any confirmation by its re-appearance in our system, although there seems to be little or no doubt of the accuracy of their results; the attractions of Jupiter and Saturn having in all probability so far changed the nature of its orbit, as to render it in future invisible to us in its approach towards the sun. If the period

of a comet's revolution were known, we should have one important element of its orbit, and the rest might be found with comparative ease: but, this being unknown, we have the whole to compute from a small number of geocentric observations, which renders the problem in this case very difficult. The apparent motion of a comet is the combined effect of its own motion and that of the earth: it is therefore extremely irregular and intricate; and, on this account, it is difficult to deduce the heliocentric positions from observations made on the earth's surface. We can view the planets at all times, and in all situations; and, with regard to them, we can thus select those positions in which the heliocentric places are found immediately from observations, without any perplexed calculations: but we are deprived of this expedient in the case of comets, which continue visible for a short time only, and in a small part of their orbit:

In order to evade the difficulties attending a direct consideration of the problem, and to obtain an approximate solution at least, Sir Isaac Newton proposed to take a small portion of the orbit for a straight line described with a uniform motion. On this supposition the projections of the comet on the plane of the ecliptic will lie in one straight line as well as the real places in the heavens; and the several parts of both lines will have the same proportions as the intervals of time between the observations: so that in order to find the projection of a comet's trajectory on the plane of the ecliptic, we have only to draw a straight line which shall cut the several straight lines whose positions are determined by the observed longitudes in such a manner that the intercepted segments shall have given proportions. With three observations only this problem is indeterminate, or admits of innumerable solutions."

When four observations are employed, the problem (generally speaking) is determinate, and is easily solved: but even here again it happens, in the case to which we want it to apply, that it is still as indeterminate as in the former case. This was first noticed by Boscovich, who shewed that, in the actual state of the data, owing to the earth and the comet being both in motion, the problem is as indeterminate when four observations are employed, as we have already remarked it to be for three observations only;- at least so long as the earth and the comet are each supposed to move in right lines; and, since this is so nearly the actual state of the data during the short period of a comet's remaining visible, it is obvious that, if we even avoid

this part of the supposition, the data will approach so near to the indeterminate case of the problem, that the conclusion becomes quite uncertain. We fall on the indeterminate case when we suppose both the earth and the comet to move in straight lines, with uniform velocities; and the very same hypothesis will be found to render evanescent the small co-efficients which enter in the other case:

There are however some solutions of this problem to which the preceding observations must not be applied. Of this kind is the method of M. Boscovich; that of the celebrated Laplace; and those which Legendre has more lately published; all of which have been found useful in practical astronomy. The method of Boscovich owes its utility as an approximation to the circumstance of introducing the velocity in the orbit as a principal condition: for that velocity depending upon the proportion of the distances of the earth and the comet from the sun, limits the other conditions, and places the orbit in its proper situation. The same thing may be said of the methods of Laplace and Legendre: and, in general, we may affirm that no solution of this problem can be free from the imperfections we have pointed out, in which the velocity in the orbit, or some equivalent property, does not enter as a principal condition.

In order to place what has been said in a clearer light, it is to be observed that three complete observations of a celestial body are sufficient for determining the species, the magnitude, and the position of the curve in which it moves round the sun. On this account there is a superfluity of conditions when we suppose the orbit to be a parabola: because, in this case, the velocity in the orbit furnishes an equation without introducing any new unknown quantity. Thus it happens, that in the problem of the comets there is one equation more than there are quantities sought and by combining those equations in different ways, various solutions of the problem may be obtained. But it ought likewise to be observed, that if we set aside the equation derived from the nature of the orbit, the remaining ones, in the actual state of the data will nearly coincide with what would result from the hypothesis of a uniform motion in a straight line: and although, theoretically speaking, we can solve the problem by means of those equations, yet we shall thus infallibly introduce co-efficients that are small and ill defined, and unfit for any practical purpose. It is therefore necessary to include the velocity in the orbit, or some equivalent property, if we wish to obtain a solution useful in practical astronomy; and even when this mode of solution is adopted, it is still necessary to examine with care the quantities introduced by combining the other conditions, in order to exclude the faulty co-efficients we have been speaking of.'

Such is the nature of the problem which Mr. Ivory has proposed to investigate, and which his well known analytical talents so well qualify him to pursue with success: but which it is impossible for us to illustrate within the contracted limits of a review. We can therefore only recommend the memoir

Ee 4

to

to the attention of astronomers; who, if they possess the re quisite proficiency in analytical investigations, will find themselves amply compensated for an attentive perusal of it.

Further Experiments on the Light of the Cassegrainian Telescope, compared with that of the Gregorian. By Captain Henry Kater, Brigade-Major. We have already had occasion to detail the interesting experiments of Captain Kater on this subject in Vol. lxxiv. of M. R. p. 155.; and, as the present may be considered merely as a continuation of the former paper, it will only be necessary to state the results hence deduced. In the author's first memoir, he gave the result of two sets of experiments made on different Gregorian telescopes, as compared with the same Cassegrainian; in the present instance, the comparison has been made with a new Cassegrainian, and the latter of the Gregorians used in his former experiments. The result is that the comparative light of the two telescopes, when reduced to the same aperture and magnifying power, is as 678 to 290; or as 234 to 100 nearly.

In the first of the preceding set of experiments, the proportion was as 235 to Ico, but in the second set as 148 to 100:

The surprising agreement of the first and third experiments with each other, excites an inquiry as to the cause of the difference observable in the second, as equal care and attention were bestowed on all.

