SiGERSON — On the AtmospJiere. 
13 
In the present case there are two 'normal axes,' and all vibrations 
of the body are compounded of those about the ' normal axes.' 
The position of the 'normal axes' is determined by a quadratic 
equation, whose roots are the squares of the semi-axes of a certain 
section of the momental ellipsoid. 
An ellipsoid is to be drawn whose axes are in the same direction as 
the axes of the momental ellipsoid, and proportional to their squares. 
The ^normal axes' are the common conjugate diameters of the sec- 
tions in which this ellipsoid and the momental ellipsoid are cut by the 
* conjugate plane.' 
Hence the ' normal axes' are parallel to the sides of the parallelo- 
gram formed by the four points of intersection of the ellipses. 
In general, the ' normal axes' are not at right angles, but the ver- 
tical planes drawn through the 'normal axes' are always at right 
angles. 
If the centre of gravity lie in one of the principal planes, the cor- 
responding principal axis is one of the 'normal axes', and the other 
axis is perpendicular to it. 
If the moments of inertia be equal about two of the principal axes, 
one of the ' normal axes' is perpendicular to the plane containing the 
centre of gravity and the third principal axis, and the other is in that 
plane. 
If the centre of gravity lie on either of a certain pair of lines, 
passing through the point of suspension, the times of vibration about 
the ' normal axes' are equal, and the body vibrates isochronously 
under all initial circumstances. 
The ' ellipsoid of equal energy' becomes a cylinder in this case, and 
the common conjugate diameters of the sections of the cylinder and the 
momental ellipsoid by the ' conjugate plane' are the ' normal axes.' 
The identity of the two constructions is easily seen. 
The motion of the instantaneous axes in the ' conjugate plane' is 
one of oscillation. 
The motion of the centre of gravity is compounded of two simple 
harmonic vibrations at right angles to each other. 
Some apparently exceptional cases are discussed. 
V. — MiCEO- Atmospheric Eeseaeches. Ey Geoege Sigeeson, M. J}., 
Ch. M., F. L. S. (Plates lY., Y., YI., & YII.) 
[Eead January 24, 1870.] 
About a year ago I commenced a series of Microscopic Researches on 
the Atmosphere, the results of which are represented by the drawings. 
Until I had completed them, I confess that the labours of others 
in a similar direction had escaped my notice. These researches have 
obtained thereby the character of an independent investigation. Hav- 
ing been commenced with no foregone conclusion, nor any reference to 
