318 
MR. AIRY’S ACCOUNT OF THE HARTON EXPERIMENT 
34. The next correction is that for the density of the atmosphere. If we adopt 
Sir George Shuckburgh’s elements (which are abundantly accurate for this pur- 
pose), the barometer-reading being B (expressed in English inches) at the tempera- 
ture f of Fahrenheit, its reading at temperature 53° would be 
g 
2 ^ (29-27 -t— 53 X 0-002615) = B(l — 53 X 0*0000896). 
The proportion of the weight of air in this state to that of air at barometer-reading 
29‘“'*27, thermometer 53° (Sir George Shuckburgh’s standard elements), will be 
X (l +5|^') =^,{1 -7=^X0-002173) 
= 2^(1-006519 — 50X0*002173). 
With the elements 29'"*27 and 53°, the weight of air is ^ that of water; and, with 
1 1 
Kater’s specific gravity 8*469, the weight of air is X §.409 that of the pendulum ; 
the effect of this on the vibrations of the pendulum, adopting Colonel Sabine’s factor 
1*655 of the statical buoyancy, will be to diminish them by the part 
Bx 1*655 
1672 X 8*469 X 29*27 ^ ^ 50X0*002173). 
In the small term multiplied by t — 50, we may consider Then the diriii- 
29*27 25* 
nation of the number of vibrations will be 
B X 1*655 X 1*006519 
1672x8*469x29*27 ‘ 
50 
0*00226 X 1*655 
1672x8*469 ’ 
or B X 0*00000401 9 — ^ - 50 X 0*00000026. 
In order to correct the number of vibrations observed, so as to produce the number 
of vibrations which would take place in vacuum, we must multiply the number 
observed by 1 -f B X 0*000004019 - 50 x 0*00000026. 
35. Combining this factor with the factor depending on the temperature of the 
pendulum, or l-f-^ — 50x0*00000501, the complete factor is 
1 -fB X 0*000004019+^—50x0*00000475, 
or (1 + B X 0*00000401 9) X (1+^— 50 X 0*00000475). 
The logarithms of these factors are B X 0*000001 7453 and 50x0*000002063. The 
following Tables will suffice for the examination of the corrections in the succeeding 
Section. 
