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TRANSACTIONS 


OF THE 


WO CAnSER LS H ACADEMY, 


VOLUME XXII. 


PART I. 


SSS 
ye - SN 


SEATS 
SAS eS 


DUBLIN: 
PRAUN aD Boy, Mee Hs Gui alc, 


PRINTER TO THE ROYAL IRISH ACADEMY. 


SOLD BY HODGES AND SMITH, DUBLIN, 
AND BY T. AND W. BOONE, LONDON. 


MDCOCXLIX. —— /vs 


\\ 


Tue Acapemy desire it to be understood, that they are not answerable for any 
opinion, representation of facts, or train of reasoning, that may appear in the 
following Papers. The Authors of the several Essays are alone responsible for 


their contents. 


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CONTENTS. 


SCIENCE. 
ART. 

I. On the Relation between the Temperature of Metallic Conductors, and 
the Resistance to Electric Currents. By the Rev. Toomas Romney 
Rosinson, D.D., M.R.1.A., 5c. Read November 30, 1848. 

II. On the Theory of Planetary Disturbance. By the Rev. Brick Bronwiy. 
Read November 30, 1848. =) PM 8 | UR 

III. On the Mean Results of Observations. By the Rev. Humpurny Lioyn, 
D.D., Preswwent, 2. S., Jc. Read June 12, 1848. 

IV. Results of Observations made at the Magnetical Observatory of Dublin, 
during the Years 1840-43. [First Series—Magnetie Declination. | 
By the Rev. Humeurey Luoyp, D.D., Present, #.R.S., fc. Read 
May 11 and 25, 1846. 

V. On a Classification of Elastic Media, tind the Tape of Plas W aves pro- 
pagated through them. By the Rev. Samuet Havueuton, Fellow and 
Tutor of Trinity College, Dublin. Read January 8, 1849. 

VI. On the Rotation of a Solid Body round a fixed Point ; being an Account 
of the late Professor Mac Cutiacu’s Lectures on that Subject. Com- 
piled by the Rev. Samurt Haucuton, Fellow and Tutor of Trinity 
College, Dublin. Read April 23, 1849. . 


PAGE, 


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TRANSACTIONS 


OF THE 


ROYAL*TRISH ACADEMY. 


L—On the Relation between the Temperature of metallic Conductors, and their 
Resistance to Electric Currents. By the Rev. THomas Romney Ropryson, 
DO Meh, TA, Ge: Ge 


Read November 30, 1848. 


Iw the year 1821, Sir H. Davy discovered that metallic wires resist a voltaic 
current more as their temperature is raised ; and that this is the case whether 
they be heated by the current itself or some other means. His memoir con- 
tains many remarkable facts; but the imperfect state of rheometric knowledge 
at that time, and the unsteady action of the batteries which were then in use, 
prevented him from determining the law of the change. More recently the 
subject has been examined by E. Becquerel and Lenz, who found the increase 
of resistance proportional to the temperature. Their researches (to which 
however, I have not an opportunity of referring) were, I believe, made at tem- 
peratures little above that of boiling water; and it seemed desirable to extend 
them through a wider range, as facts of this nature have an unequivocal rela- 
tion to the molecular forces and atomic structure of matter. 

The transference of electricity through a wire has nothing in common with 
the movement of material fluids in a tube, except the analogy of the effects 
produced by enlarging the section of the conductor. A much more probable 
view of its nature is that which refers it to a successive change of tension in 

B2 


4 The Rey. T. R. Rozinson on the Relation between the Temperature of 


each molecule, acting by induction through the interval between them in a way 
corresponding to the charge and disruptive discharge of a coated plate. This 
in some degree accounts both for the heat produced by the current, and for its 
increasing with the resistance. It also seems to explain the increase of resis- 
tance; for the distance increases with the expansion, and the intensity required 
for discharge increases with the distance. That intensity must, by the ordi- 
nary theory, be as the square of the distance between the particles; and, 
therefore, the resistance is in the same ratio. Calling it A and the distance z; 
if this latter become by expansion z+ ¢, the proportional change of resistance 
AP Ae 


A a oeoes 


or, if 1 +¢P be the length of the expanded wire /, 


Rye e 


It will, therefore, increase faster than the expansion. 

Or the transfer may be regarded in another view, as merely a momen- 
tary change of condition propagated in rapid succession like a wave, and 
modifying as it passes the normal action of the forces which keep the 
molecules in their state of equilibrium. A statement of this kind is of neces- 
sity vague, in our present imperfect knowledge (or rather conjectures) ; yet we 
are not without grounds for believing, that when these forces exert any specific 
action, they become less efficient as to others, which, under different circum- 
stances, they would have maintained with energy. Thus, light interferes with 
affinity, and this with cohesion; thus also, pressure developes heat and electri- 
city. It is, therefore, possible, that while producing thermic effects they may 
be unable to contribute to electric conduction. If so, we may expect that the 
change will be proportionate to its cause, to the heat developed in the con- 
ductor. 

However this may be, whatever tends to throw light on a question so im- 
portant cannot be without its use; and I hope the experiments which I have the 
honour to lay before the Academy may in some degree answer this purpose. 

The rheometer and rheostat which I employed have been described by 


metallic Conductors and their Resistance to Electric Currents. 5 


me in @ previous communication*. To these is added a pyrometer, which 
measures the temperature by the expansion of the platinum wire which is the 
subject of experiment. It is shown at figs. 1 and 2. The wire w, 5.4 


oe SES 


Fie. 1. Fie. 2. 


inches long, is held above by a clip attached to the binding-screw a, which 
slides in the piece 0, and can be pinched in it at any position. Below, the wire 
is passed round the cylinder c, and secured in front by a screw. The arbor g, 
which carries the cylinder, has also an arm d, provided with a sectoral arc e, 
grooved on the exterior to lodge the silk thread /, attached to its lower extre- 
mity, and coiled above on the arbor 7. This is furnished witha pulley h, on 
which is wound another thread bearing a counterpoise: it also carries the 
index n, which plays on a dial divided into sixty parts. It will easily be un- 
derstood from this, that the counterpoise tends to pull up the arm d, and roll 
the wire on the cylinder ¢, but is resisted by its tensile force. If now the wire 


* Transactions R. I. A. vol. xxi., Science, p. 291. 


6 The Rev. T. R. Rosryson on the Relation between the Temperature of 


be elongated by expansion, the counterpoise will descend, and the index n 
will describe an are of the dial proportional to that expansion. A strong pla- 
tinum wire screwed into the lower part of ¢ dips in the mercury-cup 7, and 
by connecting this and the binding-screw a with a battery, any required cur- 
rent is passed through the wire w. Since the mass of the cylinder ¢, and its 
arbor, is very great in comparison of that part of the wire which is in con- 
tact with it, besides being connected with the metallic frame of the pyro- 
meter, it is scarcely heated; and, therefore, its expansion may be neglected. 
The effective length of the wire may, therefore, be taken as the distance be- 
tween the centre of the arbor and the bottom of the clip. Calling this /, the 
number of the pyrometer divisions P, and the value of one of them (in units of /) 
= e, the machine gives eP equal to the expansion—not of /,—but of a portion 
of it l’, whose length, when expanded, is equal to l. We have, therefore, 


U=l—eP, 
and obtain the expansion of / itself by the equation 
eP xl eP 
d=; = P(1+57-+6«.) 


In the instrument which I constructed, the length of d=3".00; the radius 
of ¢=0'.208; and the diameters of the arbor 7 and the dial are respectively 
01783 and 31.24. As each of the divisions =0'. 17 nearly, the value of e is 
0.208 0.18 
3.00 © 3.24’ 
was more exactly determined by lowering the clip an amount measured by a 
micrometer microscope, which gives as a mean of eighteen trials corresponding 
to 147”, 0.09516, or, 


Optix or 0.00065; and tenths of this are easily estimated. It 


e= 0.000643. 


The diameter of the counterpoise-pulley = 0'.437, and, therefore, any weight 
applied there causes a tension of the wire 35.3 times as great. The counter- 
poise consists of a weight m= 31.3 grains, which equilibrates the arm d and 
its sector; and of a piece of chain 0 which gives the tension. The use of this 
arrangement is, that when the wire is heated, and unable to bear much strain, 
the chain descends and rests on the bottom of the pyrometer, so that as it 


metallic Conductors and their Resistance to Electric Currents. 7 


approaches the fusing point of platinum the tension has almost ceased. The 
front and back of the instrument are brass ; the sides are glazed, but, except in 
photometric experiments, the glass is covered inside with slips of bright tin, to 
lessen the effect of radiation. The top is mahogany, to insulate the screw a; 
from its low conducting power this becomes very hot, and therefore exerts a 
cooling power on the wire much less than what acts at its other end. 

To deduce the temperature from the corrected expansion, I have used the 
expansibility of platinum given by Dulong and Petit.* They assign 


Mean absolute dilatation from 0° to 100° Cent. = cy 
37700 

P ) Ci a! ies 1 
from 0° to 300° Cent. = 36300" 


The corresponding temperatures, being measured by an air thermometer, might 
require a slight correction for the coefficient of gaseous expansion, which was 
Gay Lussac’s; but such refinement is needless in the present research. The 
expansion-rate of the metal evidently increases with the temperature; its law is 
unknown, but we shall probably not err far by assuming 


e=at+B.t, 
and the above values give 


0.0000088418 = a x 180° + B x (180°), 
0.0000091828 = a x 180° + 38 x (180°); 


the degrees being Fahrenheit’s, but their origin at the freezing point of 
water. Hence 


a = log! (4.68282); B = log! (0.72118). 
But since « is the absolute increase, divided by the length, we have 
eP 
apa siMat, 
F being ® =log" (6.03836), and =<. 
This quadratic may be solved in each experiment, or its positive root tabu- 


* Annals of Philosophy, 1819. 


8 The Rev. T. R. Rozryson on the Relation between the Temperature of 


lated for a decimal progression of P, and the intermediate values got by in- 
terpolation. 

As these temperatures are reckoned from 32°, but the reading sets out 
from the actual temperature of the atmosphere, a correction is applied by adding 
to it the required amount. 

When the heat was expected to be powerful, an additional resistance, 
sometimes as much as 1500*, was included in the circuit, and gradually lessened 
till the full current passed. If this precaution be not attended to, the momen- 
tum which the counterpoise, &c., acquires in its rapid descent, is sufficient to 
produce a permanent elongation of the wire in its softened state, so that the 
index will not return to zero. 

The battery used was at first on Daniell’s principle, the acting surface of 
each metal being fifty-four square inches. With small wires this acts very well ; 
but I found that, when the resistance of the circuit is little, the sulphate of 
copper is expended more rapidly than it can be supplied. In this respect, as 
also in giving a more powerful current, the chloride of copper is a better 
charge. Afterwards I used Grove’s cells, each having 19.3 inches of platinum, 
and found them much more convenient. When the negative charge is 2 
nitric acid, 2 water, and 1 sulphuric acid, they exceed in power twice as 
many of the others, and for a long time there is no extrication of nitric oxide. 
All inconvenience from this may be avoided by arranging them outside the 
window, and bringing the conductors through its wood-work. 

When the circuit is completed through the pyrometer, its index moves 
very rapidly at first; several seconds, however, elapse before the wire becomes 
luminous, and 30 or 35* are necessary for its attaining its full heat: when it 
becomes stationary, a few light taps are given to the stand, to loosen any 
friction of the pivots. The ignition never extends to the extremities of the 
wire, especially the lower one; and the upper part of the wire is evidently the 
hottest, both for the cause already noticed, and the ascending current of heated 
air. It is a curious circumstance, that, when the temperature is above zero, 
the wire, which is then dazzling white, seems enlarged to three or four times 
its real diameter, an effect of irradiation which disappears when it is viewed 
through a darkly coloured glass. By reducing the current, and with it the 
intensity of the ignition, the dark portion at the bottom of the wire extends, 


DIURNAL VARIATION oF tHe MAGNETIC DECLINATION . 


Summer Half Year Seale 0.1 Inch=1. Minute 


Easterly Detlections of’. 


ates Correspond to 


Positive Orden 


Vorth end of Magnet. 


TRANS.RIAVOL Xx2. 


MEAN 


DIURNAL VARIATION of tHe MAGNETIC DECLINATION. 


Winter Half Year — Scale 0.1 Inch] Mimute. 
Positive Ordinates Correspond tolasterly Dthections North end. of “Magnet 
TRANS.RILAVOL 221. 


ALM. PM 
| m2 2 a Ea 5 o 7 é ga jo WN a 7, z 3 ¢ s o 7 a OSB! Ae | 
em ated aes i 2S eos Pee icra T a 
| T i T ; : 4 
) L = +o + + + + II 
| | 
t : + — + ~ . | 
= : , : 7 T | 5 i = + — 4 | 
t 


TS ee Le Eat es 


Ss I En nn i 


MEAN 


1 
5 ae 


Pe, 


Sg 
pe 


a) s vay 
WEP! a Pi wt 
or. 


s A a gat 


ANNUAL VARIATION of THE MAGNETIC DECLINATION. 


TILIV.V. V1. Scale 0-2 Inch =] Mmute 
Fasitive Ordinates Correspond to Westerly Dc lections ot North and of Magnet . 


EI. 


SCIENCE PI. 


TRANS.RIA VOL. XX. 


metallic Conductors and their Resistance to Electrie Currents. 9 


the upper one remaining nearly as before. If the room be completely darkened, 
this proceeds till only the upper inch of it is visible, and the least additional 
decrease of ignition makes all disappear, when the pyrometer shows about 
550°. 

The first used was originally +1, of an inch diameter; but during the nu- 
merous preliminary experiments it was stretched till its thickness was only 
3a: the results obtained are arranged in the following table, each being a 
mean of ten trials: 


| No, Battery. ¢. |Current.| P. die A, REMARKS. 
|; 1 | One D; 40°.8 | 0.809] 12.1 | 289.7} 305.5 
2 | One G weak.| 42°.0 | 0.858] 13.4 | 319.9] 320.8 
3 | Two D. 44°.1 | 0.957] 24.1 | 559.3| 385.2 
4 | Three D. 48.2 | 1.168] 41.6 | 930.9] 497.9 
5 | Four D. 49°.0 | 1.214] 45.9 |1020.6| 523.8] Ienition visible in full day. 
6 | Five D. 51°.3 | 1.357| 55.7 1215-0) 591.6|) Ignition strong red. 
7 | Seven D. + p.| 52°.0 | 1.404} 62.1 |1338.7| 643.8|| 48 resistance added. 
|} 8 | Six D. 53°.7 | 1.515| 67.8 |1447.0| 666.4 
| 9 | Eight D.+p. | 54°.0 | 1.538] 73.1 |1545.6| 706.2|| 78.7 resistance added. 
10 | Seven D. 57°.0 | 1.794| 85.0 |1761.9| 7374|| Yellow heat. 
11 | Eight D. 59°.0 | 2.089] 96.6 |1966.4| 793.9|| Almost white. 
12 | Six G. 60°.0 | 2.200) 105.4 |2116.0) 840.5] Observed at night and doubtful. 
13_| Nine D. 60°.2 | 2.222) 108.4 |2166.2| 827.8 
14 | Twelve D. 61°.7 | 2.318| 126.4 2461.6) 898.2|| Pure white and dazzling. 
! L 


The column headed ¢ contains the deflection of the rheometer; the next 
gives the intensity of the current, its unit being that which deflects the rhe- 
ometer to 45°, and disengages in a voltameter 6.57 inches of gases, at their 
normal temperature and pressure, in five minutes. The two next columns 
give P, the reading of the pyrometer corrected for the temperature of the air, 
and T, the temperature of the wire computed from it. The last gives A, the 
resistance of the wire expressed in revolutions of the rheostat. 

The great increase of the resistance to more than four times its original 
value, and its steady progress at such high temperatures, are very remarkable. 

The pyrometer was then placed in vacuo for a purpose that shall be subse- 
quently noticed. As I feared that the sudden change of temperature might 
fracture a glass receiver, a box of strong copper was used, the lid of which was 

VOL. XXII. c 


10 The Rev. T. R. Rosrnson on the Relation between the Temperature of 


easily made air-tight by Whitworth’s scraping process. ‘T'wo apertures glazed 
with strong plate glass enabled me to read the index and inspect the wire ; 
and an insulated wire passing through the top, and dipping in a mercury cup 
formed in the binding-screw a, connected it with the battery. The box was 
connected by a screw with the air-pump, which, however, was at the time not 
in good order. The following results are also each a mean of ten: 


No. Battery. Pressure.| . |Current.) P. T. A. || REMARKS. 


15 |OneG. weak. | 0464 | 41°.2 | 0.825] 22.7 | 531.4) 390.1] Charge had been used. 


16 | One G. 01.42 | 43°.3 | 0.916] 32.3 | 738.7| 438.8 
17 | Two G. weak. | 0.60 | 45°.5 | 1.025| 45.0 |1002.3| 515.4 
18 | Two G. 040 | 50°.9 | 1.334] 62.5 |1346.4| 606.2 
19 | ThreeG.weak.| 0.51 |... .|. . .| 69.6 |1480.7| 674.5 || N. charge, 1 nit. acid + 1 water. 
20 | Three G. 0.40 | 56°.0 | 1.716} 89.4 |1839.9| 750.8 
21 | Four G. 0446 | 57°.2.| 1.898| 105.3 |2116.0| 829.5 
22 | Five G. 0.47 | 60°.8 | 2.211] 123.2 |2410.4| 892.5 


The currents required to produce a given temperature are less, but the 
resistance is the same; its increase is therefore not due to any intrinsic quality 
of the current. 

On attempting to pass the current of six Groves the wire gave way. 

Another piece was substituted, to try whether feeble currents were simi- 
larly resisted, its diameter being 7},. On passing a current 0.279, the lowest 
which the actual position of the rheometer permitted me to measure, the wire 
was heated 24°, and its resistance =189.4. Increasing the current to 0.315, 
the wire was heated 9° more, and the resistance became 195.4. In fact, I be- 
lieve it is impossible to pass any current whatever without changing the resist- 
ance in some degree; and think it highly probable, that this has given rise to 
the opinion entertained by some philosophers, that the resistance is a function 
of the current. 


This wire failed also in an attempt to obtain higher temperatures,* and was 


* In the first trial the zero of pyrometer was, before contact, —7.2 ; P’= 148.8 ; zero after, 
425.2. If the whole of the lengthening took place during the cooling, P= 159.9 and 7'= 2981.3. 
The resistance = 967.1. In a second trial with an additional resistance of 50 in circuit, zero 


metallic Conductors and their Resistance to Electric Currents. ll 


replaced by one ;!5 diameter. The counterpoise was changed till, after several 
trials, it was found that a tension of four ounces at zero of the pyrometer, was 
sufficient. I was surprised to find that a given battery produced nearly the 
same ignition in this as in the smaller wire, the increased current compensating 
the greater mass ; but, from the greater quantity of heat evolved, the upper 
part of the pyrometer became very hot, so that the clip which holds the top of 
the wire was blued. This apparently made the resistance greater than the 
truth ; but is not likely to have affected its changes, as the experiments were 
made in the inverse order of the table, so that the highest temperature was ob- 
tained first. After five results the wire was broken by an accident close to the 
cylinder ; and as I had no more of that diameter, I rejoined it bya loop, which, 
being beyond the part that is ignited, might be expected not to interfere with 
the temperature produced. 
Each result is a mean of five. 


No. Battery. g- |Current.) P. | 1 A. | ReEMARKs. 


| 


23 | One G. +83. | 60°.0 | 2.200) 15.1 | 359.0| 107.3 


24) .... +50. | 62°.7 | 2.437] 20.3 | 476.8] 107.5 
25 | OneG. 67°.9 | 3.261} 31.9 | 730.2) 116.4 
26 | TwoG.+50.| 70°.1 | 3.768] 46.4 |1030.9| 135.0 ||Not visible in strong day-light. 


27 | TwoG. 72°.5 | 4.824] 60.4 |1306.5| 151.0)|Full red. 
28 | FourG.+105.) 73°.9 | 4.827] 70.3 |1493.8 | 173.2 |) 
29 |.... +48.| 75°9 | 5.654| 86.9 |1795.5 189.1 | Yellow heat. 


30 | Four G. 77°.1 | 6.272| 99.3 |2012.2| 188.1 || White heat. 
| 31 | Six G.+20. | 77°.7 | 6.588] 106.5 |2134.6| 196.0 | 


32 | Six G. 79°.0 | 7.286 | 121.9 poses 201.9 || Splendid in bright sunshine. 


i 


The increase is evident here also, although the discordances are greater 
than in the last series. 

Lastly, a wire of ;'; was used. At No. 40 the pyrometer was immersed in 
diluted alcohol, to ascertain whether the resistance increased with the cur- 
rent when the wire was kept cool. The fluid boiled round it with a sharp 


=~-4.6; P’=140.0 ; zero after, + 24.0. On the same supposition, P = 148.1; 7 =2803.0; and 
the resistance = 953.0. In the third trial it gave way ; the ends, however, were not fused, though 
a very little more would certainly have melted it. The temperature of the centre of the wire in 
the first of these experiments must haye exceeded 3200°. 


o2 


12 The Rev. T. R. Rosrnson on the Relation between the Temperature of 


snapping, and its refraction may make the reading doubtful one or two tenths 
of a division. All but the last are means of five; that only of two, which, how- 
ever, agree tolerably. 


