are the largest. They correspond to the central portion of the
glacier. Hence, these measurements conclusively establish, not only
the fact of glacier motion, but that _the centre of a glacier, like
that of a river, moves more rapidly than the sides_.
152. With the aid of trained engineers M. Agassiz followed up these
measurements in subsequent years. His researches are recorded in a
work entitled "Système glaciaire," which is accompanied by a very
noble Atlas of the Glacier of the Unteraar, published in 1847.
153. These determinations were made by means of a theodolite, of
which I will give you some notion immediately. The same instrument
was employed the same year by the late Professor Forbes upon the
Mer de Glace. He established independently the greater central
motion. He showed, moreover, that it is not necessary to wait a
year, or even a week to determine the motion of a glacier; with a
correctly-adjusted theodolite he was able to determine the motion
of various points of the Mer de Glace from day to day. He affirmed,
and with truth, that the motion of the glacier might be determined
from hour to hour. We shall prove this farther on (162). Professor
Forbes also triangulated the Mer de Glace, and laid down an excellent
map of it. His first observations and his survey are recorded in a
celebrated book published in 1843, and entitled "Travels in the Alps."
154. These observations were also followed up in subsequent years,
the results being recorded in a series of detached letters and essays
of great interest. These were subsequently collected in a volume
entitled "Occasional Papers on the Theory of Glaciers," published in
1859. The labours of Agassiz and Forbes are the two chief sources of
our knowledge of glacier phenomena.
§ 21. _The Theodolite and its Use. Our own Measurements._
155. My object thus far is attained. I have given you proofs of
glacier motion, and a historic account of its measurement. And
now we must try to add a little to the knowledge of glaciers by
our own labours on the ice. Resolution must not be wanting at
the commencement of our work, nor steadfast patience during its
prosecution. Look then at this theodolite; it consists mainly of a
telescope and a graduated circle, the telescope capable of motion
up and down, and the circle, carrying the telescope along with it,
capable of motion right and left. When desired to make the motion
exceedingly fine and minute, suitable screws, called tangent screws,
are employed. The instrument is supported by three legs, movable, but
firm when properly planted.
156. Two spirit-levels are fixed at right angles to each other on
the circle just referred to. Practice enables one to take hold of
the legs of the instrument, and so to fix them that the circle shall
be nearly horizontal. By means of four levelling screws we render it
_accurately_ horizontal. Exactly under the centre of the instrument
is a small hook from which a plummet is suspended; the point of the
bob just touches a rock on which we make a mark; or if the earth be
soft underneath, we drive a stake into it exactly under the plummet.
By re-suspending the plummet at any future time we can find to a
hairbreadth the position occupied by the instrument to-day.
157. Look through the telescope; you see it crossed by two fibres
of the finest spider's thread. In actual work we first direct the
telescope across the glacier, until the intersection of the two
fibres accurately covers some well-defined point of rock or tree at
the other side of the valley. This, our fixed standard, we sketch
with its surroundings in a note-book, so as to be able immediately
to recognise it on our return to this place. Imagine a straight line
drawn from the centre of the telescope to this point, and that this
line is permitted to drop straight down upon the glacier, every point
of it falling as a stone would fall; along such a line we have now to
fix a series of stakes.
158. A trained assistant is already upon the glacier. He erects
his staff and stands behind it; the telescope is lowered without
swerving to the right or to the left; in mathematical language it
remains _in the same vertical plane_. The crossed fibres of the
telescope probably strike the ice a little away from the staff of the
assistant; by a wave of the arm he moves right or left; he may move
too much, so we wave him back again. After a trial or two he knows
whether he is near the proper point, and if so makes his motions
small. He soon exactly strikes the point covered by the intersection
of the fibres. A signal is made which tells him that he is right; he
pierces the ice with an auger and drives in a stake. He then goes
forward, and in precisely the same manner takes up another point.
After one or two stakes have been driven in, the assistant is able to
take up the other points very rapidly. Any requisite number of stakes
may thus be fixed in a straight line across the glacier.
159. Next morning we measure the motion of all the stakes. The
theodolite is mounted in its former position and carefully levelled.
The telescope is directed first upon the standard point at the
opposite side of the valley, being moved by a tangent screw until the
intersection of the spider's threads accurately covers the point.
