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Part I. Price One Shilling, and Vol. I. Price 5s., cloth lettered) of a



Second Edition, revised and enlarged, with Several Hundred Additional Illustrations.

Being a series of treatises composed in a popular and generally intelligible style,
independently of the language and symbols of mathematics.





To be issued in Eighteen Monthly Parts at One Shilling, forming Four Volumes, price 5s, each

cloth lettered.

* # * A Prospectus and Specimen may be had on application.





Formerly Professor of Natural Philosophy and Astronomy in University College, London.










CHAP. I. 1. The Almanack. 2. The Calendar. 3. The contents
of an Almanack Predictions. 4. Its , prophetic character
abused. 5. Saints' Days. 6. Date of the* year. 7. Christian
era. 8. Discrepancy between the reckoning of Astronomers and
Chronologists. 9. When a century begins and ends. 10. Com-
mencement and duration of the Seasons. 11. Beginning of the
year. 12. Fixed and moveable Feasts. 13. Easter. 14. Not
dependent on the phases of the Moon. 15. By what rule deter-
mined. 16. Rule not generally understood. 17. Equinox.
18. Ecclesiastical Moon. 19. Age of the Moon. 20. Full Moon.
21. Error in the expression of the rule. 22. Lunar cycle.

23. Average length of civil and astronomical cycles agree.

24. Fictitious moon never far distant from real moon. 25.
Golden Number. 26. Epact. 27. Used to determine the date
of Easter. 28. Amount of separation of fictitious from real
moon. 29. Limits of variation of date of Easter. 30. Earliest
possible. 31. Latest possible. 32. Paschal Moon ... 1

CHAP. II. 33. Paschal moon sometimes gives a different Easter from
real moon. 34. Occasion of public controversies. 35. Professor
De Morgan points out error in Act of Parliament. 36. Other
moveable Feasts. <37. Extract from De Morgan's Book of
Almanacks. 38. Whit-Sunday. 39. The Indiction. 40. Solar
Cycle. 41. To find the year of the current solar cycle.
42. Dominical or Sunday Letter. 43. How affected by Leap-
year. 44. Sunday Letter ; of the year 1 A.D. 45. To find
Sunday Letter for any year. 46. Eras. 47. Julian Period.
48. Its commencement determined. 49. Its use in chronology.
50. Contents of the Calendar. 51. Aspect of the Heavens.
52. Times of rising and setting of celestial bodies. 53. Distor-
tion produced by the atmosphere. 54. Other effects. 55. True
and apparent sunrise. 56. The sun seen before it rises.

57. Conventional meaning of the terms sunrise and sunset.

58. Refraction. 59. The Equinoxes 60. Day and night rarely

of the same length. 61. How modified by refraction . .17

CHAP. III. 62. Noon. 63. Clock time and sun time. 64. Decli-
nation of s\m. 65. Tropics. 66. Solstices. 67. Dog days.
68. Why Midsummer is not the hottest season. 69. Unequal
intervals between the equinoxes. 70. Signs of the Zodiac.
71. Their designations. 72. Tropics of Cancer and Capricorn.




73. Change of position of constellations. 74. Zodiac. 75.
Ecliptic. 76. Other contents of Almanack. 77. Astronomical
terms. 78. Conjunction. 79. Opposition. 80. Quadratures.
81. Morning and evening star. 82. Further illustrations.
83. Lunar changes. 84. When said gibbous . . .33

CHAP. IV. 85. Full moon. 86. Last quarter. 87. Moon's age. 88.
Eate of motion variable. 89. Causes thereof. 90. "May moon,"
"March moon," &c. 91. Confusion arising from this form of
expression. 92. The epochs of chronology. 93. Anno Mundi.
94. Era of Nabonassar. 95. The Hegira .... 49


CHAP. I. 1. Colours depend upon reflected lights. 2. Bodies lumin-
ous and non-luminous. 3. Luminaries. 4. Non-luminous bodies.
5. Transparency and opacity. 6. Transparency never perfect.
7. Opacity never perfect. 8. Bodies rendered visible by reflected
light. 9. Irregular reflection. 10. Reflecting powers vary.
11. The blackest body reflects some light. 12. Irregular reflec-
tion necessary to vision. 13. Use of the atmosphere in diffusing
light 57

