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William Angus Knight.

Pro patria et regina; being poems from nineteenth century writers in Great Britain & America, issued in aid of Her Majesty Queen Alexandra's fund for soldiers & sailors online

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From the foregoing observations it may be conduded with tolerable
safety that the animals of the Order MarsupiaUa' preaent a peculiar condi-
tion of dental succession, uniform throughout the order, and distinct from
that of all other mammals. This peculiarity may be thus briefly ex-
pressed. The teeth of Marsupials do not vertically displace and succeed
other teeth, with the exception of a single tooth on each side of each jaw.
The tooth in which a vertical succession takes place is always the corre*
sponding or homologous tooth, being the hindermost of the premolar series*,
whidi is preceded by a tooth having the characters, more or less strongly
expressed, of a true molar.

It has been usual to divide the class Mammalia, in regard to the mode of
formation and succession of theirteeth, into two groups — i\it Monophyodont9^
or those that generate a single set of teeth, and the DiphyodontB, of those
that generate two sets of teeth ; but even in the most typical diphyodonts
the suocessional process does not extend to the whole of the teeth, always
stopping short of those situated most posteriorly in each series. The
Mwrsupials occupy an intermediate porition, presenting as it were a rudi-
mentary diphyodont condition, the suocessional process being confined to a
single tooth en each side of each jaw. This position, however, is by no
means without analogy among the mammals of the placental series. In
the Dugong and the existing Elephants the suocessional process is limited

* The oonvenient distinction between fidse moUur» or premolars and true molars, is
always weU marked in the form of the ^srown, espedallj in the upper jaw, in the
Marsupials.



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466 Mr. W. H. Flower on the Development [May 9,

to the incisor teeth. It is questionable whether the first premolar of those
animals of this groap which have four premolar teeth, as the Hog, Dof; (man-
dible), &c., ever has a deciduous predecessor, at all events so far advanced
as to have reached the calcified stage. But the closest analogy with the
marsupial mode of succession is found among the Rodents. Here the indsoni
appear to have no deciduous predecessors ; and in the Beaver, Poreopiney
and others, which have but four teeth of the molar series, t. e. three true
molars and one premolar, the latter is, exactly as in the Marsupials, the
only tooth which succeeds a deciduous tooth. The analogy, however, does
not hold in those Rodents which have more than one premolar, as the Hare ;
for in this case each of these teeth has its deciduous predecessor.

In the preceding account I have used the term " permanent " for those
teeth which remain in use throughout the animal's life, or, if they fall oat
(as do the rudimentary canines and the premolars of the Maeropodid4e\
do not give place to successional teeth ; and I have therefore assumed that
the milk or temporary dentition of the typical diphyodont mammals is re-
presented in the Marsupials only by the deciduous molars. It may be held,
on the other hand, that the large majority of the teeth of the Marsupials are
the homologues of the milk or first teeth of the diphyodonts, and that it b
the permanent or second dentition which is so feebly represented by the
four successional premolars. This view is supported by many general
analogies in animal organization and development, such as the fact that the
permanent state of organs of lower animals often represents the immature
or transitional condition of the same parts in beings of higher organisation.

Looking only to the period of development of the different teeth in some
of the marsupial genera, we might certainly be disposed to place the soc-
cessional premolar in a series by itself, although, indeed, all its morphological
characters point out its oongruity with the row of teeth among which it
ultimately takes its place, the reverse being the case with its predecessor.
It is, however, almost impossible, after examining the teeth of the young
Thylacine described and figured in the paper, to resist the eonclasion
originally suggested. The unbroken series of incisors, canines^ premolars,
and anterior true molars of nearly the same phase of development, with
posterior molars gradually added as age advances, form a striking contrast
to the temporary molar, so rudimental in size, and transient in duration.
I can scarcely doubt that the true molars of this animal would be iden-
tified by every one as homologous with the true molars of the diphyodonts,
which are generally regarded as belonging to the permanent series, although
they never have deciduous predecessors. Now, if the homology between
the true molars of the Thyladne and those of a Dog, for instance, be
granted, and if the anterior teeth (incisors, canines, and premolars) of the
Thylacine be of the same series as its own true molars, they must also be
homologous with the corresponding permanent teeth of the Dog.

It may be objected to this argument, that the true molars of the diphyo-
donts, not being successional teeth, ought to be r^;arded as members of the



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1867.] ^ and Succession of the Teeth in the Marsupialia, 467

first or milk- series ; but, in tratb, the fact that tbej baye themselves no
predecessors does not make them serially homologous with the prede-
cessors of the other teeth, while their morphological characters, as well as
their habitual persistence throughout life, range them with the second or
permanent series.