The telescope is then lowered to the first stake, beside which our
trained assistant is already standing. He is provided with a staff
with feet and inches marked on it. A glance shows us the stake has
moved down. By our signals the assistant recovers the point from
which we started yesterday, and then determines the distance from
this point to the stake. It is, say, 6 inches; through this distance,
therefore, the stake has moved.
160. We are careful to note the hour and minute at which each stake
is driven in, and the hour and the minute when its distance from its
first position is measured; this enables us to calculate the accurate
_daily motion_ of the point in question. The distances through which
all the other points have moved are determined in precisely the same
way.
161. Thus we shall proceed to work, first making clear to our minds
what is to be done, and then making sure that it shall be accurately
done. To give our work reality, I will here record the actual
measurements executed, and the actual thoughts suggested, on the
Mer de Glace in 1857. The only unreality that I would ask you to
allow, is that you and I are supposed to be making the observations
together. The labour of measuring was undertaken for the most part
by Mr. Hirst.
§ 22. _Motion of the Mer de Glace._
162. On July 14, then, we find ourselves at the end of the Glacier
des Bois, not far from the source of the Arveiron. We direct our
telescope across the glacier, and fix the intersection of its
spider's threads accurately upon the edge of a pinnacle of ice. We
leave the instrument untouched, looking through it from hour to
hour. The edge of ice moves slowly, but plainly, past the fibres,
and at the end of three hours we assure ourselves that the motion
has amounted to several inches. While standing near the vault of the
Arveiron, and talking about going into it, its roof gives way, and
falls with the sound of thunder. It is not, therefore, without reason
that I warned you against entering these vaults in summer.
163. We ascend to the Montanvert Inn, fix on it as a residence, and
then descend to the lateral moraine of the glacier a little below the
inn. Here we erect our theodolite, and mark its exact position by
a plummet. We must first make sure that our line is perpendicular,
or nearly so, to the axis or middle line of the glacier. Our
instructed assistant lays down a long staff in the direction of
the axis, assuring himself, by looking up and down, that it is the
true direction. With another staff in his hand, pointed towards
our theodolite, he shifts his position until the second staff is
perpendicular to the first. Here he gives us a signal. We direct our
telescope upon him, and then gradually raising its end in a vertical
plane we find, and note by sketching, a standard point at the other
side of the glacier. This point known, and our plummet mark known, we
can on any future day find our line. (To render the measurements more
intelligible, I append on the next page an outline diagram of the Mer
de Glace, and of its tributaries.)
164. Along the line just described ten stakes were set on July 17,
1857. Their displacements were measured on the following day. Two of
them had fallen, but here are the distances passed over by the eight
remaining ones in twenty-four hours.
DAILY MOTION OF THE MER DE GLACE.
First Line: A A' upon the Sketch.
East West
Stake 1 2 3 4 5 7 9 10
Inches 12 17 23 26 25 26 27 33
165. You have already assured yourself by actual contact that the
body of the glacier is real ice, and you may have read that glaciers
move; but the actual observation of the motion of a body apparently
so rigid is strangely interesting. And not only does the ice move
bodily, but one part of it moves past another; the rate of motion
augmenting gradually from 12 inches a day at the side to 33 inches a
day at a distance from the side. This quicker movement of the central
ice of glaciers had been already observed by Agassiz and Forbes; we
verify their results, and now proceed to something new. Crossing the
Glacier du Géant, which occupies more than half the valley, we find
that our line of stakes is not yet at an end. The 10th stake stands
on the part of the ice which comes from the Talèfre.
[Illustration: OUTLINE PLAN, SHOWING THE MEASURED LINES OF THE MER DE
GLACE AND ITS TRIBUTARIES.]
166. Now the motion of the sides is slow, because of the friction of
the ice against its boundaries; but then one would think that midway
between the boundaries, where the friction of the sides is least, the
motion ought to be greatest. This is clearly not the case; for though
the 10th stake is nearer than the 9th to the eastern or _Chapeau_
side of the valley, the 10th stake surpasses the 9th by 6 inches a
day.
167. Here we have something to think of; but before a natural
philosopher can think with comfort he must be perfectly sure of his
facts. The foregoing line ran across the glacier a little below the
Montanvert. We will run another line across a little way above the
hotel. On July 18 we set out this line, and to multiply our chances
of discovery we place along it 31 stakes. On the subsequent day five
of these were found unfit for use; but here are the distances passed
over by the remaining six-and-twenty in 24 hours.
