12. A Demonstration of the Rule for finding the Place of a
Meteor, in the second Problem, page 218 o/* this Volume,
[pp. 437—439.]
VOLUME FOURTH. PART FIRST.
Published in 1818.
13. On a Mistake which exists in the Solar Tables of Mayer,
Lalande, and Zach* [pp. 2, 3.]
14. On the Calculation of the Oblateness of the Earth, by
Means of the observed Lengths of a Pendulum in
different Latitudes, according to the Method given by
motions of a pendulum thus suspended, and the very curious experiments of Professor Dean,
who explains, in this mode, the apparent motion of the earth as seen from the moon, engaged
Dr. Bowditch in the examination of the theory of these motions. The result has been, he
adds, " une recherche tres interessante." " Comme ce memoire merite d'etre mieux connu,
et qu'il ne I'est pas generalement, vu la difSculte de se procurer des livres americains, nous
en donnerons la traduction dans un de nos cahiers."
* Dr. Bowditch states, that " The attraction of Jupiter produces an equation in the
expression of the Sun's distance from the Earth, and a Table is given for its computation,
by Mayer, in 1770," &c. ; " and ever since this Table was first published, which is about fifty
years, an error of six signs has always existed in the argument by which the correction is
found ; so that, when the equation is really svhtractive, it will frequently be found by the
Table to be additive, and the contrary." — "In De Lambre's Solar Tables, published in 1806,
the form of the table is wholly altered, the method of entry by a double argument being used ;
and by thus taking a different path, the error is avoided, without noticing that it really does
exist in the other works."
Baron Zach, in his Monatliche Correspondenz, Vol. VIII. p. 449, A. D. 1803, says
that Bowditch, an American astronomer, has called his attention to this mistake ; and, after
admitting its importance, frankly adds, " Allen Astronomen, welche sich mit Verfertigung
der Sonnen-Tafeln beschaftigt haben, einen La Caille, Tob. Mayer, La Lande, De
Lambre und mir ist dieser Fehler entgangen."
MEMOIR. 51
Laplace, in the Second Volume of his "Micanique
Cileste;*' tcith Remarks on other Parts of the same
Work relating to the Figure of the Earth. [pp. 3—24.]
The object of this communication is to correct certain errors in
the article " Earth " in Recs's Cyclopaedia, to the end that currency
should not be given to inaccurate ideas on the subject, by that popular
work.
15. Method of correcting the apparent Distance of the Moon
from the Sun, or a Star, for the Effects of Parallax
and Refraction. [pp. 24 — 31.]
This is but the rule given in the Practical Navigator, making all
the corrections in question additive. It is another instance of the
simplicity at which he always aimed in his rules and formulas.*
16. On the Method of computing the Dip of the Magnetic
Needle in different Latitudes, according to the Theory
of Mr. Biot. [pp. 31—36.]
17. Remarks on the Methods of correcting the Elements of the
Orbit of a Comet, in Netcton^s ^^Principia" and in
Laplace* s ^^ Micanique Celeste." [pp. 36 — 48.]
This communication proves that two equations in the Principia,
the accuracy of which several commentators upon that work had
• In Zach's Monatl. Carres., Vol. XVII. p. 411, A. D. 1808, this method is mentioned
as being in the Appendix to the New American Practical Navigator, printed at Newburyport,
1804 ; and the editor says, " Der Verfasser ist ein Americaner, Bowditch, und Delambre hat
69 der Muhe werth gehalten, eine umstandliche Darstellung dieses Verfahrens zu geben."
Then follows a somewhat minute account of the method. — See note to article 1.
52 MEMOIR.
attempted to prove, and as to which no doubts had jet been expressed
or insinuated, always made the corrections in question " double of
what they ought to be," and restricts the method of Laplace as
appropriate only where the number of observations is small.
18. Remarks on the usual Demonstration of the Permanency
of the Solar System, with Respect to the Eccentricities
and Inclinations of the Orbits of the Planets, [pp. 48 — 51.]
19. Remarks on Dr. Stewarfs Formula for computing the
Motion of the Moon^s Apsides , as given in the Supplement
to the Encyclopcedia Britannica. [pp. 51 — 61.]
This is a very curious and interesting communication. A method
which, notwithstanding doubts had been expressed respecting it,
had been sanctioned as accurate by Dr. Hutton, by Lalande, and
Playfair, — the latter of whom even considered its accuracy to have
been demonstrated, — is in this memoir proved to have been true only
in the particular case supposed ; and it is shown that, as a general
method, it wholly fails.