CHAP. II. 14. Diffusion of light by all visible objects. 15. Decom-
position of light by visible objects. 16. Experimental proof of
the composition of light. 17. The prismatic spectrum. 18. The
composition of solar light 19. The recomposition of light by
prism. and concave reflector. 20. The same by prism and lens.
21. The same with artificial colours. 22. Light of the same
colour may have different refrangibilities. 23. Colours produced
by combining different rays of the spectrum. 24. Comple-
mentary colours. 25. Colours of natural bodies generally
compound. 26. Method of observing the spectrum by direct
vision. 27. Why objects seen through prism are fringed with
colours. 28. The prismatic colours, not all simple. 29. Sir D.
Brewster's analysis of the spectrum ..... 65


CHAP. I. 1. Great importance of the subject in relation to all the
effects of vision. 2. Explanation of how an object is seen with
the naked eye. 3. Images produced by plane reflectors.
4. How rays are reflected 'from such surfaces. 5. Experimental
verifications of this. 6. Image of a point in a plane reflecting
surface. 7. Image of an object in the same. 8. Real and
imaginary images. 9. Images produced by spherical reflectors.
10. By a concave reflector. 11. Experimental verification.
12. Variation of position, and magnitude of image. 13. Images
in convex reflectors. 14. Images produced by transparent bodies.
15. Refraction. 16. Cases in which light will not enter a
transparent body. 17. Reflection of objects in water. 18. The



fallacy of the fable of "the Dog and the Shadow." 19. Objects
seen at the bottom of a transparent body. 20. Case of water
and glass. 21. Broken appearance of a rod immersed in water.
22. Cases in which rays cannot emerge from a transparent
body. 23. Experimental verification. 24. Reflection by a
rectangular Prism. 25. Images produced by lenses. 26. Six
kinds of lenses. 27. The axis of a lens. 28. Example of each
kind of lens. 29. Optical image produced by a convex lens.
30. Relative position of the object and image . . .81

CHAP. II. 31. Experimental verification. 32. Variation of the
magnitude of the image. 33. Principal focus and focal length.
34. Variation of position, and magnitude of image. 35. When
images real, and when imaginary. 36. Images produced by
concave lenses. 37. Focal length varies with refracting power.
38. Refracting power depends on material of lens. 39. Sphe-
rical aberration. 40. Images produced by lenses not absolutely
clear and distinct. 41. Series of images. 42. Nebulous and
confused effect. 43. Spherical aberration greater near the
borders. 44. Increases with the curvature. 45. And with
the magnifying power. 46. Spherical distortion. 47. Curved
images. 48. How to diminish spherical aberration. 49. Lenses
made from diamonds and other precious stones. 50. Ineffectual
attempts at improvement by this means. 51. Methods of dimi-
nishing spherical aberration by proper adaptation of curvatures.
52. Aplanatic lenses. 53. Chromatic aberration. 54. White
light compound. 55. Coloured lights sometimes compound.
56. Images produced by homogeneous lights. 57. Images pro-
duced by compound light. 58. Lenses always produce several
images of a natural object. 59. Why they are not always so
confused as to be useless for vision. 60. Dispersion. 61. Dis-
persion increases with refraction. 62. Dispersion different with
different material . . . . . . .. .97

CHAP. III. 63. Experimental illustration. 64. Dispersive powers.
65. Dispersive power does not necessarily increase with refrac-
tive power. 66. Example of the diamond. 67. Achromatic
lens. 68. Achromatic combination of flint and crown-glass.
69. Form of the compound lens . . . . .113


1. Though common and familiar, little understood. 2. Image of an
object produced by it vertically erect, but laterally inverted.
3. Image of an object parallel to the looking-glass. 4. Image of
an object inclined to the reflector. 5. Series of images formed
by two reflectors. 6. Example in rooms furnished with several
mirrors. 7. Reflection by a looking-glass takes place at the
posterior surface' silvering. 8. Analysis of the effect of a
looking-glass upon the light falling on it. 9. Conditions on
which the goodness of a looking-glass depends. 10. Effect of
mirrors flush with the floor. 11. Best method of cleaning


mirrors. 12. Light reflected from the silvered surface. 13.
How a double image is produced. 14. Why one image is much
more faint than the other. 15. Positions in which the two
images are visible. 16. The image usually seen produced by the
posterior surface. 17. Effect of light absorbed by the glass.
18. Glasses rendered unfaithful in their tints. 19. A good
glass must have its surface parallel. 20. Defects of low-priced
glasses ' . . . -120


Their correspondence with the lunar phases known at an early
period. 2. Erroneous notions prevalent as to their causes. 3.
Not caused by the moon's attraction. 4. But by the inequality
of its attraction.- 5. Calculation of this inequality. 6. Solar
tides. 7. : Difference between the power of the sun and moon to
produce a tide.' 8. Spring and neap tides. 9. Why the tides
are not directly under the moon. 10. Establishment of the port.
11. Effects of the form of the coasts upon the local tides.