No. Battery. g. |Current.) P. T. A, REMARKS. 
33 | One double G. +155.| 56°.1 | 1.522| 15.4 | 365.9} 127.8 
34]... . . +88. | 58°.4] 2.020) 20.5 |} 481.3] 144.9 
35|. . ... . +18. | 61°.9| 2.411) 31.4 | 719.6) 169.0 
| 36 | Two G. + 22.6. 65°.1 | 2.758} 46.0 |1020.7 | 212.0 
37 | Three G. + 80. 68°.1 | 3.226} 60.6 |1310.4| 238.7 
Weis Woaeo. vs + 37.6. 69°.8 | 3.699} 71.6 |1518.0) 270.1 
| 39 | Four G. 72°.9 | 4.352| 91.9 \1883.9| 318.6 
| 40 | Five G. 81°.3 | 9.548 8.6 | 207.8) 93.8 
41 | Ditto. 73°.9 | 4.821 | 110.8 |2206.7| 346.0 
42 | Six G. 74°9 | 5.230| 119.8 (2355.1 | 361.4 | { Battery nearly exhausted and) 
{zero unsteady. 


In examining these tables it is evident, 
1. That the increased resistance is not occasioned by any condensation of 
the current. In No. 40 it passes more easily than in No. 33, though of six-fold 
power, and able to fuse a far thicker wire in air. It is also worth notice, that 
in these two cases the productions of heat are as 29: 1; and, therefore, it is not 
by the mere employment of molecular forces in the production of that agent, 
but by its accumulating and becoming sensible, that conduction is impeded. 
2. The magnitude of the change prevents me from attributing it to a mere 
change of molecular distance. On this hypothesis we have seen that it will be 
A'-A %P ¢P 
B lc aaa 
1 


mG 30), 


Now in No. 14, the highest of the set, Ze = 0.1, which will give A 4 


l 


whereas it really = 4.68. 

3. Nor is it proportional to the expansion: up to a certain point it may be 
expressed by the formula A =a + bP, but less accurately than by making it 
depend on the temperature ; and 

4. It appears to be correctly determined by the equation 


Aaebe- (1) 


where a is the resistance at 32° of Fahrenheit, and 6 its change for one degree. 


metallic Conductors, and their Resistance to Electric Currents. 13 


Before endeavouring to deduce the values of these constants for each 
wire, it is to be remarked, that the resistances given in the preceding tables 
are too small, and require to be corrected for the heating effect of the current 
on the rheostat and resistance coils by which they were measured. The 
thickness of the wire in the former, and the immersion of the others in alcohol, 
might seem to guard against this danger ; but, with powerful currents, both be- 
come warm to the touch. If we assume the truth of (1), the resistance 
measured is not A, but A (1+0’¢’), supposing all reduced to the freezing point. 
Now the heat generated is as A x square of current ; and I have found by ex- 
periment, that the temperature of a wire follows the same law under 100°. 
Hence, for 1+0’t’, we may write 1+¢.A.C?, and (1) becomes 


A=a+bT—c.A*.C*. 


Each result furnishes an equation of condition, which may be grouped to- 
gether, and either by minimum squares or ordinary elimination the values of 
a, b, and e determined. 

If the twenty-two that belong to the wire z3q be thus combined, we have 


the equations 
442.19 =a+bx 674.1—cx 195855.0, 
660.53 =a +b x 1447.9 — e x 1002800.0, 
833.382 =a +b x 2153.8 —¢ x 3141477.0. 


Hence 
a=198.4; b= 0.3412 ; ¢ = 0.00003182. 


Computing with these the apparent values of A, and subtracting them from 
the observed, I have arranged the results according to 7. 


No. T. |Obs.—Cal.|! No. T. |Obs.—Cal.|| No. T.  |Obs.— Cal.) 
i} 
1} 289.7 | +10,2 6 | 1215.0 | + 4.0 || 11 | 1966.4-| +10.5 
2{| 320.0 | +15.7 7 | 1338.7 | 415.3 || 12 | 2116.0 | +289 
15 | 531.4 | +13.6 || 18 | 1346.4 | -30.8 || 21 | 2116.0 | -12.0 
3| 559.3 | + 80 8 | 1447.0 | + 4.1 13 | 2166.2 | — 2.0 | 
16 | 738.7 | + 7.0 |] 19 | 1480.7 | — 3.3 || 22 | 2410.4 | - 4.4 | 
4! 930.9 | +68 9 | 1545.6 | +180 || 14 | 2461.6 | -21 | 
M7) L002!) | 3-23) || 10 || W61t9 | =" 10 | 
5 | 1020.6 | + 5.5 || 20] 1839.9 | -11.3 | 


14 The Rev. T. R. Rosryson on the Relation between the Temperature of 


With the exception of 18 and 12, the agreement between the formula and 
observation is sufficiently close ; and even in them the error is not remarkable, 
if we consider that a degree of the pyrometer represents 20° of Fahrenheit, and 
that a little oxidation in the connexions may affect the resistance of an entire 
set. It even seems to me that this principle affords a very effectual method of 
measuring high temperatures in the arts. 

With the wire 7, the three equations are 


114.55=a+bx 424.25—cx 130725.0, 
171.10 =a+6 x 1531.98 —e x 753848.0, 
195.83 =a +b x 2178.70 — ec x 1741069.0. 
Hence, 
a=91.4; b6=0.05898 ; c = 0.0000141. 

The value of a is certainly too large. I have mentioned the probable effect 
of the oxidation of the clip ; possibly while looping the broken wire, the con- 
tact may have been improved, for I found afterwards, that by trying its resis- 
tance under water while attached to the clip, with a current = 2.743, the 
resistance was 76.1. On making the contact perfect it was only 46. 

The values of observed — calculated resistances are 


| ! 
No. Ts Obs.—Cal.'| No. ae Obs. — Cal. 
eres (per oe (eae etal 
23 359 — 4.5 28 1494 + 3.6 
24 477 -11.1 29 1796 +7.9 
25 730 —16.1 30 2012 — 2.4 
26 1031 -13.5 31 2135 +2.2 
| 27, 1306 —-11.6 32 2389 +0.1 


Part of the errors of the first five are, I think, accounted for ; and the rest 
1s unimportant. 
Lastly, for the wire ;/, the equations are 


147.22 =a+bx 522.27-—ex 96511, 
240.27 =a+b x 1283.03 —e x 644327, 
338.67 =a +b x 2148.57 — ¢ x 2694208. 


Hence, 
a= 81.9 ; b=0.1261; ¢c = 0.000007188. 


metallic Conductors and their Resistance to Electric Currents. 15 


In these equations No. 40 is not included from the uncertainty of P. The 
comparison with observation gives, 


No. T. |Obs.—Cal.|| No.| 7.  |Obs. — Cal, 
33 366 0.0 |38| 1518 | +20 | 
34 481 +3.2 || 39 | 1884 | + 9.3 
35 720 =D 640 209 | -10.1 
36 | 1021 +3.2 || 41] 2207 | + 0.5 
37 | 1310 -5.3 | 42| 2355 | - 9.7 | 


Here also the conformity to observation is very satisfactory. 

If we divide the values of b by a (assuming a’= 46), we obtain 0.0017, 

0.0013, and 0.0015, taking the mean of which we have for a platinum wire, 
A=a(1+0.0015 x T), (2) 
a being, as before, the resistance at 32°. 

It would be desirable to extend these experiments to other metals ; but I 
could not find any determination of their expansions similar to that which 
Dulong and Petit have given for platinum, except what those philosophers 
have given for iron and copper. The first of these metals, however, I found 
to oxidate so rapidly in the pyrometer, that I could get no consistent results. 
It should for this purpose be surrounded by dry nitrogen. Copper also oxi- 
dates; but the film of oxide acts as a coating, and protects the interior, so that 
its diameter does not change up to 900°. The wire used was of the same 


diameter as the last platinum one, 45. Each result is a mean of three closely 
agreeing. 


No. | Battery. gd. Current. 72 Le A, Obs. — Cal. 


| 


43 |1G.+196} 56°.9 1.808 11.1 102.3 30.1 + 0.3 
44)...+4105|] 64.3 2.640 21.6 195.0 33.4 +0.3 


45 |...+50 70°.6 3-902 40.0 348.9 37.8 —0.6 
46 |... +30 72°.9 4.352 53.0 452.4 41.8 - 0.2 
47|1G. 75°.8 5.608 81.0 664.1 49.6 +0.2 


When the current was increased to produce ignition, 7=919.8, A = 68.8; 
but the zero changed, and the wire stretched till its diameter became 3). 


16 The Rey. T. R. Roprnson on the Relation between the Temperature of 


For this metal the coefficients of expansion are a= log’ (5.03826) ; 
6 = log! (1.40598). As the resistance was measured by the rheostat alone, 
the correction cA’C” need not be applied, and the equations are 


33.77 =a +) x 215.40, 
45.90 =a+b x 558.25. 
Hence, 


a = 26.37; 6 =0.0348 ; - = 0.00133. 


bss ; 2 4 
The value of 7 18 so near that of platinum as to make it an object of interest 


to ascertain whether the same equality prevails in other metals. The difference 
of conducting power in copper and platinum appears very strikingly here. At 
32° the resistances are as 1: 3.1; but in Nos. 46 and 39, when the current is 
the same, as 1:7.6. It may also be remarked, that these constants give, as the 
probable values of the correction cA*C*, quantities closely agreeing with those 
computed by the values of ¢ given above. 

The facility of bringing the wire of the pyrometer to a given temperature, 
and maintaining it, makes it a convenient source of light in photometers ; but 
as the heat is not uniform along it, it seems worth inquiry according to what 
law it varies. Each section of the wire is traversed by the same current, and, 
therefore, under similar circumstances, would be equally heated: but the heat 
thus excited is dissipated by three cooling agencies. The first of these is radia- 
tion, which, though lessened by the bright metallic surface of the pyrometer, 
below what it would be in free space, is still very powerful. The second is 
the presence of air ; and the third the conducting power of the wire itself, by 
which a portion of the heat escapes to the metallic supports which attach it 
to the instrument, in this case chiefly to the lower one. As long as their 
combined effects are inferior to the heating power of the current, the tempe- 
rature must increase: while doing so, however, the resistance also increases, and 
with it (as shall be immediately shown) the heating power, the current being the 
same. On the other hand, the cooling causes also augment in energy, and in 
a still higher ratio. An equilibrium of these powers is therefore attained, to 
which belongs the thermic state shown by the pyrometer: it is, therefore, ex- 


metallic Conductors, and their Resistance to Electric Currents. 17 


pressed by equating to cypher the differential equation, which expresses the 
rate of cooling for a differential section of the wire in function of the time. 
Calling « the distance of a point from the extremity of the wire, y the excess of 
its temperature above the surrounding medium, and f(y), f(y), the heating 
power of the current, and that cooling one which depends on its surface, and on 
the surrounding media, the differential equation becomes 

0=H fly) - Lf (y) - S22. 
The integral of which will determine y the temperature at x. 

The heating power of a given voltaic current is known to be proportional to 
the resistance which it overcomes ; but in all the experiments which have es- 
tablished these laws, the change of resistance which I have been considering was 
overlooked, because the conductors were kept at a comparatively low tempe- 
rature. It might, therefore, be a question, whether the resistance to be used 
is the intrinsic (that at a given temperature) or that increased by heat. It is 
easily proved to be the latter by means of the apparatus (fig. 3). A isa 
thin jar, in whose neck are cemented copper 
wires terminating in the binding screws C, C. 
Their other ends are connected by platinum 
wire, W, of so inch diameter, and 5.4 inches 
long. Over the wire is inverted another jar, 
B, formed of thin tube. If water be now 
poured in, B acts asa diving-bell, and the wire 
W is in contact with air. Passing a current 
through it, it may be intensely heated, and its 
resistance of course increased; but the heat 
which it gives off is employed in heating the 
glass and water by which it is surrounded, and 
can be measured by a thermometer immersed 
in the water. At low temperatures Newton’s 
law of cooling is exact, and, therefore, the li 
rise of the thermometer is proportional to the NEL 


thermic power of the current, A single result will be sufficient. The jar 
VOL. XXII. D 


18 ‘The Rev. T. R. Ropinson on the Relation between the Temperature of 


containing 5.5 cubic inches of water, a current = 3.527 was passed for twelve 
minutes, the air and water being both nearly 72°. The thermometer rose 77°.5, 
and the resistance A = 257.6. The wire was almost white, and its temperature 
must have been near1500°. The instrument was then cooled, filled with water 
(which, by inclining it, was made to fill B), a resistance = 165.6 added in the 
circuit, and a current = 3.558 passed for twelve minutes. Now the thermome- 
ter rose only 29°.7, and the resistance = 89°.0. Here all was the same, except 
the increase of A by the heat; and that determined the greater heating power 
in the first experiment. The second was repeated, but without any inter- 
posed resistance in the circuit: bubbles of steam formed round the wire, 
which were condensed with sharp snapping; the current = 6.045, which would 
have melted it in air; the resistance = 94.5; and the rise of the thermometer 
= 83°.2. 

From this it follows that f(y) = a(1+ ry). 

The function /’(y) is far from being so easily determined. Fourier and 
Poisson, in their celebrated investigations, have assumed it = ky, following New- 
ton. This, however, is quite at variance with observation. Dulong and Petit, in 
their memoir, have assigned expressions for the effect of the air and radiation, 
which represent their observations very exactly. According to them the effect of 
radiation is as 1.0077 7—1, and that of the air as 7°. The heated body which they 
employed was the bulb of a thermometer enclosed ina globe of copper a foot 
in diameter, blackened on its interior surface, and kept at an invariable tempe- 
rature. The highest range was under 500°, and of course far below the point 
at which light is given off,—an agent which, doubtless, interferes with heat. 
Accordingly, their law of radiation fails altogether in my experiments, but the 
other is nearly exact. We are enabled to infer this from the law already men- 
tioned, that the heating power of the current is as its square multiplied by the 
resistance.* Now in the experiments Nos. 1-14, the wire is in contact with 
air, while in Nos. 15-22, which were made in vacuo, the effect of that medium 


* This law has been often verified, but the experiments just described gave a good illustration 
of it. In the first and third, the ratio of the heats excited is 1 : 1.074; while that of AC? is 
1: 1.077; the difference arising from this, that, the temperature being higher in the last, more 
was lost. It may also be mentioned as evidence of the heating power of that current, that it gene- 
rated in the wire as much heat as would have ignited eight ounces of platinum to strong redness. 


metallic Conductors and their Resistance to Electric Currents. 19 


is nearly insensible. If from the first we deduce by interpolation the currents 
and resistances which correspond to the temperature of the vacuum series, we ob- 
tain one in which radiation and conduction must be the same as in it; and the 
difference between the AC? for the same temperature is evidently the measure 
of the cooling due to air. Comparing them with the corresponding values of 7, 
I find that they are as its first powers. The deficiency from the experiment 
of Dulong and Petit proceeds, probably, from the air being heated. 

In the vacuum series AC? must be as the combined effects of radiation and 
conduction. Omitting No. 15 as too low, if we divide AC? by 7’, we obtain 
the numbers 


Nor 20 um rns eel gure 
Dik, Magee cla Xe" ROG 
205 wh Rae + EE 
DOP eae ee Ge 
18, S21 + TAL 3 3, O99 
17 te 0 1) 8 Le oe 
Le er ane SES 


And if we allow for the residual air and the conduction, we may assume the 
radiation in this pyrometer to be as the square of the temperature. Hence, 
F'(y) = Gy + Ly’, and as G is less than H.ar, the equation becomes, 

d’y 
ae = my’ — ny — p, 
in which it must be remembered that m, the quotient of the coefficient of radi- 
ation by that of conduction, is constant for a given wire, but m and p vary with 
the current. The integration of this is facilitated by considering, that the effect 
of conduction must cease at a certain distance from the origin, beyond which y 
is constant. Let this value of y be 6, then we must have, 


m0? — nd = p, (3) 
substituting which, and writing pw” for 2m6 — n, and u for 6 — y, we have, 


& 
Ta =u (w — mu). 


D2 


20 = The Rev. T. R. Rosinson on the Relation between the Temperature of 
Integrating 
du” _ ay. 
ca) = (2 — $mu), 
which requires no arbitrary constant, because du vanishes with wu. 
Integrating again, ¢ being the base of the Neperian logarithms, 
6.2 1 
ie ¢ areal gs ot ) 
As y vanishes when 2 = 0, we have then 


62 il 


O= x yuk pe\ 29 (4) 
ere) 
and hence deduce 
. y fi % el ae eahey? 
fi) =1 et (1 a GEER : (5) 


which determines the thermic condition of any point z. 
As the pyrometer gives only 7, the mean temperature, we must find its 
expression for any length z: 
_fydz _ 6 1 ; 
a pent tines eemy i)» 
In strictness this should be taken from 0 to the centre of that portion of 
the wire which is of uniform heat, supposing both supports to cool it equally; but 


as this part extends close to the upper support, I prefer taking it from 0 to A, 
the place where the heat declines; in this instrument A is five inches. 


Thence 
1a 1 i Gre)? 
fala (item SE). (6) 


It then remains only to determine 0, w, and ¢“*. 

In (3) the quantity » is the difference of two quantities ; one the heating 
power due to the increase of resistance by heat, which, being proportional to p, 
may be called rp, r being, as we have seen, 0.0015; the other representing the 


metaihe Conductors and their Resistance to Electric Currents. Di 


air’s cooling power, which, like m, is constant, and therefore = ms. Equation 
(3) then becomes 

me? — 0 (rp — ms) = p, 
which, combined with py? = 2m0 — n, gives 


tam (are 
a Lene)” 


From the series in air and in vacuo already referred to, it appears that s = 
0.2822 ; it may, therefore, be neglected, and then 


re 1+ 40 
y= 2mo (542), (7) 


Substituting this in (4), we obtain 


5 + 2r0 5 + 2rby? \ ; 
SER as teed ot SS i) 
f Seen a leeas a (8) 


Whence it appears, that though » and 0 increase, ¢~“* is confined in narrow li- 
mits, ranging from 0.105 to 0.268, while @ passes from 0 to infinity. 


Since the loss of heat must equal its production, we have m6? + smé 
as AC”, or, 
P+ s0= qA (ys 


and as s is small, @= Y(qgAC*). Hence the highest temperature attained is 
as the current, not as its square; and also as the square root of the resistance. 
If we tabulate an equidistant series of 0, and compute for each the values of 


2 UK 
rep oda dai elas etl ) x ¥(2m) 
2m be 


=g; and assume y= A x (2m), 


the equation (6) gives 


_ gy Lee es 
6-T= g(a NN xv =). 
Now taking any two observed values of 7, where A and C are known, we 
have the ratio of the 6s; assuming one the other is known, and the other 
quantities can be taken from the table. A few trials of this kind show that 


22 The Rev. T. R. Rosinson on the Relation between the Temperature of 


vy must be a number less than unity, and that ev”** must be so large that 
the last term of the equation may be neglected, whence 
@—T= g 
‘ (9) 
B= x* Vv, ‘fF. 


When v is known @ is easily found ; for, entering the table with 7 as argu- 
ment, we get a first approximation, with which as argument the true value is 
obtained. 

A still more accurate mode of obtaining this quantity is by observing the 
value of x at which the wire assumes a given temperature. That which I se- 
lected is the point at which platinum begins to be visible in total darkness. It 
is unknown ; but by varying the current, so as to have different lengths of 2, 
we may equate the values of yin (5). I measured « by a screen moved by a 
rack, which was lowered till it cut off all ight. Its pinion was moved bya gra- 
duated head, and I found the measures very consistent. 

With the wire 4 I obtained 

T = 539.3; C=2.213; A = 150.9; no light visible. 
GED ec 129 Oi Oe OOO) 
T= 850-5); to Oa — Drie — a9) 


From these I find y= 0.3 nearly, and with this value 
6 


6 = 710.9; 7 = 262. 
6’ 

= 9115 5 Fy = 2855 y' = 739.7. 
6” 

0 = 995.5 ; F7= 28.6 5 y= 733.2. 


R being = V/A x C. 

The light of the wire is like Herschel’s lavender ray, and is, perhaps, rather 
a phosphorescence than a true ignition. 

For the wire +4, the same process gives v = 0.4 nearly, as might be ex- 
pected from its being proportional to Ym; the temperature is also some- 


metallic Conductors and their Resistance to Electric Currents. 23 


thing higher, probably from the smaller quantity of light requiring a greater 
intensity to be visible. 

I will conclude with a summary of the principal facts which I have endea- 
voured to establish in this memoir :— 

1. When a wire of platinum is heated by a voltaic current, its resistance 
to the passage of that current increases without limit to the verge of its fusion. 

