Mr. Ivory on the astronomical refractions. 427 
melting ice, is to the specific gravity of mercury at the same 
temperature, as 1 to 10467: hence we have p = o. 76 ,p = 
t = o; and, by the substitution of these numbers, we get, 
/= 10467 x 0.76 metres, 
or, in English fathoms, 
l = 4349 - 8 . 
This is the length of l at the temperature of melting ice ; 
but, if the temperature be changed, it will vary directly as 
the volume of the air, and inversely as that of the mercury. 
If now we take for the radius of the earth ( = a ) , a mean 
between half the polar axis and the radius of the equator, 
and reduce the foregoing value of / to the mean temperature 
of 50° of Fahrenheit, we shall get, 
/= 45 ° 4.8 | fathoms 
£=3481280 J 
4 -= -001294 ; Log. — 3.1119343. 
The value of (x, or the height through which the thermo- 
meter must be carried at the earth’s surface, in order to de- 
press the mercury one degree, has not been determined with 
much certainty or exactness. The greatest irregularity is 
found to prevail, in regard to this element, in observations 
made on different heights and at different times. This is, no 
doubt, to be attributed in part to local peculiarities affecting 
the thermometer. The most accurate way of determining 
this element would be by means of observations made in 
balloons elevated to moderate heights. Ramond, from 38 
barometrical measurements, makes the mean depression for 
one centesimal degree equal to 164.7 metres, or 90 fathoms; 
Humboldt found 161 metres, or 88 fathoms ; and the ascent 
