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neration for the great and illustrious propounder of these laws.
We do not, however, approve of all that the learned professor has said relatively to this second law of motion. In proving the law, or rather in rendering probable the truth of the law, considered as a physical law, he introduces arguments to which we are unable to affix any precise notion. We instance one: A force, which we know to act equably, produces equal increments of velocity in equal times, whatever these velocities may be.' What kind of force does the author allude to? Does he know any thing of the equable action of the force, except from the fact of equal increments of velocity'? We suspect the proposition, if it means any thing, is tautological; but besides this objection, the professor's manner of writing is here very faulty: he ought not obscurely and allusively to have couched in general terms the results of particular experiments; but plainly and particularly to have stated those experiments, and then to have drawn his inferences.
But our objections and censures are not at an end: we like still less than the part just reprehended, what the author has said relatively to the question of the forces vives; we thought this question had been settled, and that every philosopher understood the dispute to be verbal, and why it was verbal. Dr. Robison might have learnt this from a writer he often quotes, from Dalembert: for, if our memory does not fail us, he has shown that according as you define force, its measure may the mass into the velocity, or the mass into the square of the velocity; that is, the measure of force A, or of moving force, may be mu, and the measure of force B, or of mechanical force, may be mu1: from applying the same term (force) to two different things, great mistakes arise; and, for a moment to descend from our grave chair of criticism, the cause of Master Slender's mis ake was somewhat similar, when he carried off, instead of Anne Page, a lubberly boy dressed like her, in white.
We find some difficulty in conceiving how Dr. Robison, who in many parts so clearly explains what the mathematician ought to understand by the terin force, could dictate the following passage.
The same conclusion may be deduced from our notions of a constant or invariable force; it is surely a force which produces equal effects, or changes of motion, in equal times. Now equal augmentations of motion are surely equal augmentations of velocity. We find this notion of an invariable accelerating force confirmed by what we observe in the case of a falling body. This receives equal additions of velocity in equal times; and we have no reason to think that this force is variable. We should therefore infer, that whatever force it imparts in one second, it will impart four times as much in four seconds. So it does, if we allow a quadruple
velocity to indicate a quadruple force; but in no other estimation of force.' P. 112.
On the subject of the composition of forces, Dr. Robison properly animadverts on those faulty proofs by which the composition of forces is immediately inferred from the composition. of motions; and he notices the more rigorous demonstrations of Daniel Bernouilli, Foncenex, and Dalembert. We are rather surprised that the professor should have passed over unnoticed the demonstration of Laplace; and that he should have let slip so fit an occasion for the exercise of his acuteness and sagacity, and (we may add) for the indulgence of his spleen, against that great mathematician. It is hardly fair to give our opinion without the grounds of it: but we cannot briefly enter into particulars; the demonstration of the author, in our opinion, is not free from objection..
In the section concerning accelerating and retarding forces, the author, notwithstanding his own arguments, seems not entirely delivered from verbal thraldom. He says: "Indeed all that we know of force is, that it is something which is always
proportional to 'this is indeed all that is necessary to be
known; and if the author had been under the influence of the same good sense that dictated the preceding sentence, he would not have swelled his book by attempting to prove that no finite change of velocity is generated in an instant, by any accelerating or retarding force.'
On the subject of deflecting forces, and of central forces, the author gives several of the propositions contained in the second section of Newton; the first proposition in the eighth, the first and second propositions of the ninth, and some of the first propositions of the eleventh, section. He then passes on to plane astronomy, which he treats with great neatness and perspicuity, particularly the subject of the calendar; and we subjoin an extract rather for its perspicuity, its easy and flowing style, than for its novelty of information and depth of thought.
Astronomy, like all other sciences, was first practised as an art. The chief object of this art was to know the seasons, which, as we have seen, depend either immediately, or more remotely, on the sun's motion in the ecliptic. A ready method for knowing the season seems, in all ages, to have been the chief incitement to the study of astronomy. This must direct the labours of the field, the migrations of the shepherd, and the journies of the traveller. It is equally necessary for appointing all public meetings, and for recording events.
Were the stars visible in the day-time, it would be easy to mark all the portions of the year by the sun's place among them. When he is on the foot of Castor, it is midsummer; and midwinter, when he is on the bow of Sagittarius. But this cannot be done, because his splendour eclipses them all.
The best approximation which a rude people can make to this, is to mark the days in which the stars of the zodiac come first in sight in the morning, in the eastern horizon, immediately before the sun-rise. As he gradually travels eastward along the ecliptic, the brighter stars which rise about three quarters of an hour before the sun, may be seen in succession. The husbandman and the shepherd were thus warned of the succeeding tasks by the appearance of certain stars before the sun. Thus, in Egypt, the day was proclaimed in which the Dog-star was first seen by those set to watch. The inhabitants immediately began to gather home their wandering flocks and herds, and prepare themselves for the inundation of the Nile in twelve or fourteen days. Hence that star was called the Watch-dog, Thoth, the Guardian of Egypt.
This was therefore a natural commencement of the period of seasons in Egypt; and the interval between the successive apparitions of Thoth, has been called the natural year of that country, to distinguish it from the civil or artificial year, by which all records were kept, but which had little or no alliance with the seasons. It has also been called the Canicular year. It evidently depends on the sun's situation and distance from the Dog-star, and must therefore have the same period with the sun's revolution from a star to the same star again. This requires 365d 6h 9' 11", and differs from our period of seasons. Hence we must conclude that the rising of the Dog-star is not an infallible presage of the inundation, but will be found faulty after a long course of ages. At present it happens about the 12th or 11th of July.
