Rodolfo Amedeo Lanciani.

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E, Loomis on Solar Spots, Magnetic Decimation, etc, 171

1. Those cases in which the observers were not entirely con-
fident that there was any auroral display.

2. Those cases in which the corresponding observations of
the solar spots were very incomplete ; and

3. Those cases in which auroras were observed on two or
three successive days, when I have generally selected the most
remarkable aurora, and made but one entry for that period.

The number of auroras which I have thus discussed is 251.
In order to famish a specimen of these numbers, the table on
page 170 is given, in which the arrangement is the same as in
the table on page 168. At the bottom of the table are given
the averages of these numbers for each of the 13 columns ; and
in another line are given the corresponding averages for the
whole number of 251 auroraa

These final averages are represented by the upper curve line
in the figure page 169, from which it wdl be seen that there is
a well-markea maximum of solar disturbance corresponding to
the date of an auroral display. The small fluctuations during
the preceding and following days, bear some resemblance to the
fluctuations attending magnetic storms, but they are so small in
amount that no importance is attached to them. The entire
fluctuation within 6 days extends from 50*3 to 60*5, or 20 per
cent of the whole quantity ; a number so large and derived
from so many cases that it is thought to indicate a law of na-
ture. Hence we conclude that

Auroral displays in the middle latitudes of America are gen-
erally accompanied by an unusual disturbance of the sun's sur-
face on the very day of the aurora, and are, therefore, subject
to some influence which emanates immediately from the sun.

These conclusions may be modified by a comparison of a
longer series of observations, and especially by more accurate
observations which furnish for each aay an exact measurement
of the extent of the sun's spotted surface. Such observations
have been made for several years at the Kew observatory, and
it is hoped that when published they will furnish the materials
for the desired comparison. The observations for 1862 and
1863 have already appeared in the Philosophical Transactions
for 1869, pp. 23-44; and it is expected that the observations
for the subsequent years will soon follow.



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172 J. W. French on a new Period m Chronology.



Art. XVLL — On a new Period in Chronology^ called the Precession
Period; by J. W. French. (In a letter to the Editors.)

I PROPOSE in the place of the Julian Period in chronology,
another which I will call the Preeession-PerioA

This latter wUl be found to have all the advantages of the
other without its defects, and beyond these comparative utilities,
to have chronological uses of its own which are great and vari-
ous, both for the subdivisions of history, and for the vaat cycles
contemplated by scienca

The Julian reriod in chronology consists of 7,980 Julian
years, that number beinf formed by the continual multiplica-
tion of 28, 19 and 15 ; that is to say, of the cycle of the sun, the
cycle of the moon, and the cycle of indiction. The first year
of the Christian Era is made the 4,714th of the Julian Period.
By such an arrangement we can find for any year its golden
number, its number for the solar cj^cle, and tnat for its Koman
Indiction. Also, we have a fixed period reaching back in history
among the local and broken cycles of different peoples and
countries. These certainly are great advantages, and have se-
cured for that Period acceptance and commenc&tion.

But some of its defects are these. L It has an artificial de-
ment, that of the Boman Indiction, instead of having its found-
ation whoDy in astronomy. 2. It is soon exhausted, and in
the past, it aoes not reach far enough even for the Septuagint
Chronology in history. 8. It Aimishes no unit nor cycle for
science.

The period which I propose is founded wholly on astronomy,
is exhaustless by being recurrent, has its initial point sufficient-
ly fer back for any conceivable historical purposes, gives to sci-
ence a worthy unit for the vast durations it contemplates, and
with these inestimable advantt^es, has the two practical utilities
of the Julian Period ; — that of giving the elements needed in
the almanac for every year, and that of extending into the past
a long and unaltering standard for tima

Ipropoee to iakcj as the chronological unit, ffie time for Ae preceS'
sion of the equinoxes^ 26,872 years. By a singular felicity, that
number can be formed from the fiwjtors 28, 84, and IL Now,
28 is the number of the solar cycle ; 84 is a lunar cycle em-
ployed formerly by the Jews, and having peculiar uses in esti-
mating long series of lunations. The ouier number, 11, is a lu-
nar cycle employed by the early Christians, the errors of which
almost exactly counteract those of the cycle of 84 years. These
three multiplied together form 26,872. A suborainate felicity
will at once be seen by a complete mathematician. Tlie num-
ber 26,872 can be divided and mbdivided to the last, without a re-
mainder, by a large number of divisors.



