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same direction, viz. in that of the sun's rotation, and not far from the plane of his equator. A phenomenon so remarkable cannot be the effect of chance and it obviously indicates one general cause, which has determined all these motions. To estimate the probability with which this cause is pointed out, it must be considered, that the planetary system, such as we now see it, is composed of eleven planets and eighteen satellites; and that the rotation of the sun, of six planets, of the satellites of Jupiter, of the ring of Saturn, and of one of his satellites, are all known. These movements, taken in conjunction with those of revolution, make a total of forty-three-all in the same direction. Now, by the calculation of probabilities, it will be found that there are more than 4 millions of millions to wager against one, that this disposition is not the effect of chance; a probability much superior to that of the historical events about which we entertain the least doubt. We must therefore believe at least with equal confidence, that One Primitive Cause has directed all the planetary motions; especially when we consider, that the greater part of these motions are also nearly in the same plane."
Our author proceeds, then, to offer some conjectures concerning the physical cause to which these motions are to be ascribed. He brings together a great number of facts, from Dr Herschell's observations concerning the nebula, which, com
bined with the preceding, seem to point out the solar atmosphere as the most probable cause. But where the facts lie so far out of the reach of accurate observation as many of these do, and when the supposed cause has ceased so entirely to act, the evidence we can have is so slight, and the difficulties so many, that even the author of the Mécanique Céleste must fail in giving weight and durability to his system.
In those sciences which are in a great measure conjectural, such as medicine, agriculture, and politics, the calculus of probabilities may be employed for discovering the value of the different methods that are had recourse to. Thus, to find out the best of the treatments in use in the cure of a particular disease, the comparison of a number of cases, where the circumstances have been as much alike as possible, will enable us to judge of the accidental causes that in each particular case assisted or impeded the cure these last will make a compensation for one another; and if the number of cases is sufficiently great, will leave the efficacy or inefficacy of the remedies distinctly visible.
"The same," he adds, " may be applied to political economy; with respect to which, the operations of governments are so many experiments, made on a great scale, and calculated to throw light on the conduct to be pursued on similar occasions. So many unforeseen, concealed, and inappreciable causes, have an
influence on human institutions, that it is impossible to judge a priori of their effects.-Nothing but a long series of experiments can unfold these effects, and point out the means of counteracting those that are hurtful. It would conduce much to this object, if, in every branch of the administration, an exact register were kept of the trials made of different measures; and of the results, whether good or bad, to which they have led."
He concludes with a maxim, which the circumstances of the times in which he has lived, must have but too deeply engraven on the mind of every Frenchman.
"Ne changeons qu'avec une circonspection extrême nos anciennes institutions et usages auxquels nos opinions et nos habitudes se sont depuis longtems pliées. Nous connaissons bien par l'expérience du passé les inconvéniens qu'ils nous présentent; mais nous ignorons quelle est l'étendue des maux que leur changement peut produire."
These are safe and just maxims; and we are glad to think that he who expresses them holds a high situation in the government of his country. There is, however, another maxim. grounded also on the doctrine of Probability, which we should think hardly less necessary than this, viz. that the rulers of mankind, in order to remove as much as possible all chance of sudden and great revolutions, would strike at the roots of the causes which so of
ten render them inevitable, by taking care that all political institutions are gradually and slowly corrected, as their errors are found out, or as new circumstances in the situation of the world render them inapplicable. The negative precept, of not changing things but slowly, is not alone sufficient; it is necessary to add the affirmative precept, of changing them slowly, but readily, when reason for such change appears. In this way, the causes that tend to disturb the public order are prevented from accumulating, so as to create, or even to justify, the spirit of revolution; and by gradual reformations, which may be made without danger, those great changes are avoided which cannot happen without incalculable mischief.
One of the most important applications of the doctrine of Probability, is to determine the most probable mean, or average, among a number of observations. The most accurate experiments and observations are liable to errors, which must affect the truth of the results obtained from them. To make these disappear as much as possible, observations must be greatly multiplied, in order that the errors in defect and in excess may destroy one another, and the mean, of consequence, become nearly correct. Still, however, the manner of striking this mean to the greatest advantage, remains to be examined, as also the degree of error to which, after all, it must be liable.
For a long time mathematicians were contented with taking the arithmetical mean as the true result of the observations; that is, they added them all together, and divided the sum by the number of observations. This was sufficient when the observations appeared to be all equally good, and entitled to equal weight in the determination of the result. This, however, was far from being always the case; and Cotes was the first, as Laplace remarks, who thought of a method by which each observation should have an influence in the determination of the results proportioned to its real value. Suppose that it is the position of an object that is required to be found by astronomical observation; let the place given by each individual observation be found, and at each of these conceive a weight to be placed proportional to the accuracy, or inversely as the error which it is reasonable to assign to that particular observation; the centre of gravity of all these weights is the true, or the most probable place of the object. This was in fact a generalization of the common method of taking an arithmetical mean; for it is only conceiving, that if one observation A, was twice as good as another observation B, then, instead of A, there should be accounted two observations of the same value with B, and giving the same result with A, and so on in any other proportion, even if the proportion were expressed by a fraction. The principle here is, that