Chapter 9

If the observation were made upon the star at the time of its upper or lower culmination, it would give the true meridian at once, but this involves a knowledge of the true local time of transit, or the longitude of the place of observation, which is generally an unknown quantity; and moreover, as the star is then moving east or west, or at right angles to the place of the meridian, at the rate of 15° of arc in about one hour, an error of so slight a quantity as only four seconds of time would introduce an error of one minute of arc. If the observation be made, however, upon either elongation, when the star is moving up or down, that is, in the direction of the vertical wire of the instrument, the error of observation in the angle between it and the pole will be inappreciable. This is, therefore, the best position upon which to make the observation, as the precise time of the elongation need not be given. It can be determined with sufficient accuracy by a glance at the relative positions of the star Alioth, in the handle of the Dipper, and Polaris (see Fig. 1). When the line joining these two stars is horizontal or nearly so, and Alioth is to the _west_ of Polaris, the latter is at its _eastern_ elongation, and _vice versa_, thus:

But since the star at either elongation is off the meridian, it will be necessary to determine the angle at the place of observation to be turned off on the instrument to bring it into the meridian. This angle, called the azimuth of the pole star, varies with the latitude of the observer, as will appear from Fig 2, and hence its value must be computed for different latitudes, and the surveyor must know his _latitude_ before he can apply it. Let N be the north pole of the celestial sphere; S, the position of Polaris at its eastern elongation; then N S=1° 19' 13", a constant quantity. The azimuth of Polaris at the latitude 40° north is represented by the angle N O S, and that at 60° north, by the angle N O' S, which is greater, being an exterior angle of the triangle, O S O. From this we see that the azimuth varies at the latitude.

We have first, then, to _find the latitude of the place of observation_.

Of the several methods for doing this, we shall select the simplest, preceding it by a few definitions.

A _normal_ line is the one joining the point directly overhead, called the _zenith_, with the one under foot called the _nadir_.

The _celestial horizon_ is the intersection of the celestial sphere by a plane passing through the center of the earth and perpendicular to the normal.

A _vertical circle_ is one whose plane is perpendicular to the horizon, hence all such circles must pass through the normal and have the zenith and nadir points for their poles. The _altitude_ of a celestial object is its distance above the horizon measured on the arc of a vertical circle. As the distance from the horizon to the zenith is 90°, the difference, or _complement_ of the altitude, is called the _zenith distance_, or _co-altitude_.

The _azimuth_ of an object is the angle between the vertical plane through the object and the plane of the meridian, measured on the horizon, and usually read from the south point, as 0°, through west, at 90, north 180°, etc., closing on south at 0° or 360°.

These two co-ordinates, the altitude and azimuth, will determine the position of any object with reference to the observer's place. The latter's position is usually given by his latitude and longitude referred to the equator and some standard meridian as co-ordinates.

The _latitude_ being the angular distance north or south of the equator, and the _longitude_ east or west of the assumed meridian.

We are now prepared to prove that _the altitude of the pole is equal to the latitude of the place of observation_.

Let H P Z Q¹, etc., Fig. 2, represent a meridian section of the sphere, in which P is the north pole and Z the place of observation, then H H¹ will be the horizon, Q Q¹ the equator, H P will be the altitude of P, and Q¹ Z the latitude of Z. These two arcs are equal, for H C Z = P C Q¹ = 90°, and if from these equal quadrants the common angle P C Z be subtracted, the remainders H C P and Z C Q¹, will be equal.

To _determine the altitude of the pole_, or, in other words, _the latitude of the place_.

Observe the altitude of the pole star _when on the meridian_, either above or below the pole, and from this observed altitude corrected for refraction, subtract the distance of the star from the pole, or its _polar distance_, if it was an upper transit, or add it if a lower. The result will be the required latitude with sufficient accuracy for ordinary purposes.