The Cassegrainian telescope used on that occasion I have been unable to procure again, but from the inquiries I have since made, there is some reason to believe that, in addition to the polish of the specula having been somewhat impaired, as remarked in my last paper, its convex mirror was too small to receive the whole cone of rays, and to this circumstance principally I am inclined to attribute the deficiency of light in the second experiment when compared with the first and third.

If the mean of all three experiments be taken, the relative quantity of light will be as 20 to 1o; but, if the second experiment be rejected, and the mean of the first and third be considered as correct, the light will be very nearly as 23 to 10 in favour of a telescope of the Cassegrainian form compared with one of the Gregorian

construction.'

The author closes his memoir with an appendix, detailing a number of interesting experiments, connected with the same subject; which were principally designed to ascertain, in a direct manner, whether any rays are lost in crossing each other at the place at which the image is formed. It was on this principle that Captain Kater deemed it probable that the great difference in the light of the two telescopes was to be explained: an hypothesis which these latter experiments tend very much to confirm.

Astronomical

Astronomical Observations relating to the sidereal Part of the Heavens, and its Connection with the nebulous Part; arranged for the Purpose of a critical Examination. By William Herschel, LL.D. F.R.S.-The reader will form an idea of the nature of this paper from the Doctor's introductory page, which serves as a sort of preface to his memoir :

In my paper of observations of the nebulous part of the heavens, I have endeavoured to shew the probability of a very gradual conversion of the nebulous matter into the sidereal appearance. The observations contained in this paper are intended to display the sidereal part of the heavens, and also to shew the intimate connection between the two opposite extremes, one of which is the immensity of the widely diffused and seemingly chaotic nebulous matter; and the other, the highly complicated and most artificially constructed globular clusters of compressed stars.

The proof of an intimate connection between these extremes will greatly support the probability of the conversion of the one into the other; and in order to make this connection gradually visible, I have arranged my observations into a series of collections, such as I suppose will best answer the end of a critical examination.'

Dr. H. then proceeds to the arrangement and classification of his observations, which he divides into twenty different heads, viz. 1. Of Stars in remarkable Situations with regard to Nebula. 2. Of two Stars with Nebulosity between them. 3. Of Stars with Nebulosities of various Shapes attached to them. 4. Of Stars with nebulous Branches. 5. Of nebulous Stars. From the observations reported in the latter articles, Dr. Herschel thinks he has reason to conclude that stars grow; that, in the two former cases, they are receiving fresh accumulation of matter from the contiguous nebulosity; and that, in the latter, having already received their due quantity, they are merely acquiring a higher degree of condensation. 6. Of Stars connected with extensive Windings of Nebulosity. 7. Of small Patches consisting of Stars mixed with Nebulosity. 3. Of Objects of an ambiguous Construction. 9. Of the sidereal Parts of the Heavens. 10. Of the Aggregation of Stars. 11. Of irregular Clusters. 12. Of Clusters variously extended and compressed. From the latter set of observations, the author wishes to draw the conclusion that, after the generation and complete formation of stars, they have then a tendency, from their mutual - attractions, to form themselves into distinct systems. Articles 13, 14, 15, 16, 17, and 18. relate to differently formed clusters, and article 19. to a Recurrence of the ambiguous Limit of Observation.

Dr. Herschel thus concludes this part of his memoir :

The extended views I have taken, in this and my former papers, of the various parts that enter into the construction of the heavens,

have

have prepared the way for a final investigation of the universal arrangement of all these celestial bodies in space; but as I am still engaged in a series of observations for ascertaining a scale whereby the extent of the universe, as far as it is possible for us to penetrate into space, may be fathomed, I shall conclude this paper by pointing out some inferences which the continuation of the action of the clustering power enables us to draw from the observations that have been given."

The Doctor's last article relates to the breaking up of the milky Way; which he considers to be in a state of gradual dissolution. Such conjectures and hypotheses would certainly be rejected as chimerical, were they to proceed from a less celebrated observer than Dr. Herschel.

We hope to attend to Part II. in our next or the following Number.

[To be continued.]

ART. VIII. State of the Prisons in England, Scotland, and Wales, extending to various Places therein assigned, not for the Debtor only, but for Felons also, and other less criminal Offenders. Together with some useful Documents, Observations, and Remarks, adapted to explain and improve the Condition of Prisoners in general. By James Nield, Esq., one of his Majesty's Acting Justices of the Peace for the Counties of Buckingham, Kent, and Middlesex, &c. 4to. pp. 700. 21. 2s. Boards. Printed by Nichols

and Son. 1812.

FEW

EW of our readers are unacquainted with the name of Mr. Nield, who may be called the successor of the philanthropic Howard, in his benevolent attentions to the state of our prisons and the situation of their unfortunate tenants; and the public has learnt with regret that this worthy man has, within a few months, gone to obtain the reward of a well spent life. In recalling to mind his past labours, and lamenting that the world cannot profit by his future efforts, it occurred to us that we had overlooked his last important publication, on the subject so near to his heart *; and though we are sorry for our temporary neglect, we have satisfaction in even thus tardily discharging our duty, by now devoting to it the notice which it amply merits. Yet we greatly fear that many readers will turn over unread the pages which we allot to it, because it treats

We must remark that the knowlege and circulation of this vo lume has been strangely and injudiciously obstructed, by its not being sold through the usual medium of a publisher, and by the usual allowance to booksellers being denied if they have orders to procure it. A more efficacious mode of rendering the publication nugatory could scarcely be contrived. It is keeping the work in prison, and render. ing access to it difficult.

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