o f Edinburgh , Session 1881-82. 401 
disturbed atmosphere ; or (getting quit of the intolerable British 
inch), 
R 2 = cos 2 lat x -08 cm. 
Now the height of the barometer corresponds always to the mass 
of the air over a given horizontal area of the locality, independently 
of the temperature of the air ; and, in averages for the different 
places, no doubt independently of the wind also.* Thus for every 
centimetre of higher or lower mercury in the barometer, there is 
more or less mass of air over the locality to the extent of 1 3 *596, 
or say 14 grms. over every square centimetre of horizontal surface. 
Thus the second diagram with its angle of 30° (corresponding to 
c 2 = 60°) represents the state of things, as regards the quantity of 
air over different parts in the circle of any parallel of latitude, or at 
all events of any circle farther from the pole than 60° north or south 
latitude. It represents the state of things for every parallel of lati- 
tude in the imagined elliptic spheroid, constituting the terms we have 
to deal with in the spherical harmonic expression of the actual effect : 
and definitively, if we suppose half the excess of the greatest above 
the least radius of the elliptic spheroid in the diagram to be equal to 
the square of the sine of the latitude multiplied into ’08 cm., the 
diagram shows the distribution of a mass of matter of the same 
density as mercury, over the whole surface of the earth, which 
would experience the same resultant couple from the sun as does the 
earth’s atmosphere in reality. To evaluate this couple we may use 
the known formula ( Thomson and Taifs Natural Philosophy , vol. i. 
§ 539) relative to the mutual attraction between a mass M, not con- 
* In strong winds the barometer may stand sensibly above or below the 
proper value for the weight of the atmosphere over the place, according as the 
room containing the barometer is more exposed by openings on the windward 
or on the leeward side of the house in which it is placed. The error due to 
this cause may be sensible in the diurnal averages for one particular barometer, 
because of the daily periodic variations in the direction of the wind ; but it is 
not probably large for any well-placed barometer, and, such as it is, it must be 
fairly well eliminated in the averages for different barometers in variously 
arranged buildings and in different parts of the world. In passing, it may be 
remarked, that it is probably not a matter of no importance that the barometer- 
room of a well-appointed meteorological observatory should be as nearly as 
may be symmetrically arranged in respect to openings to the external air in 
different directions, and in respect to shelter against wind from other parts of 
the building. 