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J. W. French on a new Period in Chronology. 178

Making the years Gregorian, and calling the initial year of
the Christian Era, 0, 1 pujux the beginning ^ the Precession Period
at 12,698 B. G.

Instantly we have by that arrangement, the advantages which
have brought the Julian Period into favor.

We can find the solar cycle, the golden number, the Eoman
Indiction ^correctly as we would &om the Julian Period) by
the following simple rules :

1. To express any year before or after Christ in the corres-

S indent number in the Precession-Period : For any year before
hrist, deduct from 12,698, the figures of the year B. C. : For
any year after Christ, add to the same number (12,698) the fig-
ures of the year A. D.

Thus 752 B. C. (758 historical reckoning) is 11,941 P. P. The
present year 1870 A. D. is 1,870+12,693=14,568 P. P. (We
use P. P. as abreviation for Precession-Period.)

2. To find the Golden Number, Solar Cycle, and Roman In-
diction for anj year before or afler Christ : 1. Turn the ycM* by
the first rule mto the correspondent number of Precession Pe-
riod : 2. Divide that number by 19 for the golden number, by
28 for the solar cvcle, and by 15 for the Roman Indiction. In
the three remainders you have the answer.

Thus the present year 1870 A. D., is 14,568 P. P. Dividing
this latter number by 19, I find a remainder of 9 ; by 28, a re-
mainder of 8 ; and by 15, a remainder of 18. Opening the Al-
manac for this year, I find the answer correct It gives the
Golden Number as 9, the Solar Cycle as 8, the Roman Indiction
as 18.

The Precession-Period has then in this particular, equal util-
ity with the Julian.

The other advantage, that of a fixed standard of time ex-
tending back in past history, it possesses, and adds the great
benefit of adequate length in botn directions, to 12,693 B. C,
and on to 18,179 A. D. ; the whole forming one precession.
And this precession is not like the Julian Period, an arbitrary
straight line stretched over a small portion of duration. It is
a definite circle marked on the face of the heavens. The pre-
cession begins at 12,693 B. C. with the point of the vernal equinox
in the Zodiac near Spica Virgints, a brilliant star, forming a good
point of departure. When the whole circle of the Zodiac is
swept, and the first decree of celestial longitude is again by
Spica Virginis^ the pericS is completed.

Surely it is better to adopt such a period for our almanacs
and histories than the infenor one called the Julian.

But beyond the historical and chronological uses in the sub-
divisions of the Precession-Period, are the advantages of that
period as a unit for Astronomy and Geology. We want a unit



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174 F. W. Clarke on the Atomic VoluToeof Compcnmds.

larger tlian the year. A precession is a good one. Instead of
cumbering a line of page with bewildering cyphers we can sa^
40, 100, or 1,000 precessions. Thus 40 precessions (and forty is
a number easily remembered) would, by another felicity of this
period, make a million of years, with a little over. We might
call it a miUionade, and give that again multiplications to form
an age. An " age " might be 400 precessions.

Should we adopt any thing like this plan, we should have the
same delightful surprise which we often experience, by finding
that ancient races and nations have been along the same path-
way which we imagined ourselves to be for the first time break-
ing and exploring. Six days, such as are His, who in His times
as in His nature, must be what others are not ; six immense

Eeriods are reckoned in the Creative work not only in Genesis,
ut in Oriental Recorda Take 100 precessions. Divide them
by that number, six You have the veiy periods recognized by
the Brahmins of India, each about 430,000 years.
West Point, June 7, 1870.



Art. XVin.«— fTpon the Atomic Volumes of Solid Compounds;
by Frank Wigglesworth Clarke, S.B.

In studying the atomic volumes of solid compounds, the
materials at my command have been in some respects quite co-

f)ious, and in others quite limited. Having been unable, through
ack of opportunity, to make any new determinations of spe-
cific gravities, I have been forced to content myself with the
data which are scattered through the various scientific publica-
tions. These, apart fi-om the views expressed in nearly a hun-
dred papers written by various chemists upon atomic volumes,
consistea of about 1,900 determinations of the specific gravities
of 912 different solids of definite constitution, exclusive of al-
loys. Much of this material had to some extent been already
worked over, although the larger part of it had never been ex-
amined in this direction. In some cases there are data covering
a whole series of compounds, in others only one or two mem-
bers of a series have oeen studied, while again, for many im-
portant substances no detenninations of specific gravity have
ever been taken. Again, for some compounds there are many
determinations by different authorities, and these bodies can l>e
studied with much certainty ; while for other compounds only
single observations of specific gravity have been made, and
these often with no pretence to ngid accuracy.