Second Line: B B' upon the Sketch.
West
Stake 2 3 4 5 6 7 8 9 10 11 12 13
Inches 11 12 15 15 16 17 18 19 20 20 21 21
Stake 15 16 17 18 19 20 21 22 23 24 25 26
Inches 23 23 23 21 23 21 25 22 22 23 25 26
East
168. Look at these numbers. The first broad fact they reveal is the
advance in the rate of motion from first to last. There are however
some irregularities; from 23 inches at the 17th stake we fall to 21
inches at the 18th; from 23 inches at the 19th we fall to 21 inches
at the 20th; from 25 inches at the 21st we fall to 22 inches at the
22nd and 23rd; but notwithstanding these small ups and downs, the
general advance of the rate of motion is manifest. Now there may have
been some slight displacement of the stakes by melting, sufficient to
account for these small deviations from uniformity in the increase
of the motion. But another solution is also possible. We shall
afterwards learn that the glacier is retarded not only by its sides
but by its bed; that the upper portions of the ice slide over the
lower ones. Now if the bed of the Mer de Glace should have eminences
here and there rising sufficiently near to the surface to retard the
motion of the surface, they might produce the small irregularities
noticed above.
169. We note particularly, while upon the ice, that the 26th stake,
like the 10th stake in our last line, stands much nearer to the
eastern than to the western side of the glacier; the measurements,
therefore, offer a further proof that the centre of this portion of
the glacier is not the place of swiftest motion.
§ 23. _Unequal Motion of the two Sides of the Mer de Glace._
170. But in neither the first line nor the second were we able to
push our measurements quite across the glacier. Why? In attempting
to do one thing we are often taught another, and thus in science, if
we are only steadfast in our work, our very defeats are converted
into means of instruction. We at first planted our theodolite on the
lateral moraine of the Mer de Glace, expecting to be able to command
the glacier from side to side. But we are now undeceived; the centre
of the glacier proves to be higher than its sides, and from our last
two positions the view of the ice near the opposite side of the
glacier was intercepted by the elevation at the centre. The mountain
slopes, in fact, are warm in summer, and they melt the ice nearest to
them, thus causing a fall from the centre to the sides.
171. But yonder on the heights at the other side of the glacier we
see a likely place for our theodolite. We cross the glacier and plant
our instrument in a position from which we sweep the glacier from
side to side. Our first line was below the Montanvert, our second
line above it; this third line is exactly opposite the Montanvert;
in fact, the mark on which we have fixed the fibre-cross of the
theodolite is a corner of one of the windows of the little inn. Along
this line we fix twelve stakes on July 20. On the 21st one of them
had fallen; but the velocities of the remaining eleven in 24 hours
were found to be as follows:--
Third Line: C C' upon the Sketch.
East West
Stake 1 2 3 4 5 6 7 8 9 10 11
Inches 20 23 29 30 34 28 25 25 25 18 9
172. Both the first stake and the eleventh in this series stood
near the sides of the glacier. On the eastern side the motion is
20 inches, while on the western side it is only 9. It rises on
the eastern side from 20 to 34 inches at the 5th stake, which we,
standing upon the glacier, can see to be much nearer to the eastern
than to the western side. _The united evidence of these three lines
places the fact beyond doubt, that opposite the Montanvert, and for
some distance above it and below it, the whole eastern side of the
glacier is moving more quickly than the western side._
§ 24. _Suggestion of a new Likeness of Glacier Motion to River
Motion. Conjecture tested._
173. Here we have cause for reflection, and facts are comparatively
worthless if they do not provoke this exercise of the mind. It
is because facts of nature are not isolated but connected, that
science, to follow them, must also form a connected whole. The mind
of the natural philosopher must, as it were, be a web of _thought_
corresponding in all its fibres with the web of _fact_ in nature.
174. Let us, then, ascend to a point which commands a good view
of this portion of the Mer de Glace. The ice-river we see is not
straight but curved, and its curvature is _from_ the Montanvert;
that is to say, its convex side is east, and its concave side is
west (look to the sketch). You have already pondered the fact that a
glacier, _in some respects_, moves like a river. How would a river
move through a curved channel? This is known. Were the ice of the
Mer de Glace displaced by water, the point of swiftest motion at the
Montanvert would not be the centre, but a point east of the centre.
