sodium per annum is, therefore, 131*5 x 10 6 tonnes.

We have now to return to the numerator, and apply
to it such corrections as may be necessary. The
assumption made above, that about one-third of the
chlorine in the rivers is really derived from the ocean,
involves that the true, denudative supply of chlorine
to the ocean by the rivers has been 56*5 x 10 6 tonnes
per annum ; the cyclical chlorine (28'2 x 10 6 tonnes)
being subtracted from the total chlorine (84'7 x 10 s
tonnes). This has been the constant rate of supply



URANIUM AND THE AGE OF THE EARTH. 243

since the beginning of denudative processes, so that its
integral over geological time represents what has heen
brought from the land. If we call the annual supply
of chlorine c and the time X, the quantity is cX. Now,
if we make deduction of this from the total chlorine in
the ocean, we are left with a quantity of chlorine which
must for want of any alternative hypothesis be sup-
posed to have existed in the primeval atmosphere of the
earth, and, probably combined with hydrogen, to have
effected a rapid denudation of the earth-crust. If C
is the existing amount of chlorine in the ocean, the
primeval chlorine is C - cX.

Such a primeval acid denudation would undoubtedly
be responsible for the comparatively rapid introduction
of chlorides into the original ocean. We can make
some estimate of the quantities involved. Thus, if we
ascribe to the original lithosphere a composition similar
to that of the average igneous lithosphere of to-day, we
have (again quoting Clarke) :

Aluminium, . . . 7 '90 per cent.

Iron, . . . 4'43 ,,

Calcium, . . . 3 "43 ,,

Magnesium, . . . 2*40 ,,

Potassium, . . . 2 '45

Sodium, . . . 2-43 ,,

We here refer only to such substances as might be
supposed to enter into combination with the chlorine
present. Assigning to these elements their combining
proportions of chlorine, it is found that only 6*7 per
cent, of the chlorine is used in bringing sodium into
the primitive ocean. The total quantity of sodium

R2



244 RADIOACTIVITY AND GEOLOGY.

thus introduced into the ocean, at the dawn of the
denudative period, was

. 6-7 23



the last factor serving to convert the chlorine into its
equivalent of sodium. This, when simplified, becomes
(G - cX} 0-044. The quantity of sodium which has
been supplied by the rivers is found by subtracting the
above amount from what is now in the ocean. If this
last quantity be denoted by N, and n be the annual
sodium discharge from rivers (as previously corrected),
we have for the determination of geological time the
equation :

_ N - 0-044(ff - cX) _ N- 0-044(7
n n - 0"044c

In this equation N = 1,555 x 10 13 ; and from
Dittmar's analysis of average sea-water, we get for
the total chlorine in the ocean 28,769 x 10 12 = C. For
n we have found 131-5 x 10 6 , and for c, 56'5 x 10 6 , all
in tonnes. The value of X determined from these
figures is 111 millions of years. This is the period
required for the accumulation of the sodium in the
ocean, according to Murray's average composition of
river- water and his statement of its total amount ; the
corrections already described being applied.

It is probable that this is the best result at present
attainable according to the method of solvent denu-
dation. It may be contended by some that a longer
duration of denudation might be arrived at if we
allowed for a greater circulation of ocean salts from



URANIUM AND THE AGE OF THE EARTH. 245

the sea to the land. As we cannot be sure of the
precise correction to apply for this source of error,
it is important to show that a fixed and definite limit
can be assigned to the effect of this correction upon
the duration arrived at.

We have seen that in the ocean there is an excess
of chlorine over sodium, so that only 82 per cent, of
the chlorine can be combined with sodium. Now, let
us suppose that all the chlorine in rivers is derived
from the ocean, and, taking 82 per cent, of it, subtract
the equivalent sodium from the average river content
of that element ; regarding the balance only as due
to denudation. This procedure evidently constitutes
a maximum allowance for the circulation of salt : an
allowance obviously excessive, for we ignore the various
sources of chlorine rocks, volcanoes, springs, lodes,
ancient salt deposits (not marine), etc., which must
contribute some part of the chlorine, as well as the
possibility that free chlorine is evolved from the ocean.

When we carry out the calculation for the geological
age, proceeding as before, and making c = 0, we find the
period of denudation to be 141 millions of years. On
Murray's data this is a major limit to geological time.