2. That increase of resistance is not caused by the mere increase of the 
current. 

3. It is not caused by the increased distance of the molecules. 

4. It is not caused by the employment of the molecular forces in generating 
heat. 

5. It is exactly proportional to the increase of temperature of the wire. 

6. The same is the case with copper till the oxidation of the metal inter- 
rupts the experiment. 

7. In both those metals a given elevation of temperature produces the 
same proportionate change of resistanee. 

8. This change of resistance must always be attended to in rheometry; and 
the neglect of this precaution may explain some objections that have recently 
been made to the theory of Ohm. 

9. The heat evolved by a current passing through a wire is as the square of 
the current, and as the actual resistance of the wire (that increased by the heat). 

10. The highest temperature attained by any part of it is, however, as the 
current x square root of resistance. 

11. The loss of heat by the air is as the difference of the temperatures of 
the air and wire. 

12. That by radiation is in this pyrometer as the square of that difference 
nearly. 

13. Thermic equation of the wire ; from which it follows, that the tem- 
perature rises very rapidly in receding from the lower end of the wire, till at a 
small distance it becomes constant. 

14. This constant temperature exceeds that given by the pyrometer by an 
amount varying from a seventh to a tenth. 

15. The following is the table of the quantities involved in this equation: 


\ 


24 The Rev. T. R. Roprnson on the Temperature of metallic Conductors, §e. 


| @ rs f 9 
400 0.1313 325.0 25.10 
600 0.1422 457.9 32.03 
800 0.1521 581.8 38.21 

1000 0.1603 700.0 43.85 
1200 0.1678 814.3 49.11 
1400 0.1736 925.8 54.00 
1600 0.1788 1035.3 58.69 
1800 0.1839 1143.2 63.03 
2000 0.1882 1250.0 67.21 
2200 0.1922 1355.8 TAB} 
2400 0.1957 1460.9 75.08 
2600 0.1990 1565.3 78.79 
2800 0.2020 1669.2 82.38 
3000 | 0.2047 1772.6 85.87 


OBSERVATORY, ARMAGH, 
Nov. 8, 1848. 


I1.—On the Theory of Planetary Disturbance. By the Rev. Brice BRonww. 
Read November 30, 1848. 


1. In this paper I shall consider, with M. Hansen, the disturbance as af- 
fecting the radius vector (or rather the mean distance ) and the mean longitude ; 
and I shall first, after his manner, employ two times. Various formule not 
noticed by him (one of them fundamental) are given, in the hope that they 
may some time be made useful. The principal equations are investigated in 
a way that leads to some very elegant formule, and the elimination of the 
quantities containing both the times is effected in a very simple manner. In 
finding the latitude, I propose to introduce the latitude itself and the reduction 
into the disturbance function ; by which means the part of that function de- 
pending on the inclination of the orbit to the fixed plane is greatly simplified, 
and the determination of the latitude and reduction rendered easier. But it is 
not my intention in the present paper to develope the functions in series of sines 
or cosines. 
The well-known differential equations of a planet's motion, referred to the 
plane of the orbit, are 
Chain Ce) ON 


a tpt Ge ao o 
d LR 
r 7 Sh =i — — dt, 
mr mm aa! + yy! + 22’ 
zi mote X= (r? — 2r’r cos x + r*)#? ge rr / 


where z, y, and z are the rectangular co-ordinates of the disturbed (z=0), and 
a’, y’, and 2’ those of the disturbing body. The meaning of the other symbols 
is obvious. 

VOL. XXII. E 


26 The Rev. Brick Bronwin on the Theory of Planetary Disturbance. 
When m’ = 0, let the integrals of (1) be 
=f (t, Go, 0) To, €0), Yo= P (Ft, Ao, C0, Mo &)- 
And when the disturbing force is restored, let 
m= f(t a, en 7, €), U = (1,4, 2, 7, €). 
Thus rand v are the same functions of ¢ as when m’=0, the elements a, e, &c., 


being variable, and determined in the usual manner. And, rt being a new time, 
we make 
p= (% 42,7, 6); N= @ (zane, x, ©): 
We further suppose, 
t= (28) ei mse) 8) = Olea, erm te ys 
=f (g Qe), M) €,)» A= (% A), @,, Ty ei 
the elements a,, ¢,, &c., and h,, to be presently introduced, being constants, z a 
function of ¢, and ¢ a function of t and ¢. To these we must add the assumed 
relations, 
r=r,B, p=p,é v=v, + Ent, N=X, + Ent. 
By changing 7 into ¢, we change p into r, A into v, p, into r,, A, into v,, 
— into B, and ¢ into z 
l Z eae 
From what has been given above, we have necessarily 7; T= h,, 
, ar : : 
p i =h,. And from the way in which a, e, &., are found, & = 0, tv =0, 
the characteristic 6 denoting the variation relative to a, e, &c.; therefore, 


—=h. 
dt 
GON apt N, a ON RG dg Og. 
But p 7e = pé 7 = pe de == Sie oe Consequently /,é Ps h; or, 
de eh 
ie ae (2) 
Also 12 = te 4 eng? = rip eS 5 en Per = ng SE + Envi =/p5 Oe 
dz nln iire 
: (3) 


dt hip Sir 


/ 


The Rev. Brice Bronwiy on the Theory of Planetary Disturbance. 27 


The two theorems now found are fundamental. The latter is not no- 
ticed by M. Hansen; the former, or one equivalent to it, is employed by 
him. But there is another fundamental theorem which he has not found ; for 
we have necessarily 


—4-=+5=0, 


as in an undisturbed orbit ; because, since d operates on 7 only, the elements 
and h may vary in any manner whatever, and this equation will still hold. 
Ga os wane. ae ip de Sab Ath “dp, 2). 
Now ih qt oat ates at dr de * fe ac’ PY (2); and 
dp _  @é dp,d¢dt h dp,dé h ap,dg_ ME hh dp dt ; 
de Pde de de de hE dg dr * he de! de = de the aC. ay’ PY (2)3 
ME W dp, 


=P) 75 + ap de by the same. 


ad? h? > or 2 2 : 
But Py — i+ ie =0. Therefore, substituting for on and ay their values, 
de pt pp dz de 
I? h? 
a ie and =! ae we have 
pp a 


or, since ep > = p?, 
K PE ie ” 
2 


ae _ oe (W? 
ano (a4): a 
There are still two other theorems to be investigated, which are given by 


M. Hansen ; but found by him in a manner very different from that which I 
shall employ. 


which easily reduces to 


1 _# pe soe LM Hope 
7 het Fp 08 (¥ — =) gives ——= =F cos (v — 2) = 
pe ‘ 2 
RB (cos 7 cos v + sin x sin v). 


E2 


28 The Rev. Brice Bronwin on the Theory of Planetary Disturbance. 


And differentiating relative to ¢, 


Tdr oye. dv. : Ce 
Sat pF a et) ig Oe ecen an 
5 =e sin (v — 2) = (cos » sin v — sin x cos”). 
Whence we easily deduce 
sk tine 

(- 2) cos v + FG, sin v = 73 COs ™ 

Ip dr 

=i Fi) Sn Oe egy COP ge 


In like manner, 


tt) cosh 
(| -%| cos A + ee A= ag COS ™ 
py alle eee 
( -4) sin A re cosA = 72 in 
Equating the two sets of values of J cos 7 and a sin 7, 


i ya ldr . (eee ldp : 
(tf) cos 0+ 57 sno = (Ff cosA +77" sin A, = 
Lg Nias ldr ay fo ye ldp 

aoe sin v— 79, c08 0= (5 —F BEL Ng ae CORN: 


Multiplying these by cos v, sin v, cos A, and sin A, and adding and sub- 
tracting results, 


== (2-f) cos 0) +5 Fain 2), 
r= —(5— fh) iB O=0) +5 FeO A-P - 
; = (Ef) 208 (a= 0) — | Gain 2) 
rea (e-) sO a) ook aces (A v) 


The Rev. Brice Bronwin on the Theory of Planetary Disturbance. 29 


The equations (5) may be put under the following form : 
d : d ; _p : 
a (r sin v) — om (p sind) = I (cos v — cos A). 
d d Via aul fs 
= (7 cos v) — ze (pcos A) = 7 (sin A — sin v). 


The first and second of (6) may be written thus: 


1 ld ; 

— =F, (1 =cos (A—v)} + 5 Ftp sin (A—v)}; 
hp JP sc d , ; 
777] Se (A— v) + = jp cos (A — v)}. 


These, and the third and fourth of (6), are very elegant equations, and are 
deserving of notice on the ground that, possibly, some use may be made of 
them. I shall only employ the third of (6). Differentiating it relative to ¢, 
there results, 


ldp_(2u 2 \o+ 1dr 1dh . dr 
aaa — Fx Cos (A—v) +{5 a 08 (A v) — Ba a a- o) bF 


| PNG er ei NY 
+ (Bla 9) + Ge tae) 9 O— 0) 
ep Wee 


Eliminating ds 7 bY the third and fourth of (6), and substituting for ©" ee 


F = its value from (1), we find 


ldp_1dpdxr Dea es 0 Uc te Lee , ak 
pdt TER t sth (gtp) oO) [ie ae 


Multiply this by A, put for = its value from (1), and for © 5 in the first 


member its value = ; then making 


r={G+ i) oS (Cg lr (+ ) fae — Si 0) Se 


we have 


30 The Rev. Brick Bronwin on the Theory of Planetary Disturbance. 


dp dX dp dr _ 
dds dr a” 7) 
which is a very remarkable equation. 
From this we deduce successively, 
dp dX, _dp dr dp 


Gi de de ae wet a, 


h, (dp dg dp d¢ dp 
a (ESF 4 Sines 
but 
dp ede dp, dg dp_ dé p, AC 
ae det © ae di? dr =n gree S. 


Therefore, by substitution in the above, 


dé dg dé dé dp 
(ES-ES =T+in—. (8) 
This again is a very remarkable ie and has a remarkable corres- 
pondence with (7). Dividing it by + ng a ee == we have 
dg 
dz dé| dt el dp 
di dr \ae| ~ 5, ea Hig Pg 3 
dr 
or, 
[a 
dew i Ené d(p?) dé 
de he + oR de * ae ae (9) 
dt 
Equation (7) multiplied by 2p gives 
ae dX dpdrX_. 
Cad "aan 


; A r 
But differentiating p? “= =h, relative to t, we have 
iP 


, BR dp da _ dh 
geip ae aiaree ay 


The Rev. Brice Bronwin on the Theory of Planetary Disturbance. 31 


The above, subtracted from this, gives 
2 ON dp dr_ dh 
O dri” Par de ae Ph 


d(,dr\_ ah 
a(S) =o mor. (10) 


or, 


This is singular, and very worthy of notice. This theory, as we have 
treated it, gives rise to many very interesting formul. 


dx dx dX, dé 2 dé 
2 aa) 4 2 ¢2 2 id | 2 = 2-8 7.02 
Bue a! op een Se dé dt Onis lye ia ae 


Therefore (10) becomes 


Or, since h,@ = — 


de’ 
= 
4 
d{dt\ 1dh 1 En d(p?) 
z= K |i aa | = (11) 
ze 


2. In the preceding section we have found all the fundamental formule, 
and indeed more than are absolutely required. We now proceed to discuss 
some points preparatory to integration. 

We might immediately integrate (11) relative tot; but the integral of the 
second member would contain a very great number of terms with 7 in their 
coefficients, or of the form tf (t). We must, therefore, proceed otherwise. 


Make z=¢+o, (=7+¢. Then diye ear. Substituting 


these values in (9) and (11), neglecting terms involving the fourth power of 
the disturbing force, and putting 


1 éné d(pt) 1 dh 1 én dp?) _ 
ici) Sir al iy a ee aaa 


they become 


32 The Rev. Brice Bronwin on the Theory of Planetary Disturbance. 


dé _p,didb dé dp do 

i dz dt dz dt dz’ | 

Lp _ dp do dp de (1) 
Te ral ee ae of). | 


Let the integrals of these relative to ¢ be 


b=f(t) + Wnt), 4 aE F=f) + $(7,t): 
f(z) and f(7) being the arbitraries of the integration. If we make m’ = 0; 
then €=0,andA=A,. But in this case A is a function of 7 without ¢ Con- 
sequently, A,, ¢, and @, are functions of 7 without ¢; and, therefore, = = UL 


Hence, all the terms in the second members of (1) vanish, and we have 


= f(r), = h(n); 
dy 


& and —~ being the values of € and de when m’ = 0. 
dr 2 dr 


Now if we make the disturbing force to vanish in (2) and (4) of the first 
section, they become 


dé ho ) 


PE bE hoe 
da? i -&,), | (2) 


mie 


the last of these being derived from the first by putting for ¢ its value. These 
equations, being integrated, give us ¢ and &, or & and do- 


4 2 

To integrate the second of these, make & = 2 (1+ ¥), when it becomes 
dy 3 Dy : 

dat ist= 0, or 75 ga + moby = 0. 


To abridge, make te =1+eEL, +E, + &c., where E,, F,, &c., are known 
0 


The Rev. Brick Bronwin on the Theory of Planetury Disturbance. — 33 


functions of the cosine of mot + € — ™ and its multiples ; and assume 
y=B+eB, +B, + 


By substitution, and equalling separately to nothing the terms multiplied by 

the different powers of e, we have 
vB a B, a’B 
qe tm B=, es + 1B + Ey = = 0; &e. 

The first of these gives B = c cos (m7+). This value substituted in the 
second, it will give P,; and so on. But in reducing the periodicals to one ar- 
gument, we should have a series of sines and another of cosines, unless we make 
k=&—m7. In this case we must have « —™ =e,—7,, and making nm = 
n, (1+6), we must develope thus: 


COS (MT + € — 7%) = COS (N/T + & — MH) — bn7 sin (N,7 + & — ™m) — Ke. 


The use of this is, by suitably determining 4, to take away an improper 
term. In some cases, perhaps, both sines and cosines may be necessary. 
But perhaps this will be more ees ae done thus: 
i 
— \1+ @ cos Os) 5 


Py 


=m (ite, cos (A,,o— 7,)}- 
ButA,.=A.- Therefore we must have m=7,, or we should have both 
sines and cosines. And then we shall have 


h? ) 1 h’ 1 
— —1)— =cos (A, — = cos (A, , — ={|— —1)-; 
(Fe — 1) | = 008 (Ro — mo) = c08 (Ro —m)) =(A 12, 
or, after a little reduction, 

Hrapelie eas Ar (EE eo 


U 


PPo €,  MP,0 &, 
But po =p,of- Substituting this value, we easily find 


i>. €\ - I? e& 
? z=(1- 2) pot pe ei 


i _&—% Pio ae (1 =3 
& Ll —e? age, ae, (1—e@’) 
VOL. XXII. FE 


or, 


34 The Rev. Brice Bronwin on the Theory of Planetary Disturbance. 


Make e =e,(1—a), @ being a small quantity of the order of the disturbing 


force ; and we may write 
1a 
OA Se pene 

& Ao Ao 


To which we may add from the third of (2) ; 


dy _ ay C 


dr até 
A, B, and C being functions of ¢ and a easily found. But p,.o, a function of 
A), and, therefore, a function of m7, must be converted into a function of #7 
by Taylor’s theorem. The results obtained are much more simple than those 
obtained by M. Hansen in the same case, and I think also more convenient. 
If we wish to make m = 7, + y, we have 


cos (Ay — 7%) = cos 9 Cos (Ay — 7) + Sin 7 Sin (Ay — 7), 
hy d, : : : 
a se = sin (A, — ™) = cos 7 sin (A, — z,) — sin 9 cos (A, — 7,), 


he 1 
cos (A,,, — 7,) = cos (A, — 2,) = hie 1 = 
40 ! 


Between these we may eliminate sin (A, — 7,) and cos (A, — 7,,) and obtain 
a result involving a but I shall not pursue the subject further. 
its 
We may satisfy (2), and all the requisite conditions, by simply making e, = ¢,, 


a : ; 

(y= Gp = =o and n,€,=m,t; but this would not leave us any arbitrary con- 
/ 

stant except a,, and we might have an unsuitable term which we could not 


get rid of. 
We must now proceed to another class of formule, some of which will be 
wanted. But I shall not confine myself to these. 


dé 1 : : : Je 
Let (=) Fi (=) denote that + is to be changed into ¢ in these quantities, 


after the operation of differentiation is performed. And thus this change will 
be denoted in other cases. Thus from (2) of the first section we have 


(4) maa 
a a | (3) 
BOY ee) 
(#) am hp? ; | 
Eliminating iF between the first of these and (3) of the first section, there 
results 
(4) dz ae 
Se pe 
or, (4) 
(dg _ dw fe Enr* | 
( jain ae 
But it is obvious that ($) + (ZF) = —— Therefore, 
do Enr® P 
(ir) - aaat ©) 
dp_ di, .dpdt 
Per ap Pag FE ae ae Whence 


(dp\_ [dé dé 
()=" ) z+ +e% @). 
But (Z) =5= 0, from the manner in which the variable elements are 


ded 
found ; and us = = s Therefore, 


dé do 
“(F) a) + + 0g (2)- °, 
(de _ &nr dr, 
di) =k de} cS) 
and since also we necessarily have 
* (d&\  [dk\ dp. 
) +a) =a 


F2 


which by (5) gives 


36 The Rev. Brice Bronwin on the Theory of Planetary Disturbance. 


therefore, 


dé\ dp €nrdr, 
(Ge) -F-ee Ce 


The preceding are all the formule of this kind that are really wanted ; but 
I shall give some others, on the ground that they may possibly be some time 
found useful. If we could change 7 into ¢ in higher differentials than the first, 
we might, perhaps, by differentiating the fundamental theorems, or any of the 
others, relative to 7 or ¢, and then changing 7 into ¢, find some new theorems 
which might be made available for simplification, or some way useful. 


From (2), section (1), or os = —1, putting + + @ for ¢ we have 
dp Dh dé 
et Therefore, 
ep. DP els /dé\ : 
( = “has ae) 
or by (7), 


ap\ 2h dp. Enh d(r?) 
(a) 


=~ ph dt wiiee age. (8) 
Equation (4), section (1), gives immediately 


And from (2), referred to above, after putting + + @ for ¢, and differentiating 
relative to t, we have 

Gp 1 dh_ 2h dé 

drdt he® dt he dt’ 


@p\ 1 dh 2h /dé\_ 
drdt) hp dt h,p® \dt)’ 


or, by substitution from (6), 


(=) 1 dh _ €nh d(r?) 


drdt]~ hp dé Wp dz ° ca) 


I might extend this list, but not without some difficulty ; and as I am not 
sure of its utility, I shall here leave it. 


The Rev. Brtce Bronwuy on the Theory of Planetary Disturbance. 37 


We now turn to the equations (1) of this section. The first contains both 
é and @; the second only ¢. This last, therefore, is preferable ; and as we 
do not want them both, we shall take this, which reduces to 


to, ao (ee ae dp ap (1 z= 3 


dzdt \dr d7* dv dr 


dja ag drdt \dr dz dt dv 
For the first and second power of the disturbing force only, 


ap dpd'¢ dpdo | dp dp dp 
hE ce aia deat 8 a ae as 


Putting this value in the second member of the above, we have 


Pb _ dd db dp dd dp ag : 
dedi "8 ot ae ae dt Oe a Nes. 
fy 42H _ (2 , —y) VA8F sin (nv) 20ER _ Ende") | 
B=) 14a —(; + 3s )ecos( 0) bay tsin(n Soe ere 


3. The values of @ and é would be very troublesome to find ; for they 
would contain a great number of terms having + —t¢ in their coefficients, and 
which in w and 6 would vanish ; and many which, when 7 is changed into ¢, 
would unite with others. If, therefore, we could get rid of these quantities, 
we should greatly diminish the labour of integration. This, happily, we are 
able to effect. To accomplish it we will develope § relative to these quantities. 

‘ SIU ate wie dp\* ht , do, .d¢? 
Equation (2) of section (1) gives STi ( + +) i (1 si 435). 
dp) _ d(2)_ nde) od#)_ Up de , dle) hdl) 
pe Te de Weutaeg ehage te Sad ae ad Fe 


odl( &) 
P, dr ~ 
changed p into p,é, v into v, + nt, and A into A, + Ent. Make, therefore, 


5 hi 2up, 2 Qu 1 dR 2 2p, dk 
(S)={5 “it~ (5 + Fh) 9.08 2) } aa + sin (A, — 0) 2 
én apt) 


h dr 


4 


These values are to be substituted in that of S, after we have 


, and 


38 The Rev. Bricr Bronwin on the Theory of Planetary Disturbance. 


up, (25 2h le dk 2p, dR _ 
= tee ie - (7+ f) p, cos (A, — v,) ian do + sin (A,— ”) aye 7 = 
1dR €n d(p?) 
Sa ae Tae 
d(p*) 


Putting the above values of € and [a in that of S, after developing rela- 
T 


tive to £; we have, making p? the value of p, (a function of + + @) when ¢ is 


made perk 3 
ee 5 Wt én ,d(& 


ho ds 


ap 2 ay Enp, dp 9 
Od a ae i) 3 h, de ¢ 2) = 


(s)-(7) (3 ay 4%). poe (1-258) 4 Se Me ED G5 


dz dt h, Pda dr h, dt dy? 


