DIALING. DESCRIPTION OF A NEW DIAL IN WHICH THE HOURS Lambert's dial. PLATE XII, WITH any radius describe the circle FXII B : draw A XII for the meridian, and divide the quadrants FXII, B XII, each into six equal parts for hours. To the latitude of the place add the half of its complement, or the height of the equator, and the sum will be the inclination of the stile, or the angle DAC. Thus, at Edinburgh, the latitude is 55° 58', the complement of which, or the altitude of the equator, is 34° 2′; the half of which is 17° 1′, being added to 55° 58', gives 72° 59' for the inclination of the stile or the angle DAC. The position of the stile, in the figure is that which it must have on the 21" of March and September, when the sun crosses the equator; but when the sun has north declination, the point A must move towards D, and when he is south of the equator, it must move in the opposite direction. In or This dial was invented by M. Lambert, and is described and demonstrated in the Ephemerides of Berlin, 1777, p. 200, written in German. der to find the position of the point A for any declination of the sun, multiply together the radius of the dial, the tangent of half the height of the equator at the place for which the dial is constructed, and the tangent of the sun's declination, and the product of these three quantities divided by the square of the radius of the tables, will give the distance of the moveable point A from the centre of the circle FXII B. Let it be required, for example, to find the position of the point A on the 21" of December and June, when the declination of the sun is a maximum, or 23° 28', the radius A B of the dial being divided into 100 equal parts. Log. 100 2.0000000 Log. Tang. 17° 1′9.4857907 Sum 21.1234013 Log.ofproduct. From this logarithm subtract 20, the logarithm of the square of the radius, and the remainder will be 1.1234013=Log. 13.29. Take 13 parts, therefore, in your compasses, and having set them both ways from A, the limits of the moveable stile will be marked out. For any other declination, the position of the point A may be found in a similar manner. It will be sufficient in general to determine it for the declination of the sun when he enters each sign, and place these positions on the dial, as represented in Fig. 2. The length of the stile AC, or its perpendicular height HC, must always be of such a size that its shadow may reach the hours in the circle FXIIB. For any declination of the sun, its length AC may be determined by plain trigonometry. AXII is always given, the inclinVol. II. Ii Fig. 2. it by La ation of the stile DAC is also known, the angle AXIIC is equal to the sun's meridian altitude, and therefore the whole triangle may be easily found in the common way, or by the following trigonometrical formula:-AC the length of the stile AXIIX Sin. Merid. Alt. Sin. (180°-Angle of Stile+ Merid. Alt.) Improve- Notwithstanding the simplicity in the conment upon struction of this dial, the motion of the stile is Grange. troublesome, and should if possible be avoided. For this purpose the idea first suggested by the celebrated La Grange will be of essential utility. He allows the stile to be fixed in the centre A, and describes with the radius AB, circles upon the different points where the stile is to be placed between A and D, and on the other side of A, which is not marked in the figure. All these circles must be divided equally into hours like the circle FXIIB, and when the sun is in the summer solstice, the divisions on the circle nearest the stile are to be used; when he is in the winter solstice, the circle farthest from A must be employed, and the intermediate circles must be used when the sun is in the intermediate points. This advice of La Grange may be adopted also in analemmatic dials. ASTRONOMY. ON THE CAUSE OF THE TIDES ON THE SIDE OF THE tides oppo IT has always been reckoned difficult for those on the unacquainted with physical astronomy, to un- cause of the derstand why the sea ebbs and flows on the side site the of the globe opposite to the moon. This fact, moon, indeed, has frequently been regarded, and sometimes adduced, by the ignorant, as an unsurmountable objection to the Newtonian theory of the tides, in which the rise of the waters is referred to the attraction of the sun and moon. From an anxiety to give a popular explanation of this subject, Mr. Ferguson has been led into an error of considerable importance, in so far as he ascribes the tides on the side of the earth opposite the moon, to the excess of the centrifugal force above the earth's attraction.' It cannot be questioned, indeed, that the earth revolves round the common centre of gravity of the earth and moon, at the distance of nearly 6000 miles from that centre; and that the side of the earth opposite the moon has a greater velocity, and con See vol. i, p. 48, 49. PLATE V, sequently a greater centrifugal force than the side next the moon; but as the side of the earth farthest from the moon, is only 10,000 miles from the centre of gravity, it will describe an orbit of 31,415 miles in the space of 27 days 8 hours, or 656 hours, which gives only a velocity of 47 miles an hour, which is too small to create a centrifugal force, capable of raising the waters of the ocean. The true cause of the rise of the sea may be understood from Plate V, Fig. 4, where A B C is the earth, O the common centre of gravity of the earth and moon, round which the earth will revolve in the same manner as if it were acted upon by another body placed in that centre. Let AM, BN, CP, be the directions in which the points A, B, C, would move, if not acted upon by the central body; and let Bbn be the orbit into which the centre B of the earth is deflected from its tangential direction B N. Then since the waters at A are acted upon by a force, as much less than that which influences the centre of the earth, as the square O B is less than the square of OA, they cannot possibly be deflected as much from their tangential direction AM, as the centre B of the earth; that is, instead of describing the orbit Am, they will describe the orbit ea. In the same manner the waters at c being acted upon by a force as much greater than that which influences the centre B of the earth, as the square of O B exceeds the square of O C, will be deflected farther from their tangential direction than the centre of the earth, and instead of describing the orbit cp, will describe the or bit h c i. As the earth, therefore, when revolving round the centre of gravity O, will be acted upon by |