The question as to whether Murray's average sodium
content of river-water will be confirmed with increase
of our knowledge of the subject, is a most important
one. We see, also, that the ratio of the sodium to
the chlorine is important, if we desire to refine upon
the result obtained by treating the whole of the
sodium as derived by denudation. A knowledge of
average inland rain-water, so far as its sodium content



246 RADIOACTIVITY AND GEOLOGY.

is concerned, would, however, make us independent of
the chlorine content of rivers. We shall probably have
these data before very many years have gone over. It
is of interest meanwhile to note that recent advances
do not appear to suggest any very wide departure from
the results for the age which Murray's figures have
afforded. I am indebted to Professor Sollas for the
following computation, in part founded on Clarke's
collection of North American river analyses. 1

Professor Sollas allows for the wind-borne sodium by
deducting from the several rivers the sodium equivalent
of all the chlorine present. The balance appears in
the column headed " Sodium." We have first to recall
that this is an excessive reduction, for even on the
assumption that all the chlorine came from the ocean,
we are only entitled to suppose that 82 per cent, of it
brought in sodium. And of course even this is too
great an allowance.

Discharge per
annum, cubic miles. Sodium ; tons.

St. Lawrence, . . 70'591 . 1,093,000

Androscoggin, . . 0'652 . 3,537

Merrimac, . . 0'911 . 8,187

Mohawk, . . 1-290 . 12,285

James, . . 2*144 . 16,235

Cahaba, . . 0'394 . 2,990

Mississippi, . . 132-355 . 1,322,550

Rio Grande, . . 0'298 . 33,700

Pecos, . . 0-083 . 14,640

Colorado, . . 5 '746 . 1,832,000

Snoke, . . 1-557 . 74,410

Sacramento, . . 7 '613 . 211,960

223-634 4,625,494

Clarke : The Jjuta of Geochemistry, p. 60, 6t seq.



URANIUM AND THE AGE OF THE EARTH. 247

Dividing the total sodium by the total annual dis-
charge of these rivers in cubic miles, we get a sodium
content of 20,684 tons per cubic mile. Murray's data
after deduction of the sodium chloride afford 17,501
tons of sodium per cubic mile. The new data obviously
point to a diminished result when applied to the calcu-
lation of geological time.

"We see, then, clearly that, going on collective facts
of any authenticity, the denudation period must be
less than 150 millions of years, taking a round number.
And so far as we know, this is reached only by excessive
assumptions. A subtractive correction of a few millions
of years might be called for on the score of direct
marine denudation of the coasts and shore deposits.
It is not probably a large correction, for the land area
exposed to denudation is, compared to the coastal area,
enormous. A primeval accelerated denudation, at the
time when the heat conducted to the surface of the
earth was greater than now, might entail a further
subtractive correction on the " age " ; for, as in the case
of coastal denudation, here, too, sodium is brought into
the ocean otherwise than by the rivers. These are minor
corrections, but they tend one way. Taking all into
account, until we know more about the origin of river-
borne chlorine, the computation which gave us 111
millions of years seems the best estimate we can
make.

The method of determining the geological age by the
sodium content of the rivers and ocean receives con-
firmation in the fact that moderate estimates of the



248 RADIOACTIVITY AND GEOLOGY.

mass of the detrital rocks, taken along with their
average deficiency in sodium as compared with the
parent igneous materials, will account for the sodium in
the sea. In a previous chapter (Chapter VI) this has
been referred to in another connexion. This fact brings
vividly before our minds the perseverance of those
denudative processes which, age by age, attended the
formation of the sediments and brought the soluble
substances into the ocean.

As regards the uniformitarian basis which underlies
this method and the method by sedimentation, it is to
be observed that there now is (and possibly always has
been) an excess of land area beyond what denudation
seriously affects, i.e., the riverless or rainless regions of
the earth. This rainless area now amounts to about
one-fifth of the entire land surface. Hence the eleva-
tion of the continents can only shift the area of
denudation, and their depression cannot seriously
lessen it, until it has proceeded so far that more than
one-fifth the present land surface is submerged.

As to the legitimacy of prolonging into the past
climatal conditions similar to those which at present
prevail upon the earth, the testimony of the rocks, and
the evidence to be derived from their fossil remains, are
at one. Sir Archibald Geikie brings the geological
testimony on this point forcibly before us in his
opening address to Section C at the British Association
meeting of 1899. Geologists, he points out, have found
no confirmation for the view that greater denudative
activity existed in the past : " On the contrary, they



URANIUM AND THE AGE OF THE EARTH. 249

have been unable to discern any indication that the
rate of geological causation has ever, on the whole,
greatly varied during the time which has elapsed since
the deposits of the oldest stratified rocks." He instances
the evidence of measured tranquillity in the deposition
of the ancient Torridonian sediments, and the fact that
the same tale, with endless additional details, is told all
through the stratified formations down to those which
to-day are in course of accumulation.

