the genus, is that by observing such stars as are occulted by the moon; for, notwithstanding the bore of computation, the difficulty of identifying a small star, and other irregularities, it affords one of the readiest and easiest methods of finding a longitude; and, when taken at a fixed station, with rigid accuracy, affords also facilities for investigating the figure of the earth, and correcting the lunar tables. An occultation, indeed, may be denominated the perfection of a lunar distance, because it is released by nature from all instrumental errors. But there are various clogs upon this admirable process, which bear hard upon ultimate precision; such as the state of the tables, which, though assumed to be correct in declination, contain errors in latitude often greater than those in longitude. There is also a small uncertainty about parallax, to the amount, perhaps, of 2" or 3"; and after all the diameters, semi-diameters, and augmented ditto, it is difficult to find a real centre for the moon; for nobody has hitherto positively determined on her apparent diameter. But to those who prefer accuracy to facility, and endeavour by corresponding observations to fix positions, we recommend the formation of an equation, involving corrections of all the quantities that can be supposed liable to error, viz. :—

The assumed longitude of the place.

The star's AR. and declination.

The moon's AR., N.P.D., parallax, and semidiameter. If this is done at the two places where the occultation is observed, the comparison of the two equations will give a relation between the error in the assumed longitude, and the other errors. As there have been complaints that this problem has been neglected by navigators, because there are difficulties in obtaining the limits in latitude of the predicted phenomena, we will give an easy method of knowing them. Enter the traverse table with the moon's equatorial parallax as a distance, and the difference in declination of the moon's and star's limbs as a departure; the corresponding course is an angle, which, applied to the declination of the star, gives the limit in latitude at the conjunction in AR.; and cos. lat. at conj. x cos. inclin. orb.=sin. lat., or greatest latitude of the same name with the declination of the star. For the opposite latitude, add the inclination of the orbit to the quantity found from the traverse table. For accurate work, the latitude thus found should be employed for correcting the equatorial parallax and angle of the vertical, and the calculation repeated with logarithms to five places. And we recommend computers of minor calibre to use the geocentric tables, on account of their excellence, and also because they never can mistake the sines of their quantities.

Of all the foregoing, the most popular problem in theory is that of determining the difference of meridians by the mean right ascension of the moon; but if Maskelyne had considered it worth attention, he would certainly have noticed it when he was racking his brains to discover the best practical solution of the question, as to the relative position of the moon and a celestial object at a given instant. In proportion to the moon's angular velocity is her value in terrestrial longitudes, hence it becomes necessary so to manage her agency, that the apparent velocity shall be the greatest possible. Therefore, if an arc between that luminary and a fixed star could be measured in the plane of her apparent orbit, the maximum accuracy from her agency could be

obtained. But we must take the firmament as we find it, and compare the velocity with the stars in the zodiac nearest the orbit, of sufficient lustre for observation. In making this comparison we are beset with difficulties, and with many probable errors,-as from the angular instrument, the figure of the earth, parallax and refraction, and incidental defects of reading and observation. We have to reduce these to a minimum; and one of the ways for the accomplishment of this object is, to select a triangle that may enable us to evade some, and diminish others. Now, cæteris paribus, small errors in altitude are less in the distance, in proportion as that distance is less than 90°.

β

a

The angle at the zenith (Z) is constant. varies as a and ß. Differentiating (♪ = the distance.) ▲ sin d=▲ a (cos Z, cos a, sin ß-sin a cos B) + AB (cos ß, cos Z, sin a-sin ß, cos a) ...d varies as its sine, and ... Ad, the error becomes less as the distance diminishes. 6 and are charged with parallax and refraction, which, in common with d, are measured by the instrument; but the latter is involved in the numerical computation, and therefore lessens the influence of A and ▲ 6. It is also obvious that Ad is least, and A, Aß greatest, when d is small, and « and ß great.

A

δ

B

a

This is not always the case in the proposals for adopting this method, but when the objects are in the prime vertical ▲▲a+Aẞ nearly. Therefore in latitudes North or South, beyond the tropics, when the moon's declination is of the same name with the latitude, the problem may be employed, if the earth's radius at the place of observation is taken into account, and the objects are 15° above the horizon, on or near the prime vertical. But even here the method will be far below that by the distance, for the latitude must be rigorously known, for the AR as well as the time; the ratio of the moon's orbital motion, with the diurnal motion of the earth on its axis, is involved, instead of the direct measure of the moon from a fixed celestial object; and it is defective, moreover, because beyond the tropics more than half a lunation is lost. We admit that near the equator it may sometimes be employed with advantage, supposing the objects are on the same side of the meridian, and the lower at least 15° above the horizon; because the difference of the errors can only influence the AR of the moon ; or if one is East and the other West, the AR will be charged with the

sum.

