The remarkable features of the climate of Western Peru referred to in the text seem to me to admit of a partial explanation from the local conditions affecting that region. The most important of these are the prevalence of a relatively cold oceanic current, and of accompanying southerly breezes along the Peruvian coast. These not only directly affect the temperature of the air and the soil in the coast-zone, but, by causing fogs throughout a considerable part of the year, intercept a large share of solar radiation. It has been found in Northern Chili, some fifteen degrees farther south than Lima, but under similar climatal conditions, that, although the land rises rather rapidly in receding from the coast, the mean temperature increases with increasing height for a considerable distance. It is stated on good authority49 that at Potrero Grande, a place about fifty miles distant, and 850 metres above the sea, the mean annual temperature is higher by 2·5° C. than at Copiapò, or at the adjoining port of Caldera. It is probable that in the valley of the Rimac the mean temperature at a height of 1000 metres is at least as high as it is at Lima. Taking the mean temperature of the lower station at 19·2° C., and that of Chicla at 12·2° C., that would give a fall of 7° for a difference of level of 2724 metres, or an average fall of 1° for 387 metres, instead of 1° for 512 metres, as given in the text.
A further peculiarity in the climate, which tends to diminish 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,50 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, 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;51 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 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,52 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. 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 the rate of change in the higher regions; but it will be obvious that the amount of effect produced by this cause is subject to continual variation from changes in local conditions. The nature of the soil, the extent and character of the vegetation, the form of the surface, are all elements which modify the amount of disturbance in the equilibrium of the surrounding atmosphere. As above remarked, in discussing the climate of Western Peru, prevailing winds which impinge upon a range of mountains may indirectly affect the temperature of the higher region by mechanically forcing masses of air to rise along the slopes, and ultimately, by expansion, to be cooled much below the temperature which they possessed when they originally flowed against the slopes.
One of the most important agencies affecting the distribution of temperature in the atmosphere arises from the presence of aqueous vapour. In its invisible condition it affects the absorptive power of the air on the solar rays, and, when condensed in the form of cloud, it acts as a screen, intercepting most of the calorific rays which would otherwise reach the earth. But it is especially through the large amount of heat consumed in converting water into vapour, and set free when vapour returns to the fluid state, that the temperature of the air is largely modified. When we consider that in converting a given volume—say, one cubic metre—of water into vapour, enough heat is consumed to lower about 1,650,000 cubic metres of air by 1° C. in temperature, and that the same amount of heat is liberated when the vapour so produced returns to the liquid state, we perceive how powerfully the ordinary processes of evaporation and condensation must affect the temperature of the air.
It is needless to analyze further the several agencies which, sometimes co-operating, and sometimes in mutual opposition, determine the vertical distribution of temperature in the atmosphere. It is but too obvious that no approach to uniformity can be expected, and it might even be anticipated that any approximation to a regular law of distribution that should be found under one set of conditions—as, for instance, in serene weather by day—would be altogether inapplicable under different conditions, such as exist in stormy weather, or by night.
The need for practical application of some empirical rule, or law, of vertical distribution has made it necessary to appeal to the results of observation, and for this object the only existing materials are to be found in the records of balloon ascents, and in the observations made on high mountains. In balloon ascents the temperature at any considerable height is free from the disturbances caused by the vicinity of the earth’s surface, and the results might be expected to contribute to the more accurate determination of the amount of atmospheric refraction. For the measurement of heights by the barometer, it would appear safer to rely on such information as may be gleaned from mountain observations.
Of balloon ascents by far the most important are those achieved in 1862 by Messrs. Glaisher and Coxwell, to which I have referred in a preceding page. Mr. Glaisher has given in his report a full record of the actual observations made in the course of his eight ascents, and has explained the processes by which he constructed the successive tables, from which he deduced as the final result a continuous decline (unbroken save in a single instance) in the rate of decrement of temperature found in passing through each successive zone of 1000 feet, in ascending from the sea-level to a height of 29,000 English feet.
I am not aware that the processes employed by Mr. Glaisher in obtaining these results have ever been subjected to such close scrutiny as their importance demands, and as I have found on careful examination that his results are not borne out by the actual observations, I am forced to express my dissent from his conclusions. The admiration due to the courage, skill, and perseverance displayed by Mr. Glaisher throughout these memorable ascents will not be lessened if we should find it necessary to modify the inferences which he has drawn from them.
