be -34 of that of air similarly circumstanced ; 

 this U only an admU.ion. at most, of iu being somewhere bet. 



9936 and SIS. And that which we call an exact meamireoMnt of a 

 length may for one purpose mean within a hundredth of an inch, for 

 another within a thousandth, and to on ; but no penon dreami of 

 having attained absolute truth. This being well known, and every 

 process used in observation being nibjeet to error, it u the buaineat of 

 the observer to repeat obwrration* many time*, and to extract a remit 

 a* dear to the truth a* may be, from the man of discordant material* 

 which the repetition will furnish. 



The necessary errors of observation arise from the imperfection of 

 our perceptions and of the instruments which we use, and also from 

 hasty or otherwise incorrect conclusions. The subject requires the 

 separation of these errors into three rlissru. which may be mixed up 

 with one another in result*, and may be mistaken for one another. We 

 may call them jtrtd. pmonal, and camal. 



By a.itnri error we mean one which is inherent in the instrument 

 or method employed, so that it must exist, and, all other things 

 remaining the same, must have a given magnitude. Thus, if the axis 

 of an equatorial (supposing such an instrument to be employed for 

 absolute measurements) do not absolutely coincide with that of the 

 heavens, the right ascension and declination of a given star, measured 

 when at a given distance from the meridian, must have a given error. 

 It might be precisely the same in numerical effect, and would certainly 

 produce an error of the same class if the observer used a wrong 

 formula in the reduction of his observations. Thus, it would be 

 perfectly possible to give to one observer an incorrect instrument 

 and a correct formula, and to another a correct instrument and an 

 incorrect formula, in such manner that their final results should 

 coincide. 



Errors of this kind cannot be detected by multiplying similar obser- 

 vations, since there can be no tendency to destroy error in the mere 

 repetition of it. There are many modes of detecting fixed errors, and 

 of allowing for them ; but the only mode of avoiding them is by taking 

 advantage of the construction of the instrument to use it for the same 

 purpose under different circumstances, in such manner that measure- 

 ment* which are too large in one set of result* must be as much too small 

 in the other. If the same number of observations be contained in each 

 set, thin, as we shall presently see, U really a reduction of the fixed 

 error to the class of casual one* ; or rather, a destruction of the fixed 

 error by the same process which gives the highest probability of 

 destroying the casual errors. 



All instruments must be more or leas erroneous in every particular. 

 In the science of observation, as now understood, and in any mat d-r in 

 which the utmost attainable exactness is requisite, the assumption ,.f 

 perfection in an instrument, in any [mint whatsoever, is looked upon as 

 nothing but the expression of the observer's unwillingness to take 

 trouble. For even if ninety-nine successive days' trials have shown 

 that any particular error does not exist to any sensible amount, 

 it is not conclusive against the observations of the hundredth day 

 being affected by some new circumstance, necessary or accidental, in 

 which the instrument has been placed in the intermediate time. 



By a i-frvatal error is meant one of the same character as a fixed 

 error, but arising from the temperament or habit* of the observer, 

 and not from the instrument. Thus if A should, in noting tin- tin,.- 

 of a phenomenon by the clock, have a tendency to accelerate the 

 moment of it* happening, and B a similar tendency to retard it, the 

 result* of the two would differ by the sum of their personal 

 errors. It has been discovered that two individuals, observing 

 the same phenomenon with the same species of instruments may 

 differ sensibly (though but little) from each other; and thi< n.'t 

 once or twice, but nearly always, and in such a manner as to make 

 the average of a set of observations of one observer differ from 

 that of the other. For anything we can know to the contrary, 

 this species of error may exist in every observer'; and its absolute 

 quantity must be unknown until we can compare the observations 

 of men subject to it with those of some other beings who are not If 

 indeed the persona) error be purely casual, so that where one person 

 measures too much, another measures as much too little, the average 

 of the results of a large number of observers would give the truth or 

 very near it But should it be the case, which is not impossible, that 

 all men are subject to an error of the same kind, some more and some 

 less, namely, that all measure more or less too much, or else, that all 

 measure more or less too little, the average above mentioned would 

 give, not the truth, but the truth affected by the average error of all 

 the observers. Nor would the result* obtained ever enable us to dis- 

 tinguish whether personal errors have a fixed average or not ; for 

 suppose the fact observed to be that A, one time with another, mea- 

 sures more than B ; this way mean either of several things : either A 

 measures truly, and B too little ; or B measures truly, and A too 

 much ; or B measures too little, and A too much ; or both measure 

 too little, but B more than A ; or both measure too much, but A more 



than B. Now, if A and B were to observe together for a century, the 

 mere comparison of their observations, though it would settle their 

 average amount Jof difference, would never enable a* to give the least 

 guess which of the preceding oases is the true one. If indeed we could 

 convert the observer, as we have previously mentioned might generally 

 be done with the instrument, into another observer with an error of 

 the opposite kind, a true result, or one sensibly true, might be obtained. 

