178 
ME. M. W. CROFTOX OX THE PROOF OF 
astronomers, not content with the degree of accuracy they had reached, prosecuted their 
researches into the remaining sources of error, they found that, not three or four, but a 
great number of minor sources of error, of nearly coordinate importance, began to reveal 
themselves, having been till then masked and overshadowed by the graver errors which 
had been now approximately removed* *. It was as if a small number of forest trees had 
been cut down, leaving an innumerable growth of shrubs and brushwood at their feet, 
remaining to be cleared. There were errors of graduation, and many others, in the 
construction of instruments; other errors of their adjustments; errors (technically so 
called) of observation ; errors from changes of temperature, of weather, from slight 
irregular motions and vibrations ; in short, the thousand minute disturbing influences 
with which modern astronomers are familiar, and which it is superfluous to recapitulate 
here. Many of these are known and allowed for, or eliminated, at least approximately, 
in practical astronomy ; still we seem to be justified in considering the error which 
remains as the result of a great number of yet minuter errors, each inconsiderable in 
itself. Thus a cursory view of the nature of astronomical errors, and the light which 
this throws on various cognate classes of observations, seem to lead to the conclusion 
that the above hypothesis will be found to hold, generally, in the case of refined and 
delicate observations. No doubt much more would be necessary to justify us in asserting 
instance, is certainly not a simple error, but one resulting from the joint action of several causes, one or more 
of which we can conceive detected and allowed for, leaving the others in operation. An error may thus arise 
from the superposition of only three or four component errors, which at first sight are of simple origin, but in 
reality represent each a group of minor errors ; and the hypothesis would then hold. It is questionable whether, 
among the causes which in practice vitiate any observation, any simple error ever does enter, of considerable 
magnitude and importance as compared with the others combined ; such, for instance, as would be the error 
produced in the time (or through the time on some astronomical magnitude) by the pendulum being -Aj- 0 f an 
inch too long or too short, every thing else being pretty accurate. If it be said that ignorance or negligence 
might produce such a result, we may answer that such negligence or ignorance would make itself felt in other 
ways also : one such error would not stand alone. Isolated acts of neglect by a careful observer would come 
under the head of occasional errors, as explained further on. 
It seems very difficult to discern, a priori, the nature of the errors incurred in estimating magnitudes by the 
eye, or of errors arising from the imperfection of our senses, such as those incurred in pointing to a star with 
the naked eye. It is quite possible that such errors may arise each from several sources, though their nature be 
hidden from our view. 
* A similar law to that mentioned above seems to prevail in many kindred cases. Thus in the successive 
improvements in artillery, machinery, &c., in proportion as the greater sources of imperfection and inaccuracy 
are understood and remedied, the number of minor disturbing influences which are thus rendered perceptible, 
and still vitiate the results, though to a less extent, increases rapidly. We may even trace a sort of analogy^ 
here in various phenomena both of the moral and material universe, which apparently have no bearing on the 
point we are considering. Thus the principal wants of human nature, the necessaries of life in fact, are very 
few ; and so long as these are supplied with difficulty, minor wants are scarcely felt, as we see in uncivilized 
communities : but when the greater wants are satisfied, the number and variety of the secondary requirements 
of our nature are visible in the multitudinous productions of civilized life. The diseases which mainly operate in 
shortening human existence are very few in number ; but could they be extirpated, the number of minor causes,' 
of nearly coordinate importance, which still would influence the rate of mortality would be very large. The 
statistics of crime, and many other phenomena, would give rise to remarks of a similar nature. 
