OF METHODS OF OBSERVATION.
APHORISM XXVIII.
_The Methods of Observation of Quantity in general are_, Numeration,
_which is precise by the nature of Number; the_ Measurement of Space
_and_ of Time, _which are easily made precise; the_ Conversion of
Space and Time, _by which each aids the measurement of the other;
the_ Method of Repetition; _the_ Method of Coincidences _or_
Interferences. _The measurement of Weight is made precise by the_
Method of Double-weighing. _Secondary Qualities are measured by
means of_ Scales of Degrees; _but in order to apply these Scales,
the student requires the_ Education of the Senses. _The Education of
the Senses is forwarded by the practical study of_ Descriptive
Natural History, Chemical Manipulation, _and_ Astronomical
Observation.
1. I SHALL speak, in this chapter, of Methods of exact and
systematic observation, by which such facts are collected as form
the materials of precise scientific propositions. These Methods are
very various, according to the nature of the subject inquired into,
and other circumstances: but a great portion of them agree in being
processes of measurement. These I shall peculiarly consider: and in
the first place those referring to Number, Space, and Time, which
are at the same time objects and instruments of measurement.
2. But though we have to explain how observations may be made as
perfect as possible, we must not forget that in most cases complete
perfection is unattainable. _Observations are never perfect._ For we
{146} observe phenomena by our senses, and measure their relations
in time and space; but our senses and our measures are all, from
various causes, inaccurate. If we have to observe the exact place of
the moon among the stars, how much of instrumental apparatus is
necessary! This apparatus has been improved by many successive
generations of astronomers, yet it is still far from being perfect.
And the senses of man, as well as his implements, are limited in
their exactness. Two different observers do not obtain precisely the
same measures of the time and place of a phenomenon; as, for
instance, of the moment at which the moon occults a star, and the
point of her _limb_ at which the occultation takes place. Here,
then, is a source of inaccuracy and errour, even in astronomy, where
the means of exact observation are incomparably more complete than
they are in any other department of human research. In other cases,
the task of obtaining accurate measures is far more difficult. If we
have to observe the tides of the ocean when rippled with waves, we
can see the average level of the water first rise and then fall; but
how hard is it to select the exact moment when it is at its greatest
height, or the exact highest point which it reaches! It is very
easy, in such a case, to err by many minutes in time, and by several
inches in space.
Still, in many cases, good Methods can remove very much of this
inaccuracy, and to these we now proceed.
3. (I.) _Number_.--Number is the first step of measurement, since it
measures itself, and does not, like space and time, require an
arbitrary standard. Hence the first exact observations, and the
first advances of rigorous knowledge, appear to have been made by
means of number; as for example,--the number of days in a month and
in a year;--the cycles according to which eclipses occur;--the
number of days in the revolutions of the planets; and the like. All
these discoveries, as we have seen in the History of Astronomy, go
back to the earliest period of the science, anterior to any distinct
tradition; and these discoveries presuppose a series, probably a
very long series, of observations, made {147} principally by means
of number. Nations so rude as to have no other means of exact
measurement, have still systems of numeration by which they can
reckon to a considerable extent. Very often, such nations have very
complex systems, which are capable of expressing numbers of great
magnitude. Number supplies the means of measuring other quantities,
by the assumption of a _unit_ of measure of the appropriate kind: but
where nature supplies the unit, number is applicable directly and
immediately. Number is an important element in the Classificatory as
well as in the Mathematical Sciences. The History of those Sciences
shows how the formation of botanical systems was effected by the
adoption of number as a leading element, by Cæsalpinus; and how
afterwards the Reform of Linnæus in classification depended in a
great degree on his finding, in the pistils and stamens, a better
numerical basis than those before employed. In like manner, the
number of rays in the membrane of the gills[1\3], and the number of
rays in the fins of fish, were found to be important elements in
ichthyological classification by Artedi and Linnæus. There are
innumerable instances, in all parts of Natural History, of the
importance of the observation of number. And in this observation, no
instrument, scale or standard is needed, or can be applied; except
the scale of natural numbers, expressed either in words or in
figures, can be considered as an instrument.
