"The immense distance of the fixed stars from our earth, and from each other, is of all considera- tions the most proper for raising our ideas of the works of God. Modern discoveries make it pro-^ bable that each of these stars is a sun, having planets and cbmdts revolving round it, as our sun has the earth and other planets revolving round him. — A ray of light, though its motion is so quick as to be commonly thought instantaneous, takes up more time in travelling from the stars to us, than we do in making a West-India voyage. A sound, which, next to light, is considered as the quickest body we are acquainted with, would not arrive to us from thence in 60,000 years. And a cannon-ball, flying at the rate of 480 miles an hour, woidd not reach us in 700,000 years.
" From what we know of our own system, it may be reasonably concluded, that all the rest are with equal wisdom contrived, situated, and provided with accommodations for rational inhabitants.
" What a sublime idea does this suggest to the human imagination, limited as are its powers, of the works of the Creator! Thousands and thou- 378 or ASTRONOMY. [USSAY sands of suns^ multiplied without end, and ranged all around us, at immense distances from each other, attended by ten thousand times ten thousand worlds, all in rapid motion, yet calm, regular and harmonious, invariably keeping the paths prescrib- ed them: and these worlds peopled with myriads of intelligent beings, formed for endless progres- sion in perfection and felicity! ** The thought that would immediately occur to a dispassionate man in listening to this statement, would be. What a vast deal am I here called on to believe!
Now the first rule of sound and sober judgment, in encountering any story, is that, in proportion to the magnitude and seemingly incredible nature of the propositions tendered to our belief, should b^ the strength and impregnable nature of the evidence by which those propositions are supported.
It is not here, as in matters of religion, that we are called upon by authority from on high to be- lieve in mysteries, in things above our reason, or, as it may be, contrary to our reason. No man pre- tends to a revelation from heaven of the truths of astronomy. They have been brought to light by the faculties of the human mind, exercised upon such facts and circumstances as our industry has set before us.
To persons not initiated in the rudiments of as- tronomical science, they rest upon the great and high-sounding names of Galileo, Kepler, Halley XXI.] OF ASTRONOMY. 879 and Newton. But, though these men are eminently entitled to honour and gratitude from their fellow-* mortals, they do not stand altogether on the same footing as Matthew, Mark, Luke and John, by whose pens has been recorded "every word that proceedeth out of the mouth of God.** The modest enquirer therefore, without pretend- ing to put himself on an equality with these illus- trious men, may be forgiven, when he permits him- self to suggest a few doubts, and presumes to exa* mine the grounds upon which he is called upon to believe all that is contained in the above passages.
Now the foundations upon which astronomy, as here delivered, is built, are, first, the evidence of our senses, secondly, the calculations of the mathe- matician, and, in the third place, moral considers* tions. These have been denominated respectively^ practical astronomy, scientific, and theoretical.
As to the first of these, it is impossible for us on this occasion not to recollect what has so often oc- curred as to have grown into an every-day observa- tion, of the fallibility of our senses.
It may be doubted however whether this is a just statement. We are not deceived by our senses, but deceived in the inference we make from our sensa- tions. Our sensations respecting what we call the external world, are chiefly those of length, breadtli and solidity, hardness and softness, heat and cold, colour, smell, sound and taste. The inference which the generality of mankind make in relation to these 380 OF ASTRONOMY. [ESSAY sensations is, that there is something out of our- selves corresponding to the impressions we receive; in other words, that the causes of our sensations are like to the sensations themselves. But this is, strictly speaking, an inference; and, if the cause of a sensation is not like the sensation, it cannot pre- cisely be affirmed that our senses deceive us. We know what passes in the theatre of the mind; but we cannot be said absolutely to know any thing more.