We have now got rid of € Let (S°) and (T°) be the values of (S) and 
(7) when @ is made nothing, or ¢= 7; then, by Taylor’s theorem, 


1 2 2S? 
(S)= oo aS 


(ry a Ao ) 


(2) 


neglecting higher powers of the disturbing force ; since we exclude those of the 
fourth order. Now ¢ enters nowhere but where it appears. 


a Gh dR : 
And putting = for — ae for convenience, 


1 dh | €n d(p”) 
0) — (.@0 ee ut D 
Ge OO eet pamaee 


d(T") _d(S®) , &n api?) 


dr dr h, dv 


Therefore, 


1 dh d(S°) nd En d(p”) pect d°(p"’) 


Pat Og. fh, a ae es eS @) 


Put in (1) the value of (S) given by (2), and that of (7) given by (8) ; 


and we have 


The Rev. Brice Bronwin on the Theory of Planetary Disturbance. 39 


’ r i dg? 1(S° di 1 dh d a 
S=(S°) (1-3 ace qa) + og (1-4 Z) -ae ie) 
En d(pr) dp (1 pt) oe Enp? dp (1-22) + En d(p) dp Fe 
h, 


Qh, dr dr © de dr dt h, dr dr 


g? 2S) Eng a°(p?) dp. 
2 deh, de dr’ 


and 


dr dr 2h dt dr 


en d(p'?) dp* énp” dp Bp 
2h, dr de h, dz dr’ 


on ee dr} "" dr dr 2h dt dr 


g tb _ = (8°) ($ S) RES d(S*) dp _ 1 dh dg’ 


/ 


We must now put these values of S and Ss a in (11) of the last section, 


and we shall find as the result, 


em do ze ee i d¢ 1 dh do ‘ dg 
drdt ne (1 ere dt a eres, Pe dz) 2h dt dr T+4 dt 
do d* 1 db\ &n dl) do ie 1 Ip ai Ds ap re dp ‘ gp a? 8 
dt dr? \~ dr) 2h, dr dr 4dr } dr) "2 


h, dv 
tn POP) 6 db , en dee) op A 
Riis Wea) ie eae ) 


We can do nothing with the last in its present form, on account of the 
terms which contain ¢ and a . But happily these may be driven out by a little 


transformation. Neglecting terms containing the third power of the disturbing 
force, (4) gives 


go) (S°) do ” d(S°) db @? ‘p 1 dhdb_ Enp? db 
dz 


‘0 =—_-]} 
(2) dzdt 


dt dz dz +9, dt dt h, dv 
en d(pit) de 
2h, dz de = 
lo do &p Gp dpdd 1 dhdp €Enp” d’o re En d(pr) do 


ie aime Vas dt det Sh i dv A dh Oh cde as 


With this value we eliminate (S°) from (4), in those terms where the dis- 
turbing force rises above the first power, and we thus find 


40 The Rev. Brice Bronwin on the Theory of Planetary Disturbance. 


a - ve 1¢° do d? 
dco) (5 apt yt 9 9828p pO 


dzdt Pea sis dz dr d+ 
1 dh fd dp, _d° eae 5 a\ dp) 
aa {t(t-tg)- eee h, Va = tia ede 
En et) { db _, 46) &b] é 
oh aie Wide Ce Saye ae (5) 


This has been put under the simplest form. It still contains three terms 
which we cannot manage; but these may be easily eliminated. Neglecting the 
powers of the disturbing force above the first, and integrating relative to ¢, add- 


doy 


ing the correction — de? the value of - = when the disturbing force is made 


to vanish, we have 


— = ae + {(S°) dt = W suppose. (6) 
Now if we include both the first and second powers of the disturbing force, 

we have 

dp _ aw de — dob dh | Enp (d? ¢ | én d(p) (do 

P= WHt toe NE Eta mbes eh, de ‘Nee 


dt 


which gives us neue 


2 2 02 
dp _ ; ee 2 wee dh ee "ee Ap én d(p) Le ae 


dz * dr dr d h, Jdr 2h, dr Jdr 
And 
op 2 do & p a ma ie ey dp br sh 
Teh pede ns? aoa en a 
Make 
d de’ P : 
~ i d? 978 =e 


Now as all the terms in the value of X after W are of the second order, 
and will be multiplied in (5) by quantities of the first order, we may put W 


for 2 in the value of this quantity. Then 
OT 
ae oe ener. dw én d(p°”) 5 
A C= We se \—. ~ Bh, ae | Wat, (7) 


and (5) will become 


The Rev. Bricr Bronwin on the Theory of Planetary Disturbance. 41 


#0 (949 (4 a Ms - 36 58-1958) 


drdt dr dr T 
gels ale A Ee. - , np dX (8) 
Qh dt 2h, dr h, dr’ 


2 


We must now eliminate — ee &e. For this purpose we take 


do _ 19° | ao 
dey sae tO ae 


which squared, neglecting terms above the third order, gives 
a x744Xx° g = c ot 
X44 5 i # ag 


X? 4 3W? 42g — 


is 


—-W?+2W2 ccumeneeal 


Tp AX deo, €O_ 
Wade ae Oe ae 
dX aw s@w 


ea ee ES 


Substituting these values in (8), it becomes 


os d dX dw 2 
dh €n Up) x En? dX 


dt 2h, dr h, dr’ 
7 dX 
€ 
— Wes gwx— yx — FAD par 4 orp (ed. (9) 


By means of this the integral of the preceding is 
2 aw. 
ae =W+o (7+ +4WOr) + eS vee (10) 


VOL. XXII. G 


42 The Rev. Brice Bronww on the Theory of Planetary Disturbance. 


Since (2) -2 i. — ; changing 7 into #, we have 
/ 


2 2 

i =H) = _ ‘A ese LW =) nee (G G@aE ee) Gi 
We have now got entirely quit of and @; and 7 is contained only in p? and 

XA’, which are the same functions of 7 and a,, ¢,, &c., as in an undisturbed orbit ; 

and we may everywhere put them without the sign of integration, and then 

change 7 into ¢. Thus we have virtually got rid of 7, and the result may be 

put under the same form as if it were obtained with only the ordinary time t. 
If we change z into ¢ + w, (3) of section (1) gives 


and 
ht dw €nr 
— n 
p= ja{1- (Et a) + 8}, 


which will give B when ae is known. And we may change £ into e*, and take 


the logarithm of both members, if we wish to have a result in the experimental 


form, which is that of M. Hansen. Or we may change f into 1 + : ; then 


/ 
we have 
r=97, +p. 


But, changing ¢ into 7+, we may employ (2) of section (1), which gives 
and 


If we wish to have a result in the experimental form, this is, perhaps, the 
most convenient. And thus changing é into e, and taking the logarithm of 
both members, we have 


h 
§=}log (7) ~ § log (1+ 58). 


The Rev. Bricz Bronwin on the Theory of Planetary Disturbance. 43 


M. Hansen employs this method, and differentiates relative to 7, by which 


h 


: h 
means he gets rid of 1 loo (“). Thus we have 
g 2 108 
/ 


vo 
Geietes de 
Gn Se do’ 
fay? 
dr 


and changing 7 into ¢, 


ad? 
dt ares 


Wipe TERS 14% 


In this form M. Hansen leaves it. But we might employ (8) of the same 
section to reduce it, or to give a distinct form; but that would introduce 
ua. 
jp again. 


/ 


4. We now proceed to the determination of the latitude, and the reduction 
to a fixed plane. Make o the sine of the latitude, 7 the inclination, and $ and 
4 the longitude of the node on the plane of the orbit and on the fixed plane 
respectively, $ having an origin fixed on the former plane. By making the 
plane of the orbit to turn round the radius vector an infinitesimal space, it is 
easily seen that, 

dS = cos idé ; (1) 
and we have the known formule, 
di 1. dR cost dR 
dt hsini dd hsini dS’ 
ds cost dR (2) 
dé hsini di’ 
G2 


44 The Rev. Brice Bronwin on the Theory of Planetary Disturbance. 


I shall give some theorems here similar to (6) of the first section, without, 
however, making any use of them. 
We have o = sin? sin (v—$) = sin 7 (sin v cos 3 — cos v sin $), 2 = sin? 
C 
_A oe BPR 
cos (v — a2 = 2 — sin? cos (v—$). Therefore, — % qm nt cos (v — $) = 


sin 7 (cos v cos $ + sin v sin $). From these we hay find 


: as o oe arte 
osinv + — — cos v= sin 2 Cos F. 
h dt 
r? do 
—ocosu+ - sin vy =sin isin 9. 
h dt 


Again, let « be the same function of + and the variable elements that o is 
of t and the same elements ; so that 


eh 


«= sin? sin (A — SJ aE den ; Sinz cos (A — $); 
P 


and, as before, we shall have 


canines Ie oN ero conte: 


h dr 


2 
= cosine = “* sin A =sinisin S. 


h drt 


Equating the two sets of values of sini cos $ and sin? sin $, 


ria 2 
asinv +” & cosy =« sin A + +5 = cosa, 
2 p dk 
o cosy — >  sinv =« cos A — & — sin A. 


By multiplying these by sin v, cos v, sin A, cos A, and adding and subtracting 
the products, we shall have no difficulty in deducing 


o = k COS (A—0) & © sin (Av), 


ale 


= =r sin (A —v) +© F cos (A — 0). 


The Rev. Brice Bronwin on the Theory of Planetary Disturbance. 45 


oe) 
x= 0 cos (A—v) +5 7 sin (A—v), 


di 
_ =—osin (A=) +7 cos (A —v). 
These two sets of equations correspond to (5) and (6) of the first section. 
From "- = sin 7 cos (v — $), = sini cos (v — $), and S = eos i 


sin (v — 3); we easily find 
de ids do .coand 
asa de tdi ent’ 
de pp de dk cos 7 
dS” hdr’ di sin 2’ 

which may be found useful. 

The part of the disturbance function depending on the inclination of the 
orbit to the fixed plane is very troublesome to express by means of 7, 5, and 8, 
and the corresponding quantities 7’, $’, and 6’, relative to the disturbing body ; 
and when either $ is expressed by means of 6, 3’ by means of 6’, or the latter 


by means of the former, would contain a great number of terms. But it may 


be expressed very simply without these quantities, by means of the latitude 
and the reduction A, and the corresponding quantities ¢’ and A’ relative to 
the disturbing body. Thus we should have v— A, and v’ — A’, and v’ — A’ for 
the longitudes on the fixed plane, and 


ha cos @ cos (v — A), # = cos ¢ sin (v — A), = =sin 9; 
ie. y Z 
77 = 0s g' cos (v' — 4’), “7 = C08 ¢’ sin (v’ — A’), 7 = sin ¢’. 
Bite "4+ 22' 
But cos x = a fi ; therefore, 


cos x= cos ¢ cos ¢’ {cos (v— A) cos (v’ — A’) +sin (v—A) sin (v' — A’)} + 
sin @ sin ¢’ = cos ¢ cos ¢’ cos (v—v' — A+ A’) +sin @ sind! = (1—o")} 
— /\2 
(1-0)! c08(v—v')4sin(o—')(A—A)—cos vv’) ATA — &e. roe! (4) 


46 The Rev. Brice Bronwin on the Theory of Planetary Disturbance. 


We suppose here that o and o’, and therefore also A and A’, are small, as in 
the case of the moon and the old planets. 

Making for a moment 7, the projection of the radius vector, and v, the 
longitude on the fixed plane, and comparing the differentials of the areas des- 
cribed on this plane and that of the orbit, we have 


ae) — 2 — 7 2 
cos 7 dy = 17 dv, =1° cos’ ¢ dv,, 
and cosi dv = cos’ ¢ dv, = cos’ @ (dv — dA); or 


dA 


= cos? 6 —. 
z dt 


; GMI? ge ONE Pra uae 
(cos p— cost) 7 =cos os OL (2sin 37 sin a) 
Whence we derive 
r? dA 


2 sin? 5= sin’ d + Wi ae cos* d, 


day eel ee 
Gores Om 5 ae 6). 


And putting o* for sin? ¢, 1 — o° for cos’ ¢, 


ey Oh g RO 4 
2 sin Reh ie ae | 
ae z 2 sin? = — 0? | ” 
di ri(1—e) 2 , | 
The equation d3=cos 7dé@ gives ee ds, andd (@—$) = ( : : -1) ds ; or, 
cost cos 7 
asin? 
d(@—S$)= aa d3. And by integration 
ae 
6—-S$=2 eT dS = a suppose. (6) 


Let A, = (v—3) —(v,— 6), where v, =v—A. Then 
sin A, = sin (v — $) cos (v, — 6) — cos (v — $) sin (uv, — 8). 


But by the well-known theorems of spherical trigonometry, sin (v — $) = 


The Rev. Brice Bronwin on the Theory of Planetary Disturbance. 47 
eu ae , sin (v,— 0) = = —f , and cos (v,— 0) = oF conse) Therefore, by sub 
sind’ cos @ 


stitution, 


SimeAy— gat : 


; 

— —— }= tan —tan @ cos (v—3$)= 
sin? tan ) 2 ? ( ) 
sin 


: F tan @ cos (v—9). 
2 cos? 


2 
, rt mek, } r° d. 
But sin A, = A, — 44%, and sin i cos (v — $) = 


o 

Wea Consequently, ,A— 
LA3 tan @ r do _ r o do _ r d Y(1 — a’) 
agi © toh ae eile) a ot dt 

Biles 2) By 

2 cos 9 2h cos 9 2h cos 9 

and A,= B ae + 4A 
2h cos’ 5 


Now A, =v—v,—-$+4+0=A—$+4+6=A +a; and, therefore 


2 


= ae At ey (7) 
1 dt o 
2h cos’ 5 


neglecting smaller quantities, observing that a is of the order of the disturbing 
ba: alt 
force multiplied by sin’ 5 


We want now to aude” > ike nd = 


To do this, we shall transpose 1A‘, 
and, after taking the sit on divide by 1 — $A’, or multiply by 
1 + 3A’; and by means of ie 


= 5 e031 cos (3) = SES, and 
a sin ¢ dt dSdt 
Zn” we shall find 
dA 7 i Oe o 
di 


, ee 
2 


48 The Rev. Brice Bronwin on the Theory of Planetary Disturbance. 


sgt 
2 sin’ = 
dA 1 1 ee aa a P ste 
a = ae (*-) i d@ i a)(+3 eo sme eta 
2 tos" 5 
2 
Sf lmmelee Seie: Dee eth ahh eae 
But - BP 3 aa = = sin’ 7 cos’ (v — $) = sin? 2 — sin’ 7 sin? (v — $) = sin*7 — o°. 
Therefore, putting this value in the preceding, we have 
2 sin? = 
aX A 1 o—sin*?z , es 2 Be a ar 
Oe cao (Gt) e)- ar ee) 
2 cos’ 


But the formulz we have obtained are not convenient for actual applica- 
tion ; it may be well, therefore, to give them im series. For this purpose we 
make sini = s, sin(v—$)=y7; theno=sy. But as, in the first differentials, 


d _ @ : 
the elements do not vary, we must make Zo ae and in = we must not dif- 


ferentiate 5. 
Now, expanding »/(1— o’) in (7), we find 


2 
Ts 


2heos* 


= 


= (ot do! + fot) — a + bas, 
9 


neglecting smaller terms. Or, 


rs? Dans. 4,05 LAs 
j= al pnt 48m + $s*n?) —a+¢ AY. 
2hcos?— 
2 
But 
Maye - ot 
1 enon 8 nel cos alle Day oa ste 
aera Te tae > = 2 +494 755% 


2 1 s Ss Se 
2cos?= 4sin?— * cos? 
2 2 2 


Substituting this value, we have at length, 


_Pe dy 


A= laut+s (37 + i) + 8 (en + 7 ter + 50)} —a+ $A’; (10) 


The Rev. Brice Bronwin on the Theory of Planetary Disturbance. 49 


where some small quantities are retained, which, perhaps, are not wanted. 
In taking the partial differential coefficients of A, it will be better to find 


dA dA 
ast and not ee 
dA 2r°s dy da 


ds hh de 21 t 8 (at dt) +9! (Bo + Boa + ent) | 4 da me 


: ‘ 1 
Write this for a moment, = =M+%t? > Transpose the last term of the 


second member. Then (1 — 3A’) = = M; whence = = M (1- 4a*y1= 
M (1+ 3A*); and 


dA 2s dh é - 
aie Ras - {ay sper (y af 37°) +84 (en + 3? at: 37)} (1 + $A’). (11) 


aA dy dv ih 

Preparatory to finding as We may observe that qi = 098 (v—$) a 
dy hws h dy 

cos (v—$); and, therefore, 7 i Ce Pour Also, qs =~ 008 


2 rt dy? : ee ‘ 
gr as and 73 apt = 00s (v—$) =1-—sin (v—$)=1-7. We 


ii 2 sin? 
dg — onlan + 8 n+ dof) + 3! (Fyn + ah + Aa’) — 


cosz 
(Lf) (d+ 5 (b+ Sy?) + 9 (Ay + eo? + Lent}. 


By further reduction, and treating the equation with regard to A as in the 
last case, 


dA 
dS SIR APH (OR + bit ta) +o (— dy — peat dd Bap) 
2 sin’ 
3A’) — — (1+ 3A’). 
(1+$a*)-—— (1 4. Ja’) 


VOL. XXII. H 


50 ‘The Rev. Brice Bronwin on the Theory of Planetary Disturbance. 


se it 
2 sin? — - 
Sa? al Deas aA INT 1 : 
= = —— = — - 1 =; - l=} 
cos 7 cos 2 COs 1 (1 — s’) 2 


Therefore, 


1A 9 9 
ogee (—$+497 +m) +5 (—3-qor to +37) {(1 + $4’). (12) 


But 


Since 2 sin’ = S = 1-cosi=1—Y(1-s*) =} + s+ hs". Putting this 


value in (5), nit developing the terms, it becomes 


—=5 ie (b-7) +8 +37 —1) +8 Get br t+ 43n'—n)}. (3) 
We will now transform (2), so as to introduce o and A, or rather y and A. 
ds : 2 cos'2 dk 1-—s' dk 


di aE “hsini dS hs dS’ 
dS cos? 2 dR 1—s dR 


dt Asint. ds = Sie- ds” 
Or, putting sy for o in R, and introducing the partial differentials of the new 
quantities, 


ds _1—s /dR dy _dRda 

a ts & ds * da 7s) 
ds Ls (die (hinds 
date ha (F + aa 7) 


| 
| (14) 


: Lag Ae 
It may not be amiss to find 2 sin* 5 separately. Thus, % being the mean 


value of 7, or its value when the disturbing force is nothing, and, therefore, a 
constant quantity; we have 


2 sin? — = =e sin’ - +2 jdsint | ‘2 sin? at fsin di = 


Bouas jet ie ie [aR dy dR da 
Sint Te eae a oN ge AS 


The Rev. Brict Bronwin on the Theory of Planetary Disturbance. 51 


1 dR dy ,1dRda y 
Make ar dy dS ate dA oes =P, to abridge. Then 


2 sin’ =2 sin? + {cos iPdt = 2 sin’ +{Pdt—2 fsin’ 5 Pat. 


But substituting this value of 2 sin* 5 under the integral sign of the second 


member, 


2 sin? - = 2 sin? 3 + cos % { Pdt — 4 ({Padt) + 2 | Padt { sin? 5 Pat 


at 
3 
By continuing these operations, we find 


2 sin’ 5 Si sin’ ® + C08 ty { Pdt —} cos % ({ Pdt)’ + 3, cos % esis &c. (15) 


This may serve to eliminate sin® 5° But since 2 sin? == =i Cos a 


¥Y(1—sin? 2) = Fsin? 7 + } sin* 7 + +), sin® i + &c., it may also serve to elimi- 
nate sin? 7 and sin 2, if we should find it convenient to do so. 

It is much easier to find r and v on the plane of the orbit, than to find the 
values of the corresponding quantities on the fixed plane; but it is more diffi- 
cult to find the latitude in the former case. It is very troublesome to find it 
directly from the variable values of the elements 7 and $; and yet we must 
have the values of these quantities separately to a considerable degree of ex- 
actness in order to find a. M. Hansen has found the latitude by means of sin7 
sin $, sin? cos $; which is a much better method; and he has found a by means 
of these latter quantities, or rather functions derived from them. But this is 
attended with a great deal of trouble. I propose to pursue a different course, 
and to find sin 7, or s, separately, by the equation given above for the purpose, 
and then to find y. To do which I shall find 


y =sin (4 — 39 — ynt), 


zx being a constant quantity. This is finding a function of $ + ynt. 


dt 
dy _st/dR dRdA 1% 4 
5 |e fav de i dAy de) fds < eS 


H2 


52 The Rev. Brice Bronwin on the Theory of Planetary Disturbance. 


It must be observed, that ynt is the uniform regression of the node, and ¥ is to 
be so determined as to take away the constant terms from Q. 

Now y% = sin (#—%,) the value when the disturbing force is made nothing . 
therefore, integrating, 


; d. 
y =sin (a — %) + Tas Qdt. 


