This historic book may have numerous typos and missing text.
Purchasers can usually download a free scanned copy of the original
book (without typos) from the publisher. Not indexed. Not
illustrated. 1896 edition. Excerpt: ...eliminated. The series of
operations thus continually raises the order of the coefficients of
the periodic terms in R. We go on with the operations until these
coefficients become sufficiently small to be neglected. Delaunay
has continued them until he has found all terms in the longitude
correctly to the seventh order inclusive; in addition, some
coefficients are calculated to higher orders when slow convergence
indicated the necessity of carrying the approximations further. The
number of operations required is very large. Delaunay retains all
terms in R up to the eighth order inclusive. He first carries out
57 operations, by means of which he eliminates all periodic terms
in R which are of an order less than the fourth. The first
operation is that outlined in Art. 195 above; then follows the
elimination of the terms with arguments 1, Ih + 2g + H-ih -2tf-21'
1, etc.--those terms whose coefficients are lowered by the
integrations being, in general, considered first. The expression
for R (in which every term produced by the successive changes of
the variables is shown separately) together with the details of
these operations occupy the greater part of Vol. i.; the expression
for R alone occupies pages 119-256. Vol. H. opens with the value of
R which remains after the 57 operations have been carried out: it
now contains no periodic term of an order less than the fourth and
the great majority of the terms are of a higher order. He then
makes 435 further operations in order to eliminate these remaining
terms. In most of these operations it is not necessary to change
the variables in R: the small changes produced are made in the
coordinates only. There are, however, five periodic terms, arising
from changes in R, to be taken into account...
|Country of origin:
Ernest William Brown
||246 x 189 x 5mm (L x W x T)
||Paperback - Trade
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