mann * 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 twohourly 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 socalled "true temperatures" for the corresponding periods.

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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

* See “Die Barometrischen Höhenmessungen und ihre Bedeutung für die Physik der Atmosphäre," Leipzig, 1870, by R. Rühlmann.

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, a 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 eccentricity 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

*I use the term "eccentricity" in the popular sense, to express the distance of the focus from the centre of the ellipse.