We have been so long accustomed to look upon the second set of teeth as
an afler-development or derivative from the first, that it appears almost
paradoxical to surest that the milk- or deciduous teeth may rather be a
set superadded to supply the temporary needs of mammals of more complex
dental organization. But it should be remembered that, instead of there
being any such relation between the permanent and the milk-teeth as that
expressed by the terms ** progeny " and " parent " (sometimes applied to
them), they are both (if all recent researches into their earlier development
can be trusted) formed side by side from independent portions of the pri-
mitive dental groove, and may rather be compared to twin brothers, one of
whiph, destined for early functional actirity, proceeds rapidly in its develop-
ment, while the other makes little progress until the time approaches when
it is called upon to take the place of its more precocious locum tenens*

Many facts appear to point to the milk-teeth as being the less constant
and important of the two sets developed in diphyodont dentition. Among
these the most striking is the frequent occurrence of this set in a rudimen-
tary and functionless or, as it were, partially developed state. The milk-
premolars of some Bodents (as the Guinea-pig), shed while the animal is
in utero, the simple structure and evanescent nature of the milk-teeth of
the Bats, Insectivores, and Seals, the diminutive first incisors of the
Dngongs and Elephants, all appear to be cases in point. On the other
hand, examples of the commencing or sketching out, as it were, of the
successors to a well-formed, regular, and functional first set of teeth, are
rarely, if ever, met with. Occasional instances of the habitual early deca-
dence, or, perhaps, absence of some of the second or so-caUed permanent
teeth occur in certain animals ; but these are rather examples of the disap-
pearance or suppression of organs of which there is na need in the economy^
and chiefly occur in isolated and highly modified members of groups in
the other members of which the same phenomenon does not occur, as in
Cheiromys among the Lemurs, Trichechus among the Seals, and the
recent Elephants (as regards the premolars) among the Proboscideans.
They form no parallel to the cases mentioned above of the rudimentary
formation of an entire series of teeth of the temporary or milk-set.

To return to the marsupials : — If this view be correct, I should be quite
prepared to find, in phases of development earlier than those yet examined,
some traces either of the papillary, follicular, or saccular stages of mOk-
predecessors to other of the teeth besides those determinate four in which,
for some reason at present unexplained, they arrive at a more mature
growdi*. Such proof as this would alone decide the truth of these specu-.

* It may be remarked that the milk-tooth, whidi alone is devdoped in the Mursu-



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468 Prof. W. J. M. Rankine on a Property of Curves. [May 9,

lations ; and I have not at present either the requisite leiaore or materials
for foliowing^ out so delicate an investigation. I trust that the facts ahreadj
elicited are sufficiently novel and important to justify my bringing them, as
they now stand, before the Society.

II. "On a Property of Carves which fulfil the condition
^ 4. ^ =0/' By W. J. Macquorn Rankine, C.E., LL.D.,
F.R.SS.L. & E. Received April 9, 1867.

1. In a paper " On Stream-Lines/^ published in the Philosophical Ma-
gazine for October 1864, 1 stated, and, in a Supplement to the same paper,
published in the Philosophical Magazine for January 1865, 1 proved the
proposition that ** all waves in which molecular rotation is null begin to
break when the two slopes of the crest meet at right angles."

2. I have now to state the purely geometrical proposition of which that
mechanical proposition is a consequence. If a plane eurve which fidJiU

the condition - ? + - ^=0 cute itself in a double point, it does so at

right angles,

3. The following is the demonstration. It is well known that the incli-
nation of any plane curve to the axes at an ordinary point is given by the
equation

dx ^ dy^ '

also that at a double point -^ and ^ both vanish, so that the inclinations
'^ dx dy

of the two branches to the axes are given by the two roots of the quadratic

equation

whence it follows that the product of the two values of -X which are the

dx

d^

two values of the tangent of the inclination to the axis ofx^ia^ ^l- I<^

a dt

dy-
a curve which fulfils the before-mentioned condition, the value of that pro-
duct is — 1 ; and when such is the case with the product of the tangents of
two angles, the difference of those angles is a right angle ; therefore the
two branches cut each other at right angles. Q.E.D.

