called a parabola, and that artillerists have nothing to do but to
calculate all about this parabola, and to deduce the range from
the initial velocity according to some simple principles depending
on the properties of the curve. All this is founded on a complete
misapprehension of the true difficulties in the way of the problem.
Only projectiles thrown with small velocity from the earth travel in
parabolic paths. A cannon-ball follows a wholly different kind of
curve. The resistance of the air, which seems to most persons a wholly
insignificant item in the inquiry, is so enormous in the case of a
cannon-ball as to become by far the most important difficulty in the
way of the practical artillerist. When a 250-lb. shot is hurled with
such force from a gun as to cover a range of six miles, the resistance
of the air is about forty times the weight of the ball—that is, is
equivalent to a weight of upwards of four tons. The range in such a
case as this is but a small fraction of that which would be given by
the ordinary parabolic theory.
As regards artillery practice in war, there are other difficulties in
the attainment of a very extended range. Cannon meant for battering
down forts cannot possibly be used in the same way that Whitworth’s was
used at Shoeburyness. If the shot flung from this gun at an elevation
of thirty-three degrees could have been watched, it would have been
found that it fell to the earth at a much greater angle—that is, much
more nearly in a perpendicular direction. On the ordinary parabolic
theory, of course, the angle of fall would be the same as the angle
of elevation, but under actual circumstances there is an important
difference. If forts are to be battered down, however, it will not
serve that they should be struck from above; our artillerists must
perforce keep to the old method of pounding away at the face of the
forts they attack. Therefore, an elevation which is all very well for
mortars—that is, when the question merely is of flinging a bomb into a
town or fortress—is utterly unsuited for ordinary artillery. With an
elevation of ten degrees, Whitworth’s cannon scarcely projected the
250-lb. shot to a distance of three miles.
The progress of the modern science of gunnery certainly tends to
increase the distance at which armies will engage each other. With
field artillery flinging shot to a distance of two or three miles,
and riflemen able to make tolerably sure practice at a distance
of three-quarters of a mile, we are not likely often to hear of
hand-to-hand conflicts in future warfare. The use of breech-loaders
will also tend to the same effect. Hitherto we have scarcely had
experience of the results which these changes are to produce on modern
warfare. At Sadowa breech-loaders did not encounter breech-loaders,
and it was easy for the victors in that battle to come to close
quarters with their enemies. But in a battle where both sides are armed
with breech-loaders, we shall probably see another sort of affair
altogether. The bayonet will be an almost useless addition to the
soldier’s arms; a charge of cavalry upon well-armed infantry will be
almost as hopeless as the famous Balaclava charge; and the artillery
on either side will have to play a game at long bowls. I venture to
anticipate that the first great European war will introduce a total
change into the whole system of warlike manœuvres.[14]
(From the _Daily News_, November 1868.)
_INFLUENCE OF MARRIAGE ON THE DEATH-RATE._
The Royal Commission on the Law of Marriage has attracted attention
to many singular and instructive results of modern statistical
inquiry. Not the least important of these is the apparent influence
of marriage on the death-rate. For several years it has been noticed
by statisticians that the death-rate of unmarried men is considerably
higher than the death-rate of married men and widowers. I believe that
Dr. Stark, Registrar-General for Scotland, was one of the first to
call attention to this peculiarity, as evidenced by the results of two
years’ returns for Scotland. But the law has since been confirmed by a
far wider range of statistical inquiry. The relative proportion between
the death-rates of the married and of the unmarried is not absolutely
uniform in different countries, but it is fairly enough represented
by the following table, which exhibits the mortality per thousand of
married and unmarried men in Scotland:—
Ages. Husbands and Widowers. Unmarried.
20 to 25 6·26 12·31
25 to 80 8·23 14·94
30 to 35 8·65 15·94
35 to 40 11·67 16·02
40 to 45 14·07 18·35
45 to 50 17·04 21·18
50 to 55 19·54 26·34
55 to 60 26·14 28·54
60 to 65 35·63 44·54
65 to 70 52·93 60·21
70 to 75 81·56 102·71
75 to 80 117·85 143·94
80 to 85 173·88 195·40
From this table we are to understand that out of one hundred thousand
married persons (including widowers) from 20 to 25 years old, 626 die
in the course of each year; while out of a similar number of unmarried
persons, between the same ages, no less than 1,231 die in each
year. And in like manner all the other lines of the table are to be
interpreted.