[Note 1\3: _Hist. Ind. Sc._ b. xvi. c. vii.]
4. (II.) _Measurement of Space._--Of quantities admitting of
_continuous_ increase and decrease, (for number is discontinuous,)
space is the most simple in its mode of measurement, and requires
most frequently to be measured. The obvious mode of measuring space
is by the repeated application of a material measure, as when we
take a foot-rule and measure the length of a room. And in this case
the foot-rule is the _unit_ of space, and the length of the room is
expressed by the number of such units which it contains: or, as it
may not contain an exact number, by a number with a _fraction_. But
besides this measurement of linear space, {148} there is another
kind of space which, for purposes of science, it is still more
important to measure, namely, angular space. The visible heavens
being considered as a sphere, the portions and paths of the heavenly
bodies are determined by drawing circles on the surface of this
sphere, and are expressed by means of the parts of these circles
thus intercepted: by such measures the doctrines of astronomy were
obtained in the very beginning of the science. The arcs of circles
thus measured, are not like linear spaces, reckoned by means of an
_arbitrary_ unit, for there is a _natural unit_, the total
circumference, to which all arcs may be referred. For the sake of
convenience, the whole circumference is divided into 360 parts or
_degrees_; and by means of these degrees and their parts, all arcs
are expressed. The _arcs_ are the measures of the _angles at the
center_, and the degrees may be considered indifferently as
measuring the one or the other of these quantities.
5. In the History of Astronomy[2\3], I have described the method of
observation of celestial angles employed by the Greeks. They
determined the lines in which the heavenly bodies were seen, by
means either of Shadows, or of Sights; and measured the angles
between such lines by arcs or rules properly applied to them. The
Armill, Astrolabe, Dioptra, and Parallactic Instrument of the
ancients, were some of the instruments thus constructed. Tycho Brahe
greatly improved the methods of astronomical observation by giving
steadiness to the frame of his instruments, (which were large
_quadrants_,) and accuracy to the divisions of the _limb_[3\3]. But
the application of the _telescope_ to the astronomical quadrant and
the fixation of the center of the field by a _cross_ of fine wires
placed in the focus, was an immense improvement of the instrument,
since it substituted a precise visual ray, pointing to the star,
instead of the coarse coincidence of Sights. The accuracy of
observation was still further increased {149} by applying to the
telescope a _micrometer_ which might subdivide the smaller divisions
of the arc.
[Note 2\3: _Hist. Ind. Sc._ b. iii. c. iv. sect. 3.]
[Note 3\3: _Ib._ b. vii. c. vi. sect. 1.]
6. By this means, the precision of astronomical observation was made
so great, that very minute angular spaces could be measured: and it
then became a question whether discrepancies which appeared at first
as defects in the theory, might not arise sometimes from a bending
or shaking of the instrument, and from the degrees marked on the
limb being really somewhat unequal, instead of being rigorously
equal. Accordingly, the framing and balancing of the instrument, so
as to avoid all possible tremor or flexure, and the exact division
of an arc into equal parts, became great objects of those who wished
to improve astronomical observations. The observer no longer gazed
at the stars from a lofty tower, but placed his telescope on the
solid ground,--and braced and balanced it with various contrivances.
Instead of a quadrant, an entire circle was introduced (by Ramsden;)
and various processes were invented for the dividing of instruments.
Among these we may notice Troughton's method of dividing; in which
the visual ray of a microscope was substituted for the points of a
pair of compasses, and, by _stepping_ round the circle, the partial
arcs were made to bear their exact relation to the whole
circumference.
7. Astronomy is not the only science which depends on the
measurement of angles. Crystallography also requires exact measures
of this kind; and the _goniometer_, especially that devised by
Wollaston, supplies the means of obtaining such measures. The
science of Optics also, in many cases, requires the measurement of
angles.
