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.
APPENDIX B
REMARKS ON MR. CROLL’S THEORY OF SECULAR CHANGES OF THE EARTH’S CLIMATE
Most scientific readers are familiar with the theory respecting the influence of changes in the eccentricity of the earth’s orbit on the climate of the globe, which has been sustained with remarkable ability by Mr. James Croll. The views originally advanced in various scientific periodicals were presented to the public in a connected form in the volume entitled “Climate and Time,” wherein the author has brought a wide knowledge of the principles of physics, and of the whole field of geological science, to the support of his theory. Even those who have not given especial attention to the subject are also acquainted with the conclusions which Sir Charles Lyell drew from the discussion of Mr. Croll’s arguments, and which are contained in the thirteenth chapter of the tenth edition of his “Principles of Geology,” and also with the more recent examination of the subject which is to be found in Mr. Alfred Wallace’s important work, “Island Life.”
I need not say that a theory so important in its bearing on some of the most obscure problems of geology has been discussed, in more or less detail, by many other writers. To most of the objections presented to his theory, Mr. Croll has replied with his usual ability; and I believe that at present the prevailing tendency among geologists is towards a partial acceptance of his views, subject to the limitations assigned by Mr. Wallace. The latter author holds, in common with Sir Charles Lyell, that geographical causes, arising from the varying distribution of land and sea, have mainly controlled the distribution of temperature over the earth’s surface; but he is disposed to go farther than Lyell in admitting the influence of periods of high eccentricity in causing those great accumulations of snow and ice which were requisite to produce the phenomena of a glacial period, whenever a sufficient area of elevated land in high latitudes coincided with the period of high eccentricity.
It would probably be of little avail, even if I were to undertake the task, that I should attempt any thorough discussion of this vast and difficult problem; and it would certainly require far more space than can here be given to it. I may, however, venture to make a few remarks upon some points which have not, to the best of my knowledge, been much noticed in the discussion.
In reading Mr. Croll’s work, which charmed many an hour during the voyage to and from South America, I found it very difficult to discover any flaw in the chain of close reasoning by which he supports his conclusions. Most of the facts on which he relies are warranted by observation, and have been accepted as well established by writers of the highest authority; and his inferences as to the results of altered conditions appeared to be in strict conformity with admitted physical principles. Nevertheless, when I reflected on the anomalies which are found at the present time in respect to the climate of many spots in the world, and the complexity of the causes which determine its actual condition, I felt a doubt whether, in his attempt to trace the result of possible changes, Mr. Croll may not have overlooked some of the elements of the problem.
Let me briefly state the leading propositions of Mr. Croll’s theory in order to make intelligible the succeeding remarks.
Estimating approximately the mean distance of the earth from the sun at ninety-one and a half millions of miles, and the eccentricity55 of the sun’s place in the orbit at one and a half million, it follows that at one period of the year, which happens to be about the winter solstice of the northern hemisphere, the earth receives from the sun a quantity of heat greater than that which reaches it in the opposite part of its orbit, in the proportion of 932 to 902, or about as 1000 to 936. Midsummer of the southern hemisphere is the season when the earth is nearest to the sun; the winter of the southern and the summer of the northern hemisphere occur when the earth is farthest from the source of heat. The conclusion seems inevitable – the southern hemisphere must have hotter summers and colder winters than our hemisphere, where the heat of summer is tempered by the greater distance, and the cold of winter mitigated by the comparative nearness, of the sun.
The next point to be considered is the effect of ocean-currents, and especially of the Gulf-stream, in modifying the climatal conditions of some parts of the earth. Following in the track of the late Captain Maury and Principal Forbes, Mr. Croll has especially insisted on the importance of the great current which, issuing from the Gulf of Mexico, and flowing northward between Florida and the Bahamas, extends across the Atlantic towards the western shores of Europe. He calculates that by this current alone an amount of heat equal to that received on the entire surface of the earth in a zone thirty-two miles in breadth on each side of the equator is carried from the tropics to the cooler regions of the northern hemisphere. Mr. Croll has, I think, victoriously replied to several of the objections opposed to this portion of his argument. His estimate of the volume of water transferred by the Gulf-stream from the tropics to the northern part of the Atlantic, which he reckons at the annual amount of about 166,000 cubic miles, is, I think, in no degree exaggerated; and I also think that he is warranted in estimating the mean initial temperature at about 65° Fahr. I am, however, persuaded that in assuming 40° Fahr. as the temperature to which, on an average, this vast body of water is reduced before it returns to the equatorial zone, Mr. Croll has gone beyond the probable limit. A large part of the stream is diverted eastward about the latitude of the Azores, and is never cooled much below 55° Fahr. before the waters enter the return current on the eastern side of the Atlantic basin; and I believe that, if we allow the water of the Gulf-stream to undergo an average loss of temperature of 20° Fahr., we shall be more likely to exaggerate than to underrate the amount of cooling.
