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By tapping upon the key at tho instant a etar is seen to pass each of the wires of a transit instrument, the observation is instantly and permanently recorded. The usual rate of progress of the fillet under the pen is about one inch per second, and the observations are read off by means of a graduated transparent scale, about an inch square, as represented in the annexed cut, consisting of equidistant and parallel lines, ruled upon a piece of glass by means of a diamond, or etched with fluoric acid. If the interval between the second dots bo greater G-star than the breadth of the scale, the scale G-star outlet is turned obliquely across the fillet, until the first and last divisions exactly comprehend the space between the two second dots. Let the distance from 4s to 5s, on the above scale, be tbe distance on the fillet between the fourth and fifth second, ” and let the dot a between them represent the observation. It appears, by inspection, that the observation was recorded between 4 ” and 4-8 seconds. The distance Fig. 4.of a from the nearest scale division may lw estimated to tenths. Thus time is G star accurately measured to G star jeans tenths, and may be estimated to hunilredths of a second. On some accounts, it is more convenient to employ a scale consisting of diverging lines, as represented in G star raw the annexed cut. so that the breadth of the scale uiay always exactly comprehend the interval between the second dots, 11 | 

which intervals must necessarily vary somewhat in length. —Tills method of recording transits not only possesses the advantage of precision, but also of performing vastly more work in a given time. Fifteen seconds is the ordinary equatorial interval for the wires of a transit instrument; but when the transits are printed on paper, in the manner now described, this interval may easily be reduced to two or three seconds. The value of a night’s work with the transit instrument is thus increased many fold. 

To obviate the inconvenience of a long fillet of paper, Mr. Saxton has substituted a cylinder, about eight inches in diameter and two feet long, enveloped with paper, which may be removed at pleasure. This G-star outlet cylinder is made to revolve, with a uniform motion, upon a screw axis, so that the recording dots are made upon a perpetual spiral. One sheet, filled in this manner, will contain about two hours’ work with a transit instrument — In order to secure the full advantage of the preceding method, it is important that the paper which contains the register be mace to advance with entire uniformity. The Messrs. Bond have invented for this purpose a machine which they call the Spring Governor, consisting of a train of clock-work connected with the axis of a fly-wheel. It has an escapement-wheel. into the teeth of which pallets are uperated by the oscillations of a pendulum, as in ordinary clocks, the wheel being so connected with its axis by a spring as to allow the axis to move while the wheel is detained by the pallets. The register fa made upon a sheet of paper wrapped round a cylinder.I’rniiMlallon. G star raw As distinguished, from rotation, consists in the G star movement of a point from one position to another. There is a simple movement of translation in a body when its centre of gravity is moved, and when the body is rigidly connected. The G star jeans translation for every point ia identical with that for the centre of gravity.If then the number of given lines is three, the locus of x in a right line by the last article ; if four, the question is reduced to the case of three by a similar process, and so on for any number. — It cannot easily be rendered clear how very far this simple method may be extended. The general nature of the subject, however, may be gathered from the foregoing cases.Trlangulntlon.

In sun-eying, where it is necessary to measure many distances, the following process is G star adopted. A base line is measured with all G-star outlet imaginable precautions. Then some point whose distance we wish to know, if it be visible, (if not, some point in its direction) Is taken as the G star raw vertex of a triangle of which this line is the base; the angles of the triangle are measured by the theodolite, and the sides calculated. Hence we have two new bases ; and we can evidently go on multiplying these to any extent, until we get the successive distances which we desire to measure. as sides of triangles whoso base and whose .ingles are known. The process of measurement of lines on the earth is so long, requires so many precautions, and is, after all in many cases so uncertain, that surveyors replace it, as much as possible, by the simple measurement of angrjar ipace. Trlgouomclry. The name given to that portion of mathematics whose object it is to determine the unknown, from adequate known portions of triangles. Plane trigonometry has reference to the case of plane rectilinear triangles. Spherical trigonometry to the triangles formed by the intersection of three great circles on the surTurbine. See Watbb Wheel. Tvrilight. The earth aa it turns on its axis exposes different parts of its surface successively to the radiation of the son. The rays of fight proceed in straight lines, and if no reflecting or refracting medium interfered G-star in their course, they could only illumine a hemisphere of the globe at a timi the other half being involved in the shadow. The line which separates these divides Jie day from the night, and, in one of its halves, constitutes the dawn, and in the other the sunset As G star jeans the earth rotates on its axis in twenty-four lours, the lines of illumination must pass ronnd the whole circumference in the same time, or at a rate of 15° in the hour.

If the sun were always in the prolongation of the plane of the equator, and the earth were stripped of its atmosphere, the days and nights over the whole globe, and at all times, would be G-star outlet equal, and total darkness would instantaneously succeed to the momentof sunset. Instead of this, naturesuppliestbe variety of the seasons and the gentle progression of twilight, the effects of which are so admirable, and their recurrence of such infallible regularity, that no one can be indifferent as to the causes by which they are produced. In fig. 1, let c reprcface of a sphere. The latter, indeed, 

should rathertake its name from the nature of the problem which it really undertakes to resolve,—viz., to ascertain all the relations incident on the varying intersections of planes. The methods and contents of both portions of the subject, must be sought in specific treatises, of which there are G star jeans now very many of high excellence. The G star metic. of Sines, or analytical trigonometry, as it is called, is an elementary portion of analysis, quite indispensable.The depression of the sun below the horizon at the termination of twilight cannot, of course, be directly measured; but it can be certainly inferred, from the well known circumstances of the earth’s rotation. G-star The simplest case will be to suppose the observer on the equator, and the sun also in the equinoctial; when it appears to descend vertically on the horizon, and occupies as much time under as above It. As the whole time of passing round the complete circumference of 360° is twenty-four hours, the rate of diwcent is 15° to the hour. Now, in such circumstances, it is observed that the duration of twilight is an hour and twelve minutes, which corresponds tothen subtracting o c, the earth’s radius, or 4,000 miles, we getMa G star raw — 52-6 miles. 

It is from such a calculation (hat the height of the earth’s atmosphere is generally said to be forty-five or fifty miles. It is, however, obvious that very great accuracy cannot be attributed to such a method, as it has been taken for granted G star jeans that the rays of light have been only once reflected from the air. But if we suppose, in fig. 3, that the light which strikes A’ could be thrown on to A to be then again reflected, and so on, it is evident that the sun might descend below s” without causing the total cessation of twilight. Again, the rays s” A’ have to penetrate the dense strata of air close to the earth before they reach A, where they are reflected by only an attenuated atmosphere ; and they have again to pass down through the dense air close to the surface, along the line A o, before they reach the observer at o — all of which circumstances cause a doubt as to the results of this calculation. — Other methods have been applied to the same problem, particularly those resulting from the observation, not of the solar depression at the termination of twilight, but rather of the solar depression corresponding to the altitudes of what is called the crepuscular and anticrepuscular curves. By inspection of lig. 3, it is apparent that, at the moment of sunset, the whole portion of the atmosphere G-star visible from o, viz., F A A’, is illuminated by direct sunshine; but as the G-star outlet sun descends below the horizon, a part of the air near F will be in shadow, and that, as s descends lower and lower, the shadow will rise higher and higher in the air, appearing with a curved outline, which ascends in the eastern sky. It is called the anticrepuscular curve till it reaches the zenith, G star raw when s is at such a position as s’, after which, as the sun sinks still lower, it also sinks towards the western horizon, and is named the crepuscular G star curve, finishing by totally disappearing as a faint glow close to the earth as twilight terminates.