For a first approximation, we ace! = =— cos (2 — 3,); and after the in- 


Sa 
tegration is performed, we may make « anything we please. We shall make 
v=v+ynt=v,+ Ent +ynt. Then y =a, and we shall have 


o = sin(v + ynt — S) sale Qadt. (16) 


After this substitution has been made for z, and v replaced by v,+ Ent, v,, being 
a given function of z, may be allowed to remain, or may be developed in terms 
of z, and z may be developed in terms of ¢. 

We may make y = sin 7 sin (a —3—-ynt) = sin 7 cos (3+ ynt) sin a—sini 
sin (3 + ynt) cos a = p sin a — q cos z. 


p =sini cos (3 + ynt), g = sini sin (3 + ynt). 


tb = cos/ cos ($+ mt — — sin? sin (3 + ynt) Gr + 7"). 
dq _ 
ee 7 sin (3 + ynt) “ = “ + sin i cos (3 + ynt) at). 


Or, 


dp cosi di ds a _pds_ ae 
dt sini dt /\de sal Fe aa NGL 


dq___ cost di ds q ds ds 
a! smi dt? (8 on): side ?\ah tr): 


We may substitute in this, for gs and ca their values from (14); but as I pre- 


dt dt 
fer the former method, I shall not pursue this further ; nor is it necessary, since 
any one who is desirous of doing it may easily carry it through. We may ob- 


The Rev. Brice Bronwin on the Theory of Planetary Disturbance. 53 


serve, however, that making ép, ég, &s, 63, the alterations produced in p, q, &e., 
by the disturbing force, we have for the first power of that force, 


whence, observing that s*= p* + q?, we have 
ete atl ke Cpe ee a 
é s 


Thus we find the alterations produced in s and $ from those produced in p 
and g. And in like manner we may find the alterations depending on the se- 
cond power of the disturbing force. 

In this section we have taken no notice of the development of 7 in the for- 
mule where it has appeared. Making r=r, B, we may either let it stand thus, 


or put from (3) section (1) its value in terms of — which we easily find to 


d 

be 
es dw €nr\~* 
emp (l+ +4) 


Then we shall have only r, and v,, besides the terms depending on the latitude, 
to develope. These are given functions of z =¢ + w,and may, therefore, be de- 
veloped together by Taylor’s theorem. 

We might have developed the value of S in (11), section (2), relative to é 
and @, differently. 

Since the difference only of A and v enters into the composition of S, we may 
change these quantities into A, and v ,, or into the anomalies A,— 7, and v,—7,. 
Using for simplicity , and v,, and making 


Te (- 5) 2cosv,dR 2sinv, dR 


Te 


h dv Fi h dr’ 


Nis 1 p»\2sinv,dR 2cosv,dRk 
Oa) Yom de Tira Wie 


we have 


54 The Rev. Bricr Bronwin on the Theory of Planetary Disturbance. 


my 2Qup\ 1 dk én d(p’) 
sa(1+ i) oS — pcosA, M — p sin A, N ——- at 
is ae de’ 
Ve eliminate < from this by putting p, ia t— +3 a for p=p,é. 


Let (S) be the value of S when p is changed into p, oe and we have 
/ 


S : hi Peeled (a dq? 
S=(S)+{ (p,cosd, I+ p, sin) mos io} (ae - 3 95) + 
4 / 


end ( , (dp d¢ 
hale eae) p 


Eliminate (p, cos A,J7 + p, sin A, NV) 3f - (f- 3 a) by 


dr *dr 


1 feats )\ dk En (pi 
oe (+ h oe) ‘dv Til, cos r, M+ P, sin A )N)- 7 au ; 


/ 


and we find as the result, 


_1dk me d(p; l dp 
sac {0-840} (8 048), 


dr da 
én d ty dp d¢ 
h, dtl? \de de? \. 
Make (P) = (8S) =s an a Then, 


. dp a’ fa! lia(de de) 
S=(8)-PUZ AZ aa dr ge as) 


We now develope p, and A, by the powers of @; so that (S°) and (P”) will 
have only p? and A’, which are elliptic functions of + only, with the constant 
elements a@,, ¢,, &¢. 
ue Me gp a(S?) | 


(S)=(S) $95? 4 EE) 


6 


The Rev. Brice Bronwin on the Theory of Planetary Disturbance. 55 


d( P’) dp? 
— 10 4 2 S07 / 
(P)=(P")+ @ dt 2 Pp—P; +o dt "i 
And by substitution, 

ia US") _ a poy Ib , En Apr) dp | Emp)? dp /, _ dp 
S55) he dr a ae iy dr dr h, dr : ae 


# POS) apo 46" _ poy UP") , Endo) dH , en Up!) dp 
9 at oe Caan mgr + aa Gis: al, a aa Pa 


To this we must add, 


LdR | én d(p@) en d%(p%) 


NRO = CER 
(=) leh aahe Wat) igh). Bare 


| 1 dR €n d(p") en d*(p%) 
0 = 0 oe ag / = / 
OS OT cael ae Ga a 


5. In concluding this paper, I will give a brief sketch of a transformation of 
the differential equations which determine the place of a disturbed planet, 
which I have never seen noticed, but which I think is deserving of some con- 
sideration. 


Make Q = — - + R; the equations with reference to a fixed plane are, 


Suppose now a plane always to make the constant angle ¢ with the fixed 
plane, 7 being the mean inclination of the orbit to this plane. And let this 
plane slide on the fixed plane in such a manner that their intersection may have 
a uniform motion equal to that of the node, or so that the intersection of the 
two planes may be always the mean place of the node. And let 6 — ant be the 
longitude of this intersection, 6 being constant. 

Let now v, and y, be co-ordinates making the angle 6 — ant with x and y; 
x, lying in the intersection of the shding and fixed planes. We have 


56 The Rev. Bricz Bronwin on the Theory of Planetary Disturbance. 
z= x, cos (6 — ant) — y, sin (@ — ant), 
y = x, sin (@ — ant) + y, cos (6 — ant). 


We form the two equations, 


cos (0 — ant) (a + =) + sin (6 — ant) (a cihiolas +o) = (1) 
— sin (0 — ant) S + =) + cos (@— ant) & Jy +o) 0. 
But 
cos (6 — ant) = + sin (0 — ant) 7 7 = 
: i a _ dQ 
— sin (@ — ant) dn + 08 (@— ant) ae 
Therefore, 
ay. dQ 
cos (6 — Pay i + sin (@ — ant) —> We tae: = 0. 
h & a 4 7Q_ 
sin (0 may ae — ant) tag =o: 


Substituting for — we and —% oe their values in x, and y,, we have 


de” ae 


dx, dQ dy, Boca 
da a ewe 
*y, , dQ da, Se ae 
de Paap eee a —an’y, = 0. 


Or dropping the distinctive marks of z, and y,, as tending to produce con- 
fusion, and as no longer necessary : 


Oe + 2 + an Yt — ante =0, | 
dt. dt | @) 
dy fos! i a 2 


We now take the new co-ordinates y, and z,, y, lying in the sliding plane, 
and z, being perpendicular to it ; and, consequently, we have 


The Rev. Brice Bronwin on the Theory of Planetary Disturbance. 57 
y=Y,COSt—2Z, 81, Z=y, sin? +z, Cosi. 


Proceeding by exactly the same steps as before, we find 


a’y, dQ dz ; : nee 
aan 2an cos Jee a’n’ cosi (y, cost — z, sin7) =0, 
pelt Ed ayes : ee 
dal a + Qan sin i= + an? sin i (y, cost — z, sin 7) = 0 


df “ dz, dt 


Or again, dropping the distinctive marks of y, and z, 


dy dQ da 71 
aa a Qan cos i= — an’ cosi (y cost — z sin?) = 0. | ie 
az, aQ dx renee ; ae at 

az + qe t2ansini s+ an? sini (ycosz —z sinz) = 0. | 


Again, x, and y, lying in the sliding plane, let «, be the angle ~ + €nt in 
advance of the line of intersection of the two planes. Then € may be so de- 
termined, that , shall lie in the mean place of the apse when projected on the 
sliding plane, or in any other position we please. And as before, 


«= x, cos (m + Ent) — y, sin (m + Ent), 
y = x, sin (m + Ent) + y, cos (x + Ent). 


Making for a moment, in order to abridge, 


= dh Oe ae ; A 
A =2an OY etnta, B =— 2an cos i= — a’n* cosi (y cos i—z sini); 


we shall have from the first of (2) and the first of (3), by exactly the same pro- 
cess as in the two former transformations, 


cos (7+ eae iP ~ +sin (7+ ent) LY ie ae ie + A cos (7+ €nt) + B sin(a + Ent) =0. 


—sin (w+ Ent) 5% +008 (4 foe sin(z + €nt)+.B cos (m+ Ent) =0. 


Px 
Or, putting for WE and” = / their values, 


VOL. XXII. I 


58 The Rev. Brice Bronwin on the Theory of Planetary Disturbance. 


a + “: +L,=0, 
oe e aa +M,=0. 
And again dropping the distinctive marks, 
tgs t h=O | : 
= +5 + +M=0. 


[irs o iz 2an cos? 5 Sore tori: 5 cos2(n-+6n!) \420n = sin? 5 sin 2 (m+€nt) — 


2,2 ee) 9 v . . @ 2 <_ igi wiles u 
af an +n’ —2abn* c0s"5 —he’n’sin?i+ (sor sin’7—2a€n? sin” 5) cos 2(7+Ent) iy 


i) 


y (ger sin*? — 2a€n* sin? 5) sin 2 (7 + nt) + a’n’ sin 72 Cos iz sin (x + Ent). 


,_ at S a at dy . ot. 
Jes Ti ae) Bn 2an cos? £4 2ansin* eos (m+ent) b- 2an 7, sin’5 sin 2(a+Ent) + 


v 2aEn* cos? Cnt Sint Jaen? sin*i+ (sor sin*i—2a€n’ sin® 5) cos2(2+Ent) \ 
x (da’n? sin’ 7 — 2a€n* sin? 5) sin 2 (a + Ent) + an’ sin 2 Cos iz cos (7+ Ent). 


The terms in Z and J containing z are of the order of the third power of 
the disturbing force multiplied by sin7, and will not be wanted in these cases 
in which 7 is large, and, I think, cannot be wanted when it is small. Most of 
the other terms are of the second order; and as 7 is constant, they are all of a 
very simple character. 

We must add from the last of (3) 


dz. aQ 
Ee 5 
oat aa —+N=0. (5) 


N= 2an sini Fa an’ sini (ycosi— z sin?). 


The Rev. Brice Bronwrn on the Theory of Planetary Disturbance. 59 


The term in N containing z is of the order of the third power of the dis- 
turbing force multiplied by sin? 7, and cannot, I conceive, in any case be 
wanted. 

We may transform the co-ordinates 2’, y/, and 2’, of the disturbing body 
in like manner to a sliding plane, and to a similar situation on that plane. 
Thus, marking all the corresponding quantities relative to this body with an 
accent, we have 


a’ = ay cos (6’ — a’n’t) — y{ sin (6 — a’n’t), 
¥ = 2, sin (6 — a’n't) + ¥{ cos ( —aln't), / = 2). 
= 2, y= y, cos? — zi sin’, 2, = Y, sind’ — z, cos 7’. 
a, = x; cos (7m +6/n't) — yj sin (7m + é'n't), 
Yo = wy sin (x! + E'n't) + y, cos (w+ €'n't), zh= zi, 


But we may transform 2’, 7’, and 2’ to the plane of the orbit of the disturbing 
body, if we please. 

To find the latitude, marking the letters in the second member with the 
number of the transformation to which they belong, we have 


Z=428ini+ z, cos 7 =a; sin 7 sin (7+ Ent) + sin i cos (7+ Ent) +2, cos i. 


But o being the sine of the true latitude, s the sine of the latitude relative 
to the sliding plane, and f the anomaly, or the longitude measured from the axis 
of x after the last transformation : 


z=Pro, t;=rcosf, y,=rsinf, and z,;=rs. 
Therefore, by substitution in the last, and dividing by r, 


o =sin? {sin (7+ Ent) cos f+ cos (++ Ent) sin f} + s cos? ; 
or, 
o=sini sin (f+7+€nt)+scosi. (6) 


Thus the latitude is very easily found. 
Still marking the letters according to the transformation to which they 
belong, 


Yi = Y2 COS 1— Z, Sin i= z, cos isin (w+ Ent) + ys; Cos 1 cos (7 + Ent) — z; sin 7. 
12 


60 The Rev. Brice Bronwin on the Theory of Planetary Disturbance. 


Let'v be the longitude on the fixed plane, measured from its intersection 
with the sliding plane, 
y, =P sin 2, 
the rest as before ; then, by substitution, 
sin v =cos i {cos f sin (7+ Ent) + sinf cos (7+ Ent)} —ssinz. 
Or, 
sin v= cos isin (f+ 7+ Ent) —s sini. (7) 
This will give the longitude when 7 is large ; and when it is small, we can 


without difficulty find v itself without finding its sine. 
I must, in conclusion, repeat what I have before said, that I think this trans- 


formation worthy of consideration. 


GuNTHWAITE Hatt, 
NEAR BARNSLEY, YORKSHIRE, 
Nov. 13, 1848. 


61 


IIL.— On the Mean Results of Observations. By the Rev. Humpurey Luoyp, D. D., 
Presipent; FF’. R.S.; Hon. F.R.S.E. ; Corresponding Member of the Royal 
Society of Sciences at Gottingen; Honorary Member of the American Philoso- 
phical Society, of the Batavian Society of Sciences, and of the Society of Sciences 
of the Canton de Vaud, &e. 


Read June 12, 1848. 


1. Tue problem in which it is sought to determine the daily mean values of the 
atmospheric temperature or pressure, from a limited number of observed values, 
is one of fundamental importance in meteorology ; and, accordingly, many solu- 
tions of it have been proposed by meteorologists. These solutions are derived, for 
the most part, from the known laws of the diurnal variation of these elements. 
Many of them are accordingly applicable only to the particular cases considered 3 
while for others, which are really general in their nature, that generality is not 
established. It is the object of the following investigation to supply this defi- 
ciency, and to show in what manner the daily and yearly means may be ob- 
tained in all the periodical functions with which we are concerned in magnetism 
and meteorology. 

2. It is known that the mean value of any magnetical or meteorological 
element, for any day, may be obtained, approximately, by taking the arithmetical 
mean of any number of equidistant observed values ; the degree of approxima- 
tion, of course, increasing with the number. A somewhat more exact mean 
may be deduced, as has been shown by Cores and Kramp, by combining the 
equidistant observed values in a different manner; and Gauss has given a me 


thod, whereby the values of the integral, [ "Cae, may be obtained with still 


greater accuracy from the observed values of the ordinate, U, corresponding to 


62 The Rev. H. Luoyp on the Mean Results of Observations. 


certain definite abscissx.* But in the case of periodical functions, it will appear 
from what follows that the refinement of Corrs is unnecessary; and, in the 
case under consideration, there are practical reasons of another kind for ad- 
hering to the method of equidistant observations, and which, therefore, deprive 
us of the advantages of Gauss’s method. 

3. Any periodical function U, of the variable z, may be represented by the 
series 


U = A, +A, sin (x +a) + A; sin (22 + q) + As sin (3x + a) + &., 


in which the first term, Ao, is the mean value of the ordinate U, and is ex- 


pressed by the equation 


+ 
Aen ah Ude. 


This is the quantity whose value is sought in the present investigation. 
It is obvious that the values of 7 return again in the same order and 
magnitude when « becomes « + 27; so that if « = at, the period is represented 


by =e If then 2x be divided into m equal parts, so that the abscissz of the 


An 2(n — 1) 
— 


: ees 2 
points of division are 7, «+ = «dp Se &e., o + z , the sum of the 


n’ 
corresponding ordinates will be 


=(U)=nA,+Aiz sin (4 +a) SASS sin} 2 («+ =) +a | 
: Qin 
+ A;> sin | 3 (2+ =) +a} + &c. 


in which 7 denotes any one of the series of integer numbers, from 0 to n — 1 
inclusive. The multiplier of 4,,, in the general term of this series, is 


>= sin {m(2 + =| + an } 
n 
: Qimn . 2imr 
= sin (mx + adn) } cos Tpawicee (mr + an) Z sin a 


* Commentationes Societatis Regie Scientiarum Gottingensis, tom. iii. 


The Rev. H. Luoyp on the Mean Results of Observations. 63 


But, when m is not a multiple of n, 


2imx . 2ima 
> cos ao =0; sin aap Oo 


and, therefore, the preceding term vanishes. When m is a multiple of n, 


2Qimx 2imx 


= cos =) Zain —— = 0;* 


and accordingly the term is reduced to 
m sin (m2 + ay). 
Hence, all the terms of the series vanish, excepting those in which m = kn, k 
being any number of the natural series, and there is 
(0) = Av A, ain (ar + dy) + Ag, sin (Qnx + ayy) + &e. 


That is, the arithmetical mean of the n equidistant ordinates is equal to the sum 
of the terms of the original series of the order kn, whatever be the value of «. 
The original series for U7 being always convergent, the derived series, 


which expresses the value of ~2(U7 ), will be much more so; and, when the 


* These results are easily established. The roots of the equation y" — 1 = 0, being 


4 > 2ir . ir : 
comprised in the formula cos —— + V¥(-1) sin —, the m* power of any one of these roots is 
n n y 


=e wa) an 2ima 


cos 


; and the sum of the m" powers of the roots is 


95 aie 
© cos SZ + (- 1) S sin A 


Now, when m is not a multiple of n, this sum = 0, and therefore 


2ima - 2tmz 
= cos ——=0, sin 
n 


7 


as above. When m is a multiple of n, the sum of the m' powers of the roots = n, and 
therefore 


2imr 2imz 


= cos =n, =sin 


This demonstration seems preferable to that derived from the general formule for the sum of 
the sines and cosines of arcs in arithmetical progression, which, in the latter of the two cases above 
mentioned, lead to illusory results. 


64 The Rev. H. Luoyp on the Mean Results of Observations. 


number 7 is sufficiently great, we may neglect all the terms after the first. 
Hence, approximately, A) = _ =(U). 


The error of this result will be expressed by the second term of the series, 
A, sin (nx + a,), the succeeding terms being, for the same reason, disregarded 
in comparison; and accordingly the limit of error willbe A,. Thus, when the 
period in question is a day, we learn that the daily mean value of the observed 
element will be given by the mean of two equidistant observed values, nearly, 
when A, and the higher coefficients are negligible ; by the mean of three, when 
A, and the higher coefficients are negligible ; and so on. 

4. The coefficient A, is small in the series which expresses the diurnal 
variation of temperature ; and, consequently, the curve which represents the 
course of this variation is, nearly, the curve of sines. In this case, then, the 
mean of the temperatures at any two equidistant or homonymous hours is, 
nearly, the mean temperature of the day. The same thing holds with respect 
to the annual variation of temperature; and the mean of the temperatures 
of any two equidistant months is, nearly, the mean temperature of the year. 
These facts have been long known to meteorologists. 

5. The coefficient A; is small in all the periodical functions with which we 
are concerned in magnetism and meteorology ; and, therefore, the daily and 
yearly mean values of these functions will be given, approximately, by the mean 
of any three equidistant observed values. ; 

In order to establish this, as regards the daily means, I have calculated the 
coefficients of the equations which express the laws of the mean diurnal vari- 
ation of the temperature, the atmospheric pressure, and the magnetic declination, 
as deduced from the observations made at the Magnetical Observatory of Dub- 
lin during the year 1843. The observations were taken every alternate hour 
during both day and night ; and the numbers employed in the calculation are 
the yearly mean results corresponding to the several hours. The origin of the 
abscisse is taken at midnight. 

6. The following is the equation of the diurnal variation of temperature : 


U — A, = + 3°-60 sin (x + 239°-0) + 0°-70 sin (22 + 67°-2) 
+ 0°26 sin (3x + 73°-5) + 0°-03 sin (4a + 102°-7) 
+ 0°-14 sin (54 + 258°-6) + 0°-09 sin (62 + 180°). 


The Rev. H. Luoyp on the Mean Results of Observations. 65 


Hence the error committed, in taking the mean of the temperatures at any two 
equidistant hours as the mean temperature of the day, is expressed nearly by 
the term 

0°70 sin (2x + 67°.2) ; 
and consequently cannot exceed 0°70. To obtain the pairs of homonymous 
hours, whose mean temperature corresponds most nearly with that of the day, 
we have only to make sin (2 + 67°-2) = 0; which gives for x the values 


z= 56°4, x= 146°.4, 
corresponding to the times 
t= 3" 46", ¢ = 9" 46". 
Accordingly, the best pairs of homonymous hours, so far as this problem is con- 
cerned, are 3°46" a.m. and 3°46"P.M., or 9°46" 4. wm. and 9* 46” P.M. 
The error committed, in taking the mean of the temperatures at any three 
equidistant hours as the mean temperature of the day, is, very nearly, 


+ 0°-26 sin (3x + 73°:5) ; 


and cannot therefore exceed 0°-26. The best hours are those in which the 
angle, in the preceding expression, is equal to 180° or 360°. The corresponding 
values of x are 

£=80-5, 7=95°-5 ; 
whence 

t= 2'99" ¢= 6 99”, 
Accordingly, the best hours of observation are 


2°22" a.m, 10°22" a.m, 6'22" pu. ; 
and 
6°22" a.m. 2°29" pw. 10*22" p yy, 

By taking the mean of any four equidistant observed values, the limit of 
error will, of course, be less. Its amount, which is the coefficient of the fourth 
term of the preceding formula, is only 0°-03; and, accordingly, the mean tempe- 
rature of the day is inferred from the temperatures observed at any four equi- 
distant hours with as much precision as can be desired. 