VOLUME FOURTH. PART SECOND.
Published in 1820.
20. On the Meteor which passed over Wilmington, in the State
of Delaware, November 21, 1819. [pp. 3— 14.]
21. Occultation of Spica by the Moon, observed at Salem,
[p. 14.]
22. On a Mistake which exists in the Calculation of Mr,
Poisson relative to the Distribution of the Electrical
Matter upon the Surfaces of two Globes, in Vol. XII.
MEMOIR. 6S
of the **M4moir€8 de la classe dea sciences mathimatiques
et physiques de TInstitut Imperial de France^* [pp. 15—17.]
23. Elements of the Comet of 1819.* [pp. 17—19.]
Besides the above contributions to the Memoirs of the American
Academy, Dr. Bowditch was the writer of several other articles,
among which may be mentioned the following : —
1. Notice of the Comet of 1807. Published in the Monthly An-
thology for December, 1807, Vol. IV. [pp. 653, 654.]
2. Review of a ^^ Report of the Committee (of Congress,) to
whom was referred, on the 25th of January, 1810, the
Memorial of William Lambert, accompanied with
sundry Papers relating to the Establishment of a First
Meridian for the United States, at the permanent Seat
of their Government" Published in the Monthly An-
thology for October, 1810, Vol. IX. [pp. 245— 266.]
This article occupies twenty-one pages, and proves very
conclusively the great advantages of continuing to estimate the
longitude from Greenwich, which Mr. Lambert considered "a sort
of degrading and unnecessary dependence on a foreign nation," and
an "encumbrance unworthy of the freedom and sovereignty of the
American people." This Memorial the reviewer shows to be " a
compilation, with needless repetitions and palpable mistakes,
evincing a great want of knowledge in the principles of the
• For a statement of Dr. Bowdilch's communications to the Memoirs of the Academy,
and an abstract of their contents, from which several of our remarks in the text are
condensed, see Mr. Pickering's Ekilogy, pp. 17 — 31.
VOL. IV.
54 MEMOIR.
calculations ; " and that, " both as respects its object and execution,
it was wholly undeserving the patronage of the National Legislature."
3. Defence of the Revieic of Mr. Lamberfs Memorial.
Published in the Monthly Anthology for January, 1811,
Vol. X. [pp. 40—49.]
Mr. Lambert having made an angry reply, charging his reviewer
with " twistical cunning," " ingenious quibbling," " zeal for the honor
of the British nation, and the convenience of British mariners,"
and challenging him " to examine his computation of the longitude
of the Capitol at Washington from Greenwich, and to point out a
mistake that can be made palpable,'''' — Dr. Bowditch, in this reply,
considers these charges of Mr. Lambert as beneath his notice,
but accepts his challenge, and proves that there is an error in every
one of the six examples he has given.
These two papers were fatal to the proposed project; and,
fortunately for the interests of science, Greenwich continues to be
the first meridian of all who speak the English language.
4. Review of ^^A Treatise on the most easy and convenient
Method of computing the Path of a Comet, from several
Observations ; by William Gibers, M. D. ; Weimar,
1797;" — and of ^^Theoria Motus Corporum Ccelestium
in Sectionibus Conicis Solem ambientium ; " by Charles
Frederick Gauss; Hamburg, 1809. Published in the
North American Review for April, 1820, Vol. X.*
[pp. 260—272.]
* A copy of this article Dr. Bowditch sent to Baron Zach, with the letter before
referred to, marJcing a part of it as written by Mr. Everett, the editor. Zach publishes
MEMOIR. 55
This article gives an account of several German astronomers
and their most noted periodical publications. Thus it contains a
notice of Dr. Olbers — " the Columbus of the planetary world " —
and of Gauss, the authors of the two works reviewed ; an account
of Bode's Astronomisches Jahrbuch, Zach's Monatliche CorrespondenZf
and the Zeitschrifi fiir Astronomie. It states tlie fact that, "out of
thirteen primary planets and satellites, discovered since the year
1781, we are indebted to persons born in Germany for twelve; and
that, in the determination of the orbits of these new bodies, they
have done more than all the other astronomers in the world.''