In insisting on the importance of the Gulf-stream in modifying the climate of Europe and the adjacent parts of the arctic zone, Mr. Croll agrees with many preceding writers; but, so far as I know, he was the first to suggest that in consequence of the greater persistency of the south-east trade-winds, which ordinarily extend up to, and, at some seasons, even north of, the equator, the warm waters of the Northern Atlantic derive a large share of the heat which is carried to the temperate and arctic zones from the southern hemisphere. Applying the same reasoning to the currents of the Pacific Ocean, Mr. Croll arrives at the general conclusion (“Climate and Time,” p. 94) that “the amount of heat transferred from the southern hemisphere to the northern is equal to all the heat falling within fifty-two miles on each side of the equator.”
I do not believe that the facts on which Mr. Croll bases this essential portion of his theory are sufficiently established. With regard to the Atlantic, I have expressed in the text (p. 344) an opinion, derived from conversations with practical seamen, that in the Atlantic the trade-winds of the northern are stronger than those of the southern hemisphere. That opinion, I am disposed, on further examination, to regard as incorrect. I believe that the north-east trade-winds often blow with greater force; but, taking the average of the entire year, I now think there can be no doubt that the south-east trade-winds extend over a wider area in the equatorial zone. However this may be, our knowledge of the currents of the Atlantic does not, I think, authorize us to conclude that the portion of heated water carried from the southern to the northern hemisphere is nearly so large as Mr. Croll has estimated. If the heat of the Gulf-stream were mainly supplied, as Mr. Croll contends, from that source, there should be a marked difference in the volume and temperature of the current, between the season when the north-east trade-winds approach the equator and that in which the south-east trades prevail to the north of the line, for which there is no evidence.
As regards the currents and winds of the Pacific, in spite of one considerable exception, to which I shall further allude, I think that the balance of evidence points to a greater prevalence of the south-east trade-winds, and to the probable transference of some portion of the equatorial waters from the southern to the northern hemisphere.
For the present discussion it is best to accept Mr. Croll’s estimate, and to compare the amount of heat which he supposes to be transferred from one hemisphere to the other with the total amount which is received annually from the sun on each hemisphere. For this purpose I have taken the known areas of the torrid, temperate, and frigid zones respectively, and, following Mr. Croll, I have adopted Mr. Meech’s estimate of the average amount of heat, per unit of surface, received from the sun in each zone, irrespective of absorption by the atmosphere. To estimate the proportion of heat which actually reaches the surface, I have adopted Pouillet’s measure of the proportion of solar radiation cut off at vertical incidence, which is 24 per cent. I assume 28 per cent. to be the average loss in the torrid zone, 50 per cent. in the temperate zone, and 75 per cent. in the frigid zone.56 The resulting figures, showing the proportional amount of heat annually received on the surface of each zone, and on the entire hemisphere, are as follows: —
Calculating, on the same basis, the amount received on a zone one mile wide at the equator, allowing a loss of 25 per cent. from atmospheric absorption, and multiplying the result by 104, I obtain the number 233·1 or rather more than one twenty-fifth part of the entire heat annually received from the sun by each hemisphere.