12. Dr. Whewell's analysis of the progress of the tidal wave.

13. Age of the tide. 14. Velocity of the tide. 15. Undulations.
- 16. Motion of the crest of a wave. 17. Bange of the tide.
18. How affected by the weather


CHAP. I. 1. Spectacle presented by the firmament. 2. Useful ob-
servations can be made without astronomical instruments. 3.
Apparent motion of the firmament. 4. The meridian. 5. View
of* the circumpolar region. 6. Permanency of the form of the
stellar groups. 7. The celestial sphere. 8. The celestial poles.
9. Orders of magnitude of the stars. 10. Number of stars of
each order. 11. Constellations. 12. Ursa major. 13. Anti-
quity of the name. 14. Sometimes called Waggon, Wain, or
Chariot. 15. Number of stars in it. 16. Proper names of stars.
17. Use of the imaginary figure to express the position of the
stars. 18. Ursa minor : the pole star. 19. How it makes a
nocturnal clock. 20. Arctic circle : origin of the name. 21.
Cassiopeia's chair. 22. Pegasus and Andromeda. 23. Perseus.
24. Auriga. 25. General view of the region of these con-
stellations : Capella, Vega, Adrided, and Altair. 26. Orioni . 145

CHAP. II. 27. Antiquity of the name of Orion. 28. Nebulae in the
constellation Orion. 29. General view of this region of the
heavens. 30. Procyon and Sirius. 31. Aldebaran : the Hyades
and the Pleiades. 32. The constellations of the zodiac. 33. Use
of celestial maps. 34. Use of a celestial globe. 35. To find the
place of an object in the heavens . . . . . .161




CHAP. I. 1. Retrospect of the solar system. 2. Inquiries beyond
its limits. 3. This system surrounded by an extensive void.
4. This proved by the absence of external perturbations. 5. And
by comets, which are feelers of the system. 6. Where then is
the vast multitude of stars which appear in the firmament ?
7. Absence of apparent parallax. 8. Illustration of the effects
of parallax. 9. Its apparent absence favoured the Ptolemaic
system. 10. Effects of parallax explained. 11. Parallax of the
planets visible 169

CHAP. II. 12. Absence of parallax obstructed the acceptance of the
Copernican system. 13. Immense distance of stars inferred from
its minuteness or absence. 14. Its greatest possible magnitude.
15. Distances of stars inferred. 16. Use of the motion of
light as a modulus of this distance. 17. Methods of ascertaining
the parallax. 18. Parallax of a Centauri. 19. Parallax of nine
principal stars. 20. The vacuum surrounding the solar system
necessary to cosmical order. 21. Classification of stars by magni-
tude arbitrary. 22. Fractional magnitudes. 23. Number of
stars of each magnitude. 24. Total number of stars in the fir-
mament. 25. Varieties of magnitude chiefly caused by difference
of distance. 26. Stars as distant from each other as from the
sun. 27. Telescopes do not magnify them. 28. Absence of a
disc proved by their occultations. 29. Meaning of the term mag-
nitude as applied to the stars. 30. Why the stars may be ren-
dered imperceptible by their distance. 31. Real magnitudes of
the stars. 32. Application of photometers or astrometers.
33. Comparison of the sun's light with that of a star. 34. Re-
lative real magnitudes of the sun and a star estimated. 35.
Comparative magnitude of the sun and the dog-star. 36. Vast
use of the telescope in stellar observations. 37. Its power to
increase the apparent splendour of a star explained . . .177

CHAP. III. 38. Telescopic stars. 39. Space -penetrating power of
the telescope. 40. Vast distances of small telescopic stars.
PERIODIC STARS : 41. Stars of variable lustre. 42. Remarkable
stars of this kind in Cetus and Perseus. 43. Table of periodic
stars. 44. Hypothesis to explain periodic stars. TEMPORARY
STARS : 45. Such stars seen in ancient times. 46. Star dis-
covered by Mr. Hind. 47. Missing stars. DOUBLE STARS :
48. Researches of Sir W. and Sir J. Herschel. 49. Stars opti-
cally double. 50. This supposition not admissible. 51. Re-
futed by the proper motion. 52. Classification of double stars.
53. Table of double stars. 54. Coloured double stars. 55.
Triple and other multiple stars. 56. Attempt to discover
parallax by double stars. 57. Observations of Sir W. Herschel 193

Fig. 1.




