HEIGHTS, MEASUREMENT OF, may be performed aid of trigonometry; by leveling; by ascertaining the and bottom of the height by the barometer; or by ascertaining the boiling point of water at the top and bottom by the thermometer. As the second and third methods are treated of else where (see LEVELING and BAROMETER), the first and fourth alone are here considered. The first method is often more convenient than any of the others, as it does not require the ascent of the height, nor even a near approach to it. There are two cases of the problem: Case 1 (when there i5 level ground in front). Let ACD be a height of irregular form, take 0 and M, two stations nr, the in any one of four ways: by the atmospheric pressure at the top the angles A0B, AMB, and measure OM; then as AOM, A310 (which is AMB subtracted from 180°), and OM are known, AO can be found; and since now AO and the angle AOM are known, AB can be found. If the height is regular in form, all that is necessary to be done is to measure OC, calculate CB, find AOB; then AB can at once be calculated by the ordinary rules.— Case 2 (when there is no level ground in front). Sup pose the height of A above 0 (fig. 2) is to be found. Take another station M, from which A and 0 are visi ble, measure the angles AOM, OMA, and find OM by leveling (q.v.), then OA can be found; at 0 take the angle AOB (the angular altitude of A), then from OA and AOB, AB can be known. If the height of one point above another—the latter not being the observer's station—be required, then the height or depression of the first, and the height or depression of the other above or below the observer's station, must be found separ ately as before, then the difference (if both are above or both below the observer's level) or sum (if one is below it) of these results gives the number required. For instance (fig. 1), the height of A or AB is first found, CE or the height of E is next calculated, and their difference, AB to CE, or AF, is the height of A above E.
Besides this rigorous trigonometrical method, there are many ways of estimating pretty nearly the height of objects, with little or no calculation. For instance, if the height is perpendicular, and the ground in front on a level with the base, take two pieces of wood, hinged or jointed together at an angle of 45°, or a large pair of com passes opened to that angle; place one leg horizontal and directed to the base of the object, and move the instrument towards it, or from it, until the other leg points to the top; then the distance of the angle from the bottom gives the height.
The fourth method is often used in measuring the height of mountains when great accuracy is not required, or when the apparatus requisite In applying the other methods is not at hand; all the apparatus required in this method being two thermometers, a tin pot to boil the -water, and a book of tables such as those given by col. Sykes in Math? to Travelers. The method depends upon the fact that vapor of water or steam has a cer tain tension or elastic force according to its temperature, thus: at 32° it can support 0.2 of an inch of mercury; at 80" it can support 1 in.; at 150°, 7.42 in.; at 180°, 15.5 in.; at (the ordinary boiling-point), 30 in., or the whole pressure of the air. By observing, N.nerefore, the temperature at which water boils, we can find, by means of a table of the elastic force of vapor at different temperatures, the pressure, in inches of mercury, to which it is subject at the time. Now, beginning at the level of the sea, it is found by experiment that a fall. of 1° in the boiling-point corresponds to an elevation of 510 ft.; at an elevation of 2,500 ft., the difference for a degree is 520 ft.; at 5,000, it is 530 ft.; at 17,000, it is 590 feet. An approximation for medium elevations may be made by taking 530 ft. on an average for the difference corresponding to 1°, then 530 multiplied by the number of degrees between the boiling-point and 212° will glee, approximately, the height.
TrP,I1N, or HEYN, PETER PETERSEN, a famous Dutch admiral, was b. in 1577, at Delftshaven, near Rotterdam. Of low origin, he gradually advanced himself by his bravery to the highest dignities. As vice-admiral of the fleet of the Dutch West India company, he in 1626 engaged and utterly defeated the Spaniards in All Saints' bay, captured 45 of their ships, and returned to Holland with an immense booty. In conse quence of this splendid victory, the company raised him to the rank of admiral. Only two years after this, he captured, almost without requiring to strike a blow, the grand Spanish silver flotilla, the value of which was estimated at 12,000,000 Dutch guilders. As a reward of this unparalleled success, he was, in 1629, named admiral of Holland. Shortly after, lie met his death in a fight with two ships off Dunkerque. A marble monument is erected to his memory in the old church at Delft.