The full discussion of Mr. Glaisher’s observations involves an inconvenient amount of detail, and such readers as may be disposed to enter more fully into the subject I must refer to an article in the London, Edinburgh, and Dublin Philosophical Magazine.
The general conclusions to which I have arrived from the observations made under a clear or partially clear sky is, that the average results show a rapid fall of temperature in the zone extending to about 5000 feet, or 1500 metres, above the earth’s surface, and that, within that limit, the rate of fall diminishes as the height increases. Above the height specified the observations prove that in each ascent the balloon passed through successive strata of air whose temperature varied in a completely irregular manner, the fall of temperature being sometimes very rapid for an ascent of a few hundred feet, and sometimes very slight in a much longer interval. In each of the higher ascents we even find instances in which the thermometer rose in ascending from a lower to a higher station, reversing the ordinary progression. These alternations occurred at various heights from 5000 to 25,000 or 26,000 feet above the sea-level.53 It seems to me very doubtful whether any safe conclusions can be drawn from averages deduced from separate series of observations so discordant, but, in any case, I may confidently assert that the results of actual observations do not bear out the conclusions deduced by Mr. Glaisher.
I desire further to point out that these balloon ascents were all executed by day, in summer, and in weather as serene as can ordinarily be found in our climate. If they did authorize us to derive from them an empirical law regulating the vertical distribution of temperature, this might, at the best, serve to approximate to the true amount of atmospheric refraction found by day in geodetical observations, but would be no guide to the conditions obtaining by night, which are those important to the astronomer.
Mr. Glaisher has not failed to notice the great difference shown by the observations made when the sky was overclouded as compared with those under a clear or partially clear sky, and has given a table showing that the mean results up to a height of 4000 feet above the sea show a nearly uniform decline of 1° Fahr. for each 244 feet at ascent. The numerical results of observations made under, or amidst, cloud appear to me of no practical value, as they depend upon conditions which are subject to constant variation.
If it be true that observations in balloon ascents, which are free from the disturbances caused by the vicinity of the earth’s surface, have hitherto failed to lead to any general results indicating a normal rate of decrease of temperature with increasing elevation, it could scarcely be hoped that observations on mountains should contribute farther to enlighten us. From what has been already said, it is apparent that the fact that the place of observation is close to the surface causes disturbances the nature and amount of which must vary with each particular spot, and with the season and the condition of the atmosphere at the moment of observation.
The intensity of solar radiation increases rapidly with increasing elevation,54 so that when the sky is clear surfaces exposed to the sun are heated much above the normal temperature. Owing to its slight absorptive power the free atmosphere is little affected; but the strata nearest the surface are heated by convection, while a contrary effect follows when the surface is no longer exposed to the sun, and radiates freely to the sky.
The air in mountain countries is rarely at rest. Even when there is no sensible breeze, the unequal heating of the surface causes ascending and descending currents, which lose or gain heat by expansion or contraction. More commonly winds are experienced which, by impinging on the inclined surfaces, force bodies of air to higher elevations, and thereby directly cause a fall of temperature.
All these causes of disturbance are complicated by the action of aqueous vapour, which, in most mountain countries, is supplied from the surface, as well as borne upwards by ascending currents. Besides the effect of raising the temperature where condensation takes place, and lowering it where clouds are dissolved in strata of dry air, the amount of aqueous vapour present at a given place affects the intensity of solar radiation, and the consequent amount of heating of the surface.
In spite of these obstacles to the attainment of accurate numerical results from which to infer the distribution of temperature in the atmosphere, we are yet, for the larger part of the earth, forced to rely on mountain observations as the only available source from which any indications of a law of distribution can be gleaned. Balloon observations have hitherto, so far as I know, been confined to a few places in Europe; and, even if the results were more conclusive than they have hitherto been, we should not be entitled to infer that they held good for all parts of the earth. In countries where the course of the seasons is more uniform, and the direction and force of the winds less inconstant, it might be expected that the distribution of temperature would exhibit some nearer approach to uniformity; and the possibility of making observations at mountain stations by night might enable us to form some conjecture as to a condition of the atmosphere very different from that which obtains when the influence of the sun is present.
It cannot be said that the observations hitherto made on mountains have done as much as they might do, if properly conducted, to contribute to our knowledge; but a few leading facts may be derived from them, and it is worth while to point them out.
