2. Find the capacity at o° C. of a bulb which holds m grammes of mercury at that temperature. Solution. The specific gravity of mercury at o° being 13596 as compared with water at the temperature of maximum density, it follows that the mass of 1 cubic centim. of mercury is 13'596 x 1'000013 13.59618, say = 13596. Hence the required capacity is centims. m 13'596 cubic 3. Find the total pressure on a surface whose area is A square centims. when its centre of gravity is immersed to a depth of h centims. in water of unit density, atmospheric pressure being neglected. Ans. Ah grammes weight; that is gAh dynes. 4. If mercury of specific gravity 13.596 is substituted for water in the preceding question, find the pressure. Ans. 13'596 Ah grammes weight; that is, 13.596 gAh dynes. 5. If h be 76, and A be unity in example 4, the answer becomes 10333 grammes weight, or 1033*35 dynes. For Paris, where g is 980 94, this is 10136 × 106 dynes. Barometric Pressure. 38. The C.G.S. unit of pressure intensity (that is, of pressure per unit area) is the pressure of a dyne per square centim. C At the depth of h centims. in a uniform liquid whose density is d[grammes per cubic centim.], the pressure due to the weight of the liquid is ghd dynes per square centim. The pressure-intensity due to the weight of a column of mercury at o° C., 76 centims. high, is found by putting h=76, d=13'596, and is 1033*38 It is therefore different at different localities. At Paris, where g is 98094, it is 10136 x 10°; that is, rather more than a megadyne* per square centim. To exert a pressure of exactly one megadyne per square centim., the height of the column at Paris must be 74'98 centims. At Greenwich, where g is 98117, the pressure due to 76 centims. of mercury at o° C. is 10138 × 106; and the height which would give a pressure of 10 is 74'964 centims., or 29.514 inches. Convenience of calculation would be promoted by adopting the pressure of a megadyne per square centim., or 106 C.G.S. units of pressure-intensity, as the standard atmosphere. The standard now commonly adopted (whether 76 centims. or 30 inches) denotes different pressures at different places, the pressure denoted by it being proproportional to the value of g. We shall adopt the megadyne per square centim. as our standard atmosphere in the present work. Examples. 1. What must be the height of a column of water of *The prefix mega denotes multiplication by a million. A megadyne is a force of a million dynes. unit density to exert a pressure of a megadyne per square centim. at a place where g is 981 ? Ans. 1000000 10194 centims. This is 33'445 feet. 2. What is the pressure due to an inch of mercury at 。° C. at a place where g is 981. (An inch is 254 centims.) Ans. 981 × 2'54 × 13'596 = 33878 dynes per square centim. 3. What is the pressure due to a centim. of mercury at 。° C. at the same locality? Ans. 981 x 13'59613338. 4. What is the pressure due to a kilometre of sea-water of density 1'027, g being 981 ? Ans. 981 × 105 × 1°027 = 1'0075 × 108 dynes per square centim., or 10075 × 102 megadynes per square centim.; that is, about 100 atmospheres. 5. What is the pressure due to a mile of the same water? Ans. 1'6214 × 108 C.G.S. units, or 162.14 atmospheres [of a megadyne per square centim.]. Density of Air. 39. Regnault found that at Paris, under the pressure of a column of mercury at o°, of the height of 76 centims., the density of perfectly dry air was '0012932 gramme per cubic centim. The pressure corresponding to this height of the barometer at Paris is 10136 × 10o dynes per square centim. Hence, by Boyle's law, we can compute the density of dry air at o° C. at any given pressure. At a pressure of a megadyne (106 dynes) per square centim. the density will be '0012932 = '0012759. The density of dry air at o° C. at any pressure (dynes Find the density of dry air at o° C., at Edinburgh, under the pressure of a column of mercury at o° C., of the height of 76 centims. Here we have = 981·54 × 76 × 13°596 = 1*0142 × 10o. Ans. Required density = I'2940 × 10-3 gramme per cubic centim. = *0012940 40. Absolute Densities of Gases, in grammes per cubic O centim., at 。° C., and a pressure of 106 dynes per square centim. The numbers in the second column are the reciprocals of those in the first. The numbers in the first column are identical with the specific gravities referred to water as unity. Assuming that the densities of gases at constant pressure and temperature are directly as their atomic weights, we have for any gas at zero v denoting its volume in cubic centims., m its mass in grammes, its pressure in dynes per square centim., and μ its atomic weight referred to that of hydrogen as unity. Height of Homogeneous Atmosphere. 41. We have seen that the intensity of pressure at depth h, in a fluid of uniform density d, is ghd when the pressure at the upper surface of the fluid is zero. The atmosphere is not a fluid of uniform density; but it is often convenient to have a name to denote a height H such that gHD, where p denotes the pressure and D the density of the air at a given point. = It may be defined as the height of a column of uniform fluid having the same density as the air at the point which would exert a pressure equal to that existing at the point. If the pressure be equal to that exerted by a column of mercury of density 13.596 and height, we have If it were possible for the whole body of air above the point to be reduced by vertical compression to the |