accounted for without calling in the aid of the supernatural. At a
recent meeting of the Photographical Society it was shown that an image
may often be so deeply impressed on the glass that the subsequent
cleaning of the plate, even with strong acids, will not completely
remove the picture. When the plate is used for receiving another
picture, the original image makes its reappearance, and as it is too
faint to be recognisable, a highly susceptible imagination may readily
transform it into the image of a departed friend. The ‘double’ is
generated by the well-known property of double refraction, obtained by
a lens under certain circumstances of unequal pressure, or sometimes by
inequalities in the process of annealing. So vanish two ghosts which
might have been more or less troublesome to those who are ready to see
the supernatural in commonplace phenomena. Will the time ever come when
no more such phantoms will remain to be exorcised?
(From the _Daily News_, March 2, 1869.)
_THE OXFORD AND CAMBRIDGE ROWING STYLES._
Whatever opinion we may have of the result of the approaching contest
(1869), there can be no doubt that this year, as in former years, there
is a striking dissimilarity between the rowing styles of the dark blue
and the light blue oarsmen. This dissimilarity makes itself obvious
whether we compare the two boats as seen from the side, or when the
line of sight is directed along the length of either. Perhaps it is in
the latter aspect that an unpractised eye will most readily detect the
difference I am speaking of. Watch the Cambridge boat approaching you
from some distance, or receding, and you will notice in the rise and
fall of the oars, as so seen, the following peculiarities—a long stay
of the oar in the water, a quick rise from and return to the water,
the oars remaining out of the water for the briefest possible interval
of time. In the case of the Oxford boat quite a different appearance
is presented—there is a short stay in the water, a sharp rise from and
return to it, and between these the oars appear to hang over the water
for a perceptible interval. It is, however, when the boats are seen
from the side that the meaning of these peculiarities is detected, and
also that the fundamental distinction between the two styles is made
apparent to the experienced eye. In the Cambridge boat we recognise the
long stroke and ‘lightning feather’ inculcated in the old treatises
on rowing: in the Oxford boat we see these conditions reversed, and
in their place the ‘waiting feather’ and lightning stroke. By the
‘waiting feather’ I do not refer to what is commonly understood by slow
feathering, but to a momentary pause (scarcely to be detected when the
crew is rowing hard) before the simultaneous dash of the oars upon
the first grip of the stroke.[15] And observing more closely—which,
by the way, is no easy matter—as either boat dashes swiftly past, we
detect the distinctive peculiarities of ‘work’ by which the two styles
are severally arrived at. In the Cambridge crew we see the first part
of the stroke done with the shoulders—precisely according to the
old-fashioned models—the arms straight until the body has fallen back
to an almost upright position; then comes the sharp drop back of the
shoulders beyond the perpendicular, the arms simultaneously doing
their work, so that as the swing back is finished, the backs of the
hands just touch the ribs in feathering. All these things are quite in
accordance with what used to be considered the perfection of rowing;
and, indeed, this style of rowing has some important good qualities
and a very handsome appearance. The lightning feather, also, which
follows the long sweeping stroke, is theoretically perfect. Now, in
the case of the Oxford crew, we observe a style which at first sight
seems less excellent. As soon as the oars are dashed down and catch
their first hold of the water, the arms as well as the shoulders of
each oarsman are at work.[16] The result is, that when the back has
reached an upright position, the arms have already reached the chest,
and the stroke is finished. Thus the Oxford stroke takes a perceptibly
shorter time than the Cambridge stroke; it is also, necessarily,
somewhat shorter in the water. One would, therefore, say it must be
less effective. Especially would an unpractised observer form this
opinion, because the Oxford stroke seems to be much shorter in range
than it is in reality. _There_ we have the secret of its efficiency.
It is actually as long as the Cambridge stroke, but is taken in a
perceptibly shorter time. What does this mean but that the oar is taken
more sharply, and, therefore, much more effectively, through the water?