8. In the measurement of linear space, there is no natural standard
which offers itself. Most of the common measures appear to be taken
from some part of the human body; as a _foot_, a _cubit_, a
_fathom_; but such measures cannot possess any precision, and are
altered by convention: thus there were in ancient times many kinds
of cubits; and in modern Europe, there are a great number of
different standards of the foot, as the Rhenish foot, the Paris
foot, the English foot. It is {150} very desirable that, if
possible, some permanent standard, founded in nature, should be
adopted; for the conventional measures are lost in the course of
ages; and thus, dimensions expressed by means of them become
unintelligible. Two different natural standards have been employed
in modern times: the French have referred their measures of length
to the total circumference of a meridian of the earth; a quadrant of
this meridian consists of ten million units or _metres_. The English
have fixed their linear measure by reference to the length of a
pendulum which employs an exact second of time in its small
oscillation. Both these methods occasion considerable difficulties
in carrying them into effect; and are to be considered mainly as
means of recovering the standard if it should ever be lost. For
common purposes, some material standard is adopted as authority for
the time: for example, the standard which in England possessed legal
authority up to the year 1835 was preserved in the House of
Parliament; and was lost in the conflagration which destroyed that
edifice. The standard of length now generally referred to by men of
science in England is that which is in the possession of the
Astronomical Society of London.
9. A standard of length being established, the artifices for
applying it, and for subdividing it in the most accurate manner, are
nearly the same as in the case of measures of arcs: as for instance,
the employment of the visual rays of microscopes instead of the legs
of compasses and the edges of rules; the use of micrometers for
minute measurements; and the like. Many different modes of avoiding
errour in such measurements have been devised by various observers,
according to the nature of the cases with which they had to
deal[4\3].
[Note 4\3: On the precautions employed in astronomical instruments
for the measure of space, see Sir J. Herschel's _Astronomy_ (in the
_Cabinet Cyclopædia_,) Arts. 103-110.]
10. (III.) _Measurement of Time_.--The methods of measuring Time are
not so obvious as the methods of {151} measuring space; for we
cannot apply one portion of time to another, so as to test their
equality. We are obliged to begin by assuming some change as the
measure of time. Thus the motion of the sun in the sky, or the
length and position of the shadows of objects, were the first modes
of measuring the parts of the day. But what assurance had men, or
what assurance could they have, that the motion of the sun or of the
shadow was uniform? They could have no such assurance, till they had
adopted some measure of smaller times; which smaller times, making
up larger times by repetition, they took as the standard of
uniformity;--for example, an hour-glass, or a clepsydra which
answered the same purpose among the ancients. There is no apparent
reason why the successive periods measured by the emptying of the
hour-glass should be unequal; they are implicitly accepted as equal;
and by reference to these, the uniformity of the sun's motion may be
verified. But the great improvement in the measurement of time was
the use of a pendulum for the purpose by Galileo, and the
application of this device to clocks by Huyghens in 1656. For the
successive oscillations of a pendulum are rigorously equal, and a
clock is only a train of machinery employed for the purpose of
counting these oscillations. By means of this invention, the measure
of time in astronomical observations became as accurate as the
measure of space.
11. What is the _natural unit_ of time? It was assumed from the
first by the Greek astronomers, that the sidereal days, measured by
the revolution of a star from any meridian to the same meridian
again, are exactly equal; and all improvements in the measure of
time tended to confirm this assumption. The sidereal day is
therefore the natural standard of time. But the solar day,
determined by the diurnal revolution of the sun, although not
rigorously invariable, as the sidereal day is, undergoes scarcely
any perceptible variation; and since the course of daily occurrences
is regulated by the sun, it is far more convenient to seek the basis
of our unit of time in _his_ motions. Accordingly the solar day (the
_mean_ solar day) is divided into 24 hours, {152} and these, into
minutes and seconds; and this is our scale of time. Of such time,
the sidereal day has 23 hours 56 minutes 4·09 seconds. And it is
plain that by such a statement the length of the hour is fixed, with
reference to a sidereal day. The _standard_ of time (and the
standard of space in like manner) equally answers its purpose,
whether or not it coincides with any _whole number_ of units.