4. The proposition just demonstrated is so simple and so obvious, that

pials, oorrespondfl homologically with that which, as a general rule, is most persistent
in the tjpioal diphyodonts, including Man, vis. the posterior milk-molar, replaced bj
the posterior permanent premolar.



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1867.] Prof. W. J. M. Rankine on a Property of Curves. 469

I was at first disposed to think it must have been known and published
previously ; and had I not been assured by several eminent mathematicians
that it had not been previously published to their knowledge, I should not
have ventured to put it forth as new.



Supplement to the preceding Paper. Received April 23^ 1867.

Professor Stokes, D.C.L., has pointed out to me an extension of the pre-
ceding theorem, viz. that at every multiple point in a plane curve which

fiUfils the condition - -£ + -j^ =0, the branehee make equal angles with
tur dy^

each other ; so that, for example, if n branches cut each other at a multiple

point, they make with each other 2n equal angles of -.

It

The following appears to me to be the simplest demonstration of the ex-
tended theorem. At a point where n branches cut each other the follow-
ing equation is fulfilled by all curves :

Let be the angle made by any branch with the axis of x ; then

But in a curve which fulfils the equation -t-|h — % =»0, we have

dy dx*

whence it follows that in such a curve the equation of a multiple point of n
branches is



|(cosa+V — l.sina)^! 0=0.



Choose for the axis of a? a tangent to one of the branches at the multiple
point. Then it is evident that the preceding equation is satisfied by the 2n
values of corresponding to the 2nth roots of unity, that is to say, by
0=0. !; 2^, &,.,.. .(2«=l1>.



fl fl



therefore the n branches make with each other 2n equal angles of -. Q.E.D.



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470 Mr. S. E. Hoskins on a Tabular Form of Anafysis. [May 9,

III. ''A Tabular Form of Analysis, to aid in tracing the Possible In-
fluence of Past and Present upon future states of Weather/' By
S. Elliott Hoskins, F.R.S., &c. Receiyed March 28, 1867.

The data upon which the present communication is founded are deriyed
from the * Greenwich Reports/ from Mr. Glaisher's papers in the Philo-
sophical Transactions, and from my own observations at Guernsey. The
latter were commenced in the autumn of 1842, in accordance with the re-
commendations of the Ck)mmittee of Physics of the Royal Society, and
were taken at the request of Professor Daniell, by whom the instruments
employed were selected. These instruments, made by Newman, were afiter
a time replaced by others, at the suggestion of Mr. Glaisher, by whom
they were compared with the standards at the Royal Obserratory.

For my own guidance in the first instance, I sought to arrange the re-
sults thus obtained in such a manner as to discover, if possible, whether
any month or class of months stood to each other in the relation of cause
and effect ; in other words, whether the atmospheric conditions of autumn
exercised any distinguishable influence upon the fruitful or unfruitful
character of ensuing seasons.

In order to attain this object, the principle seemed to be that of con-
densing within narrow limits, by means of intelligible symbols, as many
elements of weather, in the popular acceptation of the word, as might be
required. But the ordinary curvilinear form of diagram could not be so
modified as to answer this purpose, and I therefore availed myself of a plan
suggested by Mr. Galton : — that of converting the records of observations
into appropriate signs, and placing them compactly in a series of squares.

Upon this principle the annexed diagrams* are constructed, comprising
those elements of weather which more directly affect vegetation ; viz. heat,
cold, dryness, moisture, and their combinations. The same kind of pre-
paratory steps were taken for the compilation of the Greenwich as for the
Guernsey diagram, so as to render the results comparable — less, perhaps*
for the sake of mere comparison, than for the purpose of testing the value
of the latter by means of an accredited standard.

The first process consisted in copying out the degrees of monthly mean
temperature, the number of rainy days, and the days of wind, from four
directions, intermediate to the cardinal points. These several copies being
verified, the monthly average of each of the above elements for twenty
years, from 1 843 to 1 862, was taken.

' The next step was to obtain the difference between the adopted average
and the mean of each month in every year. By prefixing the plus and
minus signs to the resulting figures, the excess and defect of each element
is shown.

The third process was to separate the above-mentioned series of years

* [The diagramB are not publiahed, but are preeerred for reference in the Ardiives
of the Society.]



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Tah|



,


days


in Excess and Def
at Guernsey.


[2b/flctfp.470


'


Bct of an average of Twenty Yean,


Ayeragc






yeaM


priL


May.


June.


July.


Aug.


Sept


Oct


Not.