5. Review of ^^ A remarkable Astronomical Discovery, and
Observations of the Comet of July, 1819; by Dr. Olbers
of Bremen ; published in Bode^s Astronomisches Jahrbuch
for 1822;" [and of two other articles in the same work,
for the years 1822 and 1823, on the same subject, by
Professor Encke of the Ducal Observatory at Seeberg,
near Gotha.] Published in the North American Review
for January, 1822, Vol. XIV. [pp. 26—34.]
extracts from it in his notes upon this letter, Vol. X. p. 231, and says, " It will be interesting
to the reader to learn how men of science in America render justice to those of Germany,
while they reproach their brethren beyond the water for the little attention which they have
bestowed upon our productions." Dr. Bowdltch mentions in this review an interesting
paper which Mr. Ivory had published in the Transactions of the Royal Society of London,
1814, giving a method of his own for computing the orbit of a comet, which, " upon examination,
turns out to be nothing more than that which Dr. Olbers had published in his work above
seventeen years before, although this coincidence must have been wholly unknown to Mr.
Ivory, and to the other members of the Royal Society. We consider this as a striking
instance of the little attention paid in Great Britain to works of mathematical science printed
in Germany." The passage added by Mr. Everett was merely that which states a like
neglect of German literature.
56 MEMOIR.
A copy ot this article on Encke's comet Dr. Bowditch also sent
with the letter before mentioned, to Baron Zach, who, in his notes,
states that Dr. Bowditch " has here collected all that has been said
and done respecting this famous comet." In the concluding
paragraph of this article, the reviewer expresses his regret that,
"while Great Britain alone can boast of more than thirty public
and private observatories of considerable note, we have not, in
the whole United States, one that deserves the name." He also
speaks of the duties imposed on the importation of mathematical
instruments and scientific works, as Jines and penalties, which had
been justly called " a bounty upon ignorance," &c. This whole
paragraph is extracted by Zach, (Vol. X. p. 245,) and he says,
"Voici de quelle maniere un bon republicain exhale son chagrin
en public ; c'est au moins quelque chose,^^ &c.
6. Letter to Baron Zach, dated November 22, 1822 ; with a
Postscript, dated December 20, 1823. Published in his
Correspondance Astronomique for the year 1824,* Vol.
X. [pp. 223—230.]
7. Review, entitled ^^ Remarks on several Papers published in
former Volumes of this Journal ;" [the first being remarks
on "A New Algebraical Series, by Professor W^allace, of
Columbia, S. C. ;"] published in Silliman's Journal for
1824, Vol. VIII. [pp. 131— 139;] — and Remarks on Mr.
* This letter has been already more than once referred to, and contains many interesting
facts. The editor's comments upon it occupy twenty pages. With this letter Dr. Bowditch
had sent, besides his articles mentioned in the two last preceding items, a copy of the fifth
edition of the Practical Navigator. The editor says of him, " C'est le premier, et jusqu'a-
present le seul grand geometre en Amerique."
MEMOIR. 57
Wallace's Reply ; published in the same Journal for 1825,
Vol. IX. [pp. 293-^04.]
The reviewer expresses his surprise that any offence should have
l)een given hy the mere statement of the historical fact that this
" new series " was but the usual development of the binomial
theorem, and the same which had been given by Euler fifty years
before.*
8. Review of ^^Fundamenta AstronomicB" by Frederick William
Bessel; 1818; — of the Tables of the Moon, by M,
Burckhardt ; 1812 ; — of the New Tables of Jupiter and
* Professor Wallace, in his Reply, states that he did not claim the series as neWj and
appeals to a reference which he had made in his original article to Mr. Stainville, &c., and,
not knowing wlio his opponent was, says that he does not, like his reviewer, refer his readers
" to the Complement des Eletncns d'AIgebre, however useful as a school-book" &c. He also
states, " that the results which Euler has given do not include a single case of a transcendent
function, and were only given as examples of the applications of the simplest case of the
binomial theorem," &tc. Dr. Bowditch, in his rejoinder, mentions the vague terms in which
Mr. Stainville had been originally referred to, and says, " It now appears that Mr. Stainville
gave it as new for thejirst time in 1818, and Professor Wallace for the second time in 1824,
Euler's having been published in 1775 : " and again ; " It is believed that most persons, after
reading what Professor W. has written, would suppose he claimed some, if not a very large
portion, for his own. But the real fact is, that none of it is his. The whole of the first seven
pages, and a large portion of the two remaining pages, of Professor W.'s first communication,
are merely literal translations from Stainville and Gergonne ; and what is not copied from
tijem is quite unimportant." He also says, "It is a fact, notwithstanding the positive
declaration of Professor W. to the contrary, that Euler's demonstration is not restricted to this
very simple case, but is general for all values of the exponent, whether integer, fractional
negative, or surd ; and it is characterized by Lacroix as being elegant and rigorous." This
review will be found quite amusing and piquant. It is, like the articles on Mr. Lambert's
Memorial, both as to matter and style, a fair specimen of Dr. Bowditch's powers as a
controversial writer.