12. Since the sidereal day is thus the standard of our measures of
time, it becomes desirable to refer to it, constantly and exactly,
the instruments by which time is measured, in order that we may
secure ourselves against errour. For this purpose, in astronomical
observatories, observations are constantly made of the transit of
stars across the meridian; the _transit instrument_ with which this
is done being adjusted with all imaginable regard to accuracy[5\3].
[Note 5\3: On the precautions employed in the measure of time by
astronomers, see Herschel's _Astronomy_, Art. 115-127.]
13. When exact measures of time are required in other than
astronomical observations, the same instruments are still used,
namely, clocks and chronometers. In chronometers, the regulating
part is an oscillating body; not, as in clocks, a pendulum
oscillating by the force of gravity, but a wheel swinging to and fro
on its center, in consequence of the vibrations of a slender coil of
elastic wire. To divide time into still smaller portions than these
vibrations, other artifices are used; some of which will be
mentioned under the next head.
14. (IV.) _Conversion of Space and Time._--Space and time agree in
being extended quantities, which are made up and measured by the
repetition of homogeneous parts. If a body move uniformly, whether
in the way of revolving or otherwise, the _space_ which any point
describes, is _proportional_ to the _time_ of its motion; and the
space and the time may each be taken as a measure of the other.
Hence in such cases, by taking space instead of time, or time
instead of {153} space, we may often obtain more convenient and
precise measures, than we can by measuring directly the element with
which we are concerned.
The most prominent example of such a conversion, is the measurement
of the Right Ascension of stars, (that is, their angular distance
from a standard meridian[6\3] on the celestial sphere,) by means of
the time employed in their coming to the meridian of the place of
observation. Since, as we have already stated, the visible celestial
sphere, carrying the fixed stars, revolves with perfect uniformity
about the pole; if we observe the stars as they come in succession
to a fixed circle passing through the poles, the intervals of time
between these observations will be proportional to the angles which
the meridian circles passing through these stars make at the poles
where they meet; and hence, if we have the means of measuring time
with great accuracy, we can, by watching the _times_ of the transits
of successive stars across some visible mark in our own meridian,
determine the _angular distances_ of the meridian circles of all the
stars from one another.
[Note 6\3: A _meridian_ is a circle passing through the poles about
which the celestial sphere revolves. The meridian _of any place_ on
the earth is that meridian which is exactly over the place.]
Accordingly, now that the pendulum clock affords astronomers the
means of determining time exactly, a measurement of the Right
Ascensions of heavenly bodies by means of a clock and a transit
instrument, is a part of the regular business of an observatory. If
the sidereal clock be so adjusted that it marks the beginning of its
scale of time when the first point of Right Ascension is upon the
visible meridian of our observatory, the point of the scale at which
the clock points when any other star is in our meridian, will truly
represent the Right Ascension of the star.
Thus as the motion of the stars is our measure of time, we employ
time, conversely, as our measure of the places of the stars. The
celestial machine and our terrestrial machines correspond to each
other in their movements; and the star steals silently and steadily
{154} across our meridian line, just as the pointer of the clock
steals past the mark of the hour. We may judge of the scale of this
motion by considering that the full moon employs about two minutes
of time in sailing across any fixed line seen against the sky,
transverse to her path: and all the celestial bodies, carried along
by the revolving sphere, travel at the same rate.
15. In this case, up to a certain degree, we render our measures of
astronomical angles more exact and convenient by substituting time
for space; but when, in the very same kind of observation, we wish
to proceed to a greater degree of accuracy, we find that it is best
done by substituting space for time. In observing the transit of a
star across the meridian, if we have the clock within hearing, we
can count the beats of the pendulum by the noise which they make,
and tell exactly at which second of time the passage of the star
across the visible thread takes place; and thus we measure Right
Ascension by means of time. But our perception of time does not
allow us to divide a second into ten parts, and to pronounce whether
the transit takes place three-tenths, six-tenths, or seven-tenths of
a second after the preceding beat of the clock. This, however, can
be done by the usual mode of observing the transit of a star. The
observer, listening to the beat of his clock, fastens his attention
upon the star at each beat, and especially at the one immediately
before and the one immediately after the passage of the thread: and
by this means he has these two positions and the position of the
thread so far present to his intuition at once, that he can judge in
what proportion the thread is nearer to one position than the other,
and can thus divide the intervening second in its due proportion.