Dec








13


11


lO


II


11


12


i8


17


17
























|h-7


+9


+ 7


— 2


— o


- 6


+ 6


+4


_ I




^'-"9


-7


— 4


— O


+ 3


— o


+ I


— I


- 8




e-3


— I


— 2


+4


— o


+ 3


- 9


— o


+ 7




S coefficients of this group in different decades
is invariably one of considerable inequality.

2nd. Two cold Novembers only occur in the warm cycle, and only two
warm ones in the cold cycle.

3rd. In the second decade the proportion of warm to cold Novembers
is 8 to 2, and of dry and wet 2 to 8 .; but in the warm period warm and
wet months were prettily evenly distributed.

4th. Novembers of comparatively low temperature, such for instance as
those of 1851, 1853, 1854, 1855, 1856, 1860, 1861, and 1862, were in
each year succeeding those enumerated, followed by Mays or Junes of a
similar character. The following risumi shows the relations between the
Novembers and the Junes.

Months.



Novembers. Junee.



r, / Ist decade. 8 warm to 2 cold. 8 warm to 2 cold.

Ouornsey. 1 2nd decade. 8 cold to 2 warm. 7 cold to 3 warm.

Degrees.



Novembers. Junes.



« r Ist decade. 1 5°-7 plus to 4'*-2 minus. 1 r -5 plus to 3'-0 minus.

Guernsey. 1 2nd decade. 14° minus to 2°-8 plus. 18^-5 minus to 3°-l plus.

These contrasts and analogies seem to justify the surmise that the at-^

mospheric conditions of the former months may have exercised some in-

. fluence upon those of the latter. Whether such be the case generally is

not to be determined until a much longer series of results at Guernsey can

*be compared.

The peculiarities with respect to the Novembers may be purely acci-
dental, or confined to the period under consideration ; but that they are

2r2



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474 Cmmbra Monthly Magnetic Determinations. [May 9,

not restricted to locality is proved by the Greenwich Tables, in which
these groups stand out still more prominently (see Table YII.) ; the ratio*
between warm and cold being 9 to 1 in the first decade, and 1 to 9 in the
second. It is difficult therefore to avoid the conclusion that, during the
twenty years in question, the Novembers were exceptional months at both
places ; although at Guernsey they were more frequently followed by un-
favourable Junes.

The Greenwich diagram (Diagram II. Archives), to which I must now
briefly advert, does not exhibit so striking a contrast of light and shade as
was observable at first sight in the other diagram. But on further exami-
nation it will be found that the warm months of the first decade correspond
nearly in number with the cold months of the second, although not so
exactly as at Guernsey.

Months. Degrees.
, * ^ , » ^

n»^n«r'/«ii / 1*^ decade. 65 warm to 55 cold. 15T''5 plus to 108**-5 mmus.
ureenwicii.-j^ 2nd decade. 62 cold to 68 warm. 148^-4 minus to 116*-8 plus.

On comparing the above abstract with that in a previous page, it will be
perceived that the disparity between the general results, from both places.
IS not very considerable ; a similarity all the more remarkable, when we
consider the great difference in position and latitude of the inland and the
insular stations. See Diagram III.

It would be superfluous to enter into any further discussion of the
various alternations which the coefficients are susceptible of, in a paper
which is merely intended to direct attention to the accompanying diagrams
and analytical tables. My motive for venturing to bring them under notice
is a desire to place them in the hands of those better qualified than I am
for conducting processes o^ induction ; and as the modified plan I hare
adopted is based upon long recognized principles, which are applicable to
the investigation of atmospheric phenomena in any locality, I tmst that it
may be deemed worthy of consideration.

IV. "Monthly Magnetic Determinations^ from June to November
1 866 inclusive^ made at the Observatory at Coimbra," by Professor
J. A. DE SouzA^ Director of the Observatory. Communicated
(with a Note) by the President. Received May 8, 1867.

[Note. — These observations contain the record of the commencement
of the absolute magnetic determinations at the Coimbra Observatory, with
iostraments procured by M. de Souza at Kew, and on the system of
observation and reduction adopted at the Kew Observatory. The employ-
ment of the photographic continuously self-recording instruments at
Coimbra has hitherto been delayed by the works required for the introduc-
tion of gas into the Observatory ; but this has now been accomplished ; and
a letter, dated April 20, 1867, from the Director states that the photo-



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1867.] Coimbra Monildy Magnetic Determinations. 475

graphic records were at that date on the point of commencing. The lati-
tude and longitude of the Observatory are 40° 12'-5 N., and 8*^ 25' W.—

E. S.]

Observations of Deflection, Fiif ration, and Dip taken at the Coimbra
Observatory, 1866.