Modern philosophy has taught us, in certain cases, to controvert the position, that the causes of our sensations are like to the sensations themselves. Locke in particular has called the attention of the reasoning part of mankind to the consideration, that heat and cold^i sweet and bitter^ and odour offensive or otherwise, are perceptions, which im- ply a percipient being, and cannot exist in inani- mate substaik;es. We might with equal propriety ascribe pain to the whip that beats us, or pleasure to the slight alternation of contact in the person or thing that tickles us, as suppose that heat and cold, or taste, or smell are any thing but sensations.
The same philosophers who have called our attention to these remarks, have proceeded to shew that the causes of our sensations of sound and eolour have no precise correspondence, do not tally with the sensations,we receive* Sound is the jresult of a percussion of the air. Colour is pro- ^luced by the reflection of the rays of light; so that XXI.} M" ASTRONOMY. 381 the same object^ placed in a position^ different as to the spectator, but in itself remaining unaltered^ will produce in him a sensation of different colours^ or shades of colour, now blue, now green,: now brown, now black, and so on. This is the doctrine of Newton, as well as of Locke.
It follows that, if there were no percipient being to receive these sensations^ there would be no heat or cold, no taste, no smell, no sound, and no colour* Aware of this difference between our sensations in certain cases and the causes of these sensations, Locke has divided the qualities of substances in the material universe into primary and secondary, the sensations^^ we receive of the primary representing the actual qualities of material substances, but the sensations we receive of what h^ calls the secondary having no proper resemblance to the causes that produce them.
Now, if we proceed in the spirit of severe ana^ lysis to examine the primary qualities of matter, we shall not perhaps find so marked a distinction between those and the secondary, as the statement of Locke would have led us to imagine.
The Optics of Newton were published fourteen years later than Locke's Essay concerning Human Understanding.
In endeavouring to account for the uninterrupted transmission of rays of light through transparent substances, however hard they may be found to be, Newton has these observations.
^^ Bodies are much more rare and porous^ than is commonly believed. Water is nineteen times lighter, and by consequence nineteen times rarer, than gold; and gold is so rare, as very readily, and without the least opposition, to transmit the mag- netic effluvia, and easily to admit quicksilver into its pores, and to let water pass through it. From all which we may conclude, that gold has more pores than solid parts, and by consequence that water has above forty times more pores than parts. And he that shall find out an hypothesis, by which water may be so rare, and yet not capable of com- pression by force, may doubtless, by the same hy- pothesis, make gold, and water, and all other bodies, as much rarer as he pleases, so that light may find a ready passage thrpugh transparent substances^."
Again: '* The colours of bodies arise from the magnitude of the particles that reflect them. Now, if we conceive these particles of bodies to be so disposed among themselves, that the intervals, or empty spaces between them, may be equal in mag- nitude to them all; and that these particles may be composed of other particles much smaller, which have as much empty space between them as equals all the magnitudes of these smaller particles; and that in like manner these smaller particles are again composed of others much smaller, all which toge- ther are equal to all the pores, or empty spaces, between them; and so on perpetually till you come •' Newton, Opties, Book 11, Part III, Prop. viii.
XXI.] OF ASTRONOMY^ 883 to solid particles^ such as have no pores^ or empty spaces within them: and if in any gross body there be, for instance, three such degrees of particles, the least of which are solid; this body will have seven times more pores than solid parts. But if there be four such degrees of particles, the least of which are solid, the body will have fifteen times more pores than solid parts. If there be five degrees, the body will have one and thirty times more pores than solid parts. If six degrees, the body will have sixty and three times more pores than solid parts. And so on perpetually *^.'* In the Queries annexed to the Optics^ Newton further suggests an opinion, that the rays of light are repelled by bodies without immediate contact. He observes that: " Where attraction ceases, there a repulsive vir-* tue ought to succeed. And that there is such a virtue, seems to follow from the reflexions and in-^ flexions of the rays of light. For the rays are repelled by bodies, in both these cases, without the immediate contact of the reflecting or inflecting body. It seems also to follow from the emission of light; the ray, so soon as it is shaken off from a shining body by the vibrating motion of the parts of the body, and gets beyond the reach of attract tion, being driven away with exceeding great velo*^ city. For that force, which is sufficient to turn it back in reflexion, may be sufficient to emit it It ^ Ibid.
