The use of the boiling-point thermometer for the determination of elevations in mountainous countries appearing to me to be much underrated, I have collected the observations which I was enabled to take, and compared their results with barometrical ones.

I had always three boiling-point thermometers in use, and for several months five; the instruments were constructed by Newman, Dollond, Troughton, and Simms, and Jones, and though all in one sense good instruments, differed much from one another, and from the truth. Mr. Welsh has had the kindness to compare the three best instruments with the standards at the Kew Observatory at various temperatures between 180° and the boiling-point; from which comparison it appears, that an error of l·5° may be found at some parts of the scale of instruments most confidently vouched for by admirable makers. Dollond’s thermometer, which Dr. Thomson had used throughout his extensive west Tibetan journeys, deviated but little from the truth at all ordinary temperatures. All were so far good, that the errors, which were almost entirely attributable to carelessness in the adjustments, were constant, or increased at a constant ratio throughout all parts of the scale; so that the results of the different instruments have, after correction, proved strictly comparable.

The kettle used was a copper one, supplied by Newman, with free escape for the steam; it answered perfectly for all but very high elevations indeed, where, from the water boiling at very low temperatures, the metal of the kettle, and consequently of the thermometer, often got heated above the temperature of the boiling water.

I found that no confidence could be placed in observations taken at great elevations, by plunging the thermometer in open vessels of boiling water, however large or deep, the abstraction of heat from the surface being so rapid, that the water, though boiling below, and hence bubbling above, is not uniformly of the same temperature throughout.

On several occasions I found anomalous rises and falls in the column of mercury, for which I could not account, except theoretically, by assuming breaks in the column, which I failed to detect on lifting the instrument out of the water; at other times, I observed that the column remained for several minutes stationary, below the true temperature of the boiling water, and then suddenly rose to it. These are no doubt instrumental defects, which I only mention as being sources of error against which the observer must be on the watch: they can only be guarded against by the use of two instruments.

With regard to the formula employed for deducing the altitude from a boiling-point observation, the same corrections are to a great extent necessary as with barometric observations: if no account is taken of the probable state of atmospheric pressure at the level of the sea at or near the place of observation, for the hour of the day and month of the year, or for the latitude, it is obvious that errors of 600 to 1000 feet may be accumulated. I have elsewhere stated that the pressure at Calcutta varies nearly one inch (1000 feet), between July and January; that the daily tide amounts to one-tenth of an inch (=100 feet); that the multiplier for temperature is too great in the hot season and too small in the cold; and I have experimentally proved that more accuracy is to be obtained in measuring heights in Sikkim, by assuming the observed Calcutta pressure and temperature to accord with that of the level of the sea in the latitude of Sikkim, than by employing a theoretical pressure and temperature for the lower station.

The approximate height in feet corresponding to each degree of the boiling-point, is derived from Oltmann’s tables. The multipliers for the mean temperature of the strata of atmosphere passed through, are computed for every degree Fahrenheit, by the formula for expansion usually employed, and given in Baily’s Astronomical Tables and Biot’s Astronomie Physique.

For practical purposes it may be assumed that the traveller, in countries where boiling-point observations are most desired, has never the advantage of a contemporaneous boiling-point observation at a lower station. The approximate difference in height is hence, in most cases, deduced from the assumption, that the boiling-point temperature at the level of the sea, at the place of observation, is 212°, and that the corresponding temperature of the air at the level of the sea is hotter by one degree for every 330 feet of difference in elevation. As, however, the temperature of boiling water at the level of the sea varies at Calcutta between July and January almost from 210·7° to 212·6°, I always took the Calcutta barometer observation at the day and hour of my boiling-point observation, and corrected my approximate height by as many feet as correspond to the difference between the observed height of the barometer at Calcutta and 29·921; this correction was almost invariably (always normally) subtractive in the summer, often amounting to upwards of 400 feet: it was additive in winter, and towards the equinoxes it was very trifling.

A multitude of smaller errors, arising from anomalies in the distribution of temperature, will be apparent on consulting my observations on the temperature at various elevations in Sikkim; practically these are unavoidable. I have also calculated all my observations according to Professor J. Forbes’s formula of 1° difference of temperature of boiling-water, being the equivalent of 550 feet at all elevations. (See Ed. Phil. Trans., vol xv. p. 405.) The formula is certainly not applicable to the Sikkim Himalaya; on the contrary, my observations show that the formula employed for Boileau’s tables gives at all ordinary elevations so very close an approach to accuracy on the mean of many observations, that no material improvement in its construction is to be anticipated.

At elevations below 4000 feet, elevations calculated from the boiling-point are not to be depended on; and Dr. Thomson remarked the same in north-west India: above 17,000 feet also the observations are hazardous, except good shelter and a very steady fire is obtainable, owing to the heating of the metal above that of the water. At all other elevations a mean error of 100 feet is on the average what is to be expected in ordinary cases. For the elevation of great mountain masses, and continuously elevated areas, I conceive that the results are as good as barometrical ones; for the general purposes of botanical geography, the boiling-point thermometer supersedes the barometer in point of practical utility, for under every advantage, the transport of a glass tube full of mercury, nearly three feet long, and cased in metal, is a great drawback to the unrestrained motion of the traveller.

The following observations are selected as having at the time been considered trustworthy, owing to the care with which they were taken, their repetition in several cases, and the presumed accuracy of the barometrical or trigonometrical elevation with which they are compared. A small correction for the humidity of the air might have been introduced with advantage, but as in most barometrical observations, the calculations proceed on the assumption that the column of air is in a mean state of saturation; as the climate of the upper station was always very moist, and as most of the observations were taken during the rains, this correction would be always additive, and would never exceed sixty feet.

SERIES I.—Sikkim Observations.