To trace the results of such a transfer of heat from one hemisphere to the other, I shall adopt a mode of reasoning, sanctioned by the great authority of Sir John Herschel, to which Mr. Croll frequently resorts. It is by solar heat that the surface of the earth is raised above the temperature of space, which is assumed to be 239 degrees below the zero of Fahrenheit’s scale. Adopting Ferrel’s estimate, I take the mean temperature of the northern hemisphere at 59·5° Fahr., or 298½ degrees above the temperature of space. To maintain this temperature, it receives one-half of the amount of solar radiation which reaches the earth, and in addition, on Mr. Croll’s hypothesis, one twenty-fifth part of that which reaches the southern hemisphere. It follows that the heat available to raise the southern hemisphere above the temperature of space stands to that which is received by the northern hemisphere in the ratio of 24:26, and that the mean temperature of the southern hemisphere should be 298·5 × 12/13, or 275·5° above the temperature of space; so that, in ordinary language, the mean temperature of the southern hemisphere should be 36·5° Fahr. If the fact corresponded with this result of theory, it would not be necessary to invoke increased eccentricity of the earth’s orbit to account for the extreme cold of one hemisphere, seeing that the actual conditions would suffice to completely alter their relative temperatures.
It occurs to me, however, that, on further consideration, Mr. Croll would reduce his estimate of the volume of heated water transferred from the southern to the northern hemisphere; but even if that estimate were reduced by one-half, we ought to find in the southern hemisphere a mean temperature of 47·8° Fahr., or nearly 12 degrees lower than that of our hemisphere.
We have already seen that, so far as climate depends on the relative position of the earth and the sun, we ought to find in the southern hemisphere climates of a more extreme character, with hotter summers and colder winters, than those to which we are accustomed. If it be true that through the agency of ocean-currents a considerable amount of heat is transferred to the northern hemisphere, that circumstance might serve to account for the fact that the summers of the southern are not generally hotter than those of the northern hemisphere; but it would, at the same time, tend to aggravate the severity of the southern winters.
At the time of the publication of Mr. Croll’s earlier memoirs, there existed a general belief that the southern hemisphere was in fact notably cooler than our portion of the globe, and he naturally referred to the supposed fact as harmonizing with the general conclusions drawn by him from theory. But, imperfect as our knowledge of the southern hemisphere still is, a good deal of information has been obtained of late years. The only stations south of the fiftieth degree of latitude from which we possess continuous observations are those mentioned in the text (p. 273); but we also know with sufficient accuracy the climates of two widely separated islands lying about 50° south; and from these we derive results widely different from those to which we were led by theoretical considerations. The following table gives approximately the mean temperatures, on Fahrenheit’s scale, for the year and for the hottest and coldest months of the places referred to in the southern hemisphere, and the means for corresponding latitudes in the northern hemisphere: —
If we compare the mean results of these five stations with those for corresponding latitudes in the northern hemisphere, we find that the summers are cooler and the winters very much milder, and that in the latitudes between 50° and 55° the mean annual temperature is notably higher. In Kerguelen Land alone the mean annual temperature is lower than the normal for the same latitude north of the equator; but that island is evidently exposed to exceptional conditions.
The differences between the mean results given above are shown by the following table, in which the signs show the excess or deficiency of the southern as compared with the northern hemisphere: —
Dr. Hann has carefully discussed the question as to the comparative mean temperatures of the two hemispheres in a paper published in the proceedings of the Vienna Academy, the substance of which is given in his Klimatologie, pp. 89, et seq.; and it is difficult to refuse assent to his conclusion that so far as the available evidence goes, it shows that the mean temperature of both hemispheres is equal.
I find, then, that the same train of reasoning by which Mr. Croll has sought to explain the occurrence of glacial periods by changes in the eccentricity of the earth’s orbit, and the precession of the equinoxes, leads us to conclusions respecting the climatal condition of the different parts of the earth, at the present amount of eccentricity, which are altogether opposed to the results of observation; and I am driven to the conclusion that the causes which he has adduced have not the predominant influence which he has attributed to them, and that there must be other agencies to which he has not assigned their due importance, but which are adequate to counteract the efficiency of those which, as observation proves, fail to achieve the effects anticipated from them.