The Almanack. 2. The Calendar. 3. The contents of an Almanack
Predictions. 4. Its prophetic character abused. 5. Saints' Days.
6. Date of the year. 7. Christian era. 8. Discrepancy between the
reckoning of Astronomers and Chronologists. 9 When a century
begins and ends. 10. Commencement and duration of the Seasons.
11. Beginning of the year. 12. Fixed and moveable Feasts.
13. Easter. 14. Not dependent on the phases of the Moon.
15. By what rule determined. 16. Rule not generally understood.
17. Equinox. 18. Ecclesiastical Moon. 19. Age of the Moon.
20. Full Moon. 21. Error in the expression of the rule. 22. Lunar
cycle. 23. Average length of civil and astronomical cycles agree.
24. Fictitious moon never far distant from real moon. 25. Golden


No. 79.


Number. 26. Epact. 27. Used to determine the date of Easter.
28. Amount of separation of fictitious from real moon. 29. Limits
of variation of date of Easter. 30. Earliest possible. 31. Latest
le. 32. Paschal Moon.

1. OF all books the Almanack is the most indispensable. So
constant is the need for it, that, unlike other books, it is not
deposited on the shelf, but lies ready at hand on the table.
This general and constant utility, which ought to have exempted
it from fiscal restriction, was precisely the circumstance which
marked it out for the fatal visitation of the Stamp Office, and
raised, thereby, for many years a barrier against its improvement.
The moment of its emancipation from the Chancellor of the
Exchequer having, however, at length arrived, it was indefinitely
multiplied, assumed a thousand shapes, was offered at prices
suiting all pockets, in dresses suiting all tastes, with accessories
and appendages adapted to the exigencies of all avocations, and
was sometimes even given gratuitously as a convenient vehicle for
the commercial announcements which accompanied it.

One might imagine that a book thus so universally necessary
would be as universally understood ; nevertheless it may be fairly
questioned whether one in ten thousand of those who daily
consult it have any clear or definite notions of the import of even
those parts of it to which they refer, and it is beyond all doubt
that of many other parts they have no notion whatever. It has,
therefore, appeared to us that some explanatory notice of its
contents will not be unacceptable to our numerous readers.

ALMANACK, or ALMANACK, is an Arabic term derived from the
word MANAH, to reckon.

2. In the almanack the CALENDAR holds a prominent place,
so prominent indeed that the terms are sometimes used inter-
changeably. Nevertheless, Calendar has a more special and
limited application. The first day of the Roman months was
called CALENDS, and hence a table showing the successive days
of each month, and indicating the festivals and anniversaries
civil or religious, which fell upon them, came to be called THE

It has been already explained in our Tract on " Time," that
the word MONTH has various senses. It may mean the moon's
periodic time, that is, the time it takes to make a complete revo-
lution round the earth. It also expresses the time which elapses
between two successive new moons. This is called a LUNAR.
MONTH, and sometimes a SYNODIC MONTH. In law, four weeks
are taken to be a month. The year consists of twelve unequal parts,
which are called CALENDAR MONTHS. These are the months which
have received the names with which every one is familiar.


3. The almanack is a year-book, and is published before the
commencement of the year whose date it bears, and to which its
contents are related.

The contents of the almanack are, therefore, necessarily

The prediction of fixed anniversaries, whether civil, religious or
natural, requires no calculation, since they fall from year to year
upon the same days. The recurrence of many celestial pheno-
mena, which are of great popular and civil interest, varies from
year to year ; and some religious and civil festivals and observances
which are conventionally regulated by them, are subject to a
like variation, and the prediction of the days of their recurrence
depends on similar calculations.