7. The law of the diurnal variation of the atmospheric pressure is contained 
in the following equation : 

VOL. XXII. K 


66 The Rey. H. Luoyp on the Mean Results of Observations. 


U — Ay = + -0024 sin (a + 244°-3) + -0089 sin (2x 4 144°-4) 
+ -0008 sin (3 + 27°-9) + -0006 sin (4a + 78-5) 
+ -0001 sin (5x + 228°-7) + -0002 sin (6x + 180°). 


The second term in this formula being the principal one, the mean of the pres- 
sures observed at any two equidistant hours, so far from approaching the mean 
daily pressure, may recede from it by the greatest possible amount within the 
limits of the diurnal variation. The error committed, in taking the mean of the 
pressures observed at ¢/ee equidistant hours as the mean daily pressure, is, 
very nearly, 
+ -0008 sin (32 + 27°-9) ; 

and cannot therefore exceed -0008. It is needless to inquire into the least 
value of this quantity, which is in all cases less than the probable error. 

8. The law of the diurnal variation of the magnetic declination is ex- 
pressed by the equation 


U — A, =+4+ 3'-29 sin (a + 65°-7) + 2/-08 sin (2a + 224°-5) 
+ 0-63 sin (3% + 71°-7) + 0-30 sin (42 + 237°-5) 
+ 0'-13 sin (52 + 114°-7) ; 


the coefficient of the last term being evanescent. Hence the error to which we 
are liable, in taking the mean of the declinations observed at any three equi- 
distant hours as the mean of the day, is, very nearly, 


+ 0'.63 sin (32 + 71°-7) ; 
and cannot exceed 0’.63. This term vanishes, and the mean of the three ob- 
served values will deviate from the true daily mean, by an amount less than 
the errors of observation, when 


m= Aol Ce, 7 = VlHall 2 
that is, when 


$= 2' 25", or, t= 6" 25". 
Accordingly, the best hours of observation, for the elimination of the diurnal 


variation of the declination, are 


ASA Sitty MOP OSA eg OPO Tee 
and 


6'25" a.m, 2'25"™pm, 10°25"Pp.M.; 


The Rev. H. Luoyn on the Mean Results of Observations. 67 


which coincide, almost exactly, with the best hours for the determination of the 
mean temperature. 

By taking the mean of the declinations observed at any four equidistant 
hours, as the mean of the day, the limit of error is reduced to 0'-30. 

9. It appears from the preceding, that any three equidistant observations 
are sufficient to give the daily mean values (and, therefore, also the monthly 
and yearly mean values) for each of these elements, with nearly the requisite 
precision ; and that, by a suitable choice of the hours, the degree of accuracy 
may be augmented as much as we please. But, in determining the parti- 
cular hours for a continuous system of observations, this should not be made 
the primary ground of selection. The error of the daily means being in all 
cases reduced within narrow limits by the method already explained, we should 
choose the particular hours which correspond nearly to the maxima and minima 
of the observed elements, so as to obtain also the daily ranges. This condition 
will be fulfilled in the case of the magnetic declination, very nearly, by the hours 


64a.m., 2p.m, 10P.mM; 


which will, moreover, give nearly the maximum and minimum of temperature, 
and of the tension of vapour, together with the maximum pressure of the gaseous 
atmosphere.* And, if we add the intermediate hours, 10 a. m. and 6 P.m., we 
shall have, nearly, the principal maxima and minima of the two other magnetic 
elements. Accordingly, for a limited system of magnetical and meteorological 
observations, at places for which the epochs of maxima and minima do not 
differ much from those at Dublin, the best hours of observation appear to be 


6a.mM, 10, 2p.m, 6, 10. 


The conditions of the problem are altered, if at any place the laws of the 
diurnal variation have been already obtained from a more extended system of 


* The ternary combination above proposed possesses the further advantage of coinciding, 
nearly, with one of those deduced above, as the most favourable for the determination of the mean 
temperature and mean declination. The errors of the resulting means are found by making 
x = 90° in the third terms of the general formule ; and we thus find the error of temperature 
=-— 0°07, while that of the declination = — 020. 


Ke 2 


68 The Rev. H. Luoyn on the Mean Results of Observations. 


observations. In this case the mean of the day may be inferred from observations 
taken at any hours whatever, by the addition of a known correction; and the 
hours of observation should therefore be chosen chiefly, if not exclusively, with 
reference to the diurnal range of the observed elements. 

10. The next question which presents itself for consideration, with respect to 
the daily means, is one which affects more nearly the reduction of the obser- 
vations hitherto made at Dublin. In the extended system prescribed by the 
Council of the Royal Society in 1839, and followed at the Magnetical Obser- 
vatory of Dublin during the four years commencing with 1840, observations 
were directed to be taken twelve times, at equal intervals, throughout the day,— 
namely, at the even hours of Gottingen mean time. In a system of observa- 
tions so frequent, and extending over so considerable a time, blanks must 
unavoidably occur ; and the question which presents itself here is,—in what 
way are the daily means to be deduced in such a case? 

It has been shown that the effect of the regular diurnal variation may be 
nearly eliminated, and the mean of the day obtained, by taking the mean of 
three equidistant observed values. For the elimination of the irregular changes, 
however, the number of observations combined should be as great as possible ; 
and in the case of the magnetic elements, in which these changes are often 
very considerable, this condition is an important one. 

Now it is obvious that the twelve results of any day may be resolved into 
two groups of siz equidistant results, or into three groups of four, or into four 
sroups of three. Hence, when one result is wanting in the day, the mean may 
be inferred either from one group of six results, from two groups of four re- 
sults, or from three of three. The last of these combinations, containing nine 
separate results, is, of course, to be preferred. When two results are wanting, 
the mean may be inferred from one group of four results, or from two groups 
of three ; of which the latter combination, containing six results, is to be pre- 
ferred. When three results are wanting, the mean of the day can only be in- 
ferred (in general) from one group of three; and when more than three are 
wanting, that mean cannot be generally obtained. 

11. What has been said above applies to the irregular changes of short 
period, such, especially, as those to which the magnetic elements are sub- 
ject. But there are also irregular changes of longer duration (as, for ex- 


The Rey. H. Luoyp on the Mean Results of Observations. 69 


anple, those produced in the atmospheric pressure by the passage of the greater 
aerial waves), which complicate the problem, inasmuch as a different process 
is required for their elimination. 

In the reduction of the magnetical and meteorological observations made at 
the Observatory of Dublin, the civil day is adopted; and the observations being 
made at the odd hours of Dublin mean time, very nearly, the epoch of the 
mean of all the twelve results is mean noon. But in the case of deficient ob- 
servations, the epoch of the mean, inferred from the remaining observations, 
may deviate one or more hours from noon; and its amount, therefore (as com- 
pared with the mean reduced to noon), is affected by an error equal to the 
change which the observed element undergoes in that time. In the case of 
the atmospheric pressure, this error is often very considerable, and much exceeds 
that due to the changes of whose elimination we have hitherto spoken. 

The law of the changes here referred to being unknown, we can only deal 
with them on the assumption that their course is uniform throughout the space 
of a day; and this assumption will, probably, seldom err much from the truth. 
Upon this principle, the effect of the irregular change will be eliminated by 
taking the mean of two or more results equidistant from noon (that is, the mean 
of a forenoon and afternoon result corresponding to the hours w and 12 — w, or 
any combination of such means); and we have only to consider in what manner 
this process can be combined with the elimination of the regular diurnal change. 

Let the mean of the four equidistant observed values commencing with the 
n hour be denoted, for brevity, by IV,; then the epochs of the means IV, 
IV;, 1V;, are 10 a.m., noon, and 2 p. M., respectively; so that the two conditions 
are satisfied by the combinations 


4(IV, + IV;), and IV;. 


In like manner, the means of any three equidistant observed values being de- 
noted by III,, the epochs of the means Id],, II;, 1;, IlI,, are 9 a.m., 11, 
lp.m., and 3 respectively; so that both conditions are satisfied by the com- 


binations 
$(III, + I,), and 4 (IH, + III,). 


12. When, from the number and disposition of the blanks, none of these 
combinations can be had, and therefore both changes (regular and irregular) 


70 The Rev. H. Luoyp on the Mean Results of Observations. 


cannot be eliminated, we must attend chiefly to that which is greater in amount. 
For the purpose of comparing their magnitude, I have taken the differences of 
the successive daily means, for the declination, the atmospheric pressure, and 
the temperature, as deduced from the observations of the year 1843 ; and have 
calculated the square root of the mean of the squares of these differences. The 
results, which may be taken as the measures of the irregular changes from day 
to day, are the following: 


Mean Fluctuation from Day to Day. 


Magnetic declination, . . . Fluctuation = 1’-04. 
Atmospheric -pressure,.2, 2.03 os Sane 0-214 
Atmospheric temperature,. . . . . . . 3°07. 


Similarly, if we take the differences of the yearly means corresponding to the 
successive hours of observation, and combine them in the same way, we obtain 
the mean two-hourly fluctuations, arising from the regular diurnal change. 
These numbers are the following : 


Mean Fluctuation in two Hours. 


Magnetic declination, . . . Fluctuation = 2’.04. 
Atmospheric pressure, . . . . . . . . 0-0065. 
Atmospheric temperature, . . .. . . 1°46. 


These numbers, compared with the twelfth part of the former, serve to 
measure the relative magnitude of the regular and irregular changes to which 
the elements are subject in the same time. We thus find that, in the case of 
the magnetic declination, the irregular change (which is less than j4,th part 
of the regular) may be safely neglected; and we have only to attend to the 
diurnal changes, and to the irregular changes of short period. The daily 
means are, therefore, to be deduced from one of the combinations of Art. 10, 
giving the preference to that which contains the greatest number of indivi- 
dual results. 

In the case of the atmospheric temperature, the irregular change (which is 
less than one-fifth part of the regular) is small; aud we must attend chiefly 
to the latter. The mean of the day is, therefore, to be inferred from one of 


The Rev. H. Luoyp on the Mean Results of Observations. 71 


the combinations of Art. 10, giving the preference to those of Art. 11, whose 
epoch is noon. 

In the case of the atmospheric pressure, on the contrary, the irregular 
change (which is triple the regular) is the more important. The mean of the 
day is, therefore, to be deduced from any combination whose epoch is noon, 
giving, however, the preference to one of those of Art. 11, in which the diurnal 
change is also eliminated. 

13. I now proceed to consider the reduction of the monthly means, in the 
case of deficient observations. 

For the purpose of determining the regular diurnal variation of any magnetic 
or meteorological element, it is necessary to take the mean of an adequate 
number of separate results corresponding to each hour of observation, so as 
to eliminate the irregular and accidental changes. The results usually so com- 
bined are those of each month, Their number is, in general, sufficient for 
the purpose above-mentioned; while, on the other hand, the course of the di- 
urnal change is sufficiently different from one month to the next, to demand a 
separate determination. 

But in the case of deficient observations, the monthly means of the results 
corresponding to each hour will not exhibit, in general, the true course of the 
diurnal change without a correction. Ifa result be wanting at one hour of 
a day, in which all the results are much above the mean, it is obvious that 
the monthly mean corresponding to that hour will be too small, as compared 
with the means of the other hours ; while, on the other hand, it will be too 
great, when all the results of the day in question are below the mean. The error 
will be greater, the greater the variation of the element observed from day 
to day. In the case of the atmospheric pressure it is so considerable, that the 
uncorrected monthly means afford no approximation to the law of the diurnal 
change, in the case of deficient observations. 

The remedy which first suggests itself, in such a case, is to omit all the results 
of a day in which one or more are wanting. This process is inartificial and un- 
satisfactory. The weight of the mean is diminished in the proportion of the 
number of observations combined ; and it is therefore important to employ all 
the observed results in its deduction, provided we can obtain a correction. 
Such a correction is easily found. 


72 The Rev. H. Luoyp on the Mean Results of Observations. 


14. Let « denote the observed value of any element, at any hour on any 
day ; and let a denote its mean value for that day ; then 


r=at+é, 


in which é is the magnitude of the diurnal variation corresponding to the hour 
in question. Let there be m days of observation to be combined; then, summing 
the n results, dividing by n, and denoting the mean values by 2, a, and &, 


r=até. 


Now, at any particular hour of any day, let one of the results be wanting ; 
and let a’ denote the mean for that day; summing the n —1 results, 


Spon O S,a Ls a SidentSs 
And dividing by n—1, 


whence 


- < a — 
The correction, therefore, is + = 


Similarly, if p results be wanting, we find 


eee 
B42 

in which Sa’ denotes the sum of the means of the days on which the deficien- 

cies occur. Hence, the correction to be applied to the observed mean, 2, 
Sa’ — pa 

(= P 

15. The preceding correction depends, as might have been anticipated, on the 

difference of the daily means, for the days of deficient observations, and the 

mean daily mean. With the view of determining its probable amount, I have taken 

the differences between the mean of each day and the mean of the month, for 

the declination, the atmospheric pressure and temperature, as deduced from the 


=ar+é, 


deduced from the n —p values, is + 


The Rev. H. Luoyp on the Mean Results of Observations. 73 
observations of the year 1843 ; and have calculated the square root of the mean 


: : }=(a—a)?! 
of the squares of these differences, or the values of the expression V eee a) 
The values of this quantity, which may be denominated the mean daily error, 


are the following: 


Mean daily Error. 
Magnetic declination,. . . . Daily error = 0/-95. 
Atmospheric pressure, . .*. . . . . . 0.801. 
Atmospheric temperature, . . . . . . , 4°.95, 


Now the mean value of m in each month (the Sundays being omitted) is 26. 
Hence the mean correction, in the case of a single deficient observation, is, for 
the magnetic declination, 0’-04; for the atmospheric pressure, 0-012; and for 
the temperature, 0°-17. In the case of the two meteorological elements, and 
especially in that of the atmospheric pressure, the correction is too consider- 
able to be overlooked; in the case of the magnetic declination, and, probably, 
also in that of the other magnetic elements, it may be disregarded. 


VOL, XXII. L 


74 


1V.—Results of Observations made at the Magnetical Observatory of Dublin, 
during the Years 1840-43. By the Rev. Humpurey Litoyp, D. D., 
Presiwent; J’. R. S.; Hon. F. R.S. E.; Corresponding Member of the Royal 
Society of Sciences at Gottingen; Honorary Member of the American Philoso- 
phical Society, of the Batavian Society of Sciences, and of the Society of Sciences 
of the Canton de Vaud, §. 


Read May 11 and 25, 1846. 


FIRST SERIES.—MAGNETIC DECLINATION. 


i Tue observations at stated hours, in the Magnetical Observatory of Dublin, 
commenced in November, 1838, and were at first taken twelve times during the 
day. Throughout the greater part of the following year, they were made at 
least eight times daily, with some variations as to the precise hours; and, at the 
beginning of the year 1840, the number of assistant observers was increased 
to three, and the observations were made every alternate hour, night and day, 
according to the comprehensive scheme recommended by the Council of the 
Royal Society, and followed at more than thirty observing stations in various 
parts of the globe. This plan has been in operation at the Dublin Magnetical 
Observatory until the end of the year 1843, when it was discontinued ; four 
years’ observations having been found sufficient for the determination of all the 
phenomena connected with the diurnal changes. The observations have been 
since continued upon a different and reduced scale, and with a view to other 
classes of phenomena. 

I shall not, in this place, enter into any account of the instruments, or 
methods of observation, as these will be fully explained in the publication in 
which the observations themselves are presented in detail. I desire merely to 


The Rev. H. Lioyp on the Results of Observations, ec. 75 


lay before the Academy the principal conclusions already arrived at. In the 
present paper, accordingly, I shall give the results of the observations of the 
magnetic declination during the four years referred to;* and in those which I 
hope hereafter to communicate, I shall discuss in like manner the observations 
of the other magnetic and meteorological elements made during the same 
period. 


Diurnal Variation. 


2. A very limited series of observations is sufficient to exhibit the general 
features of the diurnal variation ; but an extended one is necessary, if it be 
desired to ascertain with accuracy the mean amount of the changes. To deter- 
mine these with precision, observations should be taken daily, at equal intervals 
not exceeding three hours, and be continued for one or more years. The 
course usually adopted in the reduction of such a series is, to combine sepa- 
rately the observations of each month, taking the arithmetical mean of all the 
results corresponding to the same hour. In this manner the course of the varia- 
tion (which alters considerably throughout the year) is deduced for each month 
separately; and when the observations extend over several years, the monthly 
means of the separate years are to be again combined, each into a single mean. 

Even this, however, is insufficient. The mean results thus obtained are 
deformed by the irregular fluctuations, which are often far greater than the 
regular changes; and it is necessary to omit the observations taken on days of 
disturbance, before we can deduce a correct mean from the results of any 
practicable series. This is proved in a striking manner by the observations of 
July, 1842. Owing to the great disturbance which took place on the 2nd and 
4th of that month, the difference of the monthly means corresponding to 5 A.M., 
when these observations are retained and when they are omitted, amounts to 
5’-76; so that the observations should be continued for fifty-seven years, in 
order to reduce the error to 0/-1. 

In the final reduction of the Dublin observations, accordingly, all the results 


* TI have taken advantage of the delay which has occurred in the printing of this paper, to 
introduce the monthly mean results of the three following years, in the deduction of the annual 
and secular changes, and to make some other minor alterations of detail. The general conclusions 
originally arrived at are, however, not affected. 


Le 


76 The Rev. H. Lioyn on the Results of Observations made at the 


obtained on days of disturbance have been omitted,—those being defined to be 
days of disturbance, in which the sum of the differences between the separate 
results,and the monthly means corresponding to the same hours, exceeds a certain 
limit, which is about the double of its mean value. The number of separate 
observations actually combined, in deducing the monthly means for each hour, is, 
on the average, 86. The total number of observations employed exceeds 12,000. 
3. The hours of observation, in accordance with the instructions of the 
Council of the Royal Society, were the even hours of Gottingen mean time. 
This being 1° 4" 50* in advance of Dublin time, the observation hours are, 
nearly, the odd hours of Dublin mean time. The following are the differences 
of the monthly mean results corresponding to each hour, and the mean of the 
twelve, expressed in minutes. The positive numbers correspond to easterly 
deviations of the north pole of the magnet, and the negative to westerly. 


Taste I, Diurnat VaRIATION OF THE MAGNETIC DECLINATION. 


1aA.M. 


January, . |41/-09 10"51 40/69 40/61 |+0"69 +4065 [+267 143714 
February, |; 1-99 }+ 1°15 |+ 1-28 + 1:46 |+ 0:92 + 0°59 1 2°14 + 2°80 
March, .. |4 2-08 + 2:49 + 2°37 2°14 1+ 1°85 + 0:58 1 2°94 |+ 2°81 
+ + 2°36 + 2°14 3:15 |4+ 4:55 [+ 2°52 + 0-91 1 1-94 |}+ 2°85 
- 1:79 1 2°54 + 3:94 4 5:16 |+ 2°14 + 0-29 }- 0-95 |+ 1°31 
+ 142-09 + 2:29 + 4:18 + 5:10 |+ 2:55 + 0:04 }+ 1:02 |+ 1-81 
- 142-06 |+ 2-54 4 4-13 + 4°31 |+ 1-99 + 0:09 + 1:49 |+ 1-98 
+1215 + 2°52 + 3:63143°70 1 1:14 + 1-05 }+ 2:06 |+ 2°37 
September, |} 1-77 |+ 2:29 |+ 1-52 + 256.4 0-85 + 2:32 + 3:02 |+ 2-91 
October, « |; 2-06 }+ 1-20 + 1-37 +: 1:30 1: 0:99 + 1:54 + 3:56 |+ 2-61 
November, |+ 1-04 |+ 1-08 }+ 0:87 |}+ 0°58 |+ 0:22 + 1:02 + 2°85 |+ 1:91 
December, |+ 0:59 |+ 0°50 |+ 0-44 }+ 0-21 |+ 0-21 + 1:07 |+ 3-03 |+ 2-37 


Summer, . }+ 2:04 }+ 2°39 } 3°43 |+ 4:23 |+ 1°87 + 0°79 |+ 1°75 |+ 2°21 
Winter, .. |+ 1°47 |+ 1:15 41°17 4+ 1°05 }+ 0°81 + 0°91 }+ 2.86 |+ 2°60 
Year,.... |+ 1.76 1+ 1°77 }+ 2:30 + 2°64 1+ 1°34 + 0°85 |+ 2°30 + 2-40 


4. The general features of the phenomenon, as deduced from these numbers, 


are the following: 
1. Between 6 A.M. and 8 A.M. (the time varying with the season) the north 
pole of the magnet begins to move westward, and, therefore, the westerly decli- 


Magnetical Observatory of Dublin during the Years 1840-43. 77 


nation increases. This movement continues until about 1 Pp. m., when the decli- 
nation attains its maximum. 

u. After 1 p.m. the north pole of the magnet moves eastward, and the de- 
clination diminishes, but at a slower rate than it had previously increased. This 
easterly movement continues until between 9 p. uw. and 11 p. M., when the decli- 
nation is a minimum. 

mt. There is a second, but much smaller, oscillation of the magnet during 
the night and morning ; the north pole moving slowly to the west for a few 
hours before and after midnight, and afterwards returning to the east until 
between 6 a.m. and 8 a. m., when the declination is again a minimum. 