Can it be then that this "water-rock," as ice is sometimes called,
acts in this respect also like water?
175. This is a thought suggested on the spot; it may or it may not
be true, but the means of testing it are at hand. Looking up the
glacier, we see that at _les Ponts_ it also bends, but that there
its convex curvature is towards the western side of the valley (look
again to the sketch). If our surmise be true, the point of swiftest
motion opposite _les Ponts_ ought to lie west of the axis of the
glacier.
176. Let us test this conjecture. On July 25 we fix in a line across
this portion of the glacier seventeen stakes; every one of them has
remained firm, and on the 26th we find the motion for 24 hours to be
as follows:--
Fourth Line: D D' upon the Sketch.
East West
Stake 1 2 3 4 5 8 7 8 9 10 11 12 13 14 15
Inches 7 8 13 15 16 19 20 21 21 23 23 21 22 17 15
177. Inspected by the naked eye alone, the stakes 10 and 11, where
the glacier reaches its greatest motion, are seen to be considerably
to the west of the axis of the glacier. Thus far we have a perfect
verification of the _guess_ which prompted us to make these
measurements. You will here observe that the "guesses" of science are
not the work of chance, but of thoughtful pondering over antecedent
facts. The guess is the "induction" facts, to be ratified or exploded
by the test of subsequent experiment.
178. And though even now we have exceedingly strong reason for
holding that the point of maximum velocity obeys the law of liquid
motion, the strength of our conclusion will be doubled if we can
show that the point shifts back to the eastern side of the axis at
another place of flexure. Fortunately such a place exists opposite
Trélaporte. Here the convex curvature of the valley turns again to
the east. Across this portion of the glacier a line was set out on
July 28, and from measurements on the 31st, the rate of motion per 24
hours was determined.
Fifth Line: E E' upon the Sketch.
West East
Stake 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Inches 11 14 13 15 15 16 17 19 20 19 20 18 16 15 10
179. Here, again, the mere estimate of distances by the eye would
show us that the three stakes which moved fastest, viz. the 9th,
10th, and 11th, were all to the east of the middle line of the
glacier. The demonstration that the point of swiftest motion wanders
to and fro across the axis, as the flexure of the valley changes, is,
therefore,--shall I say complete?
180. Not yet. For if surer means are open to us we must not rest
content with estimates by the eye. We have with us a surveying chain:
let us shake it out and measure these lines, noting the distance of
every stake from the side of the glacier. This is no easy work among
the crevasses, but I confide it confidently to Mr. Hirst and you.
We can afterwards compare a number of stakes on the eastern side
with the same number of stakes taken at the same distances from the
western side. For example, a pair of stakes, one ten yards from the
eastern side and the other ten yards from the western side; another
pair, one fifty yards from the eastern side and the other fifty yards
from the western side, and so on, can be compared together. For the
sake of easy reference, let us call the points thus compared in
pairs, _equivalent points_.
181. There were five pairs of such points upon our fourth line, D D',
and here are their velocities:
Eastern points; motion in inches 13 15 16 18 20
Western " " " " 15 17 22 23 23
In every case here the stake at the western side moved more rapidly
than the equivalent stake at the eastern side.
182. Applying the same analysis to our fifth line, E E', we have the
following series of velocities of three pairs of equivalent points:--
Eastern points; motion in inches 15 18 19
Western " " " " 13 15 17
183. Here the three points on the eastern side move more rapidly than
the equivalent points on the western side.
184. It is thus proved:--
1. _That opposite the Montanvert the eastern half of the Mer de Glace
moves more rapidly than the western half._
2. _That opposite_ les Fonts _the western half of the glacier moves
more rapidly than the eastern half._
3. _That opposite Trélaporte the eastern half of the glacier again
moves more rapidly than the western half._
4. _That these changes in the place of greatest motion are determined
by the flexures of the valley through which the Mer de Glace moves._
§ 25. _New Law of Glacier Motion._
185. Let us express these facts in another way. Supposing the points
of swiftest motion for a very great number of lines crossing the
Mer de Glace to be determined; the line joining all those points
together is what mathematicians would call the _locus_ of the point
of swiftest motion.