Commenting on the evidence supplied by the above figures, Dr.
Stark stated that ‘bachelorhood is more destructive to life than
the most unwholesome trades, or than residence in an unwholesome
house or district, where there has never been the most distant
attempt at sanitary improvement of any kind.’ And this view has been
very generally accepted, not only by the public, but by professed
statisticians. Yet, as a matter of fact, I believe that no such
inferences can legitimately be drawn from the above table. Dr. Stark
appears to me to have fallen into the mistake, which M. Quetelet tells
us is so common, of trying to make his statistics carry more weight
than they are capable of bearing. It is important that the matter
should be put in a just light, for the Royal Commission on the Law of
Marriage has revealed no more striking fact than that of the prevalence
of immature marriages, and such reasoning as Dr. Stark’s certainly
cannot tend to discourage these unwise alliances. If death strikes down
in five years only half as many of those who are married as of those
who are unmarried between the ages of 20 and 25 (as appears from the
above table), and if the proportion of deaths between the two classes
goes on continually diminishing in each successive lustre (as is also
shown by the above table), it seems reasonable to infer that the
death-rate would be even more strikingly disproportionate for persons
between the ages of fifteen and twenty than for persons between the
ages of twenty and twenty-five. I believe, indeed, that if Dr. Stark
had extended his table to include the former ages, the result would
have been such as I have indicated. Yet few will suppose that very
youthful marriages can exercise so singularly beneficial an effect.
To many Dr. Stark’s conclusion may appear to be a natural and obvious
_sequitur_ from the evidence upon which it is founded. Admitting the
facts—and I see no reason for doubting them—it may appear at first
sight that we are bound to accept the conclusion that matrimony is
favourable to longevity. Yet the consideration of a few parallel cases
will suffice to show how small a foundation the figures I have quoted
supply for such a conclusion. What would be thought, for example,
of any of the following inferences?—Among hot-house plants there is
observed a greater variety and brilliance of colour than among those
which are kept in the open air; therefore the housing of plants
conduces to the splendour of their colouring. Or again: The average
height of Life Guardsmen is greater than that of the rest of the male
population; therefore to be a Life Guardsman conduces to tallness of
stature. Or to take an example still more closely illustrative of Dr.
Stark’s reasoning: The average longevity of noblemen exceeds that of
untitled persons; therefore to have a title is conducive to longevity;
or borrowing his words, to remain without a title ‘is more destructive
to life than the most unwholesome trades, or than residence in an
unwholesome house or district, where there has never been the most
distant attempt at sanitary improvement of any kind.’
We know that the inference is absurd in each of the above instances,
and we are able at once to show where the flaw in the reasoning lies.
We know that splendid flowers are more commonly selected for housing,
and that Life Guardsmen are chosen for their tallness, so that we are
prevented from falling into the mistake of ascribing splendour of
colour in the one instance, or tallness in the other, to the influence
of causes which have nothing whatever to do with those attributes;
nor is anyone likely to ascribe the longevity of our nobility to the
possession of a title. Yet there is nothing in any one of the above
inferences which is in reality more unsound than Dr. Stark’s inference
from the mortality bills, when the latter are considered with due
reference to the principles of interpretation which statisticians are
bound to follow.
The fact is, that in dealing with statistics the utmost care is
required in order that our inferences may not be pushed beyond the
evidence afforded by our facts. In the present instance, we have
simply to deal with the fact that the death-rate of unmarried men is
higher than the death-rate of married men and widowers. From this
fact we cannot reason as Dr. Stark has done to a _simple_ conclusion.