It will be seen that, for steady sea-practice, we prefer the lunars and chronometers to every other mode of finding the longitude; but we earnestly recommend the occultations of stars, and eclipses of Jupiter's satellites, to zealous navigators. When, however, observations can be made on shore, the simplest and most correct mode of coming "to the point" is unquestionably by means of the moon-culminating stars, a process which,-notwithstanding that the uncertainty of irradiation *, and the difficulty in taking the difference in AR between the bright limb of the moon and very small stars, will necessarily limit the degree

*Although, in imitation of our mathematical betters, we use such arguments, we dislike and suspect all arbitrary corrections depending on what are called "inflexion," radiation," ," "irradiation," &c. Such admissions rather palliate than destroy errors; and we would sooner include them all "in a lump," as an addition to the final result, under the form "possible correction due to our actual ignorance of data."

1833.]

NAUTICAL ASTRONOMY.

of extreme accuracy,-may be fearlessly pronounced the best approximation to longitude hitherto promulgated.

. These remarks lead us to press the necessity of navigators making more observations on shore than they have hitherto done, so that we may no longer want good geographical positions of places where our ships have often been moored for months together; insomuch that we know an instance of an officer, not an indifferent observer at sea, who, being sent to examine a harbour, reported "Latitude not observed on account of the intervention of the land!" Now our own experience led us to reject, from a table of points, every observation which was not made on shore; and we hear that Captain Beaufort, whose talent is too well known for us to particularize, once attempted to fix the latitude of a small island in the Archipelago by meridian altitudes of the sun, taken on board, under every favourable circumstance, on different bearings; but the several results differed from that established on shore. We must, however, admit, that there are occasions in which it may be necessary to determine the position of places from a ship, when time or circumstance prevent landing; in these cases, the observations ought to be made with an East or West bearing for latitude, and a North or South one for longitude, to avoid the very erroneous method, now in use, of guessing the distance on a diagonal rhomb. Yet such necessity can happen seldom; "where there's a will, there's a way," saith the proverb. And we have never frequented a shore that did not afford an insulated rock, or a come-at-able point, where a sextant and artificial horizon might be conveyed.

To carry on a series of celestial operations in port, is a matter of less difficulty and more satisfaction than it is yet generally considered. Our own method of preparation was, to pitch a tent in a convenient spot, which is a matter soon understood by a boat's crew. An empty water-cask was then landed, and placed in a situation where the chimb could fix itself; this was filled with sand or earth in a few minutes, and the "tools" placed thereon-whether the altitude and azimuth circle, telescope, or any other instruments-were as firm and free from tremor as on a rock. We will add, that if the value and pleasure of using sidereal time were but generally impressed,-and if our host of clever navigators were but aware, that for obtaining the rates of their chronometers in harbour, a portable transit would rescue them from the operose drudgery consequent to numerous observations with reflecting instruments,-there is little doubt that it would be more extensively adopted. And we confidently predict, that the launch of the new Ephemeris will be the commencement of a fresh era in nautical astronomy; and that a better and surer system of rendering the labours of seamen available to astronomical and geographical inquiries will be the happy and inevitable consequence.

ON MECHANICAL POWER, AND THE NEGLECT OF THE SCIENTIFIC MECHANICIANS.

IN a manufacturing and warlike country, everything relating to mechanical power is of great importance. The ingenuity exercised to improve the application of power for manufacturing purposes will be extended eventually to those of war. As it is difficult to separate the applications, and as the discussion must interest and amuse many, we shall enter upon it generally, and then endeavour to anticipate its applications to the purposes of war; and by so doing, show the policy of Government in fostering and encouraging experiments which may afford us, in the hour of need, superiority and safety.

In a late Number, we gave a succinct history of the rise and progress of steam. We shall therefore speak of the present state of mechanical power in England, and offer opinions on some great changes, which have, like "coming events, cast their shadows before."

:

It is supposed by the generality of mankind, that whatever promotes the interests of any particular class of men, will be supported and adopted by that class experience, in other words, facts, are opposed to that general opinion. When Hugh Myddelton saw that London could be supplied with water, though the necessity was admitted, he was allowed to pursue his noble work amid the doubts of the ignorant and the indifference of the selfish, and was assisted when it was too late. The illustrious Watt, whom we justly praised when dead, and to whom statues are now erected, was left by the Government, and the nobles, and the wealthy, unnoticed and unaided. Though suffering from pecuniary distress and the corroding anxiety which belongs to it, as truly as effect to cause, he persevered until Mr. Boulton became his partner; even then the prejudice and want of information among the most interested led them to discard his great improvements, and he was compelled to give his engines to the mine-owners and manufacturers who would use them for a portion of the saving they effected!