Much more effectively so far as the actual conditions of the contest
are concerned. The modern racing outrigger requires a sharp impulse,
because it will take almost any speed we can apply to it. It will
also retain that speed between the strokes, a consideration of great
importance. The old-fashioned racing-eights required to be continually
under propulsion. The lightning-feather was a necessity in their
case, for between every stroke the boat would lag terribly with a
slow-feathering crew. I do not say, of course, that the speed of a
light outrigged craft does not diminish between the strokes. Anyone who
has watched a closely contested bumping-race, and noticed the way in
which the sharply cut bow of the pursuing boat draws up to the rudder
of the other as by a succession of impulses, although either boat seen
alone would seem to sweep on with almost uniform speed, will know that
the motion of the lightest boat is not strictly uniform. But there is
an immense difference between the almost imperceptible loss of way of a
modern eight and the dead ‘lag’ in the old-fashioned craft. And hence
we get the following important consideration. Whereas with the old
boats it was useless for a crew to attempt to give a very quick motion
to their boat by a sharp, sudden ‘lift,’ this plan is calculated to be,
of all others, the most effective with the modern racing-eight.
It may seem, at first sight, that, after all, the result of the
Cambridge style should be as effective as that of the other. If arms
and shoulders do their work in both crews with equal energy—which we
may assume to be the case—and if the number of strokes per minute is
equal, the actual propulsive energy ought to be equal likewise. A
little consideration will show that this is a fallacy. If two men pull
at a weight together they will move it farther with a given expenditure
of energy than if first one and then the other apply his strength to
the work. And what is more to the purpose, they will be able to move
it faster. So shoulders and arms working simultaneously will give a
greater propulsive power than when working separately, even though in
the latter case each works with its fullest energy. And not only so,
but by the simultaneous use of arms and shoulders, that sharpness of
motion can alone be given which is essential to the propulsion of a
modern racing-boat.
I have said that the two crews are severally rowing in the style
which has lately been peculiar to their respective Universities. But
the Cambridge crew is rowing in that form of the Cambridge style which
brings it nearest to the requirements of modern racing. The faults of
the style are subdued, so to speak, and its best qualities brought
out effectively. In one or two of the long series of defeats lately
sustained by Cambridge the reverse has been the case. At present, too,
there is a certain roughness about the Oxford crew which encourages the
hopes of the light blue supporters. But it must be admitted that this
roughness is rather apparent than real, great as it seems, and it will
doubtless disappear before the day of encounter. I venture to predict
that the ‘time’ of the approaching race, taken in conjunction with the
state of the tide, will show the present crews to be at least equal to
the average.[17]
(From the _Daily News_, April 1869.)
FOOTNOTES:
[15] The grip is never properly caught without the pause; but anything
beyond a momentary pause is a bad fault in style.
[16] I write this with full knowledge that many Oxford men deny the
fact. I have rowed behind Cambridge, Oxford, and London strokes, and
have several times taken the place (number 2 thwart) of a London
waterman in a four (‘stroked’ by John Mackinney) training for the
Thames Regatta. So that I have had ample opportunities for comparing
different rowing styles; and I am satisfied that the main defect of
the real Cambridge style was (and perhaps is) an _exaggeration_ of the
sound rule that a boat should be propelled rather by the body than
by the arms. The very swing in a Cambridge boat shows that this must
be so. On the other hand, the Thames watermen do too much arm-work;
and hence seem to double a little over their oars. I once rowed with
some Cambridge friends from London nearly to Oxford and back, taking a
Thames waterman as ‘help.’ We set him, at first, for our strokesman,
but we soon had to make him row _bow_, for we could none of us stand
his gripping, arm-working style.
_BETTING ON HORSE RACES: OR, THE STATE OF THE ODDS._
There appears every day in the newspapers an account of the betting
on the principal forthcoming races. The betting on such races as the
Two Thousand Guineas, the Derby, and the Oaks, often begins more than
a year before the races are run; and during the interval, the odds
laid against the different horses engaged in them vary repeatedly, in
accordance with the reported progress of the animals in their training,
or with what is learned respecting the intentions of their owners. Many
who do not bet themselves, find an interest in watching the varying
fortunes of the horses which are held by the initiated to be leading
favourites, or to fall into the second rank, or merely to have an
outside chance of success. It is amusing to notice, too, how frequently
the final state of the odds is falsified by the event; how some ‘rank
outsider’ will run into the first place, while the leading favourites
are not even ‘placed.’
