THERMOMETER FOR THE DETERMINATION OF RELATIVE HEIGHTS. 129 
It is to be observed, that the differences of height determined by the two methods 
do not differ from one another in any single case by so large a quantity as do the 
greatest and least difference of level in the fourth column, determined from the ba- 
rometric observations at the two places ; while in many the accordance is almost 
perfect. One of the most satisfactory results in this respect is, however, that derived 
from the observation No. 2. at Mogadino, which appears from Table I. to be one of 
those least likely to be correct, since it places the surface of the Lago Maggiore 
much below its possible level. This alone sufficiently shows that the accordance 
above remarked can only be taken as a general indication of the accuracy of the in- 
strument. 
Having thus shown that the instrument is perfectly capable of furnishing correct 
data for the determination of difference of level, though apparently its indications 
cannot in all cases be relied on, it becomes further interesting to inquire how far it 
may be depended on when made use of without reference to corresponding observa- 
tions at any fixed station. It is obvious that the accuracy of a series of heights thus 
obtained must, to a certain extent, be vitiated by the diurnal changes in the atmo- 
spheric pressure, but it will be seen that this source of error does not operate to the 
extent that might, a priori, be supposed probable, and that, whether from a fortuitous 
balancing of errors, or from some other cause, the discrepancies in those cases where 
the previously determined height is probably most near the truth, are less considerable 
than might be expected. In order thus to obtain the results given in the following 
Table III., it became necessary again to modify the standard formula on account of 
the instrumental error. By multiplying the correction, C=-0433, by 548 we obtain 
it in the form of a difference of altitude for each degree of observed difference of 
boiling temperature at two successive places of observation, to be added to the factor 
548 to form the constant multiplier for this particular instrument. We thus obtain 
548X 1-0433 = 57172, 
or, with sufficient accuracy, 572. 
The working formula then becomes 
H = 572(& — &').{ 1 + (7 — 32°) ’00222}. 
In the following Table, in which the results have been calculated with this formula, 
the differences of level are determined from station to station in the order in which 
the observations were made, and, in case of two or more observations having been 
made at the same station, those most approximate in time have been employed. 
Taking the station at Geneva as a starting-point, and assuming its level, derived from 
that of the surface of the lake given in the Bibliotheque Universelle de Geneve, to be 
1264 English feet above the sea level, the calculated differences have been added to 
this in succession, and the altitudes by observation obtained. 