VOL. IV. p
58 MEMOIR.
of Saturn^ by M. Boiivard ; 1808 ; — of the Tables of
the Satellites of Jupiter^ ^c, by M. Delambre ; 1817;
— of the Tables of Venus, of Mars, and of Mercury, by
B. de Lindenau ; 1810, 1811, and 1813; — and of the
Memoir on the Figure of the Earth, by M. de Laplace ;
1817 and 1818.* Published in the North American
Review for April, 1825, Vol. XX. [pp. 309— 367.] f
This brief but most comprehensive article upon modern astronomy
will be found to possess an uncommon degree of interest. It
consists of a series of biographical sketches, in which are described
all who have been remarkable for the successful cultivation of
physical science in modern times, bringing into view their actual
and relative services and merits, and awarding to each the degree
of approval to which he was entitled ; — the writer now dwelling
with enthusiasm upon his favorite Lagrange, now bestowing a
more qualified and guarded approbation, or a positive censure, upon
others inferior in powers and attainments to that distinguished
mathematician, or opposite to him in character. J It comprises,
* The titles of the particular works reviewed, are here given in an abridged form.
t In the Notes to Mr. Pickering's Eulogy, p. 95, a list is given, without comment,
of six of the above eight articles, the fifth and seventh not being noticed. All these
occasional publications of Dr. Bowditch, excepting the letter to Baron Zach, were collected
by him in two volumes, now in his library.
X Thus he says, " Upon the decease of Euler, Lagrange remained undisputedly the
greatest mathematician then living," &;c. ; while of Dr. Bradley's successor he says, " Dr.
Bliss was wholly unworthy of the office of astronomer royal. The account of his life by
La Lande is comprised in less than a dozen words — ' Bliss etait astronome royal ; il mourut
en 1765.' " This article is the one, of all Dr. Bowditch's occasional publications, which
exhibits in the clearest light his peculiar talents and acquirements. Evidently the work of one
possessing a, knowledge of the actual state of mathematical science, in its various departments,
MEMOIR. as
especially, a very full account of Dr. Bradley's observations, and
of Bessel's services in reducing them ; of the best makers of
mathematical instruments — Graham, Bird, Ramsden, Troughton,
Jones, Reichenbach, Frauenhofer, Herschel, &c. ; of the successive
astronomers royal at Greenwich, and of the other chief European
observers ; and, lastly, " it gives an account of the labors of those
mathematicians who have improved the science of astronomy by
their calculations of the effects of the mutual attractions of the
heavenly bodies."
, Dr. Bowditch was also, for many years, a contributor to the
Annalist and Mathematical Diary, solving every question there
proposed, in his usual style of simple elegance. He also wrote
or corrected various articles in the American edition of Rees*8
CyclopsDdia. And all these various publications were the
employment merely of those leisure hours which were left to him
after all the calls of active business, and all the claims of social
and domestic life, had been most fully answered; and more than
this, and notwithstanding all these duties and engagements, and
all the occasional scientific labors which have been mentioned, such
was his wonderful economy of time, that, within the same period,
he also completed what has justly been characterized as the
gigantic undertaking of making the Translation and Commentary
now before the reader, — a work upon which, almost exclusively,
will rest his fame as a man of science.*
as extensive and minute as was possessed by any individual then living, — it is, throughout, a
record of the most sound and impartial criticism. Any biography of him, which has not this
review in an appendix, must be incomplete.
• Baron Zach, in his Correspondance Astronomupu, Vol. X. p. 234, A. D. 1824, says,
** Nous finirons cette note par apprcndre a nos lecteurs ce que nous a r^v^i^ le professeur
60 MEMOIR.
Upon recurring to the Translator's Preface, in the first volume,
it will be found there stated that " the notes were written at the
time of reading the volumes, as they were successively published.
The translation was made between the years 1814 [misprinted
1815] and 1817, at which time the four first volumes, with the
several appendices and notes, were ready for publication." The
fifth volume, published by La Place twenty years after the others,
was never translated by Dr. Bowditch, though he wrote many
important notes upon it.* It was his intention, however, had he
lived, to translate the volume. Death has defeated forever
that intention. The work which he had so nearly completed, no
one lives to finish as he would have finished it; but, like the
beautiful painting from which was taken the engraving prefixed to
this memoir, and which never received the final touch of the dying
artist, it is the more interesting from the circumstances under
which it was left incomplete.