The horizontal, vertical, and total forces are calculated to English
measure.

The vertical and total forces are obtained from the absolute measures of
horizontal force and dip.

The value of log r^K determined at the Kew Observatory 18=1*64829
at temp. 62^ Fahr.

The value of log /i is =6*30487.

The values of the coefficients q and q' are respectively 0*000128,
000000030. The temperature correction was obtained from the formula
^(^0— 38)+5'(/o— 38)\ The correction for error of graduation of the
deflection-bar at 10 foot is =—0*00006, at 1*3 is =—000024. The
time of one vibration has been obtained from the mean of twenty-four de-
terminations of the time of 100 vibrations.

The angles of deflection are each the mean of two determinations. The
difference between the angles of every pair was found always less than 40".

In deducing from these observations the ratio and product of the mag-
netic moment m of the magnet, and of the earth's horizontal magnetic in-
tensity X, no correction has been required for the rate of the chronometer,
or for the initial and terminal semiarcs of vibration, the former having been
always less than 2''0, and the latter less than 70' at commencement, and
30' at end.

But the induction and temperature corrections have always been applied,
and the observed time of vibration has been corrected for the effect of tor-
sion of the suspending thread.

The torsion for 90° was found no less than 5'* 18, and no greater than
8'*67.

In the calculations of the ratio ^, the third and subsequent terms of the

P o

series 1 + — + " + &c. have been omitted. The value of the constant P
r* r*

was found to be =— 00022317, by the mean of thirty-one determinations

obtained each from two pairs of deflection observations at distances 1 '0 and

1*3 foot.

The horizontal force for each day is the mean of those calculated for

each pair of deflections at distances 1*0 and 1*3 foot.



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476



Cgimbra Monihhj Magnetic Determinations. [May 9,



o



CO

CD
(X)





1


o


3-


1


N?


OO




1


oo


oo






ON '




o


ON


o


b


ON




O












"S


H












oo


oo


On


•<*-


r^




CO


so


CO


t4


-*




>*


o^


c>




o


*r\


3


w-»


w-»


f^


ON


T^ '


>




00


OO


M


oo


OO




M


CO


On


to


^






en


CO


<*


NO


ON




«




m


OO


oo


On




t^


r-H


00


00


t>.






<^*-


•«*•


-*


<+


* ,






5-* ^


vO !->«


ON ^


^ NO


NO






w m


'«*•




•^ ^


to




o.


^ vn w-»


r^ 'd-


r^ NO


^ to


w^




s




^ m


w m


M M


M


i




so so


NO *o


VO VO


VO NO


NO


1


a


2


2








1


•<


s












•»IP»N


M H


►^ e*


w rt


W «




H


B ^


M


3-


to




^ •"

H




M


00






" o




d


r*








NO


f*


M






CO


VO


to


to






•tajoaniBA


«o


*o


*i-»


«/^








b


o


o


O




.


o o


CO CO


t< H


On on




X


to m


w-» vr»










s


c< r*


NO \0


On On


ON ON






e^ a\


OO 00


ON ON


0\ ON




U^


1


CO to


to CO


CO to


to CO




o


O O


O O


b b


O O




■sj.


ON


H


r^


NO






M


NO


On








vS ci


oo.


ON


VO


t>.






?!!«*•*


<*


r^




M




s


H





51


H




s

^


o


« ••*


'«*•


-♦




'ajni«J9aui9x


° S


p


NO






••


a 3.


1^


ON


NO




1


w


to


*0

M






1


tS '^


M


8








CJ u->


O NO


M o


^ VO






sfj^


r* *o


OO ON


U-» CO


to M




1


\rk tn


O^ ON








to


'«*• ^


CO CO


H r«


d d




^


O O


o o


P P


O O




1


0\ C7\


ON On


ON ON


ON ON






r-H M


w-» t>.


t^ c*


p I-


e


c


-oo M


r>. oo


oo VO


b to






M CO


CO M








.»0 vo


CO M


f« r-«


rt r>.




-4- -+


CO ^


M


tl




O


"


ot* *r> ^


t« »o


c* w-»







Online LibraryWilliam Angus KnightPro patria et regina; being poems from nineteenth century writers in Great Britain & America, issued in aid of Her Majesty Queen Alexandra's fund for soldiers & sailors → online text (page 59 of 68)