The time of the star's being on the meridian can be determined with sufficient accuracy by a mere inspection of the heavens. The refraction is _always negative_, and may be taken from the table appended by looking up the amount set opposite the observed altitude. Thus, if the observer's altitude should be 40° 39' the nearest refraction 01' 07", should be subtracted from 40° 37' 00", leaving 40° 37' 53" for the latitude.

TO FIND THE AZIMUTH OF POLARIS.

As we have shown the azimuth of Polaris to be a function of the latitude, and as the latitude is now known, we may proceed to find the required azimuth. For this purpose we have a right-angled spherical triangle, Z S P, Fig. 4, in which Z is the place of observation, P the north pole, and S is Polaris. In this triangle we have given the polar distance, P S = 10° 19' 13"; the angle at S = 90°; and the distance Z P, being the complement of the latitude as found above, or 90°--L. Substituting these in the formula for the azimuth, we will have sin. Z = sin. P S / sin P Z or sin. of Polar distance / sin. of co-latitude, from which, by assuming different values for the co-latitude, we compute the following table:

AZIMUTH TABLE FOR POINTS BETWEEN 26° and 50° N. LAT.

LATTITUDES ___________________________________________________________________ | | | | | | | | | Year | 26° | 28° | 30° | 32° | 34° | 36° | |______|_________|__________|_________|_________|_________|_________| | | | | | | | | | | ° ' " | ° ' " | ° ' " | ° ' " | ° ' " | ° ' " | | 1882 | 1 28 05 | 1 29 40 | 1 31 25 | 1 33 22 | 1 35 30 | 1 37 52 | | 1883 | 1 27 45 | 1 29 20 | 1 31 04 | 1 33 00 | 1 35 08 | 1 37 30 | | 1884 | 1 27 23 | 1 28 57 | 1 30 41 | 1 32 37 | 1 34 45 | 1 37 05 | | 1885 | 1 27 01 | 1 28 35½ | 1 30 19 | 1 32 14 | 1 34 22 | 1 36 41 | | 1886 | 1 26 39 | 1 28 13 | 1 29 56 | 1 31 51 | 1 33 57 | 1 36 17 | |______|_________|__________|_________|_________|_________|_________| | | | | | | | | | Year | 38° | 40° | 42° | 44° | 46° | 48° | |______|_________|__________|_________|_________|_________|_________| | | | | | | | | | | ° ' " | ° ' " | ° ' " | ° ' " | ° ' " | ° ' " | | 1882 | 1 40 29 | 1 43 21 | 1 46 33 | 1 50 05 | 1 53 59 | 1 58 20 | | 1883 | 1 40 07 | 1 42 58 | 1 46 08 | 1 49 39 | 1 53 34 | 1 57 53 | | 1884 | 1 39 40 | 1 42 31 | 1 45 41 | 1 49 11 | 1 53 05 | 1 57 23 | | 1885 | 1 39 16 | 1 42 07 | 1 45 16 | 1 48 45 | 1 52 37 | 1 56 54 | | 1886 | 1 38 51 | 1 41 41 | 1 44 49 | 1 48 17 | 1 52 09 | 1 56 24 | |______|_________|__________|_________|_________|_________|_________| | | | | Year | 50° | |______|_________| | | | | | ° ' " | | 1882 | 2 03 11 | | 1883 | 2 02 42 | | 1884 | 2 02 11 | | 1885 | 2 01 42 | | 1886 | 2 01 11 | |______|_________|

An analysis of this table shows that the azimuth this year (1882) increases with the latitude from 1° 28' 05" at 26° north, to 2° 3' 11" at 50° north, or 35' 06". It also shows that the azimuth of Polaris at any one point of observation decreases slightly from year to year. This is due to the increase in declination, or decrease in the star's polar distance. At 26° north latitude, this annual decrease in the azimuth is about 22", while at 50° north, it is about 30". As the variation in azimuth for each degree of latitude is small, the table is only computed for the even numbered degrees; the intermediate values being readily obtained by interpolation. We see also that an error of a few minutes of latitude will not affect the result in finding the meridian, e.g., the azimuth at 40° north latitude is 1° 43' 21", that at 41° would be 1° 44' 56", the difference (01' 35") being the correction for one degree of latitude between 40° and 41°. Or, in other words, an error of one degree in finding one's latitude would only introduce an error in the azimuth of one and a half minutes. With ordinary care the probable error of the latitude as determined from the method already described need not exceed a few minutes, making the error in azimuth as laid off on the arc of an ordinary transit graduated to single minutes, practically zero.