All that we can do is to show that one of _three_ conclusions must be
adopted:—Either matrimony is favourable (directly or indirectly) to
longevity, in a degree sufficient wholly to account for the observed
peculiarity; or a principle of selection—the effect of which is
such as, on the whole, to fill the ranks of married men from among
the healthier and stronger portion of the community—operates in a
sufficient degree to account wholly for the observed death-rates; or
lastly, the observed death-rates are due to the combination, in some
unknown proportion, of the two causes just mentioned.
No reasonable doubt can exist, as it seems to me, that the third is the
true conclusion to be drawn from the evidence supplied by the mortality
bills. Unfortunately, the conclusion thus deduced is almost valueless,
because we are left wholly in doubt as to the proportion which subsists
between the effects to be ascribed to the two causes thus shown to be
in operation.
It scarcely required the evidence of statistics to prove that each
cause must operate to some extent.
It is perfectly obvious, on the one hand, that although hundreds of
men who would be held by insurance companies to be ‘bad lives’ may
contract marriage, yet on the whole a principle of selection is in
operation which must tend to bring the healthier portion of the male
community into the ranks of the married, and to leave the unhealthier
in the state of bachelorhood. A little consideration will show also
that, on the whole, the members of the less healthy trades, very poor
persons, habitual drunkards, and others whose prospects of long life
are unfavourable, must (on the average of a large number) be more
likely to remain unmarried than those more favourably situated. Another
fact drawn from the Registrar-General’s return suffices to prove the
influence of poverty on the marriage-rate. I refer to the fact that
marriages are invariably more numerous in seasons of prosperity than
at other times. Improvident marriages are undoubtedly numerous, but
prosperity and adversity _have_ their influence, and that influence not
unimportant, on the marriage returns.
On the other hand, it is perfectly obvious that the life of a married
man is likely to be more favourable to longevity than that of a
bachelor. The mere fact that a man has a wife and family depending
upon him will suffice to render him more careful of his health, less
ready to undertake dangerous employments, and so on; and there are
other reasons which will occur to everyone for considering the life of
a married man better (in the sense of the insurance companies) than
that of a bachelor. In fact, while we are compelled to reject Dr.
Stark’s statement that ‘bachelorhood is more destructive to life than
the most unwholesome trades, or than residence in an unwholesome house
or district, where there has never been the most distant attempt at
sanitary improvement of any kind,’ we may safely accept his opinion
that statistics ‘prove the truth of one of the first natural laws
revealed to man—“It is not good that man should live alone.”’
(From the _Daily News_, October 17, 1868.)
FOOTNOTES:
[14] The reader need hardly be reminded of the complete fulfilment of
this anticipation, during the war between France and Germany.
_THE TOPOGRAPHICAL SURVEY OF INDIA._
At the close of the war with Tippoo Sahib, Major Lambton planned the
triangulation of the country lying between Madras and the Malabar
coast, a district which had been roughly surveyed, during the progress
of the war, by Colonel Mackenzie. The Duke of Wellington gave his
approval to the project, and his brother, the Governor-General of
India, and Lord Clive (son of the great Clive), Governor of Madras,
used their influence to aid Major Lambton in carrying out his design.
The only astronomical instrument made use of by the first survey party
was one of Ramsden’s zenith-sectors, which Lord Macartney had placed in
the hands of Dinwiddie, the astronomer, for sale. A steel chain, which
had been sent with Lord Macartney’s embassy to the Emperor of China and
refused, was the only apparatus available for measuring.
Thus began the great Trigonometrical Survey of India, a work whose
importance it is hardly possible to over-estimate. Conducted
successively by Colonel Lambton, Sir George Everest, Sir Andrew
Waugh, and Lieut.-Col. Walker (the present superintendent), the
trigonometrical survey has been prosecuted with a skill and accuracy
which renders it fairly comparable with the best work of European
surveyors. But to complete in this style the survey of the whole of
India would be the work of several centuries. The trigonometrical
survey of Great Britain and Ireland has been already more than a
century in progress, and is still unfinished. It can, therefore, be
imagined that the survey of India—nearly ten times the size of the
British Isles, and presenting difficulties a hundredfold greater than
those which the surveyor in England has to encounter—is not a work
which can be quickly completed.