I am far from pretending to be able to analyze completely the complex agencies which, by their mutual action, determine the climate of different parts of the earth, but I may briefly refer to two of them. Foremost of these is the relative distribution of land and sea, for a due appreciation of which we are indebted to the great work of Sir Charles Lyell. It is unnecessary here to discuss how far his view of the probable amount of change in past geological epochs may, in the present state of our knowledge, be subject to limitation. Mr. Wallace, who is the most strenuous supporter of the modern doctrine of the permanence of the present continents and ocean basins, recognizes the theoretical correctness of Lyell’s views, and admits that changes of level great enough to cause profound modifications of climate have actually occurred. Notwithstanding recent objections, it appears to me that Darwin’s hypothesis as to the subsidence of a great tract in the Southern Pacific is that which best accounts for the existence of the countless coral islands in that region; nor is the probability of a nearly continuous barrier of volcanic islands across the Atlantic to be completely dismissed. That such changes would have largely affected the climate of the earth cannot, I think, be doubted.
If I may venture to express my own view on this difficult subject, I must say that, although it has not been overlooked by the able men who have discussed it, the paramount importance of aqueous vapour as an agent for modifying climate has not yet been fully recognized. Mr. Croll has constantly discussed the phenomena of ocean-currents, as if their chief function were to affect climate by heating or cooling the surrounding air, which is thence diffused over the land surfaces, and he has devoted little attention to the effects of evaporation from the sea, and the subsequent condensation in some other region of the vapour produced. When we remember that as much heat is consumed in the conversion of one cubic mile of water into vapour as would raise the temperature of nearly ninety-seven cubic miles of water by 10° Fahr., we get some measure of the vast power of vapour as a vehicle of heat. Admitting, as I am disposed to do, that 166,000 cubic miles of water are annually conveyed northward by the Gulf-stream, and suffer an average loss of 20° Fahr. before returning to the torrid zone, I must point out that the entire heat requisite to maintain this great volume of water at the higher temperature would be consumed in the conversion of 3433 cubic miles of water into vapour. In point of fact, I believe that more than one-half of the quantity specified is expended in evaporation, and that the cooling of the waters of the Gulf-stream is mainly due to this agency. To follow the vapour thus produced, to ascertain where it is condensed, and where the heat disengaged in the act of condensation becomes available to raise the temperature of the air, is a task which is beyond our present resources; but it is one which must be performed before we can reason with any confidence as to the ultimate distribution of the heat carried by the Gulf-stream or any other ocean-current. Whatever part of the vapour produced by evaporation from the Gulf-stream goes to supply the rainfall of Western Europe, or to form snow in the arctic regions, acts as a vehicle to transfer heat from the tropics to the temperate and frigid zones. But it is more than probable that a large part of the vapour in question is carried back to the torrid zone, and that some of it is even restored to the southern hemisphere. The south-eastern branch of the Gulf-stream flows, at least partially, into the area of the north-east trade-winds. These winds reach the lower region as cold and very dry winds. As they advance towards the equator, and are gradually warmed, their capacity for aqueous vapour constantly increases, and there can be no doubt that in both hemispheres the trade-winds bear with them a large share of the vapour which goes to supply the heavy rainfall of the tropics.
In the Pacific region we have direct evidence to this effect, in the fact that in Hawaii, and elsewhere, the side of the islands exposed to the trade-winds is that of heavy rainfall, and is generally covered with forest. No sufficient data exist for estimating the amount of vapour thus carried back to the tropics from high latitudes on both sides of the equator, nor the amount of heat set free by its condensation; but we may form some conception of its probable amount by considering that at the moderate estimate of a mean annual rainfall of seventy-two inches for the portion of the globe between the tropics, this amounts to a yearly fall of 88,737 cubic miles, and that we can scarcely reckon the share of this great volume of water supplied by evaporation from the same part of the globe at more than one-half. Still less is it possible to calculate the amount of vapour annually transferred from the northern to the southern hemisphere, which goes to neutralize the apparent effect of the diversion of portions of the equatorial waters to the north side of the line. In the Atlantic basin it is probable that the larger part of the rainfall in the region including and surrounding the Gulf of Mexico and the Caribbean Sea is supplied by vapour carried from the temperate zone by the north-east trade-winds. There is some reason to believe that a portion of the rainfall of the great basin of the Amazons, south of the line, is also supplied from the same source. Several travellers report that during the rainy season the prevailing winds are from the west and north-west, the latter being especially predominant at Iquitos, about 4° S. latitude, and 1600 miles from the mouth of the river.
