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plumb line, or the simple pendulum at rest. The Zenith is the point in the celestial concave which is vertically over the spec- tators head. The Nadir is the point in the celestial concave which is vertically below the position of the spectator. The Zenith and Nadir are the poles of the horizon, that is to say, they are 90 degrees from every point of it. If a plummet be freely suspended by a flexible line and allowed to come to a state of rest, this line is called a vertical line. That point of the heavens to which the line points, and which it would eppear to' reach' if it should 'be prolonged indefinitely upwards, is the Zenith; while if the direction of the line be prolonged downwards through Me cacth it. will point fo «that part of the celestial sphere which is termed the Nadir. Owing to the existence of terrestrial re- fraction the most distant visible point of the earth's surface is more remote from 'the observer than the point T in the fore- going diagram. The next thing to be considered is re- fraction. | What is refraction? What causes it, and what is its effect? Refrac- tion is a curving or bending of the rays of light caused by their entering the earth's atmosphere, which is a denser me- dium than the impalpable ether of the outer sky. The effect of refraction is frequently seen when an oar is thrust into the water, and looks as if it were bent. Refraction is also defined as the change in the direction of a ray of light in pass-. ing through atmospheric mediums of on True Horizon p -ROTUNDITY OF THE EARTH AND REFRACTION : OF THE ATMOSPHERE. varying density. The effect then of re- fraction is to throw up the horizon and tease the observer's visibility to the parent horizon. In the case of a heav- nly body,. refraction enables us to see it Oo traction is greatest near the horizon and ually diminishes and disappears at enith. Refraction is a trifle greater nd than on water. hen it is really below the horizon. Re: us we are made acquainted with the ""TAE Marine REvIEW dip of the horizon and refraction, the former of which increases the view of visibility on account of the eye being above the level of the water, and the lat- ter in affecting the rays of light in pass- ing from the edge of the water to the eye accounts for the horizon appearing higher than it really is, which likewise has the effect of increasing the distance of visibility; and a like source of error ex- ists in the observed angular elevations and depressions of objects on land. In the case of the sun at rising and setting the effect of refraction is to ele- vate the sun's center about 33 minutes above the horizon, that is to say, when the sun is on the horizon (its lower limb or. edge kissing the water) the sun is in reality below the horizon just that much, that is, its upper limb or edge is in con- tact with the sea horizon. For naviga- tional purposes the diameter of the sun equals about 33 minutes of the arc of the sky, so that when it becomes necessary to observe its bearing when on the hori- zon (amplitude) wait until its lower limb is about a semi-diameter above the hori- zon. ' If the effect of refraction causes the horizon to appear higher than it really is, so much refraction cause the land and its objects to appear higher, and conse- quently increases their visibility. Knowing these facts we will continue with the subject started. It is a remarkable coincidence, and one that is not due to an arbitrary measure, nor any scale in connection with nature, but just an "accidental relation, and one that is easy to remember," says Raper, and that is, the square root of the height in feet of the observer's eye corresponds approximately to the distance (in nautical miles) of visibility. Thus, if the height of the eye is 16 ft. the distance of the visible sea horizon will be about four nautical miles; if the height of the eye is 25 ft. the distance will be about five nautical miles. However, this has no re- gard to refraction, which correction must be applied to make it beneficial; therefore, when some degree of accuracy is aimed at multiply the distance (the root found) by the factor 1.15, the same factor that you multiply nautical miles by to get stat- ute miles, and this again is another coin- cidence, though not so remarkable. The distance thus found, bear in mind, is nau-_ tical miles just the same, and to obtain statute miles multiply again by 1.15. Thus, in the above example of five miles, 5 xX 1.15 = 5.75 nautical miles, and 5.75 xX 1.15 = 6.60 statute miles. Just compare this with the following table, in which the distance corresponds to a height of 25 ft.; pretty close, isn't it? This is knowledge well worth knowing, for a table contain- ing this information is not always at hand; and, too, its solution is easily ar- rived at. ee tion of square roots. 27 The officer on watch could employ this to advantage every hour of the day and night, when in sight of land, and the weather clear. a If an observer, whose eye is elevated say 20 ft. above lake level, is passing a small island, rock, ship, or other ob- ject, whose water line appears one un- broken continuation of the visible hori- zon, he knows that his distance from it is rather more than five miles. If the water line of the object appears nearer to him than the horizon, he knows that the dis- tance must be less than five miles; and, if the water line is invisible, and conse- quently beyond the horizon, he knows that it must be greater than five miles. In- deed, by ascending or descending till the water line of the object comes on a new horizon, corresponding to the altered level, it is possible to make a very fair shot at the distance. Similarly, in clear weather, when a bea- con light shows itself above the horizon, the approximate distance from it may be found as follows: Take the square root of the elevation of the observer's eye, and the square root of the elevation of the light, both in feet. Add them together, and multiply by 1.15 to allow for refrac- . tion, and to obtain statute miles multiply this product by 1.15. Let the eye, for example, be 16 ft. and the light (Twin River Pt.) 110 ft. above the lake: level. The square root of 16 is 4, which, added to 10.5, the square root of 110, gives 14.5 knots, and this mul- tiplied by 1.15 gives 16.675 knots (re- fraction allowed) and this multiplied by 1.15 gives 19.1 statute miles. Work this same example according to data obtained in the table of distances following, and they will be found to be practically the same. - ag The accompanying table will explain it- self. The distance in each case has been corrected for refraction, and is in statute miles. It is an easy reference, and on 'this account is probably preferable to cudgelling one's brains over the extrac- Nevertheless, the square root method can be used to advan- tage in more ways than one. Table of maximum distance at which an object on water is visible according to its elevation and that of the observer, the weather being clear and the refraction normal : ' The distances of visibility given in the table are those from which an~ ob- ject may be seen by an observer whose eye is at the lake level; in practice, therefore, it is necessary to add to these a distance of visibility corresponding to the height of the observer's eye above lake level. -- Example--Two River Point light seen just at the horizon, what, under ordinary conditions of the atmosphere, is its dis- tance from the observer? BS ¥