ed its maximum, the mercury remains steady. The plate will never attain the heat of the source, as it receives it by one surface, and transmits it by the other. To which must be added the loss, in consequence of some reflexion, from the surface exposed to the light. Some further illustrations of Dr. Herschel's experiments conclude the first part.

4

The second part of this ingenious paper contains our author's theory of heat, which has been before published. It does not, however, differ greatly from the doctrines of the English chemists. He premises some well-known facts, particularly M. Pictet's experiments, to show that cold is equally reflected into a focus by a mirror, and that heat runs through nearly seventy feet in an inconceivable instant. The experiment of concentrating cold is not indeed so extraordinary as it appears; for melting ice abstracts heat rapidly, as is evident from the freezing mixtures, in which different saline bodies are added to ice; for, when the cold is most violent, the ice is in a melting state. We shall add our author's theory in his own words, though in an English dress.-Indeed the whole paper should have been translated.

Fire is a fluid, composed of particles in an agitated state: each molecule of fire, at liberty, is moved with great rapidity in different directions, so that a hot body sends forth calorific rays in every direction; and these molecules are so distant, that two or a greater num ber of currents may cross each other, like those of light, without interrupting their progress. When this constitution of fire is clearly understood, if we suppose two neighbouring spaces in which it abounds, it will appear, that, between them, there will be constant changes. If, in each, the fire is equally copious, the exchanges will be equal, and there will be an equilibrium. If one space contain more fire than another, the exchanges will be unequal: the least hot will receive more numerous particles than it imparts; and, after a time, these repeated changes will restore the equilibrium.'

We shall add only our author's own recapitulation.

To recapitulate-I say, 1. That the effect of a constant source of heat on the thermometer, in a limited time, is not in proportion to the heat of the source: 2. That we have, however, a mean of determining the heat of the source from its effect on the thermometer, because we know the law that this effect follows in its successive increments: 3. That this method is the only one we should employ, when we compare two sources of heat, from their effects in a limited time, 'less than that which is required to produce the maximum: 4. That, when we consider transmitted heat, we must distinguish that which is immediately transmitted from that which the transmitting body adds while warming it: 5. That, when we neglect this distinction, the interception of heat attributed to the lamina is only a limit of smallness, so that it remains uncertain whether the interception have not been much greater, or even total: 6. That, in applying these principles to the experiments of Mr. Herschel, the appreciation becomes more ex

act, but depends still on some accessory and undetermined circumstances: 7. That, in these experiments, the apparent difference between the interception of heat and that of light, by the same bodies, establishes no legitimate conclusion respecting the identity of heat and light: 8. That the law mentioned above (that of Kraft and Richman) is not only proved by direct experiment, but by its agreement with the true theory of heat: 9. That this theory is established on various facts wholly independent of this law, and particularly on the reflexion of cold, and is the only one which agrees with the general phænomena of nature.'

XVII. Of the Rectification of the Conic Sections. By the Rev. John Hellins, B. D. F. R. S. and Vicar of Potter'sPury, in Northamptonshire.'

This is a most ingenious and elaborate article, whose continuation, in the rectification of the ellipse and other sections of the cone, we shall receive with much gratitude. We have nothing of analysis more clear, more accurate, and judicious. The investigations are at the same time acute and profound; the corollaries drawn with precision, and the examples well chosen. We shall transcribe some remarks from the conclusion.

The utility of hyperbolic and elliptic arches, in the solution of various problems, and particularly in the business of computing fluents, has been shown by those eminent mathematicians, M'Laurin, Simpson and Landen; the last of whom hath written a very ingenious paper on hyperbolic and elliptic arches, which was published in the first volume of his Mathematical Memoirs, in the year 1780. I have indeed heard, that some improvement in the rectification of the ellipsis and hyperbola had been produced, and some of the same theorems dis covered, by a learned Italian, many years before Mr. Landen's Mathematical Memoirs were published; but, as Mr. Landen has declared that he had never seen nor heard any thing of that work, and as various instances are to be found of different men discovering the same truth, without any knowledge of each other's works, I see no reason for disbelieving him. But I have seen no writings on this subject which contain any thing more than what is very common, besides those of the three gentlemen above mentioned, and Dr. Waring's "Meditationes Analyticæ;" and, while I have no inclination to detract from their merits, I may be allowed to say that I have borrowed nothing from their works.