This observation of a star's first appearance in the year, by getting out of the dazzling blaze of the sun, is called the heliacal rising of the star. The ancient almanacks for directing the rural labours were obliged to give the detail of these in succession, and of the corresponding labours. Hesiod, the oldest poet of the Greeks, has given a very minute detail of those heliacal risings, ornamented by a pleasing description of the successive occupations of rural life. This evidently required a very considerable knowledge of the starry heavens, and of the chief circumstances of diurnal motion, and par ticularly the number of days intervening between the first appearance of the different constellations.
Such an almanack, however, cannot be expected, except among a somewhat cultivated people, as it requires a long continued observation of the revolution of the heavens in order to form it; and it must, even among, such people, be uncertain. Cloudy, or even hazy weather, may prevent us for a fortnight from seeing the stars
'The moon comes most opportunely to the aid of simple nations, for giving the inhabitants an easy division and measure of time. The changes in her appearance are so remarkable, and so distincf, that they cannot be confounded. Accordingly, we find that all nations have made use of the lunar phases to reckon by, and for appointing all public meetings. The festivals and sacred ceremonies of simple nations were not all dictated by superstition; but they served to fix those divisions of time in the memory, and thus gave a comprehensive notion of the year. All these festivals were
celebrated at particular phases of the moon-generally at new and full moon. Men were appointed to watch her first appearance in the evening, after having been seen in the morning, rising a few minutes before the sun. This was done in consecrated groves, and in high places; and her appearance was proclaimed. Fourteen days after, the festival was generally held during full moon. Hence it is that the first day of a Roman month was named Kalendæ, the day to be proclaimed. They said pridie, tertio, quarto, &c. ante calendas neomenias Martias; the third, fourth, &c. before proclaiming the new moon of March. And the assemblage of months, with the arrangement of all the festivals and sacrifices, was called a kalendarium.
'As superstition overran all rude nations, no meeting was held without sacrifices and other religious ceremonies--the watching and proclaiming was naturally committed to the priests-the kalendar became a sacred thing, connected with the worship of the gods-and, long before any moderate knowledge of the celestial motions had been acquired, every day of every moon had its particular sanctity, and its appropriated ceremonies, which could not be transferred to any other.
But as yet there seemed no precise distinction of months, nor of what number of months should be assembled into one group. Most nations seem to have observed that, after twelve moons were completed, the season was pretty much the same as at the beginning. This was probably thought exact enough. Accordingly, in most ancient nations, we find a year of 354 days. But a few returns of the winter's cold, when they expected heat, would, shew that this conjecture was far from being correct; and now began the embarrassment. There was no difficulty in determining the period of the seasons exactly enough, by means of very obvious observations.Almost any cottager has observed that, on the approach of winter, the sun rises more to the right hand, and sets more to the left every day, the places of his rising and setting coming continually nearer to each other; and that, after rising for two or three days from behind the same object, the places of rising and setting again gra dually separate from each other. By such familiar observations, the experience of an ordinary life is sufficient for determining the period of the seasons with abundant accuracy. The difficulty was to accomplish the reconciliation of this period with the sacred cycle of months, each day of which was consecrated to a particular deity, jealous of his honours. Thus the Hierophantic science, and the whole art of kalendar-making, were necessarily entrusted to the priests. We see this in the history of all nations, Jews, Pagans, and Christians.' P. 201.
Into the laborious details, the perplexing calculations, of physical astronomy; into its minute niceties, the touchstone of its truth; Dr. Robison does not enter: but he endeavours to give his reader a notion of the principle and method by which Newton ascertained the lunar inequalities to arise from the influence of the common law of gravitation; agreeably to this plan, he introduces what, in fact, is the 66th proposition of
the Principia,' the ingenious but imperfect method by which the great founder of physical astronomy solved the problem of the three bodies. Dr. Robison's method, with a few trifling variations, is the same as Newton's: in the following short extracts the author's clear and good sense shines out with great lustre.
In all this process, it is plain that we consider the heavenly bodies as consisting of matter that has the same mechanical properties with the bodies which are daily in our hands. We are not at
liberty to imagine that the celestial matter has any other properties than what is indicated by the motions, otherwise we have no explanation, and may as well rest contented with the simple narration of the facts. The constant practice, in all attempts to explain a natural appearance, is to try to find a class of familiar phenomena which resemble it; and if we succeed, we account it to be one of the number, and we rest satisfied with this as a sufficient explanation. Accordingly, this is the way that philosophers, both in ancient and modern times, have proceeded in their attempt to discover the causes of the planetary motions.' P. 273.
And again :
"We must constantly keep in mind that an explanation always means to shew that the subject in question is an example of something that we clearly understand. Whatever is the avowed property of that more familiar subject, must therefore be admitted in the use made of it for explanation. We explain the splitting of glass by heat, by shewing that the known and avowed effects of heat make the glass swell on one side to a certain degree, with a certain known force; and we shew that the tenacity of the other side of the glass, which is not swelled by the heat, is not able to resist this force which is pulling it asunder; it must therefore give way. In short, we shew the splitting to be one of the ordinary effects of heat, which operates here as it operates in all other cases.' P. 278.
Our limits do not permit us to extract what is said of Newton; of his mental character, his studies, and his inventions. We think this part ably done; and especially the beginning (Art. 434), which is written with great beauty of language and justness of thought. Dr. Robison very agreeably variegates his discussions and demonstrations with historical matter: he lays down the track of Newton's investigations and discoveries; he shows how that great philosopher employed the discoveries of Kepler, and improved on the thoughts of Hooke; and he states with precision, and fully unfolds, the argument for the truth of the law of universal gravitation: in this statement, as he must needs do, the author introduces several propositions from the 'Principia,' from the third and twelfth sections. He affirms, and truly affirms, that only in two laws, the direct and the inverse square, the attraction to a sphere is the same as if