It is in reality a simple matter to understand the betting on races (or
contests of any kind), yet it is astonishing how seldom those who do
not actually bet upon races have any inkling of the meaning of those
mysterious columns which indicate the opinion of the betting world
respecting the probable results of approaching contests, equine or
otherwise.
Let us take a few simple cases of ‘odds,’ to begin with; and, having
mastered the elements of our subject, proceed to see how cases of
greater complexity are to be dealt with.
Suppose the newspapers inform us that the betting is 2 to 1 against
a certain horse for such and such a race, what inference are we to
deduce? To learn this let us conceive a case in which the _true_ odds
against a certain event are as 2 to 1. Suppose there are three balls
in a bag, one being white, the others black. Then, if we draw a ball
at random, it is clear that we are twice as likely to draw a black as
to draw a white ball. This is technically expressed by saying that
the odds are 2 to 1 _against_ drawing a white ball; or 2 to 1 _on_
(that is, in favour of) drawing a black ball. This being understood,
it follows that, when the odds are said to be 2 to 1 against a certain
horse, we are to infer that, in the opinion of those who have studied
the performance of the horse, and compared it with that of the other
horses engaged in the race, his chance of winning is equivalent to the
chance of drawing one particular ball out of a bag of three balls.
Observe how this result is obtained: the odds are 2 to 1, and the
chance of the horse is as that of drawing one ball out of a bag of
three—three being the sum of the two numbers 2 and 1. This is the
method followed in all such cases. Thus, if the odds against a horse
are 7 to 1, we infer that the _cognoscenti_ consider his chance equal
to that of drawing one particular ball out of a bag of _eight_.
A similar treatment applies when the odds are not given as so many to
_one_. Thus, if the odds against a horse are as 5 to 2, we infer that
the horse’s chance is equal to that of drawing a white ball out of a
bag containing five black and two white balls—or seven in all.
We must notice also that the number of balls may be increased to any
extent, provided the proportion between the total number and the
number of a specified colour remains unchanged. Thus, if the odds are
5 to 1 against a horse, his chance is assumed to be equivalent to that
of drawing _one_ white ball out of a bag containing six balls, only one
of which is white; _or_ to that of drawing a white ball out of a bag
containing sixty balls, of which ten are white-and so on. This is a
very important principle, as we shall now see.
Suppose there are two horses (amongst others) engaged in a race,
and that the odds are 2 to 1 against one, and 4 to 1 against the
other-what are the odds that one of the two horses will win the race?
This case will doubtless remind my readers of an amusing sketch by
Leech, called—if I remember rightly—‘Signs of the Commission.’ Three
or four undergraduates are at a ‘wine,’ discussing matters equine. One
propounds to his neighbour the following question: I say, Charley,
if the odds are 2 to 1 against _Rataplan_, and 4 to 1 against _Quick
March_, what’s the betting about the pair?’—‘Don’t know, I’m sure,’
replies Charley; ‘but I’ll give you 6 to 1 against them.’ The absurdity
of the reply is, of course, very obvious; we see at once that the odds
cannot be heavier against a pair of horses than against either singly.
Still, there are many who would not find it easy to give a correct
reply to the question. What has been said above, however, will enable
us at once to determine the just odds in this or any similar case.
Thus-the odds against one horse being 2 to 1, his chance of winning is
equal to that of drawing one white ball out of a bag of _three_, one
only of which is white. In like manner, the chance of the second horse
is equal to that of drawing one white ball out of a bag of _five_,
one only of which is white. Now we have to find a number which is a
multiple of both the numbers three and five. Fifteen is such a number.
The chance of the first horse, modified according to the principle
explained above, is equal to that of drawing a white ball out of a bag
of fifteen of which _five_ are white. In like manner, the chance of
the second is equal to that of drawing a white ball out of a bag of
fifteen of which _three_ are white. Therefore the chance that _one of
the two_ will win is equal to that of drawing a white ball out of a bag
of fifteen balls of which _eight_ (_five_ added to _three_) are white.
There remain _seven_ black balls, and therefore the odds are 8 to 7
_on_ the pair.