384 OF ASTRONOMY* [ESSAY seems also to follow from the production of air and vapour: the particles, when they are shaken off from bodies by heat or fermentation, so soon. as they are beyond the reach of the attraction of the body, receding from it and also from one another^ with great strength; and keeping at a distance, so as sometimes to take up a million of times more space than they did before, in the form of a dense body."
Newton was of opinion that matter was made up, in the last resort, of exceedingly small solid par- ticles, having no pores, or empty spaces within them. Priestley, in his Disquisitions relating to Matter and Spirit, carries the theory one step far- ther: and, as Newton surrounds his exceedingly small particles with spheres of attraction and repul- sion, precluding in all cases their actual contact, Priestley is disposed to regard the centre of these spheres as mathematical points only.: If there is no actual contact, then by the very terms no two par- ticles of matter were ever so near to each other, but that they might be brought nearer, if a suffi- cient force could be applied for that purpose.. You had only another sphere of repulsion to conquer; and, as there never is actual contact, the whole world is made up of one sphere of repulsion after another, without the possibility of ever arriving at an end.
" The principles of the Newtonian philosophy,** says our author, " were no sooner known, than it XXI.] OF AStRONOMr. 886 was seen how feW in comparison, of the plienomena of nature^ were owing to solid matter, and how much to powers, which were only supposed to ac- company and surround the solid parts of matter. It has been asserted, and the assertion has never been disproved, that for any thing we know to the contrary, all the solid matter in the solar system might be contained within a nutshell^."
It is then with senses, from the impressions upon which we are impelled to draw such false conclu^ sions, and that present us with images altogether unlike any thing that exists out of ourselves, that we come to observe the phenomena of what we caU the universe. The first observation that it is here incumbent on us to make, and which we ought to keep ever at hand, to be applied as occasion may offer, is the well known aphorism of Socrates, that " we know only this, that we know nothing.'* We have no compass to guide us through the pathless waters of science; we have no revelation, at least on the subject of astronomy, and of the unnum-- bered inhabitable worlds that float in the ocean of ether; and we are bound therefore to sail, as the mmriners of ancient times sailed, always within sight of land. One of the earliest maxims of ordi^- d Priestley, Disquisitions, Section IL I know not by whom this illustration was first employed* Among other authors, I find, ia Fielding (Joseph Andrews, Book II, Chap. II), a sect of philoso- phers spoken of, who ''can reduce all the matter of the world into a nutshell."
2 c 366 OF ASTRONOMY. [ESSAY nary prudence, is that we ought ever to correct the reports of one sense by the assistance of another sense. The things we here speak of are not matters of faith; and in them therefore it is but reason, that we should imitate the conduct of Didymus the apo- stle, who said, ^^ Except I put my fingers into the prints of the nails, and thrust my hand into his side, I will not believe." My eyes report to me an ob- ject, as having a certain magnitude, texture, and roughness or smoothness; but I require that my hands should confirm to me the evidence of my eyes. I see'something that appears to be an island at an uncertain distance from the shore; but, if I am actuated by a laudable curiosity, and wish to possess a real knowledge, I take a boat, and pro- ceed to ascertain by nearer inspection, whether that which I imagined to be an island is an island or no.
There are indeed many objects with which we are conversant, that are in so various ways similar to each other, that, after having carefully examined a few, we are satisfied upon slighter investigatimi to admit the dimensions and character of others. Thus, having measured with a quadrant the height of a tower, and found on the narrowest search and comparison that the report of my instrument was right, I yield credit to this process in another in- stance, without being at the trouble to verify its results in any more elaborate method.