With respect to Dr. Waring, (who was well known to be a profound mathematician, and I can testify that he was a good-natured man,) he has given, in page 470 of his "Meditationes Analyticæ," (published in 1776,) these two series, as expressions of the length of an arch of an equilateral hyperbola; viz.

"Arcus hyperbolicus exprimi possit per seriem

1

1
+

2 X 3

1.3.5 7

x19, &c. ubi denotat abscissam ad asymptoton."

25.3.4.5 X 19

6

22.2×7

4

x-11, &c. quæ, quoad coefficientes

But, if pro

attinet, prorsus eandem observat legem ac præcedens." These series, as they now stand, are of little use. per corrections were applied to them, (which may easily be done from what has been shewn in this paper, and in my Mathematical Essays,) and the first of them were transformed into another series converging by the powers of they would become very useful for computing any arch of an equilateral hyperbola, when the abscissa is taken on the asymptote. This I thought it might be proper to remark, that the less experienced readers of this paper might not be misled by so great an authority as that of Dr. Waring. Whether or not he ever corrected these oversights in any of his subsequent publications, I cannot ascertain, for want of books.' P. 474.

XVIII. Catalogue of 500 new Nebulæ, nebulous Stars, planetary Nebulæ, and Clusters of Stars; with Remarks on the Construction of the Heavens. By William Herschel, LL. D. F. R. S.

Astronomers have hitherto been chiefly employed in investigating new celestial objects. It is time to arrange them; but the present is only an introductory attempt. Our author divides the heavenly bodies into twelve classes; viz. the insulated stars; the binary sidereal systems, or double stars; more complicated sidereal systems, or triple, quadruple, &c. stars; clustering stars, or the milky way; groups of stars; clusters of stars; nebulæ; stars with burs, or stellar nebulæ; milky nebulosities; nebulous stars; planetary nebulæ; planetary nebula with centres. Of each we shall give a short account.

Insulated stars are like our sun. Sirius and some others are similar. Other stars have no sensible influence on their motions, and round these alone is there any probability that a system of planetary bodies revolves. The binary systems contain two stars, which probably influence each other; and these may roll round a centre of gravity, as in fact our solar system revolves round a centre at a very little distance from the sun's limb.

That no insulated stars, of nearly an equal size and distance, can appear double to us, may be proved thus. Let Arcturus and Lyra be the stars these, by the rule of insulation, which we must now suppose can only take place when their distance from each other is not less than that of Sirius from us, if very accurately placed, would be seen under an angle of 60 degrees from each other. They really are at about 59°. Now, in order to make these stars appear to us near enough to come under the denomination of a double star of the first

class, we should remove the earth from them at least 41253 times farther than Sirius is from us. But the space-penetrating power of a 7-feet reflector, by which my observations on double stars have been made, cannot intitle us to see stars at such an immense distance; for, even the 40-feet telescope, as has been shewn, can only reach stars of the 1312d magnitude. It follows, therefore, that these stars could not remain visible in a 7-feet reflector, if they were so far removed as to make their angular distance less than about 244 minutes; nor could even the 40-feet telescope, under the same circumstances of removal, shew them, unless they were to be seen at least 24 minutes asunder. Moreover, this calculation is made on a supposition that the stars of which a double star is composed, might be as small as any that can possibly be perceived; but if, on the contrary, they should still appear of a considerable size, it will then be so much the more evident that such stars cannot have any great real distance, and that, consequently, insulated stars cannot appear double, if they are situ ated at equal distances from us. If, however, their arrangement should be such as has been mentioned before, then, one of them being far behind the other, an apparent double star may certainly be produced; but here the appearance of proximity would be deceptive; and the object so circumstanced could not be classed in the list of binary systems. However, as we must grant, that in particular situations stars apparently double may be composed of such as are insulated, it cannot be improper to consult calculation, in order to see whether it be likely that the 700 double stars I have given in two catalogues, as well as many more I have since collected, should be of that kind. Such an inquiry, though not very material to our present purpose, will hereafter be of use to us, when we come to consider more complicated systems. For, if it can be shown that the odds are very much gainst the casual production of double stars, the same argument will be still more forcible, when applied to treble, quadruple, or multiple compositions.' P. 482.