The zoological aspect of the same question is considered
by Poulton, 1 and similar conclusions are arrived at. The
evidence of fossil organisms seems to be incontestable.
It is to be read in the proportions and structures of
early woody plants and trees, in the wings of birds and
insects, and in the existence of frail insect life in early
times. And this evidence is greatly strengthened when
the remarkable influences of severe climatal conditions,
as witnessed to-day, on winged animal life, and on
arboreal life, are considered. Thus while fossil insects
from the Carboniferous display great powers of flight
(a fossil dragon-fly showing upwards of two feet of
wing-expanse), we see in storm-swept countries of the
world (e.g., Kerguelen Land) the whole of the insect
fauna rendered wingless. Similarly, while forests of
slender Cryptogams flourished in later Palaeozoic times,
we find to-day that the gales on our sea-coasts practically
inhibit arboreal life.

We conclude that the former physical conditions
must have been much as now ; and the view that
stupendous rains, hurricanes, and tides then existed

1 Poulton, Address to Section D, Brit. Assoc. Jiep. } 1896.



250 RADIOACTIVITY AND GEOLOGY.

is unsubstantiated by any records at our disposal. As
already remarked, however, had such conditions indeed
existed, an accelerated rate of denudation, and not a
retarded one, must have been the result.

The work of Sir George Darwin, based on the theory
of a genetic connexion between earth and moon, assigned
a minor limit of fifty-six millions of years to the time
since their separation. This, however, does not touch
the point at issue here. Similarly we have seen how
Kelvin's estimate of time since the consistentior status can
be lengthened by the heating effects of radioactivity.

With the denudation method of estimating the age
we close the case against the present indications of
the radioactive method. Can the nineteen rivers upon
which Murray's figures are based have given four or five
times the correct sodium average ? Here seems to be
the only possible opening for serious error. But recent
data suggest no possibility of so complete a failure of
the original estimates. And this being so, what are we
to conclude ? That the parentage of the stored helium
is not altogether to be assigned to the uranium family of
elements seems to be the most natural answer, if, indeed,
the migration of radioactive materials be proved an
inadequate explanation. With reference to the more
venerable ages arising out of the storage of lead in
primitive minerals (over and above the possibilities of
error), we must bear in mind the possibility that these
materials may date their radioactivity back, even
through many vicissitudes, to times before our denuda-
tive period began.

With an interest almost amounting to anxiety,



URANIUM AND THE AGE OF THE EARTH. 251

geologists will watch the development of researches
which may result in timing the strata and the phases
of evolutionary advance ; and may even going still
further back give us reason to see in the discrepancy
between denudative and radioactive methods, glimpses
of past aeons, beyond that day of regeneration which
at once ushered in our era of life, and, for all that went
before, was " a sleep and a forgetting."



CHAPTEK XII.

KADIUM MEASUREMENTS IN PRACTICE.

THE ELECTROSCOPE AND ITS CONSTRUCTION RATE OF ACCUMULATION
OF THE EMANATION OF RADIUM TABLE FOR REFERENCE EXPERI-
MENTAL STANDARDIZATION OF THE ELECTROSCOPE MODE OF USING
THE ELECTROSCOPE CONDITIONS OF ACCURACY IN PREPARING
SOLUTIONS TREATMENT OF ROCKS AND OTHKR SUBSTANCES PRE-
CAUTIONS AGAINST CONTAMINATION MODE OF BOILING-OFF AND
TRANSFERRING THE EMANATION SOURCES OF OCCASIONAL VARIA-
TIONS IN REPETITION EXPERIMENTS.

IN the earlier chapters sufficient has been said to
enable the general theory of radium measurement to
be understood. It is intended in what follows to give
an account of the details of apparatus and procedure,
such as will enable those having the requisite manipu-
lative training to pursue this line of research.