Here then at the very outset is a difficulty. If a substance
has a very low specific gravity, and a very mgh atomic weight,



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F. W. Clarice on the Atomic Volume of Compounds. 175

a minute error in the determination of the first value must, in
calculating the atomic volume, become greatly multiplied ; so
that ap single experimental observation onlv, may often lead to
wholly erroneous results for the atomic volume. Thus, for in-
stance, with Melene, C^^E^ an error of only 0*04 in the specific
gravity will alter the atomic volume about 24*00. And it is very
common to find the determinations of specific gravity for a single
compound diflfering more than 0*04 And, as I have already
stated, many of the specific gravities observed have never had
more than approximate accuracy claimed for them. Hence, one
of the chief oifBculties in comparing atomic volumes lies in de-
ciding how great variations can be safely ascribed to experimen-
tal error. For this purpose, instead of directly comparing the ac-
tual atomic volumes with the results of theory, I have preferred
to compare the specific gravities calculated fi?om the latter with
those really determined by experiment Evren here much care
is needful, since errors are more likely to occur with some com-
pounds than with others. Thus, there is much more danger
of error in determining the specific gravity of anhydrous mag-
nesic chlorid, than in taking that of baric sulphate.

Furthermore, many different modes of taking specific gravity
are represented by the values fix)m which I have to calculate.
Some compounds have been examined in the form of powder,
and others have been crvstallized ; some have been studied near
their melting point, and others distant therefrom. Neverthe-
less, in spite of all these possibilities of error and chances of
irr^ulanty, certain curious series of relations between atomic
volumes are easily demonstrated ; which, taken together, hint
strongly at a rather more general theory of atomic volumes
than has hitherto been enunciated.

But, to begin with, we need a brief resum^ of certain points
which have been demonstrated by other observers.

First comes the axiomatic statement of Schroder that the
atomic volume of a compound must equal the sum of the ato-
mic volumes of its constituent parta This at once suggests
questions of interest Although many compounds, especially
certain sulphids, selenids, and tellurids, have atomic volumes
equalling tne sums of those of the Jree elements composing
them, many other compounds have values lower than such sums,
thereby indicating condensation. And some iodids have ato-
mic volumes greater than the sums of those of the metal and
the iodina So here arises the question, — when a compound
possesses a greater or less volume than the elements contained
m it do in the free state, do those elements condense or expand
in equal or in different ratios ? It is really upon this point that
the study of atomic volumes hinges ; so that, stripped of all
metaphysical notions of atoms and spheres of heat, the subject



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176 F. W. Clarice on the Atomic Volume of Compounds.

simply concerns the distribution of the changes of volume un-
dergone by the various elements in uniting to form compounds.

Second. It has been shown, most definitely by Schroder and
Kopp, that, in many cases, when from the atomic volumes of
certain series of salts, oxyds, &c., we subtract the atomic volumes
of the respective metals contained in them, we obtain constant
remainders which may be regarded as representing the values of
the various radicals and of oxygen. Tnus, if fix)m the atomic
volumes of one class of oxyds we remove the values of the metals,
we obtain the remainder 2*6. With other oxyds we get 6*2, and
with still others, 10*4. These are provisionally regarded as the
atomic volumes of oxygen in its solid compounds. These dif-
ferent values for a single element are of course natural conse-
quences of the fact that the various compounds containing it,
undergo, in their formation, different degrees of condensation
from the free elements composing them. But, in assuming these
three numbers to be the atomic volumes of oxygen, one as-
sumption is made which is by no means allowable, viz : that
the metals entering into these compounds undergo no conden-
sation themselves, all the change in volume taking place in the
oxygen. But, some oxyds have atomic volumes lower than
those of the metals contained in them. And yet the remarka-
ble multiple relation between the three values quoted above
cannot be due to accident* These points will be referred to
again.