186. At Trélaporte this line would lie east of the centre; at the
_Ponts_ it would lie west of the centre; hence in passing from
Trélaporte to the _Ponts_ it would cross the centre. But at the
Montanvert it would again lie east of the centre; hence between the
_Ponts_ and the Montanvert the centre must be crossed a second time.
If there were further sinuosities upon the Mer de Glace there would
be further crossings of the axis of the glacier.
187. The points on the axis which mark the transition from eastern to
western bending, and the reverse, may be called _points of contrary
flexure_.
188. Now what is true of the Mer de Glace is true of all other
glaciers moving through sinuous valleys; so that the facts
established in the Mer de Glace may be expanded into the following
general law of glacier motion:--
_When a glacier moves through a sinuous valley, the locus of the
points of maximum motion does not coincide with the centre of the
glacier, but, on the contrary, always lies on the convex side of
the central line. The locus is therefore a curved line more deeply
sinuous than the valley itself, and crosses the axis of the glacier
at each point of contrary flexure._
189. The dotted line on the Outline Plan (page 68) represents the
locus of the point of maximum motion, the firm line marking the
centre of the glacier.
190. Substituting the word _river_ for _glacier_, this law is
also true. The motion of the water is ruled by precisely the same
conditions as the motion of the ice.
191. Let us now apply our law to the explanation of a difficulty.
Turning to the careful measurements executed by M. Agassiz on
the glacier of the Unteraar, we notice in the discussion of these
measurements a section of the "Système glaciaire" devoted to the
"Migrations of the Centre." It is here shown that the middle of the
Unteraar glacier is not always the point of swiftest motion. This
fact has hitherto remained without explanation; but a glance at the
Unteraar valley, or at the map of the valley, shows the enigma to be
an illustration of the law which we have just established on the Mer
de Glace.
§ 26. _Motion of Axis of Mer de Glace._
192. We have now measured the rate of motion of five different lines
across the trunk of the Mer de Glace. Do they all move alike? No.
Like a river, a glacier at different places moves at different rates.
Comparing together the points of maximum motion of all five lines, we
have this result:
MOTION OF MER DE GLACE.
At Trélaporte 20 inches a day.
At _les Ponts_ 23 " "
Above the Montanvert 26 " "
At the Montanvert 34 " "
Below the Montanvert 33[C] " "
[C] This is probably under the mark. I think it likely that the
swiftest motion of this portion of the Mer de Glace in 1857 amounted
to a yard in twenty-four hours.
193. There is thus an increase of rapidity as we descend the glacier
from Trélaporte to the Montanvert; the maximum, motion at the
Montanvert being fourteen inches a day greater than at Trélaporte.
§ 27. _Motion of Tributary Glaciers._
194. So much for the trunk glacier; let us now investigate the
branches, permitting, as we have hitherto done, reflection on known
facts to precede our attempts to discover unknown ones.
195. As we stood upon our "cleft station," whence we had so capital
a view of the Mer de Glace, we were struck by the fact that some of
the tributaries of the glacier were wider than the glacier itself.
Supposing water to be substituted for the ice, how do you suppose
it would behave? You would doubtless conclude that the motion down
the broad and slightly-inclined valleys of the Géant and the Léchaud
would be comparatively slow, but that the water would force itself
with increased rapidity through the "narrows" of Trélaporte. Let us
test this notion as applied to the ice.
196. Planting our theodolite in the shadow of Mont Tacul, and
choosing a suitable point at the opposite side of the Glacier du
Géant, we fix on July 29 a series of ten stakes across the glacier.
The motion of this line in twenty-four hours was as follows:--
MOTION OF GLACIER DU GÉANT.
Sixth Line: H H' upon Sketch.
Stake 1 2 3 4 5 6 7 8 9 10
Inches 11 10 12 13 12 13 11 10 9 5
197. Our conjecture is fully verified. The maximum motion here is
seven inches a day less than that of the Mer de Glace at Trélaporte
(192).
198. And now for the Léchaud branch. On August 1 we fix ten stakes
across this glacier above the point where it is joined by the
Talèfre. Measured on August 3, and reduced to twenty-four hours, the
motion was found to be--
MOTION OF GLACIER DE LÉCHAUD.