The most important of these is, perhaps, the influence of plateaux of elevated land in raising the temperature of the adjacent air. This is established by observation in all parts of the world, and it would appear that the rapid fall of temperature in the strata near the surface which is found at or near the level of the sea, is equally marked when we ascend from a plateau to an isolated summit. Both these conclusions, however, apply only to observations made in the summer of temperate regions, or in the warmer parts of the earth. Apart from this effect of a relatively heated surface which appears to extend above the surface to a height of about 1500 metres, or, in round numbers, 5000 English feet, mountain observations give but slight confirmation to the belief that the rate of decrease of temperature, in normal conditions of the atmosphere, diminishes as the elevation increases.
In endeavouring to use the available materials one difficulty arises from the fact that, in comparing the temperature of the upper with the lower stations, observers have rarely been supplied with simultaneous observations at the lower station, or that, when these have been available, the distance has been so great that the results throw little light on the probable condition of a vertical column of air near the higher station. In parts of the world where the daily range of temperature near the coast is very slight, we may with small risk of error use the mean temperature of the season at the lower station as the element of comparison, and, in places near the equator, the mean annual temperature. For this reason, observations in the Andes of Ecuador, Peru, and Bolivia present great advantages, and I think it may be useful to discuss the results so far as they are now available.
It is scarcely necessary to examine critically the results of the earlier explorations. Humboldt has given in the “Recueil des Observations Astronomiques,” etc., and in the “Memoires de la Société d’Arcueil,” vol. iii. p. 579, and elsewhere, the observations made by himself in Mexico, Colombia, and Peru, and also those of Caldas and Boussingault, and has derived from them a table which, with more or less modification, has been adopted in many physical treatises. It exhibits the mean differences of temperature found in successive zones differing in height by 500 toises, the interval corresponding to 974·6 metres, or very nearly 3000 English feet.
| Height in toises. | Mean temperature. | Number of metres corresponding to a fall of 1°C. from the sea-level. | Number of metres corresponding to a fall of 1°C. between successive zones of 500 toises. |
|---|---|---|---|
| Sea-level | 27·5 | — | — |
| 500 | 21·8 | 171 | 171 |
| 1000 | 18·4 | 216 | 287 |
| 1500 | 14·3 | 221 | 238 |
| 2000 | 7·0 | 190 | 133 |
| 2500 | 1·5 | 187 | 177 |
The first remark to be made about this table is that the observations on which it is founded are not properly comparable, being partly single observations made during an ascent, and partly the mean of numerous observations made at certain places, such as Mexico, Quito, etc. It may further be remarked that many of the heights determined by Humboldt have been considerably modified by the results obtained by more recent travellers, and cannot now be regarded as correct. The influence of plateaux is, however, very apparent, as nearly all the observations from which the estimated temperatures for 1000 and 1500 toises were derived were made at places situated on open elevated valleys or plateaux. At the utmost, the results can be regarded merely as rough approximations to the truth.
By far the most important available observations in the Andes are those of Mr. Whymper, made during his remarkable explorations in 1880; but, unfortunately, the details have not yet been given to the world, and, in endeavouring to make use of them, I have been forced to content myself with the brief summary published in the Proceedings of the Royal Geographical Society for 1881. Mr. Whymper was able to secure a register of the temperatures observed at Guayaquil during his stay in Ecuador, which will doubtless be published along with the record of his own observations; but it does not appear that he was able to obtain observations at Quito during his ascents to the higher peaks; and it seems that, in comparing the temperatures for the purpose of reducing his barometrical observations, he was forced to assume for Quito a mean temperature of 57·9 Fahr., or 14·4 C., obtained from a series of thermometric observations made during his stay at that place. There is reason to believe that the daily range of the thermometer at Quito is very moderate; and at the equator the differences of season are comparatively slight; nevertheless, the absence of simultaneous observations at that place diminishes the value of the results shown in the following table, in which Mr. Whymper’s results are reduced to metrical measure.
I have adopted the heights determined by Mr. Whymper as those deserving most confidence. They agree very well with those published by MM. Reiss and Stubel, so that the limits of error from this cause are inconsiderable. I have also adopted the height assigned to Quito—9350 feet, or 2848 metres. Where Mr. Whymper remained long enough on any summit to observe notable variations in the reading of the thermometer, I have taken the mean of the observed temperatures; but I have entered separately the results of the ascents of Chimborazo, one being made in January, the other in July, and in a separate line I have entered the mean results of the two.