Third, we come to some results which I myself published
rather more than a year ago.* In my last paper upon this sub-
ject I pointed out some curious multiple relations connecting
the atomic volumes of similar solid elements. For the proofe
of these relations I must refer to the above mentioned paper,
but the values for the elements themselves I am obliged to cite
here for further reference. I give the values for solids only.
Li 11-4, Na 22-8, K 45-6, Rb 57-0. These stand to each other
as 1 : 2:4:5. I 256, Tl 17-2, Ag and Au 10-2.

Here arises an interesting question. The atomic volumes of
Ag and Li are quite near together. Btlt the specific gravity of
lithium was determined comparatively near the melting point of
that metal, while that of silver was taken at a temperature
greatly removed from the degree at which it ftisea Now melted
silver, according to Playfair and Joule, has the specific gravity
9*206 ; and consequently an atomic volume of 11*7, nearly that
of solid lithium. May not these two metals then, under simi-
lar circumstances, and at strictly comparable temperatures, be
supposed to have equal atomic volumes ?
2*6, 5*2, 10*4 S 10*4, 15*6. Se 10*4, 15*6.(?) Te 20&
This value for S is that of the octahedral variety, prismatic
* This Journal for March and May, 1869.



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F. W. (Sarke on Ae Atomic Volume of Compounds. 177

sulphur haTiuff 16'3— 16*7. Amorphous selenium has an ato-
mic volume of 18*6.

Sr, 84-3. Ba, 34-2.

Ca, 25-8. Pb, 18-2.

As and P 12-9, Sb 17-2, Bi 21 -5. These stand as 8 : 4 : 5.
This value for P is that of the so-called " metallic " variety.
Common phosphorus has an atomic value of le'O— 17*0, (per-
haps 17*2, like Sb?) and the ordinary red modification 13*9—
14*5. Amorphous arsenic has the value IS^O. Bo 41. Van-
adium in my last paper I calculated theoretically from the ato-
mic volume of one of its oxyds, making it equal to As and
P. Since then, however, this idea has been overthrown, Ros-
coe having determined the specific gravity of the metal itself
This, 5*5, gives an atomic volume of 9*4, which differs widely
fix>m my supposititious value, and bears no definite relation
which I can see, to those of As and P.

C (graphite), 5-5, Si llO, Ti ll-O (?), Sn 16-5. These stand
as 1:2:2:3. C (diamond) 34 Zr 21-7 (perhaps 22-0, or
5-5X4)

Cr, Mn, Fe, Co, Ni, U,* and Cu, 6-9 ^

Zn, Pt, Ir, Os, Pd, Ru, and Bh, 9*2

Mo and W, 11-5

Cd, Mg, and Hg, (solid) 13*8 ,

Q\ 43,t Al 10-1-10-6, Th 30-4-30-9, Ce 16-7, In 10-2.

Before proceeding farther, it now becomes necessary for me
to allude oriefly to some regularities in atomic volumes which
have already been traced by others. First, the alums have equal
atomic volumes. To the evidence which has been cited by
other investigators in proof of this, may now be added the ato-
mic volumes of rubiaium and caesium alums, whose specific
gravities, taken by Redtenbacher, show that they follow the
regular rule. Second, a number of similar carbonates, especial-
ly those of Zn, Mff, Fe, and Mn, have e<jual atomic voiumea
Third, a similar relation connects the vitriols with 7 aq. This
series is especially important, since it contains the sulpnates of
Fe, Ni, Co, Mg, Zn, and Cd. Fourth, the oxyds alliea to Qtih-
nite, with the general formula MO, MjOs, are, with one or two
exceptions, equal in atomic volume. Fifth, many correspond-
ing phosphates and arsenates have equal values. Other series
have been traced here and there, but these are perhaps the most
striking.

Now, in the first place, we may lay it down as a general rule
that when two similar elements have equal atomic volumes, the

♦ Possibly this mnj not belong in this group, but its equal atomic volume be
merek a coincidence. The values of some of its compounds suggest this idea.

f Calculated from the lower atomic weight for GL In my last paper I U8ed the
higher.



These four values stand
afi3:4:5:6.



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178 F, W. Clarhe on the Atomic Volume of Compounds.

atomic volumes of their correspondiug compounds viU also be
equal Of the truth of this I will cite a few examples, and
point out some exceptions. For want of space I cannot adduce
all the cases I have accumulated, however, but will merely at-
tempt to illustrate the principle, and afterwards bring the excep-
tions under another rule.