Thus if he observe that at the beginning of the second the star is
on one side of the thread, and at the end of the second on the other
side; and that the two distances from the thread are as two to
three, he knows that the transit took place at two-fifths (or
four-tenths) of a second after the former beat. In this way a second
of time in astronomical observations may, by a skilful observer, be
divided into ten equal {155} parts; although when time is observed
as time, a tenth of a second appears almost to escape our senses.
From the above explanation, it will be seen that the reason why the
subdivision is possible in the way thus described, is this:--that
the moment of time thus to be divided is so small, that the eye and
the mind can retain, to the end of this moment, the impression of
position which it received at the beginning. Though the two
positions of the star, and the intermediate thread, are seen
successively, they can be contemplated by the mind as if they were
seen simultaneously: and thus it is precisely the smallness of this
portion of time which enables us to subdivide it by means of space.
16. There is another case, of somewhat a different kind, in which
time is employed in measuring space; namely, when space, or the
standard of space, is defined by the length of a pendulum
oscillating in a given time. We might in this way define any space
by the time which a pendulum of such a length would take in
oscillating; and thus we might speak, as was observed by those who
suggested this device, of five minutes of cloth, or a rope half an
hour long. We may observe, however, that in this case, the space is
_not proportional_ to the time. And we may add, that though we thus
appear to avoid the arbitrary standard of space (for as we have
seen, the standard of measures of time is a natural one,) we do not
do so in fact: for we assume the invariableness of gravity, which
really varies (though very slightly,) from place to place.
17. (V.) _The Method of Repetition in Measurement._--In many cases
we can give great additional accuracy to our measurements by
repeatedly adding to itself the quantity which we wish to measure.
Thus if we wished to ascertain the exact breadth of a thread, it
might not be easy to determine whether it was one-ninetieth, or
one-ninety-fifth, or one-hundredth part of an inch; but if we find
that ninety-six such threads placed side by side occupy exactly an
inch, we have the precise measure of the breadth of the thread. In
{156} the same manner, if two clocks are going nearly at the same
rate, we may not be able to distinguish the excess of an oscillation
of one of the pendulums over an oscillation of the other: but when
the two clocks have gone for an hour, one of them may have gained
ten seconds upon the other; thus showing that the proportion of
their times of oscillation is 3610 to 3600.
In the latter of these instances, we have the principle of
repetition truly exemplified, because (as has been justly observed
by Sir J. Herschel[7\3],) there is then 'a juxtaposition of units
without errour,'--'one vibration commences exactly where the last
terminates, no part of time being lost or gained in the addition of
the units so counted.' In space, this juxtaposition of units without
errour cannot be rigorously accomplished, since the units must be
added together by material contact (as in the above case of the
threads,) or in some equivalent manner. Yet the principle of
repetition has been applied to angular measurement with considerable
success in Borda's Repeating Circle. In this instrument, the angle
between two objects which we have to observe, is repeated along the
graduated limb of the circle by turning the telescope from one
object to the other, alternately fastened to the circle (by its
_clamp_) and loose from it (by unclamping). In this manner the
errours of graduation may (theoretically) be entirely got rid of:
for if an angle repeated _nine_ times be found to go twice round the
circle, it must be _exactly_ eighty degrees: and where the
repetition does not give an exact number of circumferences, it may
still be made to subdivide the errour to any required extent.
[Note 7\3: _Disc. Nat. Phil._ art. 121.]