 Suppose, for example, it is the observer's habit, in noting the transit 

 of a star over a fixed wire in the field of a telescope, to take the transit 

 too soon when the star comes in on the right side, and too late when 

 on the left : consequently, by making a number of observation* with 

 an inverting telescope, and an equal number with one which does nut 

 invert, the average of both set* w..uM ! as likely to give a true result 

 as if neither error had existed. [KqfiTiox, PERSONAL.] 



All the errors which precede, though called errors because they give 

 a result which is not the one intended to be obtained, yet are in fact 

 the consequences of an actually existing state of things, and their laws 

 can be determined by using the right means, or at least must be 

 supposed to arise from natural causes measurable by experiment in the 

 same manner as other consequences of existing relations. They are 

 then really measures of phenomena, called errors simply because the 

 effects of their causes are to be removed from the results. It is even 

 imsaible that they might be made intentionally in a given form, with a 

 view to prevent their occurrence in a more objectionable form. Thus, 

 suppose an observer finds himself, in correcting discordant observations, 

 apt to confound additions and subtractions, using one for the other : 

 he will set his instrument intentionally wrong to an amount which 

 casual discordances never reach, taking care, of course, to preserve 

 means of correcting the intentional error with the rest ; so that the 

 requisite correction shall always be of one kind, additive or subtractive. 

 Nevertheless this arrangement, as it should be called, would go by the 

 name of an error, simply as being to have its effect afterwards destroyed. 



By carnal errors, the only ones to which the name of errors can 

 properly be given, are meant those which are absolutely inexplicable, 

 or of which the cause and tendency are equally unknown. They must 

 be considered as equally likely to be positive or negative ; so that in 

 the long run the results which they give too great will be compensated 

 by those which are too small. If this be not the case, that is, if there 

 be a greater tendency to too much than to too little, there must be a 

 reason for this phenomenon, and a law of action, which must be sought 

 for and detected. Let us suppose this done, so that auy result of a 

 single observation, corrected for all discoverable sources of error, is in 

 itself as likely to be too small as too great 



If .ill the observations be equally good, the MEAN, or average, is 

 more likely to be true than anything else. This is even true v. itli 

 reference to fixed or personal errors which may remain, but which are 

 totally unsuspected ; for there is an even chance of such errors acting 

 in either way. In the article just cited is shown the way of finding, 

 from the observations themselves, the probable error, as it'is called, or 

 that which there is an even chance of not exceeding : with references 

 to further sources of information. This article [MEAN], together with 

 the general considerations in PROBABILITIES, THEORY OF, and WEIGHT 

 or OBSERVATIONS, will contain all we shall find it necessary to say on 

 the subject 



It might be supposed that the greater the number of observations', 

 the less, in the same proportion, the probable error of the average ; 

 but this is not true, since the probable error diminishes as the ttfuarc 

 root of the number of observations increases. Thus, suppose it to be 

 well settled that twenty observations of a given observer "ill hive an 

 average of which it is an even chance that it does not err by (say) a 

 unit : then the same observer must make four times as many ol 

 tions to get an average with an even chance of not more than half a 

 unit of error ; nine times for uno-t/ilrd of a unit, and so on. 



Those who neglect sound principles of observation are apt to over- 

 rate the effect of multiplying observations ; which, though considerable, 

 does not, as we see in the above rule, keep pace with the number of 

 observations. 



OBSERVATORIES, ASTRONOMICAL. We possess only an im- 

 perfect knowledge re#]>ectmg the institutions established in' nneient 

 times for the observation of the heavenly bodies. The olw. M .,t y ,,f 

 Alexandria is alone famous in the history of Greek astronomy. It was 

 there that the observations were first made, upon which astronomy as 

 a science, in the true sense of the term, was finally founded. With 

 the revival of science in modern Europe, the establishment of observa- 

 tories was soon felt to be indispensable to the progress of astronomy. 

 The observatory of Tycho Brand, erected in the island of Huena 

 towards the close of the 18th century, under the auspices of Frederick 

 III., king of Denmark, is memorable in the history of nstronon 

 having supplied the facts which enabled Kepler to destroy the epicy- 

 clical mechanism of the planetary movement!*, and to substitute iu its 

 stead the true theory of elliptical motion. About the same time 

 William, Landgrave of Hesse Cassel, did good service to astronomy by 

 the erection of an observatory, and the prosecution of a series of 

 observations of the heavenly bodies. The lustre shed upon his 

 country by the labours of Tycho Brahd doubtless acted as a powerful 

 incentive in stimulating the Danish sovereigns to patronise astronomy. 

 We accordingly find that the earliest national observatory of modern 

 Europe was- established in Denmark. The observatory of Copenhagen 



