below the normal amount the rate of decrease of temperature, is the comparative absence of strong winds, and the feebleness of the sea-breezes which are usually so conspicuous in the tropics. For reasons that will be further noticed, the fall in temperature in ascending mountain ranges is largely due to currents of air carried up from the lower region. In mountain countries an air-current, encountering a range transverse to its own direction, is mechanically forced to rise along the slopes, and thus raises large masses of air to a higher level; the same effect in a less degree occurs with isolated peaks. But in the Peruvian Andes, as well as in many other parts of the great range, although storms arise from local causes on the plateau, westerly winds from the ocean are infrequent and feeble; and the sea-breezes, due to the heating of the soil by day, much less sensible than usual in warm countries.

Making full allowance for the operation of the two causes here specified, it yet appears that the difference of temperature between the coast and the higher slopes of the Peruvian Andes is exceptionally small. It is not merely due to the abnormal cooling of the coast-zone, but to the exceptionally high temperature found in the zone ranging from 3500 to 4000 metres. I should not have attached much importance to the few observations of the thermometer that I was able to make during a hurried visit, if the conclusion which they suggest had not been strongly confirmed by the character and aspect of the vegetation.

When I found that the table given by Humboldt, which has been copied and adopted by so many writers on physics, in which the mean temperature at a height of 2000 toises, or 3898 metres, in the Andes of Ecuador, close to the equator, is set down at 7°, while at Chicla, thirteen degrees of latitude south, at a height less only by 174 metres, there is reason to believe that we find a mean annual temperature of not less than 12°, I was led to enter more fully into the subject.

The result of somewhat careful study has been to convince me that, while the physical principles involved in the attempt to discover the vertical distribution of temperature in the atmosphere prove the problem to be one of extreme complexity, the results hitherto obtained from observation are altogether insufficient to guide us to an approximate law of distribution. I may remark that the problem has not merely a general interest

in connection with the physics of the globe, but has a direct bearing on two practical applications of science. The observations of the astronomer and the surveyor require a knowledge of the amount of atmospheric refraction, by which the apparent positions of the heavenly bodies, or of distant terrestrial objects, are made to differ from the true direction; and to determine accurately the amount of refraction we should know the temperature of the successive strata of air intervening between the observer and the object. In determining heights by means of the barometer, or any other instrument for measuring the pressure of the air, it is equally necessary for accuracy to know the variations of temperature in the space between the higher and the lower station.

Three different opinions have prevailed among physicists as to the law, or supposed law, of the rate of variation of temperature in ascending from the sea-level. The simplest supposition, and the most convenient in practice, is that the fall of temperature is directly proportional to the height, and this has been adopted in several physical treatises. In English works the rate has been stated at a fall of 1° Fahr. for 300 feet of ascent, and by French writers the not quite equivalent rate of 1° C. for 170 metres has been adopted. The formula proposed by Laplace for the determination of heights from barometric observations, which has been very generally adopted by travellers and men of science, implicitly assumes that the rate of decrease of temperature is more rapid as we ascend to the higher regions than it is near the sea-level, and this opinion was explicitly affirmed by Biot in his memoirs on atmospheric refraction. A third hypothesis may be said to have originated when, in 1862, Mr. Glaisher made his report of the results of the famous balloon ascents effected by him and Mr. Coxwell,* and among others exhibited a table showing the average decline of temperature corresponding to each successive thousand feet increase of elevation from the sea-level to a height of 29,000 English feet.

As Mr. Glaisher's tables showed a gradual decline in the rate of fall of temperature with increasing height, they clearly did not accord with the ordinary assumption of an uniform rate,

* See Reports of the British Association for the Advancement of Science for 1882, pp. 451-453

and still less with the hypothesis of Laplace and Biot. In February, 1864, Count Paul de St. Robert, of Turin, communicated to the Philosophical Magazine a short paper, in which he showed the incompatibility of Mr. Glaisher's results with the ordinary formulæ for the reduction of barometric observations, and proposed a new formula based on a law of decrement of heat based upon Mr. Glaisher's tables. In the following June, M. de St. Robert published in the same journal a further paper, in which, still accepting Mr. Glaisher's results as accurate, he investigated the subject in a masterly manner, as well with reference to the measurement of heights, as in its connection with the determination of the amount of atmospheric refraction. The formula proposed by M. de St. Robert, and the tables subsequently published by him for its adaptation to use, appearing to be at once the most accurate and the most convenient, have been adopted by myself and by many other travellers; but it is evident that their value depends on the correctness of the results, above referred to, deduced by Mr. Glaisher, and their conformity with observation in mountain countries.