The Electroscope. The electroscope (fig. 3) is very
simple in construction, and may, in fact, be made from
a round glass flask of about 400 to 500 cubic centimetres'
capacity, by cutting off most of the neck. A cork
which has been boiled in paraffin wax is fitted to the
neck and is perforated in two places. One perforation
takes a glass tube leading to the drying-tube, through
which gas is removed or admitted to the electroscope.
The drying-tube contains phosphoric anhydride, with a
close-pressed plug of cotton wool inserted between the
powder and the flask, so as to avoid any possibility of



RADIUM MEASUREMENTS IN PRACTICE. 253

the drying material being drawn into the electroscope.
A glass stopcock at the outer end of the drying-tube
controls the entry of gas ; and for greater safety a short
length of capillary tube is inserted between it and the
dry ing- tube. This guards the electroscope from too
rapid an inflow of gas. The second perforation in the
cork takes a short length of glass tube, which in turn
carries an inner sulphur tube of fine bore about one
half millimetre supporting the gold-leaf system.




FIG. 3.

The sulphur tube is prepared as follows: Into a
length of about 30 centimetres of glass tubing, melted
sulphur is drawn ; by air-suction, one end of the tube
dipping into the vessel of sulphur. After a moment
the liquid sulphur is let run back out of the tube,
and is again drawn up ; the process being repeated
till a sufficient thickness of sulphur is deposited on



254 RADIOACTIVITY AND GEOLOGY.

the walls of the glass tube. This leaves a fine-bore
sulphur tube within the glass. Letting this stand a
few hours, it will be found that the sulphur has
shrunk away from the glass, and if now a length of
about 6 centimetres is cut from the glass tube, the
tube within may be pushed forward so as to project
a couple of centimetres from one end. This projecting
part must not be touched by the fingers at any time.
To make the sulphur tube fit air-tight in the glass,
it is requisite to put a little thick Canada balsam just
where it emerges from the glass. This creeps in
and hardens, making a perfect joint. At this stage the
glass tube supporting the sulphur tube is inserted in
the cork, in such a way that the extremity of the
sulphur reaches downwards to a point rather above the
centre of the flask. A flat piece of brass about 2J
centimetres by 0.3 centimetre is attached while hot to
the end of the sulphur tube, centrally, so that it crosses
the bore of the tube. With a warm penknife the
attachment of the brass strip is made air-tight in the
bore of the sulphur tube.

The gold leaf is finally attached. It is a little shorter
than the brass strip and about the same width, and is
attached by a trace of gum just where the brass leaves
the sulphur.

When the cork is finally inserted in the flask, the fit
must be made perfectly air-tight, by melting the paraffin
around and over the cork. It should be mentioned
that in order to earth the inner wall of the flask a
couple of tin-foil strips are brought in beside the cork
and gummed to the interior of the flask. These strips



RADIUM MEASUREMENTS IN PRACTICE. 255

bend down outside, meeting the glass where it is free
from paraffin.

The electrification of the leaves is effected by
inserting through the bore of the sulphur tube a fine
platinum wire carried in a sulphur handle. This
makes contact with the sealed-in end of the brass
strip, and when a charged body is applied to it above,
the leaves diverge. The divergence when using the
instrument should not be greater than about 30 degrees.
When the proper divergence is secured, the platinum
wire is withdrawn.

The motion of the leaf is observed by a reading
microscope, with a scale in the eyepiece, dividing the
field into 100 divisions. A good stopwatch is necessary
when the rates of discharge are rapid. The time re-
quired for the extremity of the leaf to move over, say,
ten divisions, is noted and the rate converted to so
many scale divisions per hour.

The electroscope is standardized in the following
manner : One-fifth of a gram of Joachimsthal pitch-
blende is carefully weighed out and dissolved in pure
nitric or hydrochloric acid. The solution is made up
to 200 cubic centimetres with distilled water. Thus
one cubic centimetre contains one milligram of the
ore. To effect the calibration, 5 cubic centimetres are
measured out in a pipette into a clean flask, and about
600 cubic centimetres of distilled water added. This is
boiled vigorously for twenty minutes. The flask is then
closed by a good rubber stopper, and set aside for about
twenty-four hours. At the end of , this time the contents
of the flask are again boiled, and, by a procedure to be



256 RADIOACTIVITY AND GEOLOGY.

described later, the boiled-off air and emanation are
transferred in their entirety to the electroscope.
During the time of closure of the flask (which must
be carefully noted) the radium present in the solution,
which was deprived of any original emanation by the
preliminary boiling, is generating fresh emanation, and
the amount of emanation generated is proportional to
the quantity of radium present and to the period
during which it collects.