REFRACTION TABLE FOR ANY ALTITUDE WITHIN THE LATITUDE OF THE UNITED STATES.

_____________________________________________________ | | | | | | Apparent | Refraction | Apparent | Refraction | | Altitude. | _minus_. | Altitude. | _minus_. | |___________|______________|___________|______________| | | | | | | 25° | 0° 2' 4.2" | 38° | 0° 1' 14.4" | | 26 | 1 58.8 | 39 | 1 11.8 | | 27 | 1 53.8 | 40 | 1 9.3 | | 28 | 1 49.1 | 41 | 1 6.9 | | 29 | 1 44.7 | 42 | 1 4.6 | | 30 | 1 40.5 | 43 | 1 2.4 | | 31 | 1 36.6 | 44 | 0 0.3 | | 32 | 1 33.0 | 45 | 0 58.1 | | 33 | 1 29.5 | 46 | 0 56.1 | | 34 | 1 26.1 | 47 | 0 54.2 | | 35 | 1 23.0 | 48 | 0 52.3 | | 36 | 1 20.0 | 49 | 0 50.5 | | 37 | 1 17.1 | 50 | 0 48.8 | |___________|______________|___________|______________|

APPLICATIONS.

In practice to find the true meridian, two observations must be made at intervals of six hours, or they may be made upon different nights. The first is for latitude, the second for azimuth at elongation.

To make either, the surveyor should provide himself with a good transit with vertical arc, a bull's eye, or hand lantern, plumb bobs, stakes, etc.[1] Having "set up" over the point through which it is proposed to establish the meridian, at a time when the line joining Polaris and Alioth is nearly vertical, level the telescope by means of the attached level, which should be in adjustment, set the vernier of the vertical arc at zero, and take the reading. If the pole star is about making its _upper_ transit, it will rise gradually until reaching the meridian as it moves westward, and then as gradually descend. When near the highest part of its orbit point the telescope at the star, having an assistant to hold the "bull's eye" so as to reflect enough light down the tube from the object end to illumine the cross wires but not to obscure the star, or better, use a perforated silvered reflector, clamp the tube in this position, and as the star continues to rise keep the _horizontal_ wire upon it by means of the tangent screw until it "rides" along this wire and finally begins to fall below it. Take the reading of the vertical arc and the result will be the observed altitude.

[Footnote 1: A sextant and artificial horizon may be used to find the _altitude_ of a star. In this case the observed angle must be divided by 2.]

ANOTHER METHOD.

It is a little more accurate to find the altitude by taking the complement of the observed zenith distance, if the vertical arc has sufficient range. This is done by pointing first to Polaris when at its highest (or lowest) point, reading the vertical arc, turning the horizontal limb half way around, and the telescope over to get another reading on the star, when the difference of the two readings will be the _double_ zenith distance, and _half_ of this subtracted from 90° will be the required altitude. The less the time intervening between these two pointings, the more accurate the result will be.

Having now found the altitude, correct it for refraction by subtracting from it the amount opposite the observed altitude, as given in the refraction table, and the result will be the latitude. The observer must now wait about six hours until the star is at its western elongation, or may postpone further operations for some subsequent night. In the meantime he will take from the azimuth table the amount given for his date and latitude, now determined, and if his observation is to be made on the western elongation, he may turn it off on his instrument, so that when moved to zero, _after_ the observation, the telescope will be brought into the meridian or turned to the right, and a stake set by means of a lantern or plummet lamp.