In the following table I have entered in the first column the names of the peaks ascended by Mr. Whymper; in the second, the height of each as given by him; in the third, the observed temperature in degrees Centigrade; in the fourth, the difference between the observed temperature and 27° C.—that assumed for Guayaquil; in the fifth, the average number of metres corresponding to a fall of 1° C. in rising from the sea-level to the higher station; in the sixth, the difference between the observed temperatures and that assumed for Quito—14·4°; and in the seventh, the average number of metres corresponding to a fall of 1° C. in rising from Quito to the higher station. It is obvious that the more rapid the fall the less will be the number in columns 5 and 7.
| Name of Mountain. | Height above sea-level. | Observed temperature. | Difference of temperature at sea-level. | Average number of metres for fall of 1° C. from sea-level. | Difference of temperature at Quito. | Average number of metres for fall of 1° C. from Quito. | |
|---|---|---|---|---|---|---|---|
| 1 | Chimborazo (Jan.) | 6253 | -6·1 | 33·1 | 189 | 20·5 | 166 |
| 2 | Chimborazo (July) | 6253 | -8·06 | 35·06 | 178 | 22·46 | 151 |
| 3 | Mean of (1) and (2) | 6253 | -7·08 | 34·08 | 183·5 | 21·48 | 158·5 |
| 4 | Cotopaxi | 5959 | -8·4 | 35·4 | 168 | 22·8 | 136·5 |
| 5 | Antisana | 5870 | +11·1 | 15·9 | 369 | 3·3 | 916 |
| 6 | Cayambe | 5852 | +2·5 | 24·5 | 239 | 11·9 | 252 |
| 7 | Cahihuairazo | 5035 | +4·44 | 22·56 | 223 | 9·96 | 220 |
| 8 | Cotocachi | 4965 | +2·2 | 24·8 | 202 | 12·2 | 173·5 |
| 9 | Pichincha | 4851 | +7·77 | 19·23 | 255 | 6·63 | 302 |
| 10 | Corazon | 4837 | +4·44 | 22·56 | 214 | 9·96 | 200 |
| 11 | Sara Urcu | 4718 | +10·0 | 17·00 | 284 | 4·4 | 425 |
It will at once be seen that the temperatures observed on Antisana, Pichincha, and Sara Urcu were altogether exceptional, probably due to rapid condensation of vapour; and these may best be excluded from any discussion of the general results. The temperatures noted in the second ascent of Chimborazo were probably below the mean, or at least below the mean for the hours at which most of the other observations were made. But, as opinions may differ on that point, I have also given below the results of comparison with the mean for the two ascents of Chimborazo. For a similar reason I regard the figures for Cotopaxi, where Mr. Whymper remained for twenty-six hours on the summit, as giving too low a temperature, while that observed on Cayambe is certainly too high. The mean result for these two summits is probably a near approximation to the average for that height.
In attempting to draw conclusions from the above table, we must first remark that, in consequence of its position on a plateau, the temperature of Quito is considerably higher than it would probably be if the higher peaks descended with an uniform slope to the sea-level. The difference between the means for that place and Guayaquil is only 12·6° C.; whereas, on the supposition of an uniform decrease in ascending from the sea-level, it should be 14·2°, and still greater if we supposed that the rate of fall of temperature gradually diminishes as the elevation increases. Omitting altogether the results for numbers 5, 9, and 11 in the above table, we perceive that the observations fall into three groups: (1) those for Chimborazo, at 6253 metres; (2) those for Cotopaxi and Cayambe, with a mean height of 5905 metres; (3) those for Cahihuairazo, Cotocachi, and Corazon, whose mean height is 4950 metres. To these it may be well to compare the mean of the results for the entire series, and also the rate of decrease between the sea-level and Quito. I shall designate observations included hereunder by numbers corresponding to the lines in the preceding table. The number of metres of ascent corresponding to a fall of 1° C. gives the most convenient measure of the rate of decrease.
