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POPULAR SCIENCE REVIEW. 
attempt will be made hereafter to make Delisle’s method the basis of any 
systematic series of transit operations.” 
“ The Universe of Stars,” now in its second edition, is dedicated to Adams 
and Leverrier, and aims at establishing a new theory of the universe, by 
which, “instead of separating the stars and nebulae into distinct systems, or 
rather of looking on the stellar system as a member of the system of nebulae, 
we seem compelled to look on almost every object visible even in the most 
powerful telescope as a portion of one system, which comprises within its 
range single, multiple, and clustering stars, irresolvable nebulae, gaseous 
bodies of symmetrical and unsymmetrical figure, and in all probability 
myriads of other forms of matter as yet undetected.” It gives an accurate 
account of the results obtained by Sir W. Herschel during his long and ardu- 
ous labours in the study of the star-depths. The conclusions arrived at are 
briefly that “ the sidereal system is altogether more complicated, more varied 
in structure, than has hitherto been supposed. Within one and the same 
region coexist stars of many orders of real magnitude, the greatest being 
thousands of times larger than the least. All the nebulae hitherto discovered, 
whether gaseous or stellar, irregular, planetary, ring-formed, or elliptic, exist 
within the limits of the sidereal system. They all form part and parcel 
of that wonderful system whose nearer and brighter parts constitute the 
glory of our nocturnal heavens.” It is impossible, with a theme like this, for 
a thoughtful mind not to be led on to much grand and far-reaching speculation. 
In the presence of the Three that bear witness to man’s puniness, Matter, 
Space, and Motion, once more the cry goes up to heaven so well formulated 
by Newton, as of a child picking up pebbles of knowledge on the sea-shore, 
while the great ocean of truth lies all undiscovered before him. In this book 
it takes the form of a quotation from Jean Paul which singularly reproduces 
a kindred dream of the boldest and most imaginative thinker of antiquity, 
namely the myth of the Whorls at the end of Plato’s “ Republic.” 
The “ Treatise on Cycloids and Cycloidal Curves ” stands on a somewhat 
different footing from the works above named. Whereas they are speculative 
and theoretical, this is precise and constructive. It deals primarily with 
the geometry of cycloids, curves traced out by a point in a circle rolling on a 
straight line, or on or within another circle, and trochoids, traced out by a 
point within or without a circle so rolling. 
The cycloid, long known to ancient astronomers, was first fully investi- 
gated by Galileo. By suitably selecting radii and velocities, every form of 
epicyclic curve can be obtained, including the epicycloid and the hypocycloid. 
When the radius of the fixed circle is indefinitely enlarged, or in other 
words, when the centre of the moving circle advances uniformly in a straight 
line, the curve traced out by the moving point becomes a trochoid, and may 
either be prolate , right , or curtate , according as the velocity of the moving 
centre is greater, equal to, or less than the velocity of the point around that 
centre. Lastly, if the radius of the moving circle is indefinitely enlarged, so 
that a straight line is carried uniformly round a centre while a point travels 
uniformly along the line, the curve traced out becomes a spiral of the family 
to which belong the spiral of Archimedes and the involute of the circle. 
Ancient geometers were not very successful in investigating these curves. 
u Kven Galileo was reduced to the necessity of weighing paper figures of the 