Iv. In summer the westerly movement during the night becomes nearly 
insensible. In winter, on the contrary, the easterly movement during the 
morning nearly vanishes ; and the magnet isalmost in a state of repose from 
2 A.M. to 8 A.M 

v. In summer the morning easterly elongation is greater than the evening 
one; and, consequently, the greatest range is between 7 a. M. and 1p. M. In 
winter, on the contrary, the evening easterly elongation is greater than the 
morning ; and the greatest range is between 1 p.m. and10p.u. The total range 
is greater in summer than in winter. 

These general characteristics of the diurnal variation may be most readily 
understood by a reference to Plates I. and IL 

5. In order to determine the laws of the phenomenon with more precision, 
it will be desirable to express the difference between the declination at any 
hour, and the mean of the entire day, as a function of the time. 

If A be taken to denote this difference corresponding to any time, 


A= (A; cos iz + B; sin a) 


in which z =n x 15°, n being the number of hours, and parts of an hour, in 
the time reckoned from the epoch of the first observation, and 7 any number of 
the natural series. Then, since observation gives the values of A corresponding 
to n=0, 2, 4, &c...22, we have twelve equations of condition, from which 
twelve coefficients of the periodical function may be deduced by elimination. 
The first of these, A,, = 0; the following are the values of the remaining 
eleven. 


78 The Rev. H. Lioyn on the Results of Observations made at the 


Taste II]. CoErFICIENTS OF THE EQUATION OF THE DiurNAL Curve oF DeEcirinarTION. 
B, Bs 


January, . |; 2-426|— 1:119]+ 0:313|- 0-481|— 0:059}; 0:009|- 0:260}- 0:942/— 0°362}+ 0-062\— 07121 
February, |; 2-941/— 1:322/+ 0-607} 0°313}+ 0:097|- 0:018}+ 0:264|— 0°802/— 0:257|+ 0:043|— 0-085 
March, .. |+ 3-988|- 2:110|+ 0°777|- 0°598|— 0°119}+ 0:147}+ 0°688|- 0°739|- 0:112}+ 0-297/— 0-019 
April, .. . | 4:374|- 2:912/+ 1.172|- 0:235}+ 0:009|- 0:051/+ 1-403|- 0°681}- 0°527|+ 0-133|- 0-109 
May, ...- |+ 3-747|- 2°670|+ 0-712} 0:047|- 0:034|- 0-010}+ 2:003}- 0:109|- 0°438}+ 0°173)- 0:006 
June,.... |, 3-928|- 2°597|+ 0°697|+ 0:018}+ 0:000}+ 0-044/+ 2:264|- 0°551|- 0:348)— 0:029|— 0-082 
July,.... — 2°410|+ 0°545|- 0°163|+ 0040/4 0-047} 1-919|— 0:453|- 0-248}+ 0:014|- 0-072 


August, .. |; 4:241|- 2:617|+ 0-723|- 0:238 + 1:032|— 0:121|- 0:367|+ 0-078|- 0:073 
September,|s 3-989|- 2:548|+ 0:890/— 0:233|— 0:205|-_ 0:124|- 0:128/- 0°355|— 0-282/+ 0:416|- 0-033 
October, « |+ 3:452|- 1-991|+ 0:667|— 0°316/— 0-:009}+ 0:256|- 0:335|- 0°625/— 0-285]/+ 0-374|- 0-069 
November, |+. 2:363|- 1-291|+ 0:253)— 0°369/— 0:036|+ 0-121|- 0:436|- 0°354/— 0-185/+ 0°322}+ 0-031 
December, |+ 2:053|— 1-099|+ 0.055|- 0:392|— 0-088}+ 0-064|- 0:578|- 0°737|- 0°170}+ 0:200|- 0-021 


. 1 4:047|- 2°626}+ 0-790|- 0:136|- 0:022|- 0:017}+ 1°415|— 0:379|— 0°370)+ 0°131|- 0-065 
. 14 2°871/- 1-492/+ 0:445|— 0°410/- 0:036}+ 0:097|- 0:109|- 0:698)— 0:228)+ 0-216)|- 0-049 
. ++ 3-458)- 2:058)+ 0°620\- 0°272)— eed 0:041}+ 0°653|- 0°537|— 0:298)+ 0°173\— 0-057 


6. From the inspection of the numbers of this Table, we draw two impor- 
tant conclusions : 

1. The values of the four latter coefficients, B,, A;,.B;, As, being small, 
all the terms of the series beyond the eighth may be neglected as incon- 
siderable. From this it follows, that eight observations, made at equal intervals, 
are sufficient to determine the course of the diurnal variation. — 

u. On comparison of the values of A and B for the separate months, it ap- 
pears that there is a general resemblance in the course of the diurnal variation 
in the six months from April to September inclusive, as well as in the six 
months from October to March inclusive; and that thus the curves for the 
separate months distribute themselves naturally into two groups, in one of 
which the sun is to the north, and in the other to the south of the Equator.* 

Hence,if we confine our attention to the three latter rows of the pre- 
ceding Table, which give the values of the coefficients for the summer half- 


* This fact appears likewise upon an examination of the immediate results of observation, as 
given in Table I.; and still more readily by the inspection of the curves in which these changes 


are graphically represented.—(See Plates I. and II.) 


Magnetical Observatory of Dublin during the Years 1840-43. 79 


year, the winter half-year, and the whole year, respectively, the mean value of A 
at any hour will be expressed by the following equations, in which x =n x 15°, 
n denoting the number of hours, and parts of an hour, reckoned from midnight : 


Summer Half-year. 


A, = 4/288 sin ( + 55° 44") + 2/.653 sin (20 + 231° 47’) 
+ 0'-872 sin (32 + 70° 6) + 0/-189 sin (4x + 253° 56’). 


Winter Half-year. 


A, = 2/-878 sin (« + 77° 10") + 1/-647 sin (2x + 214° 56’) 
+ 0/-500 sin (3 + 72° 7’) + 0/-463 sin (4a + 237° 47’). 


Whole Year. 


A, = 3-519 sin (a + 64° 18’) + 2/-127 sin (2x 4 295° 29) 
+ 0'-688 sin (37 + 70° 40’) + 0/-322 sin (4x + 249°97’), 


7. It is manifest that the coefficients of the equation of the diurnal curve 
may be generally expressed as periodical functions of the time, reckoned from a 
given epoch of the year. For this purpose we have only to apply to the values 
of A and B, belonging to the several months of the year (Table II.), the same 
process which has been already applied to the values of A, corresponding to 
the several hours of the day. We thus obtain the following formulz, in which 
«=n x 30°, n denoting the number of months, and parts of a month, reckoned 
from the Ist of January. The terms of the series which follow those here given 
are neglected as inconsiderable. 


A, = + 3/458 + 0/-927 sin (a + 280° 37’) + 0'-541 sin (20 + 294° 56’); 
B, = + 0-653 + 1'-382 sin (w + 297° 29’) + 0/-265 sin (2e + 110° 21’), 
A, = — 2/058 + 0'.830 sin (w + 96° 39’) + 0'.339 sin (2a + 83°41’); 

B, = — 0-537 + 0'-269 sin (w + 239° 56’) + 0/.078 sin (2x + 210°48’), 
A, = + 0'-620 + 0/264 sin (« + 297° 5’) + 0/-280 sin (2x + 281° 40’); 
B, = — 0'-298 + 0/.082 sin (@ + 119° 1’) + 0'-030 sin (2 + 20°26’); 

A, = — 0/272 + 0/194 sin (@ + 269° 36’) + 0/-100 sin (2x + 147° 17') 
By = + 0'-173 + 0'-108 sin (w + 144° 23’) + 0/-150 sin (2x + 248° 50’). 


? 


80 The Rev. H. Luoyp on the Results of Observations made at the 


8. If we calculate the values of A, corresponding to the even hours of Dublin 
mean time, by means of the formula of Art.5 and the numbers of Table IL., 
we obtain the following values, in which the positive numbers correspond to 
easterly deviations of the north pole of the magnet, as before. 


Taste III. Driurnat VARIATION OF THE DECLINATION (CALCULATED VALUES). 


10 12 


January, . 40°73 40754 +0'88 +3731 +2719 
February, +115 + 1-39 + 1:39 + 2°62 |+ 2°56 
March, Htc + 2°64 4 2°01 + 2°53 + 3°27 |+ 2:27 
April, ... 42°51 143-98 4+ 4-24 + 2°48 | 2°75 
May, .... 43°12 4 4:82 1 4:35 + 1121+ 1°53 
June,.... + 3°13 14 4:95 + 4:38 + 1:4] }+ 2:08 
July,.-.. + 3:36 + 4:48 4 3°55 + 1°80 }+ 2°05 


August,. . + 3:10 + 3:89 |+ 2:89 + 2°30 H+ 2°27 
September, 4+ 1:95 |+ 1°82 |+ 2°49 + 3°19 }+ 2°19 
October, . + 1°27 1 1:22 + 1°64 + 3:30 + 2-28 
November, + 1:08 + 0°60 |+ 0°71 + 2°69 }+ 1:25 
December, + 0°61 |+ 0:18 |+ 0°46 + 3:12 |+ 1-34 


Summer, . 4+ 2°87 + 3:97 }+ 3°67 4 + 2°04 |+ 2°15 
Winter, .. + 1:25 |+ 0:98 + 1:26 4 + 3°05 + 1:97 
Year unets + 2:05 |+ 2°49 }+ 2:46 + 2°55 |+ 2:07 


These numbers, together with those of Table I., are projected in curves in 
Plates I. and II. already referred to. Plate I. contains the curves of the six 
months of the summer half-year, together with the mean of the six ; Plate IL. 
those of the six months of the winter half-year, and the mean. The scale is 
one-tenth of an inch to a minute of arc. 

9. The hours of greatest and /east declination are deduced from the general 

dA 


equation, by making cam 0 ; they are consequently given by the formula 


i (B; cos iw — A; sin a) = 0. 


Substituting for A; and B; their numerical values (Table II.), and solving the 
resulting equations by approximation, we obtain the following results: 


Magnetical Observatory of Dublin during the Years 1840-43. 81 


Epoch of greatest Westerly Elongation. 


Summer half-year,. . . . . O* 58" P.M. 
Wanter haltyears Sige... iu) AT 
Wholevyearieetl +4 sahcns lot OF 54 
Epochs of greatest Easterly Elongation. 
Summer half-year,. . 6°50" a.m. . 11" 8" p.m. 
Winterhaltyear  . 59. ew» 9,38 
Nijhole vert. ee Phe oe a SL OUO 


The hours of mean declination (or those at which the curve crosses the 
axis of abscissz) are in like manner deduced from the equation 


= (A; cos iz + B; sin iv) = 0. 
The following are the results : 


Epochs of Mean Declination. 


Summer half-year, . . 9°36" aM. . 6" 3" P.M. 
Wanter halt-year, 9). 093000 anbed4 
Wiholeyyeant) sper tit ca79 dAn vers O59 


10. The critical hours for the separate months are given in the following 
Table: 
TastelTV. Hours or Greatest, Least, anp Mean Dectination. 


Westerly 


Elongation. Easterly Elongation. Mean Declination. 


> 


he 


January, .. 
February,. . 
March,.... 
EN ath Sooe 


September, . 
October, ... 
November, . 
December, . 


AAAAARARAARAAAH 


8 
ff 
8 
7 
6 
6 
6 
6 
U 
8 
7 
8 


wmCwmwvowunnunnownowys 


VOL. XXII. M 


82 The Rev. H. Luoyp on the Results of Observations made at the 


The numbers of the preceding Table, notwithstanding some irregularities, 
exhibit very distinctly the influence of season upon the critical hours. The 
epoch of greatest westerly elongation occurs latest about the time of the summer 
solstice; and earliest in the last quarter of the year, or between the autumnal 
equinox and the winter solstice. The same thing holds with respect to the 
epochs of mean declination, which (as might have been expected) appear to be 
governed in great measure by the time of westerly elongation. 

The epochs of greatest easterly elongation appear to be governed by the times 
of sunrise and sunset, and are, consequently, much more variable. The fore- 
noon easterly elongation is earliest about the time of the summer solstice, and 
latest at that of the winter solstice ; while the case of the afternoon easterly 
elongation is nearly the reverse. In the months of May, June, and July, in 
fact, there is no change in the direction of the movement during the night, but 
the needle is quiescent for a few hours after midnight, and then the north pole 
resumes its easterly movement until after 6 a. M. 

The critical hours of greatest constancy throughout the year are those of 
the greatest westerly elongation, and those of the forenoon mean ; the extreme 
difference between any of these hours, and the mean for the entire year, being 
twenty-eight minutes. The differences are much lessened, if apparent be sub- 
stituted for mean time. 

11. I proceed, in the next place, to state the results connected with the 
diurnal range. 

The morning easterly elongation being greater than the evening one in sum- 
mer, and less in winter, it follows that a complete view of the phenomena 
connected with the magnitude of the oscillation cannot be had, without 
taking into account the double range. This is accordingly done in the fol- 
lowing Table, the first column of which gives the range of the westerly 
movement, between 7 a.m. and 1 p.m., nearly; and the second that of the 
succeeding easterly movement, from 1 Pp. m. to 10 P.M. nearly. 


Magnetical Observatory of Dublin during the Years 1840-43. 83 


Taste V. RanceEs oF THE DECLINATION IN EACH MONTH. 


Summer Half-year. Winter Half-year. 


| - = 
Westerly Easterly 
Movement. Movement. 


Westerly Easterly 


Movement. Movement. Month. 


Month. 


13 . October, ... 
12:2 3 || November, . 
123 7 December, - 
11°6 D January, -- 
August, ... 11°8 February, . . 
September, . 10°1 q March, .... 


Mean,....-. 


It appears from the foregoing Table, that (as above stated) the greatest 
range in summer is that of the westerly movement, its mean value being 11’.9; 
while, in winter, the greatest range is that of the easterly movement, and its mean 
value is 8’.3. It is remarkable, however, that the mean ranges of the easterly 
and westerly movements, for the entire year, are precisely equal, the mean value 
of each being 9-1. 

The greatest value of the maximum range is that of April, and its amount 
is 13’-3 ; the range then decreases until about the middle of July, and after- 
wards increases, attaining a second, but smaller maximum in August. The 
least value of the maximum range is that of December, and its amount is 6/-6, 
being one-half of the greatest value. The mean value of the maximum range, 
for the entire year, is 10’-1. 

The unexpected fact, of the occurrence of the greatest ranges in April and 
August, was first noticed by Beauroy. He seemed to think, however, that 
the result was only an apparent one, and arose from the circumstance, that the 
times of observation approached more nearly the epoch of greatest elongation 
in April than in June. The fact has been since noted also by Gauss, in his 
account of the Gottingen observations. “ The differences” (of the declination 
at 8 a.m. and 1 p.m.), he observes, “ are not greatest at the time of the sum- 
mer solstice, but appear smaller in June and July than in April, May, and 
August ;” but he concludes, with Brauroy, that this was due to the accidental 


circumstance, that the whole range was not observed near the solstice, the time of 
M 2 


84 The Rev. H. Luoyp on the Results of Observations made at the 


the greatest easterly elongation being then earlier than 8 a.m. It is manifest, 
however, that such an explanation will not apply to the result deduced, as in the 
present instance, from the diurnal curve ; and there can be no longer any doubt 
of the reality of the phenomenon. 

12. The physical dependence of the changes of declination upon the sun is 
evident from the fact that they observe a diurnal and an annual period. The 
conclusion deducible from this fact has been confirmed by the leading features 
of the diurnal movement. Thus it has been long ago observed, that the time 
of greatest westerly elongation follows the sun’s meridian passage at a nearly 
constant interval ; and that the times of greatest easterly elongation, in the 
morning and evening, are in like manner connected, although not so closely, 
with the hours of sunrise and sunset. The greater magnitude of the range, in 
summer than in winter, is another obvious confirmation of the same view. 

We may, I believe, disregard, as wholly untenable, the hypothesis originally 
proposed by Couroms, in which the influence of the sun is assumed to be direct, 
and the effect of magnetic polarity in that body. It is easy to show that, if such 
an action exist at all, it cannot certainly account for the principal part of the 
observed effect. But, without dwelling on the negative side of the question, I 
hope to show that the sun acts indirectly, by means of his heating power exerted 
upon the earth’s surface. This has been assumed by Canton, and since by 
Professor Curist1e, in the hypotheses which they have severally devised to 
account for the diurnal variation of the declination ; but the evidence upon 
which it rested did not extend beyond the facts which have just been stated. 
It will appear from the following examination, that the connexion between the 
changes of declination and those of temperature is more intimate than has been 
hitherto supposed. 

13. The force which produces the deviation of the magnet from its mean 
position, at any moment of the day, is measured by the sine of the deviation,— 
or, since the deviation is small, by the angle of deviation itself, or by the ordi- 
nate of the diurnal curve; and the sum of all these forces throughout the day, or 
the integral of the diurnal action, is measured by the area of the diurnal curve. 
If, then, the diurnal variation of the declination be the result of the diurnal 
variation of temperature, we should expect to find a marked correspondence 
between the areas of the diurnal curves of the two elements,throughout the year. 


Magnetical Observatory of Dublin during the Years 1840-43. 85 


The following Table contains the computed values of these two functions, for 
the several months of the year, the units being one minute of declination, one 
degree of temperature, and one hour of time. 


Taste VI. AREAS OF THE DIURNAL CURVES OF DECLINATION AND TEMPERATURE. 


Declination, .... | 39:3 | 42-2} 64-4 79°5 | 72:5 | 76-7| 74:6 | 174: 
Temperature, .. | 38.9 | 37-6 | 72:0 93°9 | 96-9101. 91-1 | 94: 


For the purpose of comparison, the preceding numbers are graphically pro- 
jected in Plate III. figs. 1 and 2, one division of the scale corresponding to four 
minutes of declination, and to eight degrees of temperature. These curves ex- 
hibit in the clearest manner the correspondence between the two classes of 
phenomena, and leave no doubt whatever that they stand in the relation of 
effect and cause. The slight dissimilarities which exist between them are 
abundantly accounted for by the circumstance, that it is to the heating power 
of the sun, exerted upon the earth’s surface (and not upon its atmosphere), that 
we must ascribe the changes of declination ; and I venture to predict, that as 
soon as we are in possession of data respecting the diurnal changes of tempe- 
rature of the earth’s surface, sufficient for the purposes of a comparison such 
as that now made, the agreement of the laws will be found to be still more 
complete. 

The same agreement appears, also, upon a comparison of the mean yearly 
values of the same functions, calculated for the four years ; the following are 
the results. 


Taste VII. Areas oF THE DIURNAL cURVES oF DECLINATION AND TEMPERATURE, FOR 
THE SEPARATE YEARS, 


1840. | 1841. 1842. 1843. 


Declination, . ... 68:3 
Temperature,...| 84:0 


62-3 59:2 56:0 
66-0 62:7 55°6 


86 The Rev. H. Luorp on the Results of Observations made at the 


Annual and Secular Variations. 

14. The mean yearly values of the declination, for the seven years from 
1840 to 1846, inclusive, are given in the following Table; the deviation of the 
north pole of the magnet from the astronomical meridian being measured from 
the north eastward. The third column of the Table contains the differences of 
the declination in the successive years, or the yearly amounts of the secular 
change. 


Tasrte VIII. Mean Yearty VALUES OF THE DECLINATION, FOR THE YEARS 1840-46. 


Differences. 


Declination. 


1840 332° 30/69 


1841 34 -65 + 3796 
1842 43°55 + 8-90 
1843 50°10 + 6°55 
1844 53 43 + 3°33 
1845 59°75 +6 +32 


1846 333° 7:22 ap i a7 


If n denote the number of years reckoned from any epoch, D) the declina- 
nation at that epoch, and e the change from year to year, the actual declination, 
D,,, will be given by the formula 

D, = D, + me, 
on the supposition that the change of declination is proportional to the time. 
But the middle of the year 1840 being taken as the epoch, the values of D,, 
corresponding to » = 0, 1, 2...6, are given in the preceding Table ; so that 
we have seven equations for the determination of D, and e. Combining these 
equations by the method of least squares, we obtain 
D, = 332° 30.30; «= + 6-060. 

Consequently the north end of the magnet moves to the east from year to year, 
and the westerly declination therefore diminishes, by 6’-06 annually, in its mean 
quantity. The amount (as will be seen from the Table) varies considerably in 


different years. 
Subducting 3’-03 from the value of D, given above, the mean declination 


Magnetical Observatory of Dublin during the Years 1840-43. 87 


for January 1, 1840, is 332° 27’-27. Wherefore, the mean declination at any 
time 1s 
D,, = 332° 27'.27 + 6-06 x n, 

n denoting the number of years, and parts ofa year, reckoned from Jan. 1, 1840. 

