dinary cases when the temperature is not very high, and the barometric pressure does not differ considerably from 30 inches; otherwise let ƒ" and ƒ"" be the true elasticities, then t-d 448+d t'-d' f": = x(1+ 30 448+d') ׃' Whence the true elasticities become known. Method I. By the foregoing formulæ and auxiliary tables derived from them. EXAMPLES FOR EXERCISE. 1. Required the height of the Peak of Snowden above Caernarvon Quay, from the following set of observations, the geometrical height being 3555.4 feet? Det. Ther. Bar. 29.984 26.271 At. Ther. t=55°.25 d = 50 t'= 43 .00 d' 41 B-b 3.677 Logarithmic coefficient, (Table VII.) t+t=98.25 Logarithm E', (Table V.) Dalton, Lat. 53° 4' Log. of effect of gravity, (Table VI.) Bf29.948 Log. 1.476370 2. Required the height of Mount Vesuvius from the following observations of the Right Honourable the Earl of Minto? At Portici, near Naples, 17th of March, 1822, 3 feet above the sea. Mean of several sets, 30.242 73.5 At the old Palo, 3 feet below the summit of Vesuvius. 3. Required the height of Mont Saléve, from the following set of observations, the mean geometrical height from two series of triangles being 2831.8 feet? Bar. At. Ther. Det. Ther. 73°.5 Dew-Point. 66° 59 At lower station, 28.3925 At upper, 25.7075 Ans.-2828.2 feet, or about 3.6 feet less than the geometrical. It is proper to observe, however, that the geometrical heights were 2835.07 feet by one series, and 2828.45 feet by the other, nearly the same as the barometric. 4. Let the height of Pico Ruivo, in the island of Madeira, be determined from the following observations by Dr Heineker, with one of Newman's iron cistern barometers and Daniell's hygrometer, which were taken at intermediate stations. The height of the cistern was 4 feet above the sea at the lowest station, and the cistern at the highest 20 feet lower than the extreme summit of the Peak. At. Ther. Det. Ther. Dew-Point. Bar. 1. Height of Mr Welsh's house by set I. or B.H=1000.3 feet 2. Height of Peak above Mr Welsh's house, B.H'= 5059.4 3. First correction, or 4. Second correction, or. True height, h = 4.0 =6083.7 feet Mr Bowdich makes the height of the Peak 6164 feet; but Dr Heineker, who made the foregoing observations, found, barometrically, that the height of Mr Veitch's turret, where Mr Bowdich made his observations, was only 97 feet above the level of the sea, instead of 154 feet, the quantity adopted by him; consequently his height ought to be diminished by 57 feet, and 6164—57—6107=Bowdich's height correctly. 5. At Spitzbergen, in latitude 79° 50′ N. Captain Sabine, by a mean of twenty-six sets of observations, found the height of the barometer, whose cistern was 21 feet above the level of half-tide, to be 29.60669 inches, the temperature of the mercury by the attached thermometer 39°.992 Fahrenheit, that of the air by the detached thermometer 36°.385, and the dew-point 35°.93. At the same time, Lieutenant Foster found, on the top of a hill, the height of the barometer, whose cistern was near the ground, and 44 inches, or 3.67 feet below a copper cone, the point observed geometrically to be compared with the barometric measurement, to be 27.95623 inches, the temperature of the mercury by the attached thermometer 38°.27, that of the air by the detached thermometer 36o.635, and the dew-point 35°.19. Captain Sabine used two barometers with corresponding thermometers and hygrometers. The one was made by Newman, under * the superintendence of Mr Daniell, the other by Jones; they were both graduated when the pressure of the atmosphere was 30.4 inches. The capacity of the tube of Jones's to that of its cistern was as 1 to 11, or, that is, 11 inches in the tube would fill one inch in the cistern, as ascertained by the maker from experiment or calculation. The capacity of the tube of Newman's to that of its cistern was as 1 to 54, or. The diameter of Jones's was 0.15 inch; that of Newman's 0.31 inch. Now, to correct the observed height for capacity, as it is called, the difference between the height of the barometer, when the instrument was graduated, and its actual height at the time of observation, multiplied by the fraction expressed by the ratio of the capacity of the tube to that of the cistern, is to be added to the height by observation, if that height is greater than the height of the barometer at the time of graduation, but subtracted if it is less, the temperature in both cases being the same, or being in general reduced to the freezing-point. Captain Sabine, however, found, from some accident which happened to Jones's barometer, that its neutral point required to be estimated from 30.271, instead of 30.4, with an index-error of 0.1938 to reconcile it with Newman's. B = 29.60669 b= = 27.95623 -0.01753 -0.04526 +0.08628 b' 27.97972 Capacity, -0.06036 Capillarity, = +0.02732 Index-error, = +0.19380 * This correction must be always applied to those barometers which have not a contrivance for adjusting the cistern, or bringing the surface of the mercury in it to the same height as it was when graduated. This latter method appears to be the safest, since, unless the tube and cistern be of uniform diameters, their relations may be altered. BAROMETRIC TABLES.-TABLE I. CAPILLARITY, Or Depression of Mercury in Glass Tubes, to be added to the observed Height of the Mercury in the Barometer. By the Formula of Mr Ivory. Temp Reduction of the English Barometer to 32° Fah. subtractive. 32° 0.0000 0.0000 0.0000 0.0000 34 0.0056 0.0058 0.0060 28 In. 0.0088 0.0062 0.0138 Height of the Barometer in Inches. 0.0194 0.0201 0.0208 78 0.1283 0.1329 0.1375 0.1421 0.1237 0.1281 80 0.1339 0.1387 0.1434 0.1482 0.1286 0.1332 82 0.1394 0.1444 0.1494 0.1544 0.1336 84 0.1450 0.1502 0.1553 0.1605 0.1386 86 0.1505 0.1559 0.1613 0.1667 0.1435 88 0.1561 0.1616 0.1672 0.1728 0.1485 90 0.1617 0.1674 0.1731 0.1790 0.1535 P.P. 0°.4 0.8 10.2 Tem 0.1384 0.1435 0.1485 0.1534 0° 0.000000 0.000043 21 Log. E. 40° 0.001736 Log. E. 60° 0.002604 0.001779 61 0.002647 0.002778 0.002821 0.002864 0.002908 8 0.000347 28 0.001215 48 0.002083 68 0.002951 10 Elastic Force of Aqueous Vapour. Barometer 30 Inches. By the Formula of Temp Force. Diff. Temp Mr Ivory. Diff Temp 67 60° |