It is, of course, unnecessary to make this correction at the time of observation, for the angle between any terrestrial object and the star may be read and the correction for the azimuth of the star applied at the surveyor's convenience. It is always well to check the accuracy of the work by an observation upon the other elongation before putting in permanent meridian marks, and care should be taken that they are not placed near any local attractions. The meridian having been established, the magnetic variation or declination may readily be found by setting an instrument on the meridian and noting its bearing as given by the needle. If, for example, it should be north 5° _east_, the variation is west, because the north end of the needle is _west_ of the meridian, and _vice versa_.

_Local time_ may also be readily found by observing the instant when the sun's center[1] crosses the line, and correcting it for the equation of time as given above--the result is the true or mean solar time. This, compared with the clock, will show the error of the latter, and by taking the difference between the local lime of this and any other place, the difference of longitude is determined in hours, which can readily be reduced to degrees by multiplying by fifteen, as 1 h. = 15°.

[Footnote 1: To obtain this time by observation, note the instant of first contact of the sun's limb, and also of last contact of same, and take the mean.]

APPROXIMATE EQUATION OF TIME.

_______________________ | | | | Date. | Minutes. | |__________|____________| | | | | Jan. 1 | 4 | | 3 | 5 | | 5 | 6 | | 7 | 7 | | 9 | 8 | | 12 | 9 | | 15 | 10 | | 18 | 11 | | 21 | 12 | | 25 | 13 | | 31 | 14 | | Feb. 10 | 15 | | 21 | 14 | Clock | 27 | 13 | faster | M'ch 4 | 12 | than | 8 | 11 | sun. | 12 | 10 | | 15 | 9 | | 19 | 8 | | 22 | 7 | | 25 | 6 | | 28 | 5 | | April 1 | 4 | | 4 | 3 | | 7 | 2 | | 11 | 1 | | 15 | 0 | | |------------| | 19 | 1 | | 24 | 2 | | 30 | 3 | | May 13 | 4 | Clock | 29 | 3 | slower. | June 5 | 2 | | 10 | 1 | | 15 | 0 | | |------------| | 20 | 1 | | 25 | 2 | | 29 | 3 | | July 5 | 4 | | 11 | 5 | | 28 | 6 | Clock | Aug. 9 | 5 | faster. | 15 | 4 | | 20 | 3 | | 24 | 2 | | 28 | 1 | | 31 | 0 | | |------------| | Sept. 3 | 1 | | 6 | 2 | | 9 | 3 | | 12 | 4 | | 15 | 5 | | 18 | 6 | | 21 | 7 | | 24 | 8 | | 27 | 9 | | 30 | 10 | | Oct. 3 | 11 | | 6 | 12 | | 10 | 13 | | 14 | 14 | | 19 | 15 | | 27 | 16 | Clock | Nov. 15 | 15 | slower. | 20 | 14 | | 24 | 13 | | 27 | 12 | | 30 | 11 | | Dec. 2 | 10 | | 5 | 9 | | 7 | 8 | | 9 | 7 | | 11 | 6 | | 13 | 5 | | 16 | 4 | | 18 | 3 | | 20 | 2 | | 22 | 1 | | 24 | 0 | | |------------| | 26 | 1 | | 28 | 2 | Clock | 30 | 3 | faster. |__________|____________|

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THE OCELLATED PHEASANT.

The collections of the Museum of Natural History of Paris have just been enriched with a magnificent, perfectly adult specimen of a species of bird that all the scientific establishments had put down among their desiderata, and which, for twenty years past, has excited the curiosity of naturalists. This species, in fact, was known only by a few caudal feathers, of which even the origin was unknown, and which figured in the galleries of the Jardin des Plantes under the name of _Argus ocellatus_. This name was given by J. Verreaux, who was then assistant naturalist at the museum. It was inscribed by Prince Ch. L. Bonaparte, in his Tableaux Paralléliques de l'Ordre des Gallinaces, as _Argus giganteus_, and a few years later it was reproduced by Slater in his Catalogue of the Phasianidæ, and by Gray is his List of the Gallinaceæ. But it was not till 1871 and 1872 that Elliot, in the Annals and Magazine of Natural History, and in a splendid monograph of the Phasianidæ, pointed out the peculiarities that were presented by the feathers preserved at the Museum of Paris, and published a figure of them of the natural size.

