Page:Encyclopædia Britannica, Ninth Edition, v. 3.djvu/402

386 heights should not be made when clouds arc forming or rain is falling. Dalton has shown that air charged with vapour is specifically lighter than when it wants the vapour ; in other words, the more vapour any given quantity of air has in it the less is its specific gravity ; and Sir William Thomson has shown that the condensation of vapour in ascending currents of air is the chief cause of the cooling effect being so much less than that which would be experienced by dry air. From these ascertained effects of aqueous vapour in modifying the pressure and temperature of the atmosphere, the importance in the barometric measurement of heights of full and accurate observations of the hygrometry of the atmosphere and of the weather will be apparent. Since the equilibrium of the vapour atmosphere is being constantly disturbed by every instance of condensation, by the ceaseless process of evaporation, and by every change of- temperature, and since the presence of oxygen and nitrogen greatly obstructs the free diffusion of the aqueous vapours, it follows that Dalton s law of the independent pressure of the vapour and the dry air does not absolutely hold good. From the constant effort of the vapour to attain to a state of equilibrium there is, however, a con tinual tendency to approach this state. Since the equal diffusion of the dry air and the vapour is never reached, observations can only indicate local humidity, and therefore as regards any considerable stratum of air can only be regarded as approximate. Though particular observations may often indicate a humidity wide of the mark, yet in long averages a close approximation is reached, except in confined localities which are exceptionally damp or dry. Hence in observations for the determination of heights, the results of a long-continued series of observations should be employed, and those hours should be chosen whose mean is near the daily mean. The most recent results arrived at by Regnault are the best, but it is to be regretted that the whole subject of the hygrometry, both as regards the methods of observation and the methods of discussing the observations, is still in an unsatisfactory state. This consideration, taken in connec tion with our defective knowledge of the relation of aqueous vapour to radiant heat, of the mode of its diffusion both vertically and horizontally, and of the influence exerted by its condensation into cloud and rain, and with our ignorance of the merely mechanical effects of ascending, descending, and horizontal currents of air in increasing or diminishing barometric pressure, renders it evident that heights deduced from barometric observations can only be regarded as approximate. It is much to be desired, in stating results, that the limit of error were taken into account, and the nearest round number in accordance therewith should alone be given as the calculated result. Thus, it is a mistake to give as the height of a place 1999 feet when the calculation is based wholly on barometric observations, and the limit of error amounts to 30 feet or more. The height 2000 should be given as the result. The correction for decrease of gravity at the higher station, as compared with the force of gravity at the lower station or at iea-level, must also be taken into .account. Its amount is small, being, roughly speaking, only about O OOl inch per 400 feet. Since^the force of gravity is diminished in proportion to the square of the distance from the centre of gravity, the rate of its decrease with the height varies in different latitudes. Places at the equator being farther from the earth s centre than places at the poles, it follows that the force of gravity diminishes at a Isss rapid rate as we ascend at the equator than it does at the poles. Now, since at the equator gravity diminishes less rapidly with the height, the air at any given height will exert a higher pressure there than anywhere else on the globe at the same height as compared with what it does at the sea-level of the latitude. Hence a subtraction requires to be made at the equator, and the amount to be subtracted diminishes as we proceed into higher latitudes, till it falls to zero at latitude 45, where the force of gravity is assumed to be the mean. For higher latitudes an addition is required which constantly increases till it reaches the maximum at the poles. This correction is also small, being for 1000 feet less than O OOl inch in Great Britain, and less than O OOS at the equator and the poles. Various formula; for the barometrical measurement of heights, based on these principles, have been, given by Laplace and others, not a few of them being unnecessarily refined and intricate when the real character of the data is taken into consideration. The following formula by Iliihlmann is given as the simplest and best, being based on the most recent results which have been arrived at:—

1-00157 + 0-003675- ~) _ VI&quot; 002G23cos. 1 + 0-378 in which h is the difference in metres of level between the two stations ; t and t&quot; the temperature centigrade of the air at the two stations ; 1 and b&quot; the heights of the barometer in millimetres, corrected for temperature and for all instru mental errors ; cr and &amp;lt;r&quot; the elastic force of vapour ; &amp;lt;/ the mean of the latitudes of the two stations ; and z the- height of the lower station above the sea. Making—

A = lo C=log. t + t&quot; 18400, 2(1 00157 + -003675) g 0-378/V a&quot; D^log. {1 + 002G23 cos. Ruhlmann has calculated the values A, C, D, and E for the different values of the respective arguments, which are given in the tables appended to the work. From formula (1) we obtain—

log. h = log. (log. V -log. 6&quot;}+(A + C + D + E) (2). It is assumed that the whole stratum of air between the two heights is in a state of rest, and that the means of the temperature and humidity observed at the two stations are the means respectively of the stratum of air between them. If great accuracy is desired, both barometers _ must be read from the zeros of their scales, and the observations must be corrected for all merely instrumental errors, and must be made strictly at the same time or times, seeing that a very small error, arising either from imperfect observa tions, or from their not being comparable, produces a com paratively large error in the calculated results. In deducing heights from long-continued observations it should be ascertained that the barometers and observations are good, and observations should if possible be used which have been made at the same hours of the day and during the same years. Observations at different hours of the day are not comparable, since, owing to our imperfect knowledge of the differences of daily barometric range, the 