Barium and strontium, Sr Clj, sp. gr. 2*8033, Karsten. Ba Clt,
8-704, Karsten. At vols., 56-5 and 56-2.
Sria 4415, Bodeker. Balg 4-917, FilhoL At vols., 77-8 and
79-5. Sr Hj.02, 8 aq., 1-396 Filhol, Ba ffK3a, 8 aq., 1-656,
FilhoL At vols., each 190-2.
The sulphates and nitrates, bromids, carbonates, and simple
hydrates, are either doubtful or exceptions. In all these
cases the compounds of Ba have the highest values.

Iron group. Here examples are so abundant that I will only
mention a few. MnO sp. gr., 5-38, P. & J.* NiO 5*597, P.
&J. CoO 5-597-5-750, P. & J. UO 10-15, Ebelmen. CuO
6-130, Boullay. At vols., respectively, 13-0, 13*4, 13-0-
13-4, 18-4, 12-9.
OaOs 4-950, P. & J. FeaO, 4-679-5-135, P. & J. Ni 0,
4-814, P. & J. CojOs 4-814, P. & J. At vols., 30-7, 31-1
-34-2, 34-4, 34-4. Mispickel, FeSj, FeAsg 60-6-4 Gers-
dorffite, NiSa, NiAsg 5-6-6-9. Cobaltite, CoSa, CoAsj,
6-0-6-3. At vols., 50-9-54-3, 48-1-59-2, 52-6-55-3.
FeS 5-035, P. & J. : NiS 5-650, Rammelsberg; 4-601 Kenn-
gott CoS5-45. At vols., 17-5, 16-1-19 7, 16-7. Exceptions,
MnS and CuS, having sp. grs. 3*95, Dana's Min., and 4*163,
Karsten ; and at vola, 21-8 and 22*9. It is worth noting
that these two sulphids stand at the ends of the series ;
CrS and US, being (if they exist), wholly unstudied in this
direction.
One more striking exception may be found by comparing
FeS2, MnS2, and CoSj, whose atomic volumes are very dis-
similar.

Platinum group. 2KC1, PtCl4; and 2KC1, IrCU Sp. grs.
Bodeker, 3*586 and 3*546. At vola, 136*2 and 137*9.
PdPj and PtP^ have unequal values.

Molybdenum and tungsten. It has been proved by other author-
ities that MoOs and WO, have equal atomic volumes.

Cadmium group. CdO 6*9502, Karsten. HgO 11*344, P. & J.
At vols., 18*4 and 19*0. M^O has an exceptional value
which will be studied in anomer connection.

Phosphorus and arsenic CusP 6-69, Hvoslef CujAs 7*62, GrentL
At vols., 33*6 and 34*9.

P3O5 2*387, Brisson. AsjOj 4*25 Filhol ; 3*7342, Karsten.
At vols., 59-5 and 54*1-61*6.

♦ Playfair and Joule. This is the only abbreviation of the sort which I shall
have occai^ion to employ. When I give no authority for a specific gravity, it will
be found in " Dana^s Mineralogy,** last edition.



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F. W. CloTke on the Atomic Volume of Compounds. 179

Phospliates and arsenates have been compared by others,
Where their values differ, that of the arsenate is the highest
Silicon and titanium. The acids of this group will be cited far-
ther alon^. Fayalite, 2FeO SiOa 4-006. 2FeO TiOa 4-370
Hautefeuille. At vola, 50*9 and 51*7.

The only definite exception is found in comparing 2KF SiF4 ;
sp. gr. 2-6662, Stolba; and 2KF TiF4, 2 080, Bodeker. At
vols., 82-6 and 116-3.

These examples will suffice for the present, although I shall
have occasion to cite others to illustrate another point Upon
comparing all the material which I have collected, I find the
exceptions to be quite rare, although, perhaps, I have given
them undue prominence here.

Second, similar compounds of similar metals often have
equal atomic volumes, even when those of the metals them-
selves are unequal The corresponding compounds of the iron,
platinum, and cadmium groups often exemplify this most
strikingly. The exceptions to the previous rme are probably
due to tnis. Thus, although Mg and Cd have equal atomic
volumes, their oxyds show no such equality ; that of the first
metal having shaded off into approximate umformity with those
of its kindred iron group.

Of the rule under consideration, however, the most striking
case hitherto adduced is that of the vitriols. As I have already
stated, the sulphates with 7 aq. of Fe, Ni, Co, Zn and Mg, have
equal atomic volumes, while the double salts of the same class,



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