18. Connected with the principle of repetition, is the _Method of
coincidences_ or _interferences_. If we have two Scales, on one of
which an inch is divided into 10, and on the other into 11 equal
parts; and if, these Scales being placed side by side, it appear
that the beginning of the latter Scale is between the 2nd and 3rd
division of the former, it may not be apparent {157} what fraction
added to 2 determines the place of beginning of the second Scale as
measured on the first. But if it appear also that the 3rd division
of the second Scale _coincides_ with a certain division of the
first, (the 5th,) it is certain that 2 and _three-tenths_ is the
_exact_ place of the beginning of the second Scale, measured on the
first Scale. The 3rd division of the 11 Scale will coincide (or
interfere with) a division of the 10 Scale, when the beginning or
_zero_ of the 11 divisions is three-tenths of a division beyond the
preceding line of the 10 Scale; as will be plain on a little
consideration. And if we have two Scales of equal units, in which
each unit is divided into nearly, but not quite, the same number of
equal parts (as 10 and 11, 19 and 20, 29 and 30,) and one sliding on
the other, it will always happen that some one or other of the
division lines will coincide, or very nearly coincide; and thus the
exact position of the beginning of one unit, measured on the other
scale, is determined. A sliding scale, thus divided for the purpose
of subdividing the units of that on which it slides, is called a
_Vernier_, from the name of its inventor.
19. The same Principle of Coincidence or Interference is applied to
the exact measurement of the length of time occupied in the
oscillation of a pendulum. If a detached pendulum, of such a length
as to swing in little less than a second, be placed before the
seconds' pendulum of a clock, and if the two pendulums begin to move
together, the former will gain upon the latter, and in a little
while their motions will be quite discordant. But if we go on
watching, we shall find them, after a time, to agree again exactly;
namely, when the detached pendulum has gained one complete
oscillation (back and forwards,) upon the clock pendulum, and again
coincides with it in its motion. If this happen after 5 minutes, we
know that the times of oscillation of the two pendulums are in the
proportion of 300 to 302, and therefore the detached pendulum
oscillates in 150/151 of a second. The accuracy which can be
obtained in the measure of an oscillation by this means is great;
for the clock can be compared (by {158} observing transits of the
stars or otherwise) with the natural standard of time, the sidereal
day. And the moment of coincidence of the two pendulums may, by
proper arrangements, be very exactly determined.
We have hitherto spoken of methods of measuring time and space, but
other elements also may be very precisely measured by various means.
20. (VI.) _Measurement of Weight._--Weight, like space and time, is
a quantity made up by addition of parts, and may be measured by
similar methods. The principle of repetition is applicable to the
measurement of weight; for if two bodies be simultaneously put in
the same pan of a balance, and if they balance pieces in the other
pan, their weights are exactly added.
There may be difficulties of practiced workmanship in carrying into
effect the mathematical conditions of a perfect balance; for
example, in securing an exact equality of the effective arms of the
beam in all positions. These difficulties are evaded by the _Method
of double weighing_; according to which the standard weights, and
the body which is to be weighed, are successively put in the _same_
pan, and made to balance by a third body in the opposite scale. By
this means the different lengths of the arms of the beam, and other
imperfections of the balance, become of no consequence[8\3].
[Note 8\3: For other methods of measuring weights accurately, see
Faraday's _Chemical Manipulation_, p. 25.]
21. There is no natural _Standard_ of weight. The conventional
weight taken as the standard, is the weight of a given bulk of some
known substance; for instance, a _cubic foot of water_. But in order
that this may be definite, the water must not contain any portion of
heterogeneous substance: hence it is required that the water be
_distilled_ water.
22. (VII.) _Measurement of Secondary Qualities._--We have already
seen[9\3] that secondary qualities are estimated by means of
conventional Scales, which refer {159} them to space, number, or
some other definite expression. Thus the Thermometer measures heat;
the Musical Scale, with or without the aid of number, expresses the
pitch of a note; and we may have an exact and complete Scale of
Colours, pure and impure. We may remark, however, that with regard
to sound and colour, the estimates of the ear and the eye are not
superseded, but only assisted: for if we determine what a note is,
by comparing it with an instrument known to be in tune, we still
leave the ear to decide when the note is _in unison_ with one of the
notes of the instrument. And when we compare a colour with our
chromatometer, we judge by the eye which division of the
chromatometer it _matches_. Colour and sound have their Natural
Scales, which the eye and ear habitually apply; what science
requires is, that those scales should be systematized. We have seen
that several conditions are requisite in such scales of qualities:
the observer's skill and ingenuity are mainly shown in devising such
scales and methods of applying them.