| Mean height. | Difference of temperature at sea-level. | Metres for fall of 1° C. from sea-level. | Difference of temperature at Quito. | Metres for fall of 1° C. from Quito. | |
|---|---|---|---|---|---|
| Quito | 2848 | 12·6 | 226 | 0 | 0 |
| Mean of 1, 4, 6, 7, 8, and 10 | 5483·5 | 27·19 | 201·5 | 14·59 | 180·6 |
| ” 3, 4, 6, 7, 8, and 10 | 5483·5 | 27·35 | 200·5 | 14·75 | 178·7 |
| ” 7, 8, and 10 | 4946 | 23·37 | 212 | 10·77 | 195 |
| ” 4 and 6 | 5905 | 29·95 | 197 | 17·35 | 176 |
We see from this table that, in ascending from the coast to the highest peaks of Ecuador, the average fall of the thermometer was, in round numbers, 1° C. for every 200 metres of ascent, while in ascending from the sea-level to the plateau of Quito the fall was proportionately less, being at the rate of 1° C. for 226 metres. On the other hand, the fall of temperature was more rapid in ascending from Quito to the higher peaks. On an average of all the ascents, we may reckon the rate of 1° for 180 metres. But it is remarkable that, taking the average of the three peaks which rise about 2000 metres above the level of Quito, the temperature fell only at the rate of 1° for 195 metres, while in ascending to peaks higher by nearly 1000 metres, the rate of fall was 1° for 176 metres, and if we take the still higher summit of Chimborazo we may reckon the rate of fall at about 1° for 160 metres.
The apparent increase in the rate of decline of temperature in the higher region is still more clearly shown if we compare the mean of the three peaks whose average height is 4946 metres, with that of the two whose average height is 5905. For a difference in the mean height of 959 metres, we find an average fall of 6·58° C., or a fall of 1° for 145 metres. Taking the first ascent of Chimborazo as giving the most probable results, we find that between this peak and the mean of the three lower summits, with a difference in height of 1307 metres, the difference of temperature is 9·73°, or a fall of 1° for 134 metres. Again, comparing Chimborazo with the mean of Cotopaxi and Cayambe, we find, for a difference of height of 348 metres, a difference of temperature of 3·15°, or a fall of 1° for 110 metres.
I am fully aware that these observations are not numerous enough to lead to any safe general conclusions; the comparatively high temperatures found at the height of about 5000 metres may be due to exceptional local conditions, such, for instance, as the ordinary formation of clouds at about that level; but, so far as they go, the observations tend to negative the supposition that in the tropics the rate of decrease of temperature diminishes as we ascend to the higher regions of the atmosphere.
MM. Reiss and Stubel made numerous observations in the Andes of Ecuador and Peru, during a prolonged visit to that region. Lists of heights obtained by reduction from their observations have appeared in various German scientific periodicals, and more fully in the American Journal of Science, vol. ii. pp. 268, 269; but, so far as I can ascertain, the record of their observations of the barometer and thermometer has never been given to the world.
In “Copernicus,” vol. iii. p. 193, et seq., Mr. Ralph Copeland has published a summary of the results of a series of meteorological observations made by him at various stations on the line of railway connecting Mollendo on the Pacific coast with Puno in Bolivia, near the lake of Titicaca, and also at La Paz and at Tacna. Two series of observations were made at Vincocaya, the summit station of the railway, 4377 metres above the sea. All the other stations are either on elevated plateaux, or on open slopes inclining gently towards the coast. The temperatures are partly derived from numerous observations and partly by taking the mean of the maxima and minima, with corrections for each station, the reasons for which are assigned by Mr. Copeland. In most of these I am inclined to concur, but there are two from which I am forced to dissent. In reducing Mr. Copeland’s tables to metrical measure, I have therefore ventured to make some corrections, which do not, however, much alter the results.
I give below the heights above the sea, in metres, with the corrected mean temperature for each place, and the dates for each set of observations.
| Places. | Latitude. | Height. | Dates of observation. | Mean temperature, corrected. |
|---|---|---|---|---|
| Mollendo | 17° 2′ 54″ | 20 | July 2 | 16·7° C. |
| Tacna | 18° 1′ 21″ | 560 | July 7–10 | 14·2° |
| Arequipa Hotel | 16° 25′ 20″ | 2346 | Feb. 2–8 | 16·2° |
| Arequipa railway station | —— | 2300 | June 29–30 | 9·0° |
| Vincocaya, I. | 15° 53′ 56″ | 4377 | Feb. 28-March 4 | 2·83° |
| Vincocaya, II. | —— | — | June 6–27 | -2·2° |
| Puno, I. | 15° 50′ 2″ | 3840 | March 20-April 4 | 9·2° |
| Puno, II. | —— | — | April 15-June 2 | 7·8° |
| La Paz | 16° 27′ 0″ | 3645 | Feb. 12–25 | 10·7° |
Without entering into minute details, or discussing the small corrections for changes in the sun’s declination to be allowed for latitude and for the dates of observation, we perceive that on the western slope of the Cordillera the rate of decrease of temperature in this region is much below the ordinary average. Estimating the mean temperature of Mollendo at 22° at the beginning of February, we find between Mollendo and Arequipa a difference of 5·8° C., or a fall in summer of 1° for an ascent of 401 metres; while in mid-winter we obtain a difference of 7·7°, showing that an ascent of 364 metres is necessary to cause a fall of 1°. This abnormal condition is, no doubt, mainly due to the exceptionally low temperature of the coast-zone. Between Arequipa and Vincocaya we may reckon the fall of temperature on the 1st of March at 14·2° for an ascent of 2031 metres, giving the proportion of 1° to 143 metres; but in winter the decrease is less rapid, as we have at the end of June a difference of about 11·5° for an ascent of 2077 metres, or about 181 metres for a fall of 1°.
