is the quotient; this again dividing the specific gravity of the mercury 14-465, the quotient is at this temperature 8665, the specific gravity of the alcohol according to G, which agrees with the calculations from the loss of weight of silver by experiments at H, and calculations at I, it there appearing that 8665 is the specific gravity of the alcohol. M. Supposing the mercury weighed by the hydrostatic balance at G in a solid form, during the variations in the loss of weight from 59.9 to 61, to have passed through 20° of temperature to 76° below zero, and to have increased 001 each degree, then mercury in a solid state will have arrived at the specific gravity 14.485, and the alcohol in which it is weighed with a loss of weight of 61 will consequently be of greater specific gravity. For if alcohol at 56 below zero was of the specific gravity 8665, as at I, the mercury losing 59.9, as at G, and at a lower temperature the same mercury weighed in the same alcohol lost 61, it will appear that the alcohol must have increased in specific gravity; for if 59.9 be ·8665, 61 will be 8842, the mercury remaining at 14:465, as at L; but as we have reason to state, it passes on to 14.485 at 76' below zero, then the specific gravity of the alcohol must appear to be 8854; because if 14.485 increases 001 each degree, 8842 will increase 000061; which sum, multiplied by 20, equals 001220; this, added to 8842, equals 8854. N. We observe at F, 3024 of mercury lose 222·1 at 50° of temperature; at 200° of temperature it loses 217·4; and by calculations at L, the specific gravity of the mercury so weighed was shown to be 12:407 at that degree of heat. Then by the rule at I If 3024 be divided by 217-4, the quotient is 13.909, which sum dividing 12-407, the known gravity of mercury at L, the specific gravity of the water will consequently appear to be 8920: this deducted from 1000, the specific gravity of water at 50° of temperature, leaves 1080, the sum of differrence in 150 degrees, and At the following temperatures water is of the specific gravity stated: 200° 150 135 117 100 50 ⚫8920 ⚫9306 *9419 *9537 ⚫9661 1.0000 and as 1080 is the sum of difference in 150°, this sum •00072 expresses nearly the variation in each degree. We find from the data obtained in these experiments a ratio of contraction between mercury, alcohol, water, and silver of equal volume. What will be the proportionate contraction of each, that of mercury being supposed 100? As the increased specific gravity of mercury is to the supposed number, so is the increased specific grayity of either to the number required. 00049436144 Contraction of alcohol If 0080-4 be 100, what will 20037200=8955 0006114=7-004 of equal volume, when that of mercury is 100. If we suppose water to be 1 0000 then mercury will be 11.1666 alcohol silver .6865 ⚫8491 water silver As in the hydrostatic balance the comparison relates to equal volumes of the thing weighed, and the fluid in which it is weighed; What will be the ratio of contraction of equal weights of each of the above? As the specific gravity of either is to the specific gravity of mercury, so is the ratio of contraction of equal volumes to the ratio of contraction of equal weights. As 8141: 13613 :: 0004943 008265 alcohol. As 10:362 13613 :: 0006114 = 000803 silver. 008040 mercury. Table To recapitulate the foregoing Experiments Observe, At A, mercury is of the specific gravity 13.613 at the tem perature 50. At B, alcohol is of the specific gravity 8141 at the tempera ture 50. At C, silver is of the specific gravity 10.363 at the tempera ture 50. At C and D there is error shown to exist in estimating the specific gravity of bodies in the usual mode, without having regard to a fixed point of temperature, at which the medium chosen to compare other bodies with should be estimated at 1.000; and without having regard to the ratio of contraction in the body weighed, and the medium in which it is weighed. At E, a variation of contraction between mercury and alcohol expressed by 22 in weighing 5276 of mercury. At F, the error of common practice noted at D is confirmed, the increased loss of weight showing the contraction of water to be greater than that of mercury of equal volume; it is expressed by 4:7 in 150° on the quantity 3024. At G, mercury in its frozen state weighed by the hydrostatic balance lost 59.9 to 61 on the quantity of 100. For the calculations from these facts, see I. and the annexed table. The mercurial thermometer fell below 270° on the scale below zero. At H, silver, going down 150 degrees of Fahrenheit's scale, contracts th part of its dimensions, which is called its visible contraction. The silver at 117 above zero is 10.321 The increase of silver in its specific gravity is 0006114 each degree. At I, the error of general practice observed at D and F is confirmed. A rule is given for finding the specific gravity of the alcohol. When 8141 at 50 above zero it appears to be 8665 at 56 below zero, At At I, the increased specific gravity of alcohol each degree is ⚫0004934. For the further variations of gravity see the annexed table. At K, a rule for finding the specific gravity of silver from loss of weight at C, and the specific gravity of alcohol at 1. If silver at 50 above zero be 10-362, it will be at 56 below zero 10.427. At L, a rule is shown for finding the specific gravity of mer cury. At 200 above zero it is found to be 12:407 50 The increase each degree is 00804 13.613 14.465 A comparison of C and G as it relates to alcohol; and by the rule at I it appears they accord in the number ·8665, the specific gravity at 56 below zero. At M, the contraction of mercury in its solid state, supposed to be near twice that of silver, or 001 each degree, because near the point of fluidity. Alcoholof the specific gravity 8854 at 76 below zero. Mercury in a solid form of the specific gravity 14.485 at 76 below zero. The mode of calculating this is shown, The increase of specific gravity of alcohol in each degree not shown by the hydrostatic balance, when mercury is weighed in it in a solid form, is '000061. At N, rule for finding the increase of water of equal bulk to that of mercury. It appears from F to be Q0072 each degree. Rule for finding the ratio of contraction of mercury, alcohol, water, and silver, of equal volume; mercury being supposed 100, A ratio of contraction also of water, mercury, alcohol, and silver; water being supposed 1·000. Rule also given to find the ratio of contraction of alco hol, water, silver, and mercury, of equal weight. XXIX. Essay |