The reason why we admit the inference flowing from our examination in the second instance, and XXI.] OF ASTRONOMY. 387 SO onward^ with less scrupulosity and scepticism thau in the firsts is that there is a strict resemhlance and analogy in the two cases. Experience is the basis of our conclusions and our conduct. I strike against a given object^ a nail for example^ with a certain degree of force, because I have remarked in myself and others the effect of such a stroke. I take food and masticate it, because I have found that this process contributes to the sound condition of my body and mind. I scatter certain seeds in my field, and discharge the other functions of an agricultu- rist, because I have observed that in due time the result of this industry is a crop. All the propriety of these proceedings depends upon the exact ana- logy between the old case and the new one. The state of the affair is still the same, when my busi-* ness is merely that of an observer and a travell^. I know water from earth, land from sea, and moun- tains from vallies, because I have had experience of these objects, and confidently infer that, when cer- Uiin appearances present themselves to my organs of sight, I shall find the same results to all my other senses, as I found when such appearances occurred to me before.
But the interval that divides the objects which occur upon and under the earth, and are accessible in all ways to our examination, on the one hand, and the lights which are suspended over our heads in the heavens on the other, is of the broadest and most memorable nature. Human beings, in the 2 c 2 388 OF ASTRONOMY. [ESSAY infancy of the world, were contented reverently to behold these in their calmness and beauty, perhaps to worship them, and to remark the effects that they produced, or seemed to produce, upon man and the subjects of his industry. But they did not aspire to measure their dimensions, to enquire into their internal frame, or to explain the uses, far re- moved from our sphere of existence, which they might be intended to serve.
It is however one of the effects of the improve-* ment of our intellect, to enlarge our curiosity. The daringness of human enterprise is one of the prime glories of our nature. It is our boast that we un- dertake to ^^ measure earth, weigh air, and state the tides.*' And, when success crowns the boldness of our aspirations after what vulgar and timorous prudence had pronounced impossible, it is then chiefly that we are seen to participate of an essence divine.
What has not man effected by the boldness of his conceptions and the adventurousness of his spirit? The achievements of human genius have appeared so incredible, till they were thoroughly examined, and slowly established their right to general acceptance, that the great heroes of intel- lect were universally regarded by their contempo- raries as dealers in magic, and implements of the devil. The inventor of the art of printing, that glo- rious instrument for advancing the march of human improvement, and the discoverer of the more ques- XXI.] OF ASTRONOMY. 389 tionable art of making gunpowder^ alike suffered under this imputation. We have rendered the seas and the winds instruments of our pleasure^ ^^ex- hausted the old worlds and then discovered a new one," have drawn down lightning from heaven, and exhibited equal rights and independence to man- kind. Still however it is incumbent on us to be no less wary and suspicious than we are bold, and not to imagine, because we have done much, that we are therefore able to effect every thing.
As was stated in the commencement of this Essay, we know our own sensations, and we know little more. Matter, whether in its primary or se- condary qualities, is certainly not the sort of thing the vulgar imagine it to be. The illustrious Berke- ley has taught many to doubt of its existence alto- gether; and later theorists have gone farther than this, and endeavoured to shew, that each man, him- self while he speaks on the subject, and you and I while we hear, have no conclusive evidence to con- vince us, that we may not, each of us, for aught we know, be the only thing that exists, an entire uni- verse to ourselves.
We will not however follow these ingenious per- sons to the startling extreme to which their specu- lations would lead us. But, without doing so, it will not misbecome us to be cautious, and to reflect what we do, before we take a leap into illimitable space.
390 OF ASTRONOMY. [esSAY SECTION II.
" The sun,*' we are told, ^* is a solid body, ninety- five millions of miles distant from the earth we in- habit, one million times larger in cabic measure- ment, and to such a degree impregnated with heat, that a comet, approaching to it within a certain distance, was by that approximation raised to a heat two thousand times greater than that of red- hot iron."
It will be acknowledged, that there is in this statement much to believe; and we shall not be exposed to reasonable blame, if we refuse to sub- scribe to it, till we have received irresistible evidence of its truth- It has already been observed, that, for the greater part of what we imagine We know on the surface or in the bowels of the earth, we have, or may have if we please, the evidence of more than one of our senses, combining to lead to the same conclusion. For the propositions of astronomy we have no sen- sible evidence, but that of sight, and an imperfect analogy, leading from those visible impressions which we can verify, to a reliance upon those which we cannot.