[Note 9\3: B. iii. c. ii. Of the Measure of Secondary Qualities.]
23. The Method of Coincidences is employed in harmonics: for if two
notes are nearly, but not quite, in unison, the coincidences of the
vibrations produce an audible undulation in the note, which is
called the _howl_; and the exactness of the unison is known by this
howl vanishing.
24. (VIII.) _Manipulation._--The process of applying practically
methods of experiment and observation, is termed Manipulation; and
the value of observations depends much upon the proficiency of the
observer in this art. This skill appears, as we have said, not only
in devising means and modes in measuring results, but also in
inventing and executing arrangements by which elements are subjected
to such conditions as the investigation requires: in finding and
using some material combination by which nature shall be asked the
question which we have in our minds. To do this in any subject may
be considered as a peculiar Art, but especially in Chemistry; where
'many experiments, and even whole trains of research, are {160}
essentially dependent for success on mere manipulation[10\3].' The
changes which the chemist has to study,--compositions,
decompositions, and mutual actions, affecting the internal structure
rather than the external form and motion of bodies,--are not
familiarly recognized by common observers, as those actions are
which operate upon the total mass of a body: and hence it is only
when the chemist has become, to a certain degree, familiar with his
science, that he has the power of observing. He must learn to
interpret the effects of mixture, heat, and other Chemical agencies,
so as to see in them those facts which chemistry makes the basis of
her doctrines. And in learning to interpret this language, he must
also learn to call it forth;--to place bodies under the requisite
conditions, by the apparatus of his own laboratory and the
operations of his own fingers. To do this with readiness and
precision, is, as we have said, an Art, both of the mind and of the
hand, in no small degree recondite and difficult. A person may be
well acquainted with all the doctrines of chemistry, and may yet
fail in the simplest experiment. How many precautions and
observances, what resource and invention, what delicacy and
vigilance, are requisite in _Chemical Manipulation_, may be seen by
reference to Dr. Faraday's work on that subject.
[Note 10\3: Faraday's _Chemical Manipulation_, p. 3.]
25. The same qualities in the observer are requisite in some other
departments of science; for example, in the researches of Optics:
for in these, after the first broad facts have been noticed, the
remaining features of the phenomena are both very complex and very
minute; and require both ingenuity in the invention of experiments,
and a keen scrutiny of their results. We have instances of the
application of these qualities in most of the optical experimenters
of recent times, and certainly in no one more than Sir David
Brewster. Omitting here all notice of his succeeding labours, his
_Treatise on New Philosophical Instruments_, published in 1813, is
an excellent model of the kind of resource {161} and skill of which
we now speak. I may mention as an example of this skill, his mode of
determining the refractive power of an _irregular_ fragment of any
transparent substance. At first this might appear an impossible
problem; for it would seem that a regular and smooth surface are
requisite, in order that we may have any measurable refraction. But
Sir David Brewster overcame the difficulty by immersing the fragment
in a combination of fluids, so mixed, that they had the same
refractive power as the specimen. The question, _when_ they had this
power, was answered by noticing when the fragment became so
transparent that its surface could hardly be seen; for this happened
when, the refractive power within and without the fragment being the
same, there was no refraction at the surface. And this condition
being obtained, the refractive power of the fluid, and therefore of
the fragment, was easily ascertained.
26. (IX.) _The Education of the Senses._--Colour and Musical Tone
are, as we have seen, determined by means of the Senses, whether or
not Systematical Scales are used in expressing the observed fact.
