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.
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° 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° Fahrenheit, using the Calcutta and upper station observations, and 65·3° on the assumption of a fall of 1° for every 330 feet. To show, however, how great an error may accrue in individual cases from using the formula of 1° 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°, 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° 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.
In the Khasia mountains I found, from the mean of twelve stations and twenty-three observations, the multiplier as derived from the mean of the temperature at the upper station and at Calcutta, to be 75.2°, and as deduced from the formula to be 73·1°. Here, however, the equivalent in feet for 1° temp. is in summer very high, being 1°=385 feet. (See Appendix I.) The mean of all the elevations worked by the boiling-point is upwards of 140 feet below those worked by the barometer.
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.
It must be borne in mind that the comparative results given below afford by no means a fair idea of the accuracy to be obtained by the boiling-point. Some of the differences in elevation are probably due to the barometer. In other cases I may have read off the scale wrong, for however simple it seems to read off an instrument, those practically acquainted with their use know well how some errors almost become chronic, how with a certain familiar instrument the chance of error is very great at one particular part of the scale, and how confusing it is to read off through steam alternately from several instruments whose scales are of different dimensions, are differently divided, and differently lettered; such causes of error are constitutional in individual observers. Again, these observations are selected without any reference to other considerations but what I have stated above; the worst have been put in with the best. Had I been dependent on the boiling-point for determining my elevations, I should have observed it oftener, or at stated periods whenever in camp, worked the greater elevations from the intermediate ones, as well as from Calcutta, and resorted to every system of interpolation. Even the following observations would be amended considerably were I to have deduced the elevation by observations of the boiling-point at my camp, and added the height of my camp, either from the boiling-point observations there, or by barometer, but I thought it better to select the most independent method of observation, and to make the level of the sea at Calcutta the only datum for a lower station.
SERIES I.—Sikkim Observations.
| Place | Month | Elevation by Barom. or Trigonom. | Temp. B.P. | Air | Elevation by B.P. | Error |
| Great Rungeet river Bhomsong Guard House, Great Rungeet Choongtam Dengha Mr. Muller’s (Dorjiling) Dr. Campbell’s (Dorjiling) Mr. Hodgson’s (Dorjiling) Sinchul Lachoong Lamteng Zemu Samdong Mainom Junction of Zemu & Thlonok Tallum Yeumtong Zemu river Tungu Jongri Zemu river Lachee-pia Momay Palung Kongra Lama Snow-bed above Yeumtong Tunkra pass Yeumtso Donkia Mountain above Momay Sebolah pass Kinchinjow Donkia Mountain Donkia Mountain Bhomtso Donkia pass | Feb. Dec. Apr. Aug. Aug. Feb. Apr. Feb. Jan. Aug. Aug. July Dec. July July Sept. June July/Oct. Jan. June Aug. Sept. Oct. July Sept. Aug. Oct. Sept. Sept. Sept. Sept. Sept. Sept. Oct. Sept. | (feet) B. 818 1,544 1,864 5,268 6,368 Tr. 6,925 6,932 B. 7,429 Tr. 8,607 B. 8,712 8,884 8,976 Tr. 10,702 B. 10,846 11,482 11,919 12,070 12,751 13,194 13,281 15,262 15,362 15,620 15,694 15,985 16,083 16,808 16,978 17,394 17,585 17,624 18,510 18,307 18,450 18,466 | 210·7 210·2 208·1 202·6 200·6 199·4 200·1 199·4 197·0 196·4 196·3 196·1 193·4 193·6 191·8 191·3 190·4 189·7 188·8 188·5 186·0 186·1 185·4 184·1 184·6 164·1 183·1 182·4 181·9 181·9 181·0 180·6 179·9 181·2 181·2 | 56·3 58·0 72·7 65·0 68·0 41·3 59·5 47·6 41·7 54·6 77·0 58·6 38·0 52·0 54·6 52·2 48·5 43·4 26·0 47·0 42·8 48·6 45·8 41·5 44·5 39·0 15·0 41·0 47·8 46·5 47·5 37·1 38·8 52·0 45·5 | (feet) 904 1,321 2,049 5,175 6,246 7,122 6,745 7,318 8,529 8,777 8,937 8,916 10,516 10,872 11,451 11,887 12,139 12,696 13,151 13,360 14,912 14,960 15,437 16,041 15,816 16,317 16,279 17,049 17,470 17,517 18,026 18,143 18,597 18,305 17,866 | (feet) + 86 – 223 + 185 – 93 – 122 + 197 – 187 – 111 – 78 + 65 + 53 – 60 – 186 + 26 – 31 – 32 + 69 – 55 – 43 + 79 – 350 – 402 – 183 + 347 – 169 + 54 – 529 + 71 + 76 – 68 + 402 – 367 + 290 – 145 – 600 |
| Mean | – 58 |