The first cardinal particular we meet with in the above statement concerning the sun, is the term, distance. Now, all that, strictly speaking, we can affirm respecting the sun and other heavenly bodies, is that we have the same series of impressions re- XXI.] OF ASTRONOMY. 59!
specting them, that we have respecting terrestrial objects near or remote, and that there is an imper- fect analogy between the one case and the other.
Before we affirm any thing, as of our own know-- ledge and competence, respecting heavenly bodies which are said to be millions of millions of miles removed from us, it would not perhaps be amiss that we should possess ourselves of a certain degree of incontestible information, as to the things which exist on the earth we inhabit. Among these^ one of the subjects attended with a great degree of doubt and obscurity, is the height of the mountains with which the surface of the globe we inhabit is diversified. It is affirmed in the received books of elementary geography, that the Andes are the highest mountains in the world. Morse, in his American Gazetteer^ third edition, printed at Bos- ton in 1810% says, ^'The height of Chimborazzo^ the most elevated point of the vast chain of the Andes, is 20^280 feet above the level of the sea, which is 7102 feet higher than any other mountain in the known world:" thus making the elevation of the mountains of Thibet, or whatever other rising ground the compiler had in his thought, precisely 13,178 feet above the level of the sea, and no more. This decision however has lately been contradicted. Mr. Hugh Murray, in an Account of Discoveries and Travels in Asia, published in 1820, has collated * Article, Andes.
/ 392 OF ASTRONOMY. [BSSAY the reports of various recent travellers in central Asia; and he states the height of Chumularee, which he speaks of as the most elevated point of the mountains of Thibet, as nearly 30,000 feet above the level of the sea.
The elevation of mountains, till lately, was in no way attempted to be ascertained but by the use of the quadrant; and their height was so generally exaggerated, that Riccioli, one of the most eminent astronomers of the seventeeinth century, gives it as his opinion that mountains, like the Caucasus, may have a perpendicular elevation of fifty Italian miles ^. Later observers have updertaken to correct the iur accuracy of these results through the application of the barometer, and thus, by informing themselves of the weight of the air at a certain elevation, pro- ceeding to infer the height of the situation.
There are many circumstances, which are calcu- lated to induce a circumspect enquirer to regard the affirmative positions of astronomy, as they are delivered by the most approved modem writers, with considerable diffidence.
They are founded, as has already been said, next to the evidence of our senses, upon the deductions of mathematical knowledge.
Mathematics are either pure or mixed.
Pure mathematics are concerned only with abs- tract propositions, and have nothing to do with ' Rees, Encyclopedia 3 article. Mountains.
XX].] OF ASTRONOMY. 393*.
the realities of nature. There is no such thing in actual existence as a mathematical point> line or surface. There is no such thing as a circle or square. But that is of no consequence. We can. define them in words^ and reason about them. We can draw a diagram^ and suppose that line to be straight which is not r^lly straight, and that figure, to be a circle which is not strictly a circle. It is conceived therefore by the generality of observers^ that mathematics is the science of certainty.
But this is not strictly the case. Mathematics are like those abstract and imaginary existences about which they are conversant. They may con-, stitute in themselves, and in the apprehension of an infallible being, a science of certainty. But they come to us mixed and incorporated with our imper^- fections. Our faculties are limited; and we may be easily deceived, as to what it is that we see with transparent and unerring clearness, and what it is that comes to us through a crooked medium, re- fracting and distorting the rays of primitive truth*. We often seem clear, when in reality the twilight of undistinguishing night has crept fast and far^ upon us. In a train of deductions, as in the steps of an arithmetical process, an error may luive insi- nuated itself imperceptibly at a very early stage^. rendering all the subsequent steps a wandering farther and farther from the unadulterated truth. Human mathematics, so to speak, like the length of life, are subject to the doctrinie of chances. Ma* 394 OF ASTRONOMY. [ESSAY themadcs may be the science of certainty to celes- tial natures, but not to man.