4. The people of all classes in all countries seeing the precision
with which so many and such various phenomena were foretold,
were not slow to manifest a craving after like predictions of
events of quite another order ; and almanack makers were not
and are not even now wanting who pander to this demand. We
have, accordingly, almanacks including predictions of the vicissi-
tudes of weather, of the occurrence of great political events, and
in short of everything which can be imagined to gratify the
spurious appetite of the credulous. It must be admitted, to the
discredit of certain of our public bodies, that they have long con-
descended to traffic in this sort of charlatanism, and to derive a
revenue from thus imposing on public credulity. If precedent,
however, can be admitted as any extenuation of this practice, they
may claim to have sinned in good company, for Arago relates
that he had the following anecdote from Lagrange.

"The Berlin Academy, so celebrated for the vastness of physical
discoveries and researches which were consigned to its trans-
actions, formerly derived its chief revenue from the circulation of
its almanack. This publication from an early period included a
mass of pretended predictions of meteorological phenomena and
political events, like those which figure in some of our own
almanacks of much more recent date. Ashamed of sanctioning
the publication of such absurdities, the Academy, upon the pro-
position of one of its leading members, resolved at one time upon
suppressing them and supplying their place with more rational
and useful matter.

' ' The immediate consequence of the reform was the almost total
suspension of the revenues of the Academy by the great decrease
of the sale of the almanack, so that the learned body was literally
starved into compliance with the public demand, and compelled to
reissue annually a collection of pretended predictions which were
a subject of ridicule to those who invented and compiled them."

2 3


A similar circumstance occurred with respect to Moore's
Almanack, of which the sale was reduced in amount by the
omission of the column which assigned the effects produced by
the signs of the zodiac on human members.

Another of the early almanacks which owed its immense circu-
lation to the same cause, was one published at Liege, under the
name of Matthew Laensberg, a canon of that city. " When we
speculate on human credulity," observes Arago, speaking of this
almanack, " we may be confident of success. It is in yain that,
from year to year, the events are in flat contradiction to the
predictions. The public does not the less resort to the famous
almanack, so true is the saying of La Fontaine :

L'homme est de glace aux verites,
II est de feu pour le mensonge."

Arago relates a curious accidental coincidence which gave the
Laensberg Almanack prodigiously increased vogue. In the Alma-
nack for 1774, there appeared a prediction that " one of the most
favoured ladies would play her last part in the month of April."
Now, it so happened, that in the month of April, Louis XY. was
attacked at Versailles with the small-pox, and the notorious
Madame Dubarry was expelled from the palace.*

5. The religious anniversaries indicated in the calendar, con-
sisting principally of the days consecrated by the Church to the
commemoration of saints and martyrs, necessarily vary in different
Christian countries, according to the varying forms of the faith.
The personages recognised as saints in the Roman Church are at
least six times as numerous as the days of the year ; and
although the Greek Church does not recognise exactly the same
collection, their list is equally abundant. A selection has been
made by each branch of the Church, and the name of a saint
or martyr is appropriated to each of the three hundred and
sixty-five days ; and to such an extreme is this carried, that a
saint is even given to the intercalary day in bissextile years.
Thus, in the Roman Church, the intercalary day is appropriated
to St. Damien, and in the Greek branch to St. Cassian.

The identification of the days of the year severally with the
names of canonised personages, will explain the familiar allusions
to the " Saints of the Calendar."

In Protestant States, and more especially in England, this long
list of saints is greatly curtailed, all those whose canonisation
took place subsequently to the imputed corruption of the Church
being rejected. In Catholic countries, however, the names regis-

* For a more recent specimen of the effect of such an accidental coinci-
dence occurring among ourselves, see our Tract on "Weather Prognostics."


tered in the calendar have become so closely interwoven with the
national manners and customs, that it is unlikely that any refor-
mation should efface them. It is the general practice to celebrate
the anniversary of each individual, not, as with us, upon that of
his or her birth, but upon the day consecrated to the memory of
the saint whose name he or she bears* By this usage each day in
the calendar becomes as it were the peculiar property of certain
individuals, and to efface the saints would be practically to rob all
the world of their festivals. In certain times and among certain
people such a measure would excite an insurrection.

6. The very first date indicated in the Almanack, that from
which it takes its title, and which is marked upon its back, the
number designating the year, may require some brief explanation.
What is meant, for example, by the year 1855 ? "What is its
beginning ? what its end ? From what point of departure are its
units reckoned ? 1855 since when ? These are questions to which
the answers are not quite so obvious as they may seem.

7. During the first five centuries after the birth of Christ, the
Christians, comparatively few in number, and scattered among
different and distant peoples, used in their records no other mode

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