406 
NATURE 
[JANUARY 25, 1917 
Dr. Kunz cites, among the precious stones 
mentioned by Shakespeare, a number of sub- 
stances which, though they can scarcely be 
reckoned precious, have long been employed in 
jewelry, such as agate, amber, coral, jet, and 
rock-crystal. His little volume, though without 
literary distinction, contains much information on 
the subject of which it treats, and will be wel- 
comed by lovers of the great dramatist. 
IDENTIFICATION OF STARS. 
Star Identifier and Diagrams for the Graphical 
Solution of Problems in Nautical Astronomy. 
By J. E. McGegan. (London: The London 
Name Plate Manufacturing Co., and J. D. 
Potter, 1916.) Price 1os. 6d. net. 
ot the pamphlet and diagrams prepared by 
Mr. McGegan he suggests a method by 
which, when an observer has taken an altitude of 
a star the identity of which is doubtful, he can, 
if he also observes the compass bearing of the 
object at the same time, ascertain its declination 
and right ascension, and thus identify it in the 
Nautical Almanac, 
The problem is very simple, provided the data 
can be accurately observed, as the annexed dia- 
gram will show: where P is the pole, Z the zenith, 
N the place of the ob- 
server, HO the hori- a 
zon, while S is the e 
star observed which 
requires to be identi- 
fied. The arc SA will 
be its altitude, the arc 4 5 ° 
PO the latitude of 
the observer. Consequently, the are ZS will be 
its zenith distance, and the arc P Z the colatitude, 
whilst the angle P ZS will be its azimuth, which 
can be obtained by correcting the compass bear- 
ine observed to the true bearing, and then de- 
ducting the result from 180° to find the azimuth. 
There is consequently a spherical triangle P Z S, 
with two sides and the included angle known, 
to find the third side PS (the polar distance) and 
the angle ZPS (the hour angle). By applying 
the hour angle to the right ascension of the meri- 
dian of the place, readily ascertained from the 
Nautical Almanac, the right ascension of the star 
is obtained and its declination from its polar 
distance. 
To solve the problem without much calcula- 
tion Mr. McGegan has ingeniously constructed 
two diagrams on equal scales, one the diagram 
of a hemisphere divided into circles of declination 
from the equator to both poles; and into meridians 
representing sidereal hour angles, or circles of 
right ascension; a second diagram on celluloid, 
which is transparent, represents a semicircle 
marked in circles of altitude from the horizon to 
the zenith, and of arcs of azimuth 0° to go° 
east and west from the meridian. 
There is, in addition, on the diagram of right 
ascension and declination a quadrant at the side 
marked from o° to go° to represent latitude. 
NO. 2465, VoL. 98] 
Now if the position. of the star by altitude and 
azimuth be marked on the gelluloid semicircle, 
and the semicircle be placed over the diagram 
of the hemisphere in such a manner that its centre 
coincides with the centre of the hemisphere, and 
its horizon cuts the quadrant marked outside the. 
hemisphere at the latitude of the observer, then 
the position on the celluloid will show on the 
diagram of the hemisphere under it the declina-. 
tion and hour angle of the star to be identified. 
In actual practice this is seldom, if ever, neces- 
sary. Star observations at sea are only of use 
when the horizon is clear and well defined—for 
instance, at twilight morning or evening, or when 
Venus or Jupiter passes the meridian at an inter- 
val of more than 24 hours from noon. When the 
horizon is well defined the stars are nearly always 
too faint to enable compass bearings of them to 
be observed. 
Stars on or near the meridian can at twilight 
nearly always be seen through the sextant, when 
invisible to the naked eye, if their approximate 
altitude be placed on the sextant. For longitude 
only very bright stars are available at twilight, 
and navigators know well where they are situated 
and where to look for them. 
As the celluloid semicircle easily slips out of 
its place over the diagram of the hemisphere, it 
would be an advantage.if a screw-pin were placed 
through the centres of both with a clamp and 
screwed tightly, when the horizon line had been 
placed on the appropriate latitude on the side of 
the diagram of the hemisphere. 
AN ARABIC ALGEBRA. 
Compendio de Algebra de Abenbéder. Texto 
arabe, traduccién y estudio por José A. Sdnchez 
Pérez. Pp. xlviit+t117. (Madrid: E. Mastre, 
1916.) 
HIS work is “a compendium of algebra com- 
posed by the sheikh Abu Abdullah Muham- 
mad b. ‘Umar b. Muhammad, generally known 
as Ibn Badr.” Practically nothing is known about 
the author, and not much about the date of the 
treatise. The MS. on which this edition is based 
was written in a.H. 744 (=A.D. 1343), and the 
text contains a reference to Abu Kamil (trans. 
p. 57, text p. 39) and “his book about algebra.” 
The editor takes this Abu Kamil to be Abu Kamil 
Shuja‘’ b. Aslam al-Hasib (the reckoner). The 
treatise comprises a theoretical part and a col- 
lection of problems, or rather a set of numerical 
examples of particular types, followed by problems 
relating to practical affairs of commerce, etc. 
The theoretical range includes (in this order) 
quadratic equations, quadratic surds, law of in- 
tegral indices, rule of signs for multiplication 
(given without any comment), multiplication of 
ordinary polynomials, division of one monomial 
by another, rule of transposition. Among the 
problems we have cases of simultaneous equations 
of various kinds; and it is clear (p. 70) that the 
author was acquainted with the arithmetical 
theory of proportion. 