A remarkable contrast is shown when we compare the temperature at Vincocaya with that of places on the plateau surrounding the great lake of Titicaca. From Mr. Copeland’s observations we may estimate the mean annual temperature of Vincocaya at 1° C., that of Puno at 8·5°, and that of La Paz at 8·8°. These figures would give a mean difference of 7·5° for a difference in height of 537 metres between Vincocaya and Puno, or a decrease of 1° for 72 metres. Between Vincocaya and La Paz we have a difference of 7·8° for a difference in height of 732 metres, or a fall of 1° for 94 metres. The mean of the two comparisons gives a fall of 1° for 83 metres, or about twice as rapid a change as the average of the comparison between Arequipa and Vincocaya. I am not disposed to attribute this remarkable difference of atmospheric conditions exclusively to the influence of plateaux in raising the mean temperature.
In my own slight experience in the Peruvian Andes, in ascending from Chicla, at about 3700 metres, to Casapalta, at about 4200 metres, I observed so complete and rapid a change in the character and aspect of the vegetation as to satisfy me that the difference in the annual mean temperature must be even greater than that observed by Mr. Copeland for a somewhat greater difference of height between Vincocaya and Puno. It may be that, in this comparatively dry region of the Andes, the higher stations receive more frequent, though not copious, falls of rain or snow, the evaporation of which maintains a constant low temperature in the surface and the surrounding air.
In comparing observations in Peru, Bolivia, or Chili with those made in the Andes of Ecuador, it must not be forgotten that the climatal conditions are essentially different. Owing to the fact that in the latter the range of the Andes is much narrower, and on one side the main valleys descend in a nearly due easterly direction, the hot, vapour-laden, easterly winds reach the plateaux still charged with moisture, and at all seasons rain is frequent and abundant. Farther south, the winds from the Atlantic have deposited the greater part of their moisture before they arrive at the western side of the main range, and the annual rainfall must be comparatively trifling.
I have sought in vain in the records of mountain observations in other parts of the world for materials from which any probable inference may be drawn as to a law regulating the ratio of decrease of temperature with increasing height above the sea-level. There is reason to admit that isolated peaks of no great height show a more rapid decrease as compared with the plain than do considerable mountain masses. Of mountains exceeding the height of 3000 metres in the tropics, the most rapid rate of decrease is that recorded for Pangerango in Java, being 1° for 178·5 metres.
The greater mountain masses in or near the tropics show nearly the same rate of decrement, by comparison with the sea-level, that I have been led to infer from the observations in Ecuador. The average rate for the Himalayas is about 1° for 194 metres of ascent, and for the less lofty peaks of Mexico Humboldt’s observations show a decrease of 1° for 188 metres. The great irregularities due to local conditions make it impossible to derive any positive conclusions as to the comparative rate of decrease in successive zones of elevation.
In Europe and North America comparisons between the temperatures at mountain summits and the sea-level give rates of decrease varying between 1° for 160 metres, and 1° for 170 metres; but it must be remarked that the averages are mainly founded on observations made in summer, and it is certain that the rate of decrease is much slower in winter. Where the difference of height is not very great, it not uncommonly happens that in winter the phenomenon is reversed, and that we experience an increase of temperature in ascending above the plain. The same result on a small scale may often be remarked on clear cold nights, when the temperature rises for a distance of some hundred feet in ascending isolated eminences, the effect being due to the cooling effect of radiation from the surface.