Systematical Scales of sensible qualities, however, not only give
precision to the record, but to the observation. But for this
purpose such an Education of the Senses is requisite as may enable
us to apply the scale immediately. The memory must retain the
sensation or perception to which the technical term or degree of the
scale refers. Thus with regard to colour, as we have said
already[11\3], when we find such terms as _tin-white_ or
_pinchbeck-brown_, the metallic colour so denoted ought to occur at
once to our recollection without delay or search. The observer's
senses, therefore, must be educated, at first by an actual
exhibition of the standard, and afterwards by a familiar use of it,
to understand readily and clearly each phrase and degree of the
scales which in his observations he has to apply. This is not only
the best, but in many cases the only way in which the observation
can be expressed. Thus _glassy lustre_, _fatty lustre_, _adamantine
lustre_, denote certain kinds of {162} shining in minerals, which
appearances we should endeavour in vain to describe by periphrasis;
and which the terms, if considered as terms in common language,
would by no means clearly discriminate: for who, in common language,
would say that coal has a fatty lustre? But these terms, in their
conventional sense, are perfectly definite; and when the eye is once
familiarized with this application of them, are easily and clearly
intelligible.
[Note 11\3: B. viii. c. iii. Terminology.]
27. The education of the senses, which is thus requisite in order to
understand well the terminology of any science, must be acquired by
an inspection of the objects which the science deals with; and is,
perhaps, best promoted by the practical study of Natural History. In
the different departments of Natural History, the descriptions of
species are given by means of an extensive technical _terminology_:
and that education of which we now speak, ought to produce the
effect of making the observer as familiar with each of the terms of
this terminology as we are with the words of our common language.
The technical terms have a much more precise meaning than other
terms, since they are defined by express convention, and not learnt
by common usage merely. Yet though they are thus defined, not the
definition, but the perception itself, is that which the term
suggests to the proficient.
In order to use the terminology to any good purpose, the student
must possess it, not as a dictionary, but as a language. The
terminology of his sciences must be the natural historian's most
familiar tongue. He must learn to think in such language. And when
this is achieved, the terminology, as I have elsewhere said, though
to an uneducated eye cumbrous and pedantical, is felt to be a useful
implement, not an oppressive burden[12\3]. The impatient schoolboy
looks upon his grammar and vocabulary as irksome and burdensome; but
the accomplished student who has learnt the language by means of
them, knows that they have given him the means of expressing what he
thinks, and {163} even of thinking more precisely. And as the study
of language thus gives precision to the thoughts, the study of
Natural History, and especially of the descriptive part of it, gives
precision to the senses.
[Note 12\3: _Hist. Ind. Sc_. b. xvi. c. iv. sect. 2.]
The Education of the Senses is also greatly promoted by the
practical pursuit of any science of experiment and observation, as
chemistry or astronomy. The methods of manipulating, of which we
have just spoken, in chemistry, and the methods of measuring
extremely minute portions of space and time which are employed in
astronomy, and which are described in the former part of this
chapter, are among the best modes of educating the senses for
purposes of scientific observation.
28. By the various Methods of precise observation which we have thus
very briefly described, facts are collected, of an exact and
definite kind; they are then bound together in general laws, by the
aid of general ideas and of such methods as we have now to consider.
It is true, that the ideas which enable us to combine facts into
general propositions, do commonly operate in our minds while we are
still engaged in the office of observing. Ideas of one kind or other
are requisite to connect our phenomena into facts, and to give
meaning to the terms of our descriptions: and it frequently happens,
that long before we have collected all the facts which induction
requires, the mind catches the suggestion which some of these ideas
offer, and leaps forwards to a conjectural law while the labour of
observation is yet unfinished. But though this actually occurs, it
is easy to see that the process of combining and generalizing facts
is, in the order of nature, posterior to, and distinct from, the
process of observing facts. Not only is this so, but there is an
intermediate step which, though inseparable from all successful
generalization, may be distinguished from it in our survey; and may,
in some degree, be assisted by peculiar methods. To the
consideration of such methods we now proceed.
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