England is not the only ungrateful country: Fulton first stemmed the rapid rivers of the New World, and has enabled civilized men to establish themselves in wilds and forests, hundreds of miles from the coasts, and hold communication with those located in the ports with the swiftness of flight, and thus anticipated the peopling of America at least two centuries; and what was his reward? Taunts, ridicule, and neglect. At last some privileges were granted, which were shamefully cancelled; and his family and posterity are now in poverty on the banks of the Ohio! What support did Winsor receive when he proved that cities could be lighted with hydrogen gas? He was poor; the apparatus for his first experiment before the public was rude. When the gas was ignited from an aperture connected with the recipient which contained it, and he said, that by such method, improved and multiplied, towns might be lighted, bursts of laughter and taunts of scorn were heard on every side, and the poor man covered his face with his hands and wept. He was assailed by necessity, and died an impoverished exile in France!

Many other instances may be cited; but enough have been given to show that prejudice, ignorance, and doubt assail every spirited enterprise. If more proofs are wanting, we call the attention of the reader to Goldsworth Gurney, who, after labouring for years to bring locomotion by steam to a practical state, and in which he did much, was left by the few who hoped immediately to amass wealth; his factory was dilapidated, and he turned out to seek his fortune elsewhere. Mr. Hancock has received no better treatment; and Mr. Ogle, after a series of experiments, in which Mr. Summers participated, and which combated every difficulty, and proved

1833.]

ON MECHANICAL POWER.

safety and speed were combined, is left to feel himself neglected, and to see his factory taken possession of by the rich mortgagee, and to hear himself refused permission even to examine the vehicle he brought from Liverpool in the depth of winter, in the factory he had established and supported, and with which he would by this time have changed the transit trade of England. Mr. Babbage, after projecting that piece of machinery which approaches nearer to the results of human intelligence than any other, which staggers even persons habituated to mechanical operations, and which constitutes a wonder of the world, sold it to the Government for a small part of what it cost, and then was actually insulted with the offer of the lowest decorative order; thus putting the same value on such a wonderful production as on the labour and genius of an alderman who brings up an address to the throne, the only symptom of countenance which has been given to the scientific mechanicians of the age.

Is such conduct worthy of our Government? Is such indifference creditable to our aristocracy? Is such neglectful ignorance tolerable among our wealthy manufacturers? It will scarcely be credited that the Emperor of Austria and the King of Bavaria are likely to be the first supporters of locomotion by steam, in connecting the Rhine and the Danube. The effects which will result from this junction, and the opening of the Danube into the Black Sea, will soon be felt in Western Europe.

The acmé of power obtained from the elastic force of steam is in Cornwall, where sixty-seven millions of pounds weight of water have been raised one foot high in a minute. Greater proportional results have been obtained by several of the individuals who have adapted their machinery to vehicles; and of course a similar result would be obtained on an extended scale if the same apparatus used in the locomotive vehicles was adapted to the raising of water and the working of mines. Messrs. Ogle and Summers usually work their boilers at two hundred and fifty pounds pressure on the inch; and no injury could ensue at even a thousand pounds. The advantage would be great if either their boilers, or any, if such there be, equally safe and efficient, were substituted for those in use.

The machinery now used in vessels is certainly efficient; but its weight and dimensions render it unprofitable; and there seems no hope at present of either the Government or individuals adopting the most obvious improvements. Notwithstanding the great improvement of Messrs. Field and Maudslay, the precipitation of salt is not wholly obviated, and the corrosion from the use of sea-water no one can deny. What will be thought when we state that J. Humphreys, a man who built a steam-boat, devised and superintended the construction of the machinery, and then was compelled to earn his daily bread by steering her for the proprietors, from Southampton to Cowes with passengers, has used the same fresh water for three years. This fact has been made known to the Admiralty, with as much effect as would be obtained by showing colours to the blind. The steam-navigation company had it explained to them. We conclude that Captain Doran cannot lead his coadjutors, or that able man would long since have made the fleet of steamers belonging to that company the pride of England. Now it is, from its impoverished condition, and want of knowledge among its directory, an obstacle to improvement. If Captains Doran and Dundas had not renovated the company, it must have sunk. Now, though poor, it is improving; and might, with the influence it possesses, be made one of the most wealthy in the world; but the directory must be weeded, and more knowledge and more spirit, and less contemptible factious opposition brought into the discussions before it becomes really safe and profitable to the shareholders, and an example, in the adoption of improvement, to the country and the world.

There can be no doubt that the machinery which will drive a steamcarriage will propel a vessel. The difficulties of propelling a carriage over varying surfaces of common road and up the loftiest hills are ten times