It seems most probable that in the winter of the temperate and polar zones the distribution of temperature in the atmosphere is subject to conditions widely different from those prevailing in summer; and, if that be true, we should have intermediate conditions in the spring and autumn; so that even if we could arrive at comparatively accurate results for one season of the year, these would not be applicable at other periods.
The general result to which I have arrived is that to ascertain the distribution of temperature in the atmosphere in successive zones of elevation is a problem of extreme complexity, towards which the existing materials do not furnish even an approximate solution. I hold, however, that it ought to be possible to obtain much more definite knowledge than we now possess by means of properly conducted observations in various parts of the world.
Foremost of these I would suggest the importance of well-conducted balloon ascents within the tropics. In selecting stations for such ascents we are somewhat restricted by local considerations, especially the extension of forests in many regions, such as the greater part of tropical Brazil. In British India there would be no difficulty in selecting suitable stations, and there would be additional value in comparing the results obtained from ascents in Bengal, and in the very different climate of the North-west Provinces. Elsewhere in the tropics we might expect valuable results from ascents in Queensland, and from the llanos of Venezuela. It seems not impossible that, with a considerably smaller outlay, useful results may hereafter be obtained by means of improved self-recording instruments sent up in captive balloons; but in most countries such a record would be liable to interruption owing to storms.
The next desideratum is to obtain for a series of years simultaneous observations at successive stations, at vertical intervals of 500 or 600 metres, situated on the flanks and at the summits of high mountains to be chosen for the purpose. Some of these might with advantage be chosen on islands, and among these the following may be suggested:—the Peak of Teneriffe, Mauna Kea in the Sandwich Islands, Fusiyama in Japan, the Piton de Neige in the island of Réunion, and Etna in Sicily. It would add much to the value of these observations if in each case there were a double series of stations, one series being on the windward, the other on the leeward side of the mountain. It would also be important to obtain observations at similar series of stations in continental regions, removed from the immediate influence of the sea. Pike’s Peak in Colorado, which already possesses an observing station at the summit, and Mount Whitney in California, which Mr. Langley has selected as eminently suited for an observatory, both offer many advantages for the desired purpose. Another desirable station might easily be found in the Caucasus, or in Armenia, and one or more could be selected on the southern declivity of the Himalayas. In South America, where railways have been carried to such great heights, it may be hoped that regular observations may at some future time be secured at the successive railway stations. It would be worthy of the enlightened governments of Chili and Argentaria to make a commencement, by providing for such a series being obtained at the stations on the railway now in course of construction over the Uspallata Pass.
For the realization of most of these desires, as well as many others affecting the progress of human knowledge, and the general welfare of our race, we must be content to await the advent of a happier era, when the fruits of industry, and the efforts of rulers, shall no longer be mainly devoted to the maintenance and development of the arts of destruction.
While awaiting such additional knowledge as may hereafter be obtained, it is necessary in the mean time to form some provisional hypothesis on which to base the formulæ for determining the difference of heights of two stations, by barometric observations, and for ascertaining the amount of atmospheric refraction; and the subject might with advantage be discussed at a congress of scientific men. I have no authority to decide on a question of such difficulty, nor do I pretend to be thoroughly versed in the somewhat voluminous literature of the subject. I may remark, however, that in one of the fullest and most elaborate works by recent writers, Dr. Rühlmann55 has proposed a formula for the reduction of barometric observations which implicitly assumes that the rate of decrement of temperature in ascending mountains is uniform, inasmuch as he takes the mean of the temperatures observed at the higher and lower stations as the value of the mean temperature of the column of air between the two stations. It would appear that his adoption of the hypothesis of an uniform rate of decrease is merely due to the apparent impossibility of discovering a more satisfactory hypothesis. Following on a line of inquiry first suggested by the late M. Plantamour and M. Charles Martins, Dr. Rühlmann has analyzed a series of two-hourly observations of temperature made during six years at the hospice of the Great St. Bernard and at the Geneva Observatory. Treating the mean temperature of the column of air between the levels of those places as the unknown quantity, and neglecting, as unimportant, the corrections for the tension of aqueous vapour and for gravity, he has deduced the “true temperature,” as he styles it, of the intermediate column from the equation of condition between the pressures, the heights, and the temperatures of the two stations, for the average of the two-hourly periods of observation for each month. He has shown that, while on the average of the entire year the mean “true temperature” of the intermediate column of air agrees pretty well with the mean of the yearly observations at the two extreme stations, the means for the separate hours and those for the separate months usually differ widely from the so-called “true temperatures” for the corresponding periods.
