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.
In the Himalaya I invariably used distilled, or snow or rain-water; but often as I have tried common river-water for comparison, I never found that it made any difference in the temperature of the boiling-point. Even the mineral-spring water at Yeumtong, and the detritus-charged glacial streams, gave no difference, and I am hence satisfied that no objection can be urged against river waters of ordinary purity.
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.
In the following observations, the tables I used were those printed by Lieutenant-Colonel Boileau for the East India Company's Magnetic Observatory at Simla, which are based upon Regnault's Table of the 'Elastic Force of Vapour.' The mean height of the barometrical column is assumed (from Bessel's formula) to be 29.924 at temp. 32 degrees, in lat. 45 degrees, which, differing only .002 from the barometric height corresponding to 212 degrees Fahrenheit, as determined experimentally by Regnault, gives 29.921 as the pressure corresponding to 212 degrees at the level of the sea.
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 degrees, 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 degrees to 212.6 degrees, 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.
For practical purposes I found it sufficient to assume the Calcutta temperature of the air at the day and hour of observation to be that of the level of the sea at the place of observation, and to take out the multiplier, from the mean of this and of the temperature at the upper station. As, however, 330 feet is a near approach to what I have shown (Appendix I.) to be the mean equivalent of 1 degree for all elevations between 6000 and 18,000 feet; and as the majority of my observations were taken between these elevations, it results that the mean of all the multipliers employed in Sikkim for forty-four observations amounts to 65.1 degrees Fahrenheit, using the Calcutta and upper station observations, and 65.3 degrees on the assumption of a fall of 1 degree for every 330 feet. To show, however, how great an error may accrue in individual cases from using the formula of 1 degree to 330, I may mention that on one occasion, being at an elevation of 12,000 feet, with a temperature of the air of 70 degrees, the error amounted to upwards of 220 feet, and as the same temperature may be recorded at much greater elevations, it follows that in such cases the formula should not be employed without modification.
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 degree 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.