The quantity of emanation formed depends also on
the rate at which it is derived from the radium, and
the rate of its own transformation. The first rate is
a steady one over the time interval concerned, and
we may consider that the radium produces continually
n particles per second. The rate of transformation of
the emanation being relatively rapid cannot be ignored.
We may say 1 that when N particles are accumulated
the number transforming per second is \N, where A is
the radioactive constant of the emanation or fraction
transforming in one second. Obviously the number
changing is variable, increasing till the equilibrium
value is reached.

At any time t, however, the net rate of increase of
the emanation must be n - \N\ or

- -\N

The solution of this equation is :



where a is a constant.

To find the value of the constant write t = 0, and

1 See Rutherford's JRadioactivity.



RADIUM MEASUREMENTS IN PRACTICE. 257

then the first term on the right is equal to a ; and as

*Y) W

when t = 0, -2V must = 0, we have a + ^- = 0, or r- = - & ;

A A

also when t = oo, we have the first term on the right of
the equation equal to 0; and as then the maximum

number, N , is formed, we have ^ = N ; and the equation
becomes :

N-N 9 -Njru. (1)

The value of A for emanation is found by experiment
to be 216 x 10- 6 .

"We will now apply the equation to calculate the
amount of emanation accumulated during, say, twenty-
four hours. In this case t in seconds is 864 x 10 2 . The
numerical value of \t is therefore 018662.

The last member of the equation is best evaluated
logarithmically. Thus if we let x = N e~ xt , we have
logx = log^Vo - A log e.

The value of log e is 043429, and if we let N = 100,
the log of which is 2-00000, we find log a? = 1-91896 ;
from which x = 83*0. This has now to be subtracted
from 100, and finally we have from (1) N= 17. That
is to say, there is 17 per cent, of the emanation accumu-
lated in twenty-four hours.

The trouble of making this calculation each time
we calibrate the instrument, or each time we deal
with a substance which has been enclosed for less than
the time required to secure the equilibrium amount
of emanation, may be avoided by plotting a curve to
a large scale once for all, in which the abscissae are the
times since closing up the solutions, and the ordinates
the percentage collected proper to the time, derived

s



258



RADIOACTIVITY AND GEOLOGY.



by solving the equation as above. The following table
will enable such a curve to be plotted, or may be used
directly for ordinary work.



Time of collection of
emanation.


Percentage of
eqnilihrium amount of
emanation accumulated.


6 hours.


4-55


12


8-9


18


13-1


24


17-0


30


20-8


36


24-4


42


27-8


2 days.


31-1


21


37-3


3 "


42-9


"2 "


47'9


4


52-6


4J


56-8


5


60-6


5f ,,


64-2


^


67-4


6|


70-3


7


72-9


8 ,,


77-6


9


81-3


10


84-5


12


89-4


14


927


16


94-9


18


96-5


20


97-6



In standardizing the electroscope according to the



RADIUM MEASUREMENTS IN PRACTICE. 259

foregoing procedure, we, of course, require to know
the amount of radium present in the standardizing
solution. This we find by a chemical analysis of the
uraninite or pitchblende, determining the uranium
only. From this we can derive the radium, as the
proportion in which the two exist in old minerals is
constant. For every gram of uranium we have, ac-
cording to Boltwood's latest determination, 3*4 x 10~ 7
grams of radium. 1

The uranium is best determined by Patera's method,
given in Fresenius' Quantitative Analysis (vol. ii.,
p. 310). From the results of the analysis, the per-
centage of metallic uranium is calculated. For instance,
in a particular analysis, the percentage came out as
594. Taking this as 60 per cent, (as there is generally
a slight deficiency in the amount determined by
analysis), and assuming that 5 milligrams of the ore
had been used in a standardizing experiment, we have,

for the radium :
fiO
5 x 10- 3 x x 34 x 10' 7 = 1020 x 10- 13 grams.

Suppose now the time of closure of this amount of
radium had been 24 hours, then the quantity of radium
represented in the increased rate of discharge of the
electroscope would be

x 1020 v 10- 1 ' - 173 x lO' 12 .



This, in fact, is the quantity of radium which would
produce the observed effect on the electroscope, if the
emanation in equilibrium with it had been collected.

1 Boltwood, Am. Journ. Science, June, 1908, p. 504.
S2



260 RADIOACTIVITY AND GEOLOGY.

We now see that the calibration is easily completed.
For suppose the normal leak of the instrument is
15 scale-divisions per hour, and the leak, three hours
after the introduction of the emanation, was 335 scale-
divisions per hour, then the gain has been 320, and this
is due to the emanation in equilibrium with 173 x 10" 12
grams of radium. The constant of the electroscope is