From this investigation Dr. Rühlmann has shown that during the warm hours of the day, and the summer months, the “true mean temperature” is lower than the mean of the observed temperatures at the two extreme stations, while at night, and during winter, it exceeds that mean to a rather greater extent. It may be objected that the cause of the apparent discrepancy lies in the fact that, in thermometric observations, we obtain, not the true temperature of the surrounding air, but that of the thermometer, and that, however carefully screened, the thermometer cannot be completely freed from the effects of radiation to and from surrounding objects. This remark applies especially to the observations at the St. Bernard, which lies at a considerable distance from Geneva, and where the temperature is unduly depressed by surrounding masses of snow. I do not, however, attach much importance to these sources of error; and I have no doubt that under the most favourable conditions the discrepancy shown by Rühlmann will be found to a greater or less extent, but I differ from that writer in the inference that he has drawn from the facts.
If I have not misunderstood his remarks, Dr. Rühlmann concludes that the true temperature of the successive strata of air in the zone between the base and the summit of a mountain is but slightly affected by the diurnal changes that are exhibited in the range of the thermometer, and to a moderate extent only by the changes of season as shown by the range of the monthly means. He has not adverted to the fact that the differences disclosed in his tables may be the result of changes in the rate of decrement of temperature in ascending from the lower to the higher station. He shows that, on the mean of the July observations, the mean temperature of the air between the levels of Geneva and the St. Bernard is lower than the mean difference of the temperatures observed at those places by 1·57° C. But this is not inconsistent with the supposition that the thermometers have recorded the true air temperature at each station, but that the rate of decrement of temperature in ascending, at that season, diminishes rapidly in the successive vertical zones. In the same manner the fact that the true mean temperature in January is higher than the mean of the observed thermometers by 1·83° C., might be accounted for by supposing that in winter the rate of decrement is smaller in the lower strata, and increases in ascending above the surface. It is equally true that, in both cases, the facts may be consistent with such an irregular distribution of the atmosphere in successive layers, or strata, of very unequal temperature as was apparent in most of Mr. Glaisher’s balloon ascents. What is completely proved is that it is only under exceptional conditions that the hypothesis of an uniform rate of decrement of temperature, directly proportional to height above the sea-level, is approximately correct for observations in the temperate zone, where there is a considerable diurnal and annual range of the thermometer.
My own impression, as the result of such study as I have been able to give to the subject, is that, in the present state of our knowledge, the reduction of barometric observations for the height of mountains made by day, and in summer, in temperate latitudes, may best be effected by the formula proposed by M. de St. Robert; while for observations made at other seasons, and in the tropics, I should prefer the formula proposed by Mr. Rühlmann.
Before closing these remarks, I may refer to an ingenious suggestion made by M. de St. Robert in a paper published in the journal Les Mondes in Paris, in 1864, the substance of which is to be found in the Atti dell’ Academia delle Scienze di Torino for 1866, p. 193. Impressed with the difficulty of approximating in practice to a correct knowledge of the distribution of temperature in the air between the summit of a mountain and a lower station, the author sought to escape from it by seeking a phenomenon, susceptible of observation, which should give a direct measure of the mean density of the air in the space between the two stations. He pointed out that the velocity of sound supplies such a measure, and that, given the barometric pressures at the higher and lower stations, the angle of elevation of the former, measured by a theodolite and corrected for refraction, and the exact time required for sound to traverse the interval between them, the height is given with a near approximation to accuracy by a simple formula. The error arising from air currents, which increase or diminish the velocity of transmission, would be readily eliminated by discharging a fire-arm simultaneously at both stations, observing the interval between the light reaching the eye and the report becoming audible, and taking the mean of the intervals observed at both stations.
M. de St. Robert does not disguise the practical difficulty of measuring the time interval with the requisite accuracy, but he thinks that it may be obtained within a fifth of a second. The error in the result is inversely proportionate to the time required to traverse the distance, and where the stations are as distant as is compatible with the sound being audible, its amount for an error of a fifth of a second is inconsiderable.
This suggestion has not received the attention which it seems to deserve. It possesses the advantage that the observations may readily be repeated with little trouble or cost, and that the risk of error may be much diminished by taking the mean of the observed intervals of time. A comparison between observations between stations whose height is known, made under different conditions, by day and night, and in different states of weather, might, I think, contribute to diminish our ignorance as to the variable conditions of the atmosphere at different heights above the surface.