The error of the last-mentioned instrument does not probably exceed 1 mm. in excess of the true pressure, and, if the observations of the mercurial barometer were used, it would be expedient to apply to them a correction of +4·5 mm. But, in addition to the circumstances already mentioned, it must be noted that Mr. Carstensen’s observations extend over but eighteen days; while M. Beaumier’s record covers twenty-six days, from May 11 to June 5 inclusive. For these reasons it has appeared best to make use exclusively of the record supplied by M. Beaumier. His instrument was an aneroid barometer of the construction adopted by its maker (Leja), called in Paris baromètre holostérique. The readings were recorded daily at 10 A.M. and 4 P.M., and are carried to intervals of the quarter of a millimetre.
The first questions that arise in applying observations to the determination of altitudes relate to the corrections applicable to each instrument. The corrected readings of Secrétan’s aneroid at Tangiers, and during the voyage between that place and Mogador, varied from 760 mm. to 761·5 mm., and may safely be assumed to be nearly correct; but, on arriving at Mogador, they fell considerably. Inasmuch, however, as on comparison with the mercurial barometer at the British Consulate the difference was inconsiderable, the fall was attributed to the condition of the weather at that time. It was only on our return to Mogador from the interior, when a direct comparison between Secrétan’s and Leja’s instruments disclosed a difference of 7·3 mm. between the readings, and a further comparison between the recorded observations of the mercurial barometer and M. Beaumier’s instrument showed a difference of about 5·5 mm. between the scales of those instruments, that it became clear that Secrétan’s aneroid had suffered some change at or about the time of landing at Mogador. A careful comparison of all the observations leaves no ground for supposing that this arose from any gradual process; and it seems almost certain that by one of those accidents to which the best aneroids are exposed, a casual blow, received about the time of landing at Mogador, caused the fall of 7 or 8 millimetres which was then observed. It is quite possible that more complete accuracy would have been attained by applying a correction of —1 mm. to M. Beaumier’s observations; but it was thought more convenient to treat the discrepancy between the instruments as altogether due to error in Secrétan’s instrument, and to apply to its readings in South Marocco the correction +7·3 mm. So far as regards the altitudes determined by comparison with the Mogador observations, the difference between the method adopted and that above suggested is quite insensible; but with respect to the altitudes given in the following table as determined between April 29 and May 10, wherein the barometric pressure at Mogador is assumed at 760 mm., it is clear that, if the error of Secrétan’s instrument has been overcorrected to the extent of 1 millimetre, the altitudes given in the table should be increased by some 12 or 13 metres.
The next corrections requiring consideration are those arising from the temperature of the instrument at the time of observation, and in reference to this point the best makers of aneroid barometers are much open to criticism. They assert, and with approximate accuracy, that in the best instruments compensation for the effect of temperature on the instrument is provided; but they forget that in order to compare the indications of the aneroid with those of the mercurial barometer, or to apply to them any of the formulæ used for calculating altitudes, it is necessary to know at what temperature the column of mercury stands, the length of which is assumed to be shown by the scale of the aneroid. In point of fact, the scale of the latter instrument, when carefully laid down, is determined by direct comparison with the mercurial barometer under varying pressures, and the proper course would be to inscribe on the case of the aneroid a record of the temperature at which that comparison was made. From inquiries made of some of the best makers it seems probable that the best approximate correction is obtained by assuming the reading of the aneroid to correspond with that of the mercurial barometer at the temperature of 15° C., and this has been applied in the annexed table.
The height of M. Beaumier’s instrument above the sea level being about 10 metres, a small correction of +0·9 mm. has been made in order to obtain the corrected reading adopted in the following table for the ‘Mogador barometer.’
As most of our observations at stations in South Marocco were necessarily made either early in the morning or late in the evening, while those at Mogador were registered at 10 A.M. and 4 P.M., the pressure at the latter place corresponding to the hour of each of our observations has been found by intercalation. There is of course an obvious possibility of error here; but, except on a few occasions, when the changes of pressure were considerable and rapid, the amount is probably trifling.
It is familiar to all who have given attention to this subject, that one of the chief causes of error in the results obtained from barometric observations for altitude arises from the impossibility, in the present state of knowledge, of obtaining with tolerable accuracy the temperature of the stratum of air lying between the lower and the higher stations. This is especially true in climates such as that of South Marocco, where the sky is commonly clear, and the air relatively dry. The cooling of the surface at night, and the heating in the sunshine by day, have an effect on the layer of air in contact with that surface, and still more on the traveller’s thermometer, which at the best is imperfectly protected from radiation, out of all proportion to the actual cooling or heating effect on the air not in immediate proximity to the soil. As far as circumstances permitted, it was sought to take observations about an hour after sunrise and very soon after sunset, so as to diminish to the utmost this source of error.
It remains true, in the writer’s opinion, that when all these sources of error in the determination of heights by means of the barometer have been put together, there remains one surpassing all the others in amount which altogether escapes our means of correction. The formulæ employed for the reduction of observations to numerical results are, and must be, based on the assumption that a condition of equilibrium between the forces acting on the instruments at each station has been attained; whereas the utmost that can be asserted is that there is a continual tendency towards such equilibrium, requiring a variable time to effect it. But before equilibrium can be attained new changes occur, and the process of adjustment recommences. Even as regards stations near enough to be within sight of each other, repeated observations, however carefully corrected, give sensibly different numerical results, and when the stations are widely separated the discrepancies become serious in amount. The best course for a traveller in a mountain country is to endeavour to ascertain as nearly as possible the altitude of some fixed station by taking the mean of several observations compared with his distant station, and then to determine the altitude of the higher points reached near to such fixed station by comparison with an assumed reading of the barometer at the latter as derived from intercalation.
The altitudes of the stations at Hasni and Iminteli, given in the following table, derived from several comparisons with the Mogador readings, are probably nearly correct. That of Arround, as derived from comparison with Mogador at a time when the oscillations of pressure were relatively great and rapid, does not deserve much confidence; and the mean of two comparisons with Hasni has been preferred, the more readily as this nearly agrees with the result obtained from a boiling-water observation.
For the reduction of our observations the formula proposed by Count St. Robert, and first published in the Philosophical Magazine for 1864, has been preferred, and, for convenience, the tables based on that formula, published by the same author in the Memoirs of the Academy of Turin for 1867, have been used.
It is true that in the construction of the latter tables a value has been assumed for the constant expressing the rate of diminution of density in the atmosphere corresponding to uniform increase of altitude that is not constantly correct; but it would appear that the error resulting from this is but trifling. In regard to the greatest elevation attained by us in the Atlas, the difference in the measurement obtained by using the tables from that ascertained by accurate computation from the formula does not exceed 5 metres.