Notices respectiny New Books. VE 
and meeting the barycentride. Lines are drawn from O to 
the points of intersection, and the angles which they make 
with OA are inversely as the distances laid off from O along 
the perpendicular. 
Suppose the largest of these angles (marked AQ1) to be 
given. The corresponding point 1 on the perpendicular to 
OA can be found by bisecting the radius vector O1 of the 
curve at right angles, and the figure can be completed in 
accordance with the above description. We thus obtain not 
only the 4 and 1 of the given angle, but also an angle which 
is to the given angle as 1 to “2. The construction is ex- 
tremely well conditioned. 
The following values of sin 9/9 are useful for plotting the 
curve, 
et 45° =-900 | COL email rw GL 
iby "989 | GU F827 90F = 60 t 
30 code | LD, Poo 
and a check is furnished by the fact that the tangent to the 
curve at P (fig. 1) must pass through Q the extremity of the 
are AQ, of which P is the centroid. 
When the tangent at P is parallel to AO we have 
OA sin 20=OP sin 8, OA cos §=4 OP; hence OP is bi- 
sected at right angles by AH, and P and O are equidistant 
from A. The complete curve consists of an infinite series of 
convolutions, all touching OA at O; and in each convolution 
the point furthest from OA lies on the circle described round 
A with radius AO. 



IX. Notices respecting New Books. 
Cuartes NorpMann. Theses présentées a la Faculté des Sciences 
de Paris. 1*¢ These: EHssaz sur le role des ondes Hertziennes 
en Astronomie Physique et sur diverses questions qui s’y rattachent. 
Paris: Gauthier Villars. 1903. 
HIS thesis for the Paris Doctorate of Science was sustained on 
June 13th, 1903, the examiners being Profs. H. Poincaré, Pellat, 
and Moissan. It is well worth the attention of all interested in 
astrophysical speculations, if only for the wealth of references it 
contains. It treats of such varied subjects as the Solar Corona, 
Nebulae, Nova Persei, Aurora, and Terrestrial Magnetism. The 
work is mainly devoted to the exposition of the author’s theories 
as to the causes of the several phenomena discussed, and to de- 
structive criticism of other theories. Older views, such as 
Faraday’s on Terrestrial Magnetism, are not neglected, and a 
large number of recent writers (¢. g. Arrhenius, Bigelow, Birke- 
land, Deslandres, Goldstein, Lockyer, and Schuster) will find 
something to interest them. Before passing to theory, the author 
deals slightly with two positive contributions to our stock of 
scientific facts. He tried but failed to detect Hertzian waves 
proceeding from the sun, the experiment being carried out on 
