These calculations are performed by the help of logarithms. It is desirable, however, to approxi mate at least to barometrical measurements with out such aid. A very simple rule for this ob ject has been given by Professor Leslie in his Ele a 'Rents of Geometry. Since Log. 6 – = 2 M b + (aa— +6 b)3+ 5 a &c.), where M denotes the modulus of the logarithmic system. When a ap proaches to 6, the lower terms may be rejected without a —b sensible error, or Log. M ), very near ly. Wherefore, in reference to our atmosphere, the modulus is expressed by the equiponderant column of homogeneous fluid, or 60,000 X .4342945 = 26,058 feet, or only 26,000 in round numbers ; whence, as the sum of She 'mercurial columns is to their deference, so is the constant number 52,000 feet to the approximate height. Let General Roy's obser vation on Snowdon be resumed as an example : The analogy is 80.0g1 + or 56.530: 3.652 : : 52000: 8,359, the approximate ele vation, differing very little from the logarithmic result.
This mode of calculation may be deemed suffi ciently accurate for determining any altitude that exceeds not 5000 feet. But it will extend to great.. er elevations, if the second term of the series be like-. wise taken; which is done by striking off three figures, and cubing the half of this number. Thus, resum ing the mensuration of Chimboraco ; 44.895:15.105 : : 52,000:17,496, and = 670, making together 18,166 for a nearer approximation.
The calculation of barometrical measurements, in cluding the corrections required, is rendered most easy and expeditious by means of a sliding rule made by Mr Cary, optician in London. This small in strument should always go along with mountain ba rometers, and it will be found a very agreeable com panion to every geological traveller.
But portable barometers, in spite of every precau tion, are yet so liable to be broken or deranged, that other auxiliary methods are desirable for ascertaining distant elevations. In this view, the variation of the boiling point of water was proposed by Fahrenheit, as far back as the year 1724, the idea having occurred to as it had done before to Amontons, while with experiments to perfect his regard, however, seems to have been paid to the sugges tion, till De Luc and Saussure made a series of observe: tions on the heat of ebullition at different elevations above the surface. About thirty years since, Caval lo attempted to revive the scheme of Fahrenheit, but experienced much difficulty in preventing the irregular starts of the thermometer plunged in boil ing water. The best and surest way of examining the heat of ebullition, is to suspend the bulb of the thermometer in the confined steam, as it rises from the water ; and this mode, we understand, has very lately been resumed, with great prospect of success, by the Reverend Mr Wollaston.
The heat at which water boils, or passes into the form of steam, depends on the weight of the super incumbent atmosphere. By diininishing this pres
sure, the point of ebullition is always lowered. It appears that, while the boiling heat sinks by equal differences, the corresponding atmospheric pressure decreases exactly, or at least extremely nearly, in a • geometrical progression ; it being found that every time such pressure is reduced to one half, the temperature of boiling water suffers a regular diminu tion of about eighteen centesimal degrees. This beautiful relation assimilates with the law which con - nects the density and elevation of the successive strata of the atmosphere. The interval noticed between the boiling points at two distinct stations must be pro portional to their difference of al6tude above the level of the sea. We have, therefore, only to deter mine the coefficient or constant multiplier; which may be discovered either from an experiment under the rarefied receiver of an air-pump, or from an ac tual observation performed at the bottom and on the top of some lofty mountain. We shall prefer at pre sent. the observation made by Saussure on the sum mit of Mont Blanc. This diligent philosopher found, by means of a very delicate thermometer constructed on purpose, that water which boiled at 101°.62 in the plain below when the barometer stood at 30.534 English inches, boiled .at 86°.24 on the top of that mountain, while the barometer had sunk to 17.136. Wherefore the distance between the points of ebulli tion, or 15.38 centesimal degrees; must correspond to an approximate elevation of 15,050 feet; which gives 978i feet of ascent for each degree, supposing the mean temperature of the atmospheric column to be that of congelation. But it will be more convenient to assume 1000 for the constant multiplier, which corresponds to the temperature of To reduce this very simple result into practice, it would be requisite to have a thermometer with a fine capillary bore, and nicely constructed, the stem six or eight inches long, and bearing ten or a few more degrees from the boiling point ; these degrees to be divided into twenty or perhaps fifty equal parts en graved on the tube, which should be rather thick, and terminating i0 a bulb of about half an inch dia meter. This thermometer, being fitted with a brass ring two inches above the bulb, should screw into the narrow neck of a small copper flask, which holds some water, but has a hole perforated near the top for allowing the steam to escape. The water may he made to boil by the application of a lamp. The difference between the indications of the thermome ters at the two stations being multiplied by a thou sand feet, will give the elevation corresponding to a temperature of 5°. The correction for the actual mean temperature can easily be applied. If a more correct coefficient be afterwards determined, the same thousand, retained as multiplier, may easily be adapted to another temperature.