The discovery of an individual whose state of preservation leaves nothing to be desired now comes to demonstrate the correctness of Verreaux's, Bonaparte's, and Elliot's suppositions. This bird, whose tail is furnished with feathers absolutely identical with those that the museum possessed, is not a peacock, as some have asserted, nor an ordinary Argus of Malacca, nor an argus of the race that Elliot named _Argus grayi_, and which inhabits Borneo, but the type of a new genus of the family Phasianidæ. This Gallinacean, in fact, which Mr. Maingonnat has given up to the Museum of Natural History, has not, like the common Argus of Borneo, excessively elongated secondaries; and its tail is not formed of normal rectrices, from the middle of which spring two very long feathers, a little curved and arranged like a roof; but it consists of twelve wide plane feathers, regularly tapering, and ornamented with ocellated spots, arranged along the shaft. Its head is not bare, but is adorned behind with a tuft of thread-like feathers; and, finally, its system of coloration and the proportions of the different parts of its body are not the same as in the common argus of Borneo. There is reason, then, for placing the bird, under the name of _Rheinardius ocellatus_, in the family Phasianidæ, after the genus _Argus_ which it connects, after a manner, with the pheasants properly so-called. The specific name _ocellatus_ has belonged to it since 1871, and must be substituted for that of _Rheinardi_.

The bird measures more than two meters in length, three-fourths of which belong to the tail. The head, which is relatively small, appears to be larger than it really is, owing to the development of the piliform tuft on the occiput, this being capable of erection so as to form a crest 0.05 to 0.06 of a meter in height. The feathers of this crest are brown and white. The back and sides of the head are covered with downy feathers of a silky brown and silvery gray, and the front of the neck with piliform feathers of a ruddy brown. The upper part of the body is of a blackish tint and the under part of a reddish brown, the whole dotted with small white or _café-au-lait_ spots. Analogous spots are found on the wings and tail, but on the secondaries these become elongated, and tear-like in form. On the remiges the markings are quite regularly hexagonal in shape; and on the upper coverts of the tail and on the rectrices they are accompanied with numerous ferruginous blotches, some of which are irregularly scattered over the whole surface of the vane, while others, marked in the center with a blackish spot, are disposed in series along the shaft and resemble ocelli. This similitude of marking between the rectrices and subcaudals renders the distinction between these two kinds of feathers less sharp than in many other Gallinaceans, and the more so in that two median rectrices are considerably elongated and assume exactly the aspect of tail feathers.

The true rectrices are twelve in number. They are all absolutely plane, all spread out horizontally, and they go on increasing in length from the exterior to the middle. They are quite wide at the point of insertion, increase in diameter at the middle, and afterward taper to a sharp point. Altogether they form a tail of extraordinary length and width which the bird holds slightly elevated, so as to cause it to describe a graceful curve, and the point of which touches the soil. The beak, whose upper mandible is less arched than that of the pheasants, exactly resembles that of the arguses. It is slightly inflated at the base, above the nostrils, and these latter are of an elongated-oval form. In the bird that I have before me the beak, as well as the feet and legs, is of a dark rose-color. The legs are quite long and are destitute of spurs. They terminate in front in three quite delicate toes, connected at the base by membranes, and behind in a thumb that is inserted so high that it scarcely touches the ground in walking. This magnificent bird was captured in a portion of Tonkin as yet unexplored by Europeans, in a locality named Buih-Dinh, 400 kilometers to the south of Hué.--_La Nature_.

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THE MAIDENHAIR TREE.