But the growing demands of the public service have rendered it
imperatively necessary that India should be rapidly and completely
surveyed. This necessity led to the commencement of the Topographical
Survey of India, a work which has been pushed forward at a surprising
rate during the past few years. My readers may form some idea of the
energy with which the survey is in progress, from the fact that Colonel
Thuillier’s Report for the season 1866-67 announces the charting of an
area half as large as Scotland, and the preparatory triangulation of an
additional area nearly half as large as England.
In a period of thirty years, with but few surveying parties at first,
and a slow increase in their number, an area of 160,000 square miles
has been completed and mapped by the topographical department. The
revenue surveyors have also supplied good maps (on a similar scale)
of 364,000 square miles of country during the twenty years ending in
1866. Combining these results, we have an area of 524,000 square miles,
or upwards of four times that of Great Britain and Ireland. For all
this enormous area the surveyors have the records in a methodical and
systematic form, fit for incorporation in the atlas of India. Nor does
this estimate include the older revenue surveys of the North-western
Provinces which, for want of proper supervision in former years, were
never regularly reduced. The records of these surveys were destroyed
in the Mutiny—chiefly in Hazaumbaugh and the south-western frontier
Agency. The whole of these districts remain to be gone over in a style
very superior to that of the last survey.
The extent of the country which has been charted may lead to the
impression that the survey is little more than a hasty reconnaissance.
This, however, is very far indeed from being the case. The preliminary
triangulation, which is the basis of the topographical survey, is
conducted with extreme care. In the present Report, for instance,
we find that the discrepancies between the common sides of the
triangles-in other words, the discrepancies between the results
obtained by different observers-are in some cases less than one-tenth
of an inch per mile; in others they are from one inch to a foot
per mile; and in the survey of the Cossyah and Garrow Hills, where
observations had to be taken to large objects, such as trees, rocks,
&c., with no defined points for guidance, the results differ by as
much as twenty-six inches per mile. These discrepancies must not only
be regarded as insignificant in themselves, but must appear yet more
trifling when it is remembered that they are not cumulative, inasmuch
as the preliminary triangulation is itself dependent on the great
trigonometrical survey.
Let us understand clearly what are the various forms of survey which
are or have been in progress in India. There are three forms to be
considered:—(1) The Great Trigonometrical Surveys; (2) The Revenue
Surveys; and (3) the Topographical Surveys.
Great trigonometrical operations are extended in a straight course
from one measured base to another. Every precaution which modern skill
and science can suggest is taken in the measurement of each base-line,
and in the various processes by which the survey is extended from one
base-line to the other. The accuracy with which work of this sort
is conducted may be estimated from the following instance. During
the progress of the Ordnance Survey of Great Britain and Ireland,
a base-line nearly eight miles long was measured near Lough Foyle,
in Ireland, and another nearly seven miles long on Salisbury Plain.
Trigonometrical operations were then extended from Lough Foyle to
Salisbury Plain, a distance of about 340 miles; and the Salisbury
base-line was calculated from the observations made over this long
arc. _The difference between the measured and calculated values of
the base-line was less than five inches!_ As we have stated, the
trigonometrical survey of India will bear comparison with the best work
of our surveyors in England.
A revenue survey is prosecuted for the definition of the boundaries of
estates and properties. The operations of such a survey are therefore
carried on conformably to those boundaries.
The topographical survey of a country is defined by Sir A. Scott Waugh
to imply ‘the measurement and delineation of the natural features of a
country, and the works of man thereon, with the object of producing a
complete and sufficiently accurate map. Being free from the trammels
of boundaries of properties, the principal lines of operations must
conform to the features of the country, and objects to be surveyed.’
The only safe basis for the topographical survey of a country is a
system of accurate triangulation. And where the extent of country
to be surveyed is large, there will always be a great risk of the
accumulation of error in the triangulation itself; which must,
therefore, be made to depend on the accurate results obtained by
the great trigonometrical operations. In order to secure this
result, fixed stations are established in the vicinity of the great
trigonometrical series. Where this plan cannot be adopted, a network of
large symmetrical triangles is thrown over the district to be surveyed,
or boundary series of triangles are carried along the outline of the
district or along convenient internal lines. The former of these
methods is applicable to a hilly district, the latter to a flat country.
