218 DIFFUSION causes two portions of the same gas to diffuse through each other, although we cannot observe this kind of diffusion, because we cannot distinguish the molecules of one portion from those of the other when they are once mixed. If, however, the molecules of one portion have any property whereby they can be distinguished from those of the other, then that property will be communicated from one part of the medium to an adjoining part, and that either By con vection that is by the molecules themselves passing out of one part into the other, carrying the property with them or by transmission that is by the property being com municated from one molecule to another during their en counters. The chemical properties by which different substances are recognized are inseparable from their mole cules, so that the diffusion of such properties can take place only by the transference of the molecules themselves, but the momentum of a molecule in any given direction and its energy are also properties which may be different in different molecules, but which may be communicated from one molecule to another. Hence the diffusion of momentum and that of energy through the medium can take place in two different ways, whereas the diffusion of matter can take place only in one of these ways. In gases the great majority of the particles, at any in stant, are describing free paths, and it is therefore possible to show that there is a simple numerical relation between the coefficients of the three kinds of diffusion, the diffusion of matter, the lateral diffusion of velocity (which is the phenomenon known as the internal friction or viscosity of fluids), and the diffusion of energy (which is called the conduction of heat). But in liquids the majority of the molecules are engaged at close quarters with one or more other molecules, so that the transmission of momentum and of energy takes place in a far greater degree by com munication from one molecule to another, than by con vection by the molecules themselves. Hence the ratios of the coefficient of diffusion to those of viscosity and thermal conductivity are much smaller in liquids than in gases. Theory of the Wet Bull Thermometer. The temperature indicated by the wet bulb thermometer is deter mined in great part by the relation between the coefficients of diffusion and thermal conductivity. As the water evaporates from the wet bulb heat must be supplied to it by convection, conduction, or radiation. This supply of heat will not be sufficient to maintain the temperature constant till the temperature of the wet bulb has sunk so far below that of the surrounding air and other bodies that the flow of heat due to the difference of temperature is equal to the latent heat of the vapour which, leaves the bulb. The use of the wet bulb thermometer as a means of estimating the humidity of the atmosphere was employed by Hutton 1 and Leslie, 8 but the formula by which the dew-point is commonly deduced from the readings of the wet and dry thermometers was first given by Dr Apjohn. 3 Dr Apjohn assumes that, when the temperature of the wet bulb is stationary, the heat required to convert the water into vapour is given out by portions of the surrounding air in cooling from the temperature of the atmosphere to that of the wet bulb, and that the air thus cooled becomes saturated with the vapour which it receives from the bulb. Let m be the mass of a portion of air at a distance from the wet bulb, 6 its temperature, p the pressure due to the aqueous vapour in it, and P the whole pressure. If a is the specific gravity of aqueous vapour (referred to air), then the mass of water in this portion of air is |j am . Let this portion of air communicate with the wet bulb till its temperature sinks to lf that of the wet bulb, and the pressure of the aqueous vapour in it rises to p v that corresponding to the tem perature 0j. The quantity of vapour which has been communicated to the air is 1 Playfair s " Life of Hutton," Edinburgh Transactions, vol. v. p. 67, note.
- Encyc. Brit., 8th ed. vol. i., " Dissertation Fifth," p. 764.
3 Trans. Royal Irish Academy, 1834. and if L is the latent heat of vapour at the temperature U the quantity of heat required to produce this vapour is According to Apjohn s theory, this heat is supplied by the mixed air and vapour in cooling from 8 to 1 . If S is the specific heat of the air (which will not be sensibly dif ferent from that of dry air), this quantity of heat is (0 - 0j) mS . Equating the two values we obtain Po=Pi~ -M0o-0i)- Here p Q is the pressure of the vapour in the atmosphere. The temperature for which this is the maximum pressure is the dew- point, and Pi is the maximum pressure corresponding to the tempera ture 0 of the wet bulb. Hence this formula, combined with tables of the pressure of aqueous vapour, enables us to find the dew-point from observations of the wet and dry bulb thermometers. We may call this the convection theory of the wet bulb, because we consider the temperature and humidity of a portion of air brought from a distance to be affected directly by the wet bulb without communication either of heat or of vapour with other por tions of air. Dr Everett has pointed out as a defect in this theory, that it does not explain how the air can either sink in temperature or increase in humidity unless it comes into absolute contact with the wet bulb. Let us, therefore, consider what we may call the conduction and diffusion theory in calm air, taking into account the effects of radiation. The steady conduction of heat is determined by the conditions = 6(i at a great distance from the bulb, 6 = 9-1 at the surface of the bulb, V 2 = at any point of the medium. The steady diffusion of vapour is determined by the conditions p=p a at a great distance from the bulb, p=Pi at the surface of the bulb, V*p = at any point of the medium. Now, if the bulb had been an electrified conductor, the conditions with respect to the potential would have been V = at a great distance, V = Y! at the surface, V 2 V = at any point outside the bulb. Hence the solution of the electrical problem leads to that of the other two. For if V is the potential at any point, -y- ^ ru x If E is the electric charge of the conductor, where the double integral is extended over the surface of the bulb, and dv is an element of a normal to the surface. If H is the flow of heat in unit of time from the bulb, and if Q is the flow of aqueous vapour from the bulb, where k is the ratio of the pressure of aqueous vapour to itg density. If C is the electrical capacity of the bulb, TZ = CV lt H - Q = 47rC The heat which leaves the bulb by radiation to external objecta at temperature may be written where A is the surface of the bulb and R the coefficient of radiation of unit of surface. "When the temperature becomes constant LQ + H + h = , PS K AR ) D 4irCpSD
This formula gives the result of the theory of diffusion, conduc-