In tropical Australia the rainy season falls during the prevalence of the north-west monsoon, and we cannot doubt that this is mainly supplied by vapour carried from the northern hemisphere. Another region wherein the same phenomenon is exhibited on a large scale is the central portion of Polynesia, extending from the Feejee to the Society Islands over a space of at least twenty degrees of longitude. Over that wide area, as far as about twenty degrees south of the line, the regular south-east trade-wind prevails only in the winter of the southern hemisphere, while during the rest of the year, especially in summer, north and north-east winds have the predominance. Taking the mean of three stations in the Feejee Islands, of which the returns are given by Dr. Hann, I find in round numbers the very large amount of 150 inches for the mean annual rainfall, of which 105 fall during the seven months from October to April, while the five colder months from May to September supply only forty-five inches of rain. There can be little doubt that the larger part of the 105 inches falling during the warm season is derived from the northern hemisphere.
I by no means seek to account fully for the apparent contradiction between the results of theory, as developed by Dr. Croll, and the actual distribution of heat over the earth as proved by observation; but I venture to think that I have shown reason to doubt the possibility of drawing absolute conclusions as to the results of astronomical changes until we shall have fuller knowledge than we now possess of all the agencies that regulate climates.
Before concluding these remarks, I will notice one other branch of the argument in regard to which I am unable to concur with Mr. Croll. As we have seen, the essential point in his theory as to the modus operandi of changes of eccentricity, and the relative position of the poles, on the distribution of temperature, is that the currents of the equatorial zone are driven towards the pole which has the summer in aphelion, and that the cause of this shifting of the currents depends on the greater strength of the trade-winds in the hemisphere which has the winter in aphelion; the strength of the trade-winds in turn depending on the amount of difference of temperature between the equatorial and the colder zones. Taking the surface of the earth generally, the trade-winds of the southern are probably stronger than those of the northern hemisphere, and, if it were true that the south temperate and frigid zones were colder than those of the other hemisphere, it would be allowable to argue that the greater difference of temperature as compared with the equatorial zone was the cause of the greater strength of the trade-winds. But we now certainly know that the southern hemisphere between latitudes 45° and 55° is considerably warmer than the corresponding zone of the northern hemisphere, and we have good grounds for believing that the mean temperature of the whole hemisphere south of latitude 45° is higher, and certainly not lower, than that of the same portion of the northern hemisphere. We are therefore not justified in explaining the greater strength of the southern trade-winds by a greater inequality of temperature between the equator and the pole.
In my opinion the cause of this predominance of the southern trade-winds is to be sought in the fact that the southern is mainly a water hemisphere, while the northern is in great part a land hemisphere. In the south, the great currents of the atmosphere flow with scarcely any interruption, except that caused by Australia, where, in fact, the trade-winds are irregular, and lose their force. In the northern hemisphere the various winds originating in the unequal heating of the land surface interfere with the normal force of the trade-winds, and weaken their effect.
In connection with this branch of the subject, I may remark that the belief in the greater cold of the southern hemisphere mainly rests on the fact that all the land hitherto seen in high latitudes has been mountainous, and is covered by great accumulations of snow and ice. But this does not in itself justify the conclusion that the mean temperature is extremely low. It is true that the fogs which ordinarily rest on a snow-covered surface much diminish the effect of solar radiation during the summer in high latitudes, but this is compensated by the great amount of heat liberated in the condensation of vapour. The only part of the earth which is now believed to be covered with an ice-sheet is Greenland, but the mean of the observations in that country shows a temperature higher by at least 10° Fahr. than that of Northern Asia, where the amount of snowfall is very slight, and rapidly disappears during the short arctic summer. If there be, as some persons believe, a large tract of continental land surrounding the south pole, I should expect to find that the great accumulations of snow and ice are confined to the coast regions. In that case the mean temperature of the region within the antarctic circle would probably be lower than it would be in the supposition, which appears to me more probable, that the lands hitherto seen belong to scattered mountainous islands. If, from any combination of causes, one pole of the earth has ever been brought to a mean temperature much lower than that now experienced, I should expect to find that the phenomena of glaciation would be exhibited towards the equatorial limit of the cold zone, rather than in the portions near the pole. The formation of land-ice depends on the condensation of vapour, and before air-currents could reach the centre of an area of extreme cold the contained vapour would have been condensed. This consideration alone suffices, to my mind, to make the supposition of a polar ice-cap in the highest degree improbable.