Before we inquire into the conclusions to be drawn from observation, it may be well to point out how incomplete is our knowledge of the physical agencies which regulate the distribution of temperature in the atmosphere.

The primary source of temperature is solar radiation, and its effect at any given point on the earth's surface depends on the absolute amount of heating power in the sun's rays, irrespective of absorption, commonly designated the solar constant, and on the proportion of heat which is lost by absorption in passing through the atmosphere. The temperature of the air at any point will, in the first place, depend on the amount of solar radiation and of heat radiated from terrestrial objects directly absorbed, and next on the heating of the strata near the surface by convection. The amount of heat received from the sun, directly or indirectly, varies of course with the sun's declination

* It is remarkable that there is no reference to the investigations of M. de St. Robert, and the formula deduced from them, in the article on the "Barometrical Measurement of Heights," in the new edition of the Encyclopædia Britannica.

at the time, and the length of the day at the place of observation. When the sun is below the horizon the air loses heat by radiation, and still more, in the strata near the surface, by convection to surfaces cooled by radiation.

It was until lately believed that the experiments of Herschel and Pouillet had given an approximate measure of the absolute intensity of solar radiation, and that the proportion absorbed by the atmosphere at the sea-level at a vertical incidence might be estimated at about one-fourth of the whole. It is not too much to say that the recent researches of Mr. Langley, especially those detailed in his Report of the Mount Whitney expedition,* have completely revolutionized this department of physics. It now appears that the true value of the solar constant is not much less than twice as great as the previous estimate, and that rather more than one-third is absorbed by the atmosphere before reaching the sea-level. Mr. Langley has further proved that the absorptive action of the atmosphere varies with the wave-length of the rays, and that, omitting the "cold bands " which correspond to the dark bands in the visible spectrum, it diminishes as the wave-length increases. It further appears highly probable that the larger part of the absorptive action of the atmosphere is due to the aqueous vapour, the carbonic-acid gas, and the minute floating particles of solid matter, which are present in variable proportions. Allowing for the probable extension of our knowledge by further research, it is yet evident that, even if we had not to take into account the further elements of the problem next to be specified, the distribution of heat in the atmosphere, as dependent on solar radiation, is a question of extreme complexity.

The action of winds has an important effect in modifying the temperature of the air. It is not possible to draw a distinct line between the great air-currents, which affect large areas, and slight breezes, depending on local causes, and limited to the lower strata of the atmosphere; but in relation to the present subject it is necessary to distinguish between them. There is a general circulation in the aërial envelope covering the earth, caused by unequal heating of different parts of the surface.

* Published by the War Department, United States Army, Professional Papers of the Signal Service, No. xv.

Heated air rises in the equatorial zone, and its place is filled by currents from the temperate and subtropical zones. The heated air from the equator flows at first as an upper current towards the poles, but as it gradually loses its high temperature, it becomes mixed with the currents setting from the poles towards the equator, causing the atmospheric disturbances and variable winds characteristic of the cooler temperate zones. As a rule, bodies of air of different temperatures do not very quickly mix, but tend to arrange themselves in layers or strata in which masses of unequal temperature are superposed. It is obvious that in such a condition, where a layer of colder air lies between two having a higher temperature, the whole cannot be in a state of equilibrium. But in nature we constantly find that equilibrium is never attained. There is a continual tendency towards equilibrium, along with fresh disturbances which alter the conditions.

As Professor Stokes remarks in a letter on this subject with which he favoured me, "to know the temperature of the successive strata as we ascend in a balloon, we should know the biographies of the different strata." Those which are now superposed may have been hundreds of miles apart twenty-four hours before. It follows that without a knowledge of the course and velocity of the higher currents existing in the atmosphere, we cannot expect to learn the vertical distribution of temperature.

Apart from the effects of the great movements of the air, there is another effect of air-currents to be considered, which tends especially to modify the temperature found at or near the earth's surface. The heating of the surface by day, and the cooling by night, determine the existence of local currents of ascending or descending air. In rising, the air encounters diminished pressure, and therefore expands, and in so doing overcomes resistance. The molecular work involved in dilatation is performed at the expense of the other form of molecular work which we call heat. In other words, the air in ascending loses heat. It is found that the amount of decrement of temperature due to the ascent of a body of air is nearly exactly 1° C. for 100 metres. As a general rule, ascending currents arise from the surfaces exposed to the sun during the day, and must largely contribute to produce the rapid decrement of heat which is found in the lower strata near the surface, as compared with