When the district to be surveyed has been triangulated, the work of
filling-in the topographical details is commenced. Each triangle being
of moderate extent, with sides from three to five miles in length,
and the angular points being determined, as we have seen, with great
exactness, it is evident that no considerable error can occur in
filling-in the details. Hence, methods can be adopted in the final
topographical work which would not be suitable for triangulation. The
triangles can either be ‘measured up,’ or the observer may traverse
from trigonometrical point to point, taking offsets and intersections;
or, lastly, he may make use of the plane table. The two first methods
require little comment; but the principle of plane-tabling enters so
largely into Indian surveying, that this notice would be incomplete
without a brief account of this simple and beautiful method.
The plane-table is a flat board turning on a vertical pivot. It bears
the chart on which the observer is planning the country. Suppose, now,
that two points A and B are determined, and that we require to mark in
the position of a third point C:—It is clear that if we observed with
a theodolite the angles A B C and B A C, we might lay these down on the
chart with a protractor, and so the position of C would be determined,
with an accuracy proportioned to the care with which the observations
were made and the corresponding constructions applied to the chart.
But in ‘plane-tabling’ a more direct plan is adopted. A ruler bearing
sights, resembling those of a rifle, is so applied that the edge
passing through the point A on the chart (the observer being situated
at the real station A) passes through the point B on the chart, the
line of sight passing through the real station B. The table being fixed
in the position thus obtained, the ruler is next directed so that its
edge passes through A, while the line of sight points to C. A line is
now ruled with a pencil through A towards C. In a similar manner, the
table having been removed to the station B, a pencil line is drawn
through the point B on the chart towards C. The two lines thus drawn
determine by their intersection the place of C on the chart.
The above is only one instance of the modes in which a plane-table can
be applied; there are several others. Usually the magnetic compass is
employed to fix the position of the table in accordance with the true
bearing of the cardinal points. Also the bearings of several points
are taken around each station; and thus a variety of tests of the
correctness of the work become applicable. Into such details as these
I need not here enter. It is sufficient that my readers should have
been enabled to recognise the simple principles on which plane-tabling
depends, and the accuracy with which (when suitable precautions are
taken) it can be applied as a method of observation subsidiary to the
ordinary trigonometrical processes.
‘A hilly country,’ says Sir A. Waugh, ‘offers the fairest field for
the practice of plane-table surveys, and the more rugged the surface
the greater will be the relative advantages and facilities this system
possesses over the methods of actual measurement. On the other hand, in
flat lands the plane-table works at a disadvantage, while the traverse
system is facilitated. Consequently, in such tracts, the relative
economy of the two systems does not offer so great a contrast as in
the former. In closely wooded or jungly tracts, all kinds of survey
operations are prosecuted at a disadvantage; but in such localities,
the commanding points must be previously cleared for trigonometrical
operations, which facilitates the use of the table.’
In whatever way the topographical details have been filled in, a
rigorous system of check must be applied to the work. The system
adopted is that of running lines across ground that has been
surveyed. This is done by the head of the party or by the chief
assistant-surveyor. A sufficient number of points are obtained in this
way for comparison with the work of the detail surveyors; and when the
discrepancies exceed certain limits, the work in which they appear
is rejected. Owing to the extremely unhealthy, jungly, and rugged
nature of the ground in which nearly all the Indian surveys have been
progressing, it has not always been found practicable to check by
regularly chained lines. There are, however, other modes of testing
plane-table surveys, and as these entail less labour and expense in
hilly and jungly tracts, and are quite as effective if thoroughly
carried out, they have been adopted generally, while the measured
routes or check-lines have only been pursued under more favourable
conditions. Colonel Thuillier states that ‘the inspection of the work
of every detailed surveyor in the field has been rigorously enforced,
and the work of the field season is not considered satisfactory or
complete unless this duty has been attended to.’