But, if in the case of pure mathematics, we are expfosed to the chances of error and delusion, it is much worse with mixed mathematics. The moment we step out of the high region of abstraction, and apply ourselves to what we call external nature, we have forfeited that sacred character and immunity, which we seemed entitled to boast, so long as we remained inclosed in the sanctuary of unmingled truth. As has already been said, we know what passes in the theatre of the mind; but we cannot be said absolutely to know any thing more. In our speculations upon actual existences we are not only subject to the disadvantages which arise from the limited nature of our faculties, and the errors which may insensibly creep upon us in the process. We are further exposed to the operation of the uneven- nesses and irregularities that perpetually occur in external nature, the imperfection of our senses, and of the instruments we construct to assist our obser- vations, and the discrepancy which we frequently detect between the actual nature of the things about us and our impressions respecting them.
This is obvious, whenever We undertake to ^pply the processes of arithmetic to the realities of life. Arithmetic, unsubjected to the impulses of passion and the accidents of created nature, hol^s on its course; but, in the phenomena of the actual world, *^time and chance happeneth to them all."
XXI.] OF ASTRONOMY. 395 Thus it is, for example, in the arithmetical and geometrical ratios, set up in political economy by the celebrated Mr. Malthus. His numbers will go on smoothly enough, 1, 2, 4, 8, 16, 32, as repre- senting the principle of population among man- kind, and 1, 2, 3, 4, 5, 6, the means of subsistence; but restiff and uncomplying nature refuses to con* form herself to his dicta.
Dr. Price has calculated the produce of one penny, put out at the commencement of the Chris- tian era to five per (?e/i/.^ compound interest, and finds that in the year 1791 it would have increased to a greater sum than would be contained in three hundred millions of earths, all solid gold. But what has this to do with the world in which we live? Did ever any one put out his penny to interest in this fashion for eighteen hundred years? And, if he did, where was the gold to be found, to satisfy his de- mand?
Morse, in his American Gazetteer, proceeding on the principles of Malthus, tells us that, if the city of New York goes on increasing for a centuiy in a certain ratio, it will by that time contain 5,257,493 inhabitants* But does any one, for him- self or his posterity, expect to see this realised?
Blackstone, in his Commentaries on the Laws of England, has observed that, as every man has two ancestors in the first ascending degree, and four in the second, so in the twentieth degree he has more than a million, and in the fortieth the square of 396 OF ASTRONOMY. [ESSAY that number, or upwards of a million millions. This statement therefore would have a greater tendency to prove that mankind in remote ages were nume- rous, almost beyond the power of figures to repre- sent, than the opposite doctrine of Malthus, that they have a perpetual tendency to such increase as would infallibly bring down the most tremendous calamities on our posterity.
Berkeley, whom I have already referred to on another subject, and who is admitted to be one of our profoundest philosophers, has written a trea- tise s to prove, that the mathematicians, who object to the mysteries supposed to exist in revealed reli- gion, ^^ admit much greater mysteries, and even falshoods in science, of which he alleges the doc- trine of fluxions as an eminent example ^•'' He observes, that their conclusions are established by virtue of a twofold error, and that these errors, being in contrary directions, are supposed to com- pensate each other, the expounders of the doctrine thus arriving at what they call truth, without being able to shew how, or by what means they have arrived at it.
It is a memorable and a curious speculation to reflect, upon how slight grounds the doctrine of '^ thousands and thousands of suns, multiplied without end, and ranged all around us, at immense distances from each other, and attended by ten: thousand times ten thousand worlds," mentioned ? The Analyst. '' Life of Berkeley, prefixed to his Works.