To impress the method of treating such cases on the mind of the reader,
let us take the betting about three horses—say 3 to 1, 7 to 2, and 9
to 1 _against_ the three horses respectively. Then their respective
chances are equal to the chance of drawing (1) one white ball out of
_four_, one only of which is white; (2) a white ball out of _nine_,
of which two only are white; and (3) one white ball out of _ten_, one
only of which is white. The least number which contains four, nine, and
ten is 180; and the above chances, modified according to the principle
explained above, become equal to the chance of drawing a white ball out
of a bag containing 180 balls, when 45, 40, and 18 (respectively) are
white. Therefore, the chance that one of the three will win is equal
to that of drawing a white ball out of a bag containing 180 balls, of
which 103 (the sum of 45, 40, and 18) are white. Therefore, the odds
are 103 to 77 _on_ the three.
One does not hear in practice of such odds as 103 to 77. But
betting-men (whether or not they apply just principles of computation
to such questions, is unknown to me) manage to run very near the truth.
For instance, in such a case as the above, the odds on the three would
probably be given as 4 to 3—that is, instead of 103 to 77 (or 412 to
308), the published odds would be equivalent to 412 to 309.
And here a certain nicety in betting has to be mentioned. In running
the eye down the list of odds, one will often meet such expressions as
10 to 1 against such a horse _offered_, or 10 to 1 _wanted_. Now, the
odds of 10 to 1 _taken_ may be understood to imply that the horse’s
chance is equivalent to that of drawing a certain ball out of a bag
of eleven. But if the odds are offered and not taken, we cannot infer
this. The offering of the odds implies that the horse’s chance is _not
better_ than that above mentioned, but the fact that they are not taken
implies that the horse’s chance is _not so good_. If no higher odds are
offered against the horse, we may infer that his chance is _very little
worse_ than that mentioned above. Similarly, if the odds of 10 to 1 are
_asked for_, we infer that the horse’s chance is _not worse_ than that
of drawing one ball out of eleven; if the odds are not obtained, we
infer that his chance is _better_; and if no lower odds are asked for,
we infer that his chance is _very little better_.
Thus, there might be _three_ horses (A, B, and C) against whom the
nominal odds were 10 to 1, and yet these horses might not be equally
good favourites, because the odds might not be taken, or might be asked
for in vain. We might accordingly find three such horses arranged thus:—
Odds.
A 10 to 1 (wanted).
B 10 to 1 (taken).
C 10 to 1 (offered).
Or these different stages might mark the upward or downward progress
of the same horse in the betting. In fact, there are yet more delicate
gradations, marked by such expressions respecting certain odds,
as—_offered freely_, _offered_, _offered and taken_ (meaning that some
offers only have been accepted), _taken_, _taken and wanted_, _wanted_,
and so on.
As an illustration of some of the principles I have been considering,
let us take from the day’s paper,[18] the state of the odds respecting
the ‘Two Thousand Guineas.’ It is presented in the following form:—
TWO THOUSAND GUINEAS.
7 to 2 against _Rosicrucian_ (off.).
6 to 1 against _Pace_ (off.; 7 to 1 w.).
10 to 1 against _Green Sleeve_ (off.).
100 to 7 against _Blue Gown_ (off.).
180 to 80 against Sir J. Hawley’s lot (t.).
This table is interpreted thus: bettors are willing to lay the same
odds against _Rosicrucian_ as would be the true mathematical odds
against drawing a white ball out of a bag containing two white and
seven black balls; but no one is willing to back the horse at this
rate; on the other hand, higher odds are not offered against him. Hence
it is presumable that his chance is somewhat less than that above
indicated. Again, bettors are willing to lay the same odds against
_Pace_ as might fairly be laid against drawing one white ball out of
a bag of seven, one only of which is white; but backers of the horse
consider that they ought to get the same odds as might be fairly laid
against drawing the white ball when an additional black ball had been
put into the bag. As respects _Green Sleeve_ and _Blue Gown_, bettors
are willing to lay the odds which there would be, respectively, against
drawing a white ball out of a bag containing—(1) eleven balls, one only
of which is white, and (2) one hundred and seven balls, seven only of
which are white. Now, the three horses, _Rosicrucian_, _Green Sleeve_,
and _Blue Gown_, all belong to Sir Joseph Hawley, so that the odds
about the three are referred to in the last statement of the list just
given. And since none of the offers against the three horses have been
taken, we may expect the odds actually taken about ‘Sir Joseph Hawley’s
lot’ to be more favourable than those obtained by summing up the three
former in the manner we have already examined. It will be found that
the resulting odds (offered) against Sir J. Hawley’s lot—estimated in
this way—should be, as nearly as possible, 132 to 80. We find, however,
that the odds _taken_ are 180 to 80. Hence, we learn that the offers
against some or all of the three horses are considerably short of what
backers require; or else that some person has been induced to offer far
heavier odds against Sir J. Hawley’s lot than are justified by the fair
odds against his horses, severally.