Everett, que M. Bowditch a traduit en anglais toute la Mecanique Celeste de M. La Place,
avec un ample commentalre, mais qu'on n'a pu encore le persuader de publier cet ouvrage qui
ne pourrait que lui faire un honneur infini, ainsi qu'a son pays, mais nous soupconnons
qu'il attend pour cela I'ouvrage de MM. Plana et Carlini, qui est sur le metier, et qui ne
tardera pas a paraitre." A similar public announcement of this fact had been made in the
North American Review for April, 1820, Vol. X. p. 272; and the editor says that Dr
Bowditch " has not, however, yet been prevailed upon to do honor to himself and to his
country, by the publication of so great and arduous a work."
* A day or two only before his death, he received from Europe a translation, executed
by a young lady whom he had never seen, but who was soon to become his daughter,
embracing in seventy manuscript pages the first part of the fifth volume ; — a suitable offering
of filial duty to one who never lived to thank her in person for her kindness, but who left
for her at his decease an affectionate letter, written exactly a week before his death.
MEMOIR. 6|
As, in the course of publication, it became necessary to
incorporate into the notes much additional matter, owing to the
subsequent progress of mathematical science, they were all, in a
great measure, rewritten; and thus, perhaps, the present four
volumes will be found to contain almost every thing of importance
in the whole five volumes of the original work, excepting what
relates to the earth's temperature and the velocity of sound.*
Still, it was Dr. Bowditch's intention to introduce into the fifth
volume more original matter than into either of the preceding
ones, making it, as it were, the general depository alike of all the
results of his extensive theoretical investigations, and of the
practical experience of a long life. It was, especially, a source of
regret to him, that he could not prepare the Index to the work,
which he felt assured, from his intimate knowledge of its contents,
and of the relative importance of the difierent matters of which
it treats, he was more competent to prepare than any one else.
That duty, we believe, however, will at a future time be ably
performed by a friend, (Benjamin Peirce, Esq., Professor of
Mathematics in Harvard University,) whose revision of the entire
Work, when in the process of publication, and vigilance in detecting
typographical errors. Dr. Bowditch always valued as an additional
means of insuring its accuracy.
' ■ ■-•-I
It would not be our desire, were we competent to the task, to
ofTer any criticism upon the present work. It will itself speak to
every reader. A few remarks, however, upon the motives, views,
and objects of the translator may not be inappropriate.
• Mr. Pickering's Eulogy, p. 54.
VOL. IV. q
62 MEMOIR.
In the first place, then, his great design was to supply those
steps in the author's demonstrations, which were not discoverable
without much study and research, and which had rendered the
original work so abstruse and difficult, as to lead a writer in the
Edinburgh Review to say there were not twelve individuals in
Great Britain who could read it with any facility.* Dr. Bowditch
himself was accustomed to remark, *' Whenever I meet in La
Place with the words * Thus it plainly appears,' I am sure that
hours, and perhaps days, of hard study will alone enable me to
discover how it plainly appears." So important did he consider
the object which he thus had in view, that every letter which he
received, proving to his satisfaction the fact of some young man's
having read his Translation and Commentary, afforded him
much more pleasure than the favorable mention of it in popular
journals, or even than the flattering approbation bestowed by
competent judges ; since, while the one would be but an opinion,
the other would be a proof, that the great end of his labors had
been accomplished. He received several such letters. M.
Lacroix wrote to him that he had recommended the work to a
young professor at Lausanne. There can, indeed, be no doubt
* " We will venture to say, that the number of those in this island who can read that work
with any tolerable facility, is small indeed. If we reckon two or three in London and the
military schools in its vicinity, the same number at each of the English Universities, and
perhaps four in Scotland, we shall hardly exceed a dozen ; and yet we are fully persuaded that
our reckoning is beyond the truth." — Edinburgh Review, 1808, Vol. XI. p. 281.
In America, two, and perhaps three persons, besides Dr. Bowditch, were able to read the
original work critically ; but a competent judge has doubted whether the whole of it had
been so read even by one.
.^Q■'f
MEMOIR. 63
that it has been truly said by a late foreign review,* respecting
this Translation and Commentary, " a work which existed in mere