It appears, from the calculation which follows, that the probability is very considerably in favour of this combination of aquarii, which is taken for the instance. Some of these double stars have changed their situation with regard to each other, which shows a revolution round each other; and our knowledge of these systems may be increased, as their orbit subtends a visible angle. What we have said will sufficiently illustrate the more complicated sidereal systems; and, to pursue these further, will require the tables, which our author has added, to give a clearer idea of their mutual influence.

The fourth class contains very numerous stars. Between B andy Cygni, for instance, where there is a kind of division in the clusters, the stars, within the space of 5°, amount to 331,000. If we admit that they cluster in two directions, there will be 165,000 in each mass. These clusters are brighter about the middle than on their undefined borders, which may arise from a greater depth of mass, and more numerous stars in the

centre.

'A group of stars' is a collection of closely and almost equally compressed stars, without giving any clue to an imaginary centre. 'Clusters' are very beautiful collections of stars, with a suddenly-increased brightness about the middle. The stars are sufficiently compressed in the centre to afford almost the appearance of a nucleus. The whole that relates to nebula is too curious to be passed over.

• Of Nebulæ.

These curious objects, which, on account of their great distance, can only be seen by instruments of great space-penetrating power, are perhaps all to be resolved into the three last mentioned species. Clustering collections of stars, for instance, may easily be supposed sufficiently removed to present us with the appearance of a nebula of any shape, which, like the real object of which it is the miniature, will seem to be gradually brighter in the middle. Groups of stars also may, by distance, assume the semblance of nebulous patches; and real clusters of stars, for the same reason, when their composition is beyond the reach of our most powerful instruments to resolve them, will appear like round nebulæ that are gradually much brighter in the middle. On this occasion I must remark, that with instruments of high space-penetrating powers, such as my 40-feet telescope, nebula are the objects that may be perceived at the greatest distance. Clustering collections of stars, much less than those we have mentioned before, may easily contain 50000) of them; and, as that number has been chosen for an instance of calculating the distance at which one of the most remote objects might be still visible, I shall take notice of an evident consequence attending the result of the computation; which is, that a telescope with a power of penetrating into space, like my 40-feet one, has also, as it may be called, a power of penetrating into time past. To explain this, we must consider that, from the known velocity of light, it may he proved, that when we look at Sirins, the rays which enter the eye cannot have been less than 6 years and 4 months coming from that star to the observer. Hence it follows, that when we see an object of the calculated distance at which one of these very remote nebula may still be perceived, the rays of light which convey its image to the eye, must have been more than nineteen hundred and ten thousand, that is, almost two millions of years on their way; and that, consequently, so many years ago, this object must already have had an existence in the sidereal heavens, in order to send out those rays by which we now perceive it.' F. 497.

Of the eighth class, Mr. Herschel gives no satisfactory account. Milky nebulosity' sometimes arises from the very great distance of clustering stars; but the cause of this appearance is, in a few instances, nearer us, as we can notice its changes, particularly in the milky nebulosity of Orion. The source of this light, which Huygens considered as a peep into heaven, our author does not attempt to explain. Of the source of the nebulæ, in the next class, Mr. Herschel appears equally uncertain; but he seems assured that they are really fixed stars.