I have heard it asked why a horse is said to be a favourite, though the
odds may be against him. This is very easily explained. Let us take as
an illustration the case of a race in which four horses are engaged to
run. If all these horses had an equal chance of winning, it is very
clear that the case would correspond to that of a bag containing four
balls of different colours; since, in this case, we should have an
equal chance of drawing a ball of any assigned colour. Now, the odds
against drawing a particular ball would clearly be 3 to 1. This, then,
should be the betting against each of the three horses. If any one of
the horses has less odds offered against him, he is _a favourite_.
There may be more than one of the four horses thus distinguished; and,
in that case, the horse against which the least odds are offered is
_the first favourite_. Let us suppose there are two favourites, and
that the odds against the leading favourite are 3 to 2, those against
the other 2 to 1, and those against the best non-favourite 4 to 1; and
let us compare the chances of the four horses. I have not named any
odds against the fourth, because, if the odds against all the horses
but one are given, the just odds against that one are determinable,
as we shall see immediately. The chance of the leading favourite
corresponds to the chance of drawing a ball out of a bag in which are
three black and two white balls, _five_ in all; that of the next to
the chance of drawing a ball out of a bag in which are two black and
one white ball, _three_ in all; that of the third, to the chance of
drawing a ball out of a bag in which are four black balls and one white
one, _five_ in all. We take, then, the least number containing both
five and three—that is, _fifteen_; and then the number of white balls,
corresponding to the chances of the three horses, are respectively six,
five, and three, or fourteen in all; leaving only _one_ to represent
the chance of the fourth horse (against which the odds are therefore
14 to 1). Hence the chances of the four horses are respectively as the
numbers _six_, _five_, _three_ and _one_.
I have spoken above of the published odds. The statements made in the
daily papers commonly refer to wagers actually made, and therefore
the uninitiated might suppose that everyone who tried would be able
to obtain the same odds. This is not the case. The wagers which are
laid between practised betting-men afford very little indication of
the prices which would be forced (so to speak) upon an inexperienced
bettor. Book-makers—that is, men who make a series of bets upon
several or all of the horses engaged in a race—naturally seek to give
less favourable terms than the known chances of the different horses
engaged would suffice to warrant. As they cannot offer such terms to
the initiated, they offer them-and in general success—fully—to the
inexperienced.
It is often said that a man may so lay his wagers about a race as to
make sure of gaining money whichever horse wins the race. This is not
strictly the case. It is of course possible to make sure of winning if
the bettor can only get persons to lay or take the _odds he requires to
the amount he requires_. But this is precisely the problem which would
remain insoluble if all bettors were equally experienced.
Suppose, for instance, that there are three horses engaged in a race
with equal chances of success. It is readily shown that the odds are
2 to 1 against each. But if a bettor can get a person to take even
betting against the first horse (A), a second person to do the like
about the second horse (B), and a third to do the like about the third
horse (C), and if all these bets are made to the same amount—say
1000_l._—then, inasmuch as only one horse can win, the bettor loses
1000_l._ on that horse (say A), and gains the same sum on each of the
two horses B and C. Thus, on the whole, he gains 1000_l._, the sum laid
out against each horse.
If the layer of the odds had laid the true odds to the same amount
on each horse, he would neither have gained nor lost. Suppose, for
instance, that he laid 1000_l._ to 500_l._ against each horse, and A
won; then he would have to pay 1000_l._ to the backer of A, and to
receive 500_l._ from each of the backers of B and C. In like manner,
a person who had backed each horse to the same extent would neither
lose nor gain by the event. Nor would a backer or layer who had wagered
_different_ sums _necessarily_ gain or lose by the race; he would gain
or lose _according to the event_. This will at once be seen, on trial.