XXI.] OF ASTRONOMY. 397 in the beginning of this Essay, is built. It may be all true. But, true or false, it cannot be without its use to us, carefully to survey the road upon which we are advancing, the pier which human enterprise has dared to throw out into the vast ocean of Cim- merian darkness. We have constructed a pyramid, which throws into unspeakable contempt the ves^ tiges of ancient Egyptian industry: but it stands upon its apex; it trembles with every breeze; and momentarily threatens to overwhelm in its ruins the fearless undertakers that have set it up.
It gives us a mighty and sublime idea of the na- ture of man, to think with what composure and confidence a succession of persons of the greatest genius have launched themselves in illimitable space, with what invincible industry they have pro- ceeded, wasting the midnight oil, racking their fa- culties, and almost wearing their organs to dust, in measuring the distance of Sirius and the other fixed stars, the velocity of light, and ^^ the myriads of in- telligent beings formed for endless progression in perfection and felicity,'' that people the numberless worlds of which they discourse. The illustrious names of Copernicus, Galileo, Gassendi, Kepler, Halley and Newton impress us with awe; and, if the astronomy they have opened before us is a romance, it is at least a romance more seriously and perseveringly handled than any other in the annals of literature.
A vulgar and a plain man would unavoidably ask 398 OF ASTRONOMY. [esSAY the astronomers, How came you so familiarly ac- quainted with the magnitude and qualities of the heavenly bodies, a great portion of which, by your own account, are millions of million^ of miles re- moved from us? But, I believe, it is not the fa- shion of the present day to start so rude a question. I have just turned over an article on Astronomy in the Encyclopaedia Londinensis, consisting of one hundred and thirty-three very closely printed quarto pages^ and in no comer of this article is any evidence so much as hinted at. Avroc 6(|»}|. Is it not enough? Newton and his compeers have said it.
The whole doctrine of astronomy rests upon tri- gonometry, a branch of the science of matliematics which teaches us, having two sides and one angle, or two angles and one side, of a triangle given us^ to construct the whole. To. apply this principle therefore to the heavenly bodies, it is necessary for us to take two stations, the more remote from each other the better, from which our observations should be made. For the sake of illustration we will sup- pose them to be taken at the extremes of the earth's diameter, in other wbrds, nearly eight thousand miles apart from each other, the thing itself having never been realised to that extent. From each of these stations we will imagine a line to be drawn, terminating in the sun. Now it seems easy, by means of a quadrant, to find the arch of a circle (in other words, the angle) included between these lines XXlO OF ASTRONOMY. 399 terminating in the sun^ and the base formed by a right line drawn from one of these stations to the other, which in this case is the length of the earth*» diameter. I have therefore now the three particulars required to enable me to construct my triangle. And, according to the most approved astronomical « observations hitherto made, I have an isosceles tri* angle, eight thousand miles broad at its base, and ninety-five millions of miles in the length of each of the sides reaching from the base to the apex.
It is however obvious to the most indifferent ob* server, that the more any triangle, or other mathe-* matical diagram, falls within the limits which our senses can conveniently embrace, the more securely, when our business is practical, and our purpose to apply the result to external objects, can we rely on the accuracy of our results. In a case therefore like the present, where the base of our isosceles triangle is to the other two sides as eight units to twelve thousand, it is impossible not to perceive that it behoves us to be singularly diffident as to the conclusion at which we have arrived, or rather it behoves us to take for granted that we are not unlikely to fall into the most important error. We have satisfied ourselves that the sides of the triangle including the apex, do not form an angle, till they have arrived at the extent of ninety-five millions of miles. How are we sure that they do then? May not lines which have reached to so amazing a length without meeting, be in reality parallel lines? If an 400 OF ASTRONOMY. [fiSfiAT angle is never formed^ there can be no result. The whole question seems to be incommensurate to our faculties.
It being obvious that this was a very unsatisfac- tory scheme for arriving at the knowledge desired, the celebrated Halley suggested another method, in the year 1 7 1 6, by an observation to be taken at the time of the transit of Venus over the sun K