15. Subducting the mean values for each year from those of the separate 
months, we obtain a series of numbers which represent the course of the annual 
variation. During the year 1840 the declinometer was twice readjusted; and 
from this, and other causes, the monthly values of the absolute declination for 
that year cannot be relied upon with certainty. The following Table contains 
the values of the differences for the three following years, together with their 
means for the whole period : 


Taste TX. Annual VARIATION OF THE DECLINATION FOR THE YEARS 1841-43. 


Year. Jan. | Feb. | March. . 7. . . | Nov. | Dec. 


1841, ... |+0/-75 |+0/-92 |-0’70 +3/°37 |+5/.40 
1842, ...|-1.72|- 1°52 |- 0°56 H+ 4°36 |+ 5°94 
1843, .. . |+ 0:29 + 0°51 }+ 0°85 + 1:50 }+ 2°99 


Means,. .. |— 0:23 |- 0°03 |- 0:14 + 3°08 |+ 4-78 


The following Table contains the corresponding numbers for the succeeding 
triennial period, with their means, and the means of all. 


Taste X. AnnuAL VARIATION OF THE DECLINATION FOR THE YEARS 1844-46, 
TOGETHER WITH THE MEAN OF ALL. 


Year. April. | May. | June. | July. | Aug. | Sept. | Oct. | Nov. | Dec. 


1844, .... |-001 |+0/-24 +1/-13 40/08 |-1"-72 |-2"-56 -1""79 |-2/-18 |-0/-74 |+0/-46 |43/-44 113-66 

1845, ..., |- 1°14 |+0-29 |+ 0°38 |+ 0°35 |- 0:53 | 1:16 — 2:06 |- 2-15 |- 1°31 |+ 1:19 + 1-73 4°44 

1846,..- | |-1-34}- 0-73 + 0:32 + 1:99 |+ 1-06 | 1:09 — 3:14 |- 1:84 |- 0-96 |+ 0:78 +: 2:17 1+ 2°76 
| | 


Means,.. . |- 0:83 |- 0:07 + 0°61 }+ 0-81 | 0-40 |- 1-60 — 2°33 |- 2-06 |- 1-00 }+ 0°81 |+ 2-45 |+ 3:62 


Means at ~ 0:53 |-0-05 |+ 0-24 + 0-27 0-98 |- 2:06 - 2-33 | 1-92 - 0-62 |+ 1-04 |+ 2°76 + 4-20 


six years, 


88 The Rev. H. Luoyp on the Results of Observations made at the 


The mean results for the two triennial periods, together with the means of 
all, are graphically represented in Plate III. figs. 3,4, 5; the scale being 0-2 inch 
to one minute of arc. To facilitate comparisons hereafter instituted, the positive 
ordinates correspond to westerly deviations. The correspondence of the course 
of the variation during the two periods is as close as could be expected, the 
difference consisting chiefly in the epoch of the westerly maximum. 

16. The following are the laws of the changes, as deduced from the mean 
results : 

1. From the beginning of April to the beginning of July, the north end of 
the magnet moves to the west ; the maximum of westerly declination takes place 
about the 8th of July, but the epoch varies considerably in different years. 

1. During the remainder of the year (i.e. from the beginning of July to the 
beginning of April), the north end of the magnet moves to the east ; the move- 
ment, however, is very slow during the first three months of the year. 

m. The range of the westerly movement is 2-7 minutes ; and that of the 
easterly 8-7 minutes. Thus, at the end of twelve months, the north end of the 
magnet has advanced to the east, by about 6-0 minutes, as has been already 
shown. 

17. The annual variation of the declination was discovered by Cassini in 
1786.* It appeared from the observations of Cass1n1, that the north pole of the 
magnet moved to the east from the vernal equinox to the summer solstice ; 
and that, during the remaining nine months of the year, it moved to the west. 
The westerly movement, during the nine months, preponderated over the 
easterly, which took place during three ; and thus the westerly declination was 


* The determination of the annual variation is much more difficult than that of the diurnal, 
both on account of the much smaller frequency of the period, and the difficulty of preserving the 
instrument in the same unchanged condition during the much longer time, or of determining and 
allowing for its changes when they do occur. Accordingly, although the annual period may be 
traced in the observations of Gitpry, and is decidedly displayed in those of Bowprrcu, it has evaded 
the researches of recent observers. There is but a faint indication of its existence in the Gottingen 
observations, which were made at the hours of 8 A.M. and 1] p.M.; and Professor Gauss and 
Dr. Gotpscumipr find, in their analysis of these observations, no “ important fluctuation dependent 
on season.” A similar negative result is deduced by Dr. Lamonr from the Munich observations, 
which were made twelve times in the day. 


Magnetical Observatory of Dublin during the Years 1840-43. 89 


greater at the close of the year than at the commencement. The difference 
was the yearly amount of the secular change. 

The observations of Cassini were made during five years, viz. from 1784 to 
1788, inclusive. Although the annual variation at Paris was then greater than 
it is now at Dublin, the final means are less accordant ; and M. Karz deduces 
from them the existence of a double oscillation. This conclusion, however, has 
arisen from what appears to be an erroneous mean value in the month of 
October, and is therefore not a legitimate interpretation of the results. 

18. When we compare the course of the changes observed by Cassini with 
those observed at Dublin, we find that the movements are precisely opposite. 
But, it is to be observed, the directions of the secular changes at the two 
periods are likewise opposed ; and, putting together these facts, we are led to 
generalize the law as follows : 

From a little after the vernal equinox until a little after the summer solstice, the 
movement of the north pole of the magnet is RETROGRADE, or opposite in direction to 
the secular change; and during the remaining nine months of the year it is DIRECT. 

The remarkable relation between the annual and secular changes, here 
stated, may be observed on comparing the observations of Bowprrcu, in 1810, 
with those of Cassini. At this time the westerly declination was diminishing 
at Salem, in Massachusetts, by about two minutes annually ; and, in accordance 
with the preceding law, the direction of the annual movements is the inverse 
of that observed by Cassini at Paris, in 1786, and agrees with that observed at 
Dublin at the present time. M. Araco, who notices these observations (An- 
nales de Chimie, tom. xvi.), draws from them a different conclusion, and infers 
(although with an expression of doubt) that when the westerly declination 
diminishes from year to year, the period of Cassrnr is transported from Spring 
to Autumn. 

It further appears probable, that, at a given place, the amount of the annual 
variation is related to that of the secular change, and vanishes when the latter 
vanishes. This conclusion has been drawn by Araco, from the observations 
of Gitpin at London, in 1787-1793, and those of Beavroy in 1818-1820, as 
compared with those of Cassini. At the former period, in fact, the secular 
change was only +1’. 0 annually at London, and the annual variation was pro- 
portionally small; while, at the latter, both changes appeared to be evanescent. 

VOL. XXII. N 


90 The Rev. H. Luoyp on the Results of Observations made at the 


19. The phenomena just described are, it is manifest, the resultants of two 
distinct changes,—namely, the annual variation properly so called, and the secular 
change. The amount of the latter is + 0’-5 x n,n being the number of months 
elapsed. If this be subtracted from the numbers in the last row of Table X., 
reducing to the epoch July 1 (the middle of the year), we obtain the numbers 
of the following Table, which represent the course of the true annual variation. 
The positive numbers correspond to easterly deviations, as before. 


Taste XI. PeERrIoDICAL PART OF THE Mean ANNUAL VARIATION. 


April. | May. 


+2/-20 | +1199 | +. 1-52 | —0"23 | 1/81 | — 2/58 | —2”67 |—1/-87 | —0"71 | +051 | 417-45 


The following is the equation of the curve of the annual variation, in which 
x =n x 30°, n being the number of months, and parts of a month, reckoned 
from January 1. We may probably neglect, as inconsiderable, all the terms 
after the second. 


AD = 2/543 sin (a + 52°57’) + 0/-301 sin (2a + 232° 33’) 
+ 0-108 sin (32 + 117° 46’) + 0/-112 sin (42 + 26°25’) 
+ 0/057 sin (5a + 295° 7’) + 0/005 sin 62. 


The curve itself is represented in Plate III. fig. 6, the scale being 0.2 inch 
to one minute of arc. For the sake of the comparison with the annual curve 
of temperature, presently to be referred to, the signs are all changed, and the 
positive ordinates correspond to westerly deviations. 

It appears from the inspection of this curve, that the course of the annual 
variation (unlike that of the diurnal in this respect) is represented by a single 
oscillation. The minimum occurs in the beginning of February, and the maai- 
mum in the beginning of August; and the whole range of the change is 5-0 
minutes. The curve crosses the axis of the abscissez in the middle of May and 
in the beginning of November. 

To obtain the mean value of the declination corresponding to any month 
in any year, the value of AD, obtained above, must be added to that of D, 
given in Art. 14. The formula, therefore, is 


Magnetical Observatory of Dublin during the Years 1840-43. 91 
D,, = 332° 27.27 + 6.06 xn+ AD; 


n denoting, as before, the number of years reckoned from January 1, 1840. 

20. We have already seen that the diurnal changes of declination and tem- 
perature are related in a very remarkable manner ; and we should, therefore, 
naturally be led to expect a corresponding relation in the annual changes of 
the same elements. For the purpose of exhibiting it, I subjoin the differences 
between the mean temperatures of each month, and that of the entire year, as 


deduced from the observations made at the Magnetical Observatory during the 
years 1841-46. 


Taste XII. Annvat VaRIATION OF TEMPERATURE. 


Oct. 


8°38 |- 9°04 |- 6°24 | 2°-03 F 2°-95 |+ 8°-93 1+ 9°18 14 9°46 |} 122 iF 0°90 |— 4°.16 ; 7°02 


LoL ae | 


The numbers of this Table are projected in Plate III. fig. 7, immediately 
below the corresponding curve of declination, the scale being -05 of an inch to 
one degree of temperature. It will be seen, ona comparison of the two curves, 
that the annual variations of the declination and temperature present the most 
complete accordance, not only as to the hours of maxima and minima, but also 
in their entire course.* There is a slight, but systematic difference in the 
epochs of the mean values, those of the declination taking place about a 
Jortnight later than those of the temperature. This is what we should be led 
d priori to expect, on the assumption that the magnetic changes are due to the 


* Since this paper was written, I have learned that the correspondence between the annual 
changes of declination and temperature had been indicated by Horner (Gehler’s Wérterbuch) as a 
result of the Stockholm observations. The correspondence thus traced, however, does not extend 
beyond the fact, that the epochs of greatest and least declination coincide, nearly, with those of 
greatest and least temperature ; and, in fact, the results themselves, although the means of obser- 
vations extending over the space of thirty years (1786-1815), are manifestly encumbered with 
too large an amount of observation error, to render any more detailed comparison possible. The 
same remark applies, yet more strongly, to the results of the Manheim observations, as quoted by 
Kemrz. In both of these cases, the most easterly position of the needle occurs at the time of 
greatest temperature of the year, and vice versa. 


N2 


92 The Rev. H. Luoyn on the Results of Observations made at the 


changes of temperature of the earth’s crust; for it is known that the epochs of 
mean temperature, as well as those of the maximum and minimum temperature 
of the soil, are retarded, and follow the corresponding epochs for the tempera- 
ture of the air by an interval which is proportional to the depth. 

These retardations, when observation shall have determined them with 
ereater precision, will probably be found (in accordance with the results of 
Professor Forses’s experiments) to be different in different localities, depending 
upon the conductibility of the soil. 

21. It remains to notice the bearing of the remarkable relations between 
the annual and the secular changes, stated in Art. 18. It would seem to follow 
from these relations, that the two classes of changes are physically connected ; 
and therefore that the secular, as well as the annual variation, is due to the 
heating power of the sun exerted upon the earth’s crust,—although not only 
the magnitude, but even the direction of the change is different at different 
times. It is not easy to frame even a conjecture as to the nature of such an 
agency, in the case of the secular change. 


Disturbances. 


22. Having examined the periodical and the secular variations of the decli- 
' nation, it remains to consider those which, from our ignorance of their laws, 
we have been accustomed to call “ irregular.” 

Professor Krein seems to have been the first to notify the remarkable fact, 
that magnetic disturbances occur more frequently at certain hours than at 
others ; and, that the direction, as well as the frequency of these movements, 
has a dependence upon the time of the day. Colonel Sasrne has since made 
a more complete and elaborate examination of this question, in the discussion 
of the Toronto observations, and has arrived at conclusions for the most part 
confirmatory of those obtained by Professor Krern. 

In these investigations, however, those disturbances only are taken into 
account which exceed a certain arbitrary limit ; and of these the frequency 
is considered without any reference to their magnitude. In examining the 
question of the periodicity of disturbances, I have thought it advisable to pur- 
sue a different course. I have taken the differences between each result, and 
the monthly mean corresponding to the same hour, and combined these diffe- 


Magnetical Observatory of Dublin during the Years 1840-43. 93 


rences in the same manner as the errors of observation (to which they are ana- 
logous) are combined in the calculus of probabilities. The square root of the 
mean of the squares of these differences is, in fact, a quantity analogous to the 
mean error, and which we may therefore call the mean disturbance ; and it is 
evident that its values, at the several hours of the day, and at the several 
seasons of the year, will sefve to measure the probable disturbance to be ex- 
pected at the corresponding times. 

The values of this function have been deduced for the several hours of ob- 
servation, in each month of the year 1843 ;* and those for the entire year are 
obtained from them by a repetition of the same process. They are given in 
the following Table :— 


Tasre XIII. Vatues or toe Mean Disturpance. 


January, . 


— 

WE: 
Ne) No} 
— 


mS 

38S ag 
oa 

© 

oa) 


_ 
ew 


September, . 
October, .. . 
November, . 
December, . 


MR WN WNWWwWN hb 


20 
69 
43 
“Ol 
24 
“33 
96 
09 
39 
21 
03 


These numbers show that the mean disturbance follows a law of remarkable 
regularity in dependence upon the hour. During the day,—i. e. from 6 A.M. to 
6 P. M.,—it is nearly constant. At 6 p.m. it begins to increase, and arrives at a 
maximum a little after 10 p.m; and it then decreases with the same regularity, 
and arrives at its constant day-value about 6 A.M. 


* T have chosen this year, because in it the irregular changes were comparatively small ; and, 
the number which expresses their frequency, in consequence, bearing a larger proportion to that 
which denotes their magnitude, any regular law to which they are subject will be more readily 
apparent. 


94 The Rev. H. Lroyn on the Results of Observations made at the 


23. The preceding results are independent of the direction of the distur- 
bance. If, however, we take the sum of the squares of the easterly and westerly 
deviations separately, we find that the easterly disturbances preponderate during 
the night, and the westerly during the day ; the former are, however, much 
more considerable than the latter, and the difference reaches a maximum 
about 10 P.M. ; 

Let 2A,? denote the sum of the squares of the positive, or easterly distur- 
bances, and A2 that of the negative, or westerly ; then the mean values of the 
function \/ — —=2.) are the following. The values in which the easterly 
disturbances preponderate are distinguished by the positive sign, and vice versd. 


Taste XIV. M«xan VALUES OF sf ( 


ZA? - 24.) 


n 


41/43 |+1/-05 | —1718 |—1/"15 |— 107 | -0"83 -0'80|-1/12 —0"54|+1°67 


+282 | +337 


It thus appears that the mean disturbance observes a regular daily period, 
both in magnitude and direction; and this period, it is worthy of remark, is 
precisely the reverse of that of the regular diurnal movement,—the mean posi- 
tion of the magnet being nearly constant during the night, the mean disturbance 
during the day ;—the principal oscillation of the magnet, in the regular move- 
ment, being to the west during the day, while that of the irregular movement is 
to the east during the night. 

24. From these remarkable relations it seems evident that the two classes 
of phenomena are physically connected ; and I am inclined to regard the dis- 
turbance which prevails about 10 p.M., as an zrregular reaction from the regular 
day movement, and dependent upon it both for its periodical character and 
for its amount. 

If this hypothesis be a just one, it will, of course, follow that the magnitude 
of the mean disturbance will vary in some direct proportion to the daily range, 
and should, therefore, be greater in summer than in winter. This appears to 


Magnetical Observatory of Dublin during the Years 1840-43. 95 


be established by the following Table, which contains the values of / (=), 


corresponding to the several months of the year : 
Taste XV. Awnnvat VARIATION oF THE Mean Disturpance. 


June. a z Dec. 


2/01 2/11 | 3°06 | 2/42 | 2-72 | 2751 | 1763 1/67 


These numbers are somewhat irregular; but if they be combined in periods 
of three months, taking the square root of the mean of the squares, we obtain 
the following numbers, in which the existence of an annual period is evident : 


February, March, April, . . . 2/68 
May, June, Ci a are Ter, ¥ | 
August, September, October, . . . 9/-55 
November, December, January) SO V-77 


The mean disturbance, for the entire year, is 2.56. 

25. It by no means necessarily follows, from the results now stated, that all 
disturbances have a periodical character. There probably are two classes of 
disturbances, the results of distinct physical causes, of which one observes a 
period, while the other is wholly irregular ; and it is manifest that, in such a 
case, the period of the former will necessarily be impressed upon the resultant 
mean disturbance. We have, I think, also grounds for concluding that these 
two kinds of disturbances are further distinguished by the important charac- 
teristics,—that those of the former class are local (depending, as they do, upon 
the time at the place of observation), while those of the latter are universal, and 
belong to the phenomena which have hitherto so much engaged the attention 
of observers. 

Of the periodical disturbances the principal (if not the only one) is that 
which occurs about 10 p.a, and which causes the north pole of the magnet to 
deviate to the east. The epoch of the maximum of easterly deflection varies, 
however, between very wide limits, being sometimes before 8 p. M, and some- 
times later than 1 a.m; and hence it is evident, that its effect on the monthly 


96 The Rev. H. Lioyp on the Results of Observations, §c. 


mean curve is to produce a general increase of the ordinate between these limits 
of time, as well as the maximum at 10 P.M. 

We learn from the consideration of these facts, that the ordinary mode of 
grouping the observations, by taking the mean of all the results at the same 
hour,—although it truly gives the mean diurnal curve for the period embraced 
by the observations,—does not represent the average actual course of the move- 
ment during one day. In order to obtain the representative, or type curve (as it 
may be called), it seems necessary to treat the ordinates and abscisse as inde- 
pendent variables, and to take,—not the means of the ordinates corresponding 
to certain definite abscissee,—but the means, both of the abscissee and ordinates, 
corresponding to the time of the phenomenon. The former of these will give the 
mean epoch of the disturbance, and the latter its mean amount. 

We find, in this manner, that the mean epoch of the periodical disturbance 
is a few minutes before 10 p.m. Its mean magnitude is 10’-0; and its mean 
duration is an hour and a half. 


es 


V.—On a Classification of Elastic Media, and the Laws of Plane Waves propa- 
gated through them. By the Rev. Samuret Haucuton, Fellow and Tutor of 
Trinity College, Dublin. 


Read January 8, 1849. 


Ty a Memoir on the equilibrium and motion of solid and fluid bodies, pre- 
sented to this Academy in May, 1846, I deduced the laws of such bodies from 
the hypothesis of attracting and repelling molecules ; since that time I have 
been led to consider the general laws of continuous bodies, without making 
any such restriction as to the nature of the molecular action. The present 
paper contains the results I have arrived at in this investigation, and may, per- 
haps, be considered interesting on account of the classification suggested as ap- 
plicable to all elastic media. It consists of five sections ; the first contains the 
general equations applicable to all media, and the properties of plane waves 
transmitted through them, which are readily deduced from an extension 
which I have given to a theorem originally stated by M. Caucuy, for a parti- 
cular case ; the second, third, and fourth sections contain respectively the laws 
of the three groups into which elastic media may be divided; these three groups 
consisting of,—first, bodies whose molecular action consists of exclusively nor- 
mal pressures ; secondly, bodies whose molecular action produces exclusively 
tangential forces ; thirdly, bodies composed of attracting and repelling molecules. 
The fifth section contains a comparison of the mechanical theories of light pro- 
posed by Mr. Green and Professor Mac CutiaGu, with some observations on 
the present state of the science of physical optics. Whatever theoretic objec- 
tions may be made to the application of the theory of elastic media to optics, 
none such exist as to its application to solid and fluid bodies The mathematical 
VOL. XXII. 0) 


98 The Rev. S. HavcurTon on a Classification of Elastic Media, 


investigations which, in the case of light, must be hypothetical, are, in the case 
of solids and fluids, essentially positive, and may be made the object of direct 
experiment. A general inquiry into the laws of elastic media, is an interesting 
application of rational mechanics, and although it must necessarily include cases 
purely hypothetical, it is not, therefore, to be considered as unimportant. In 
this respect it is analogous to an inquiry into the general theory of central forces, 
the importance of which is not confined to the investigation of those laws, of 
which examples occur in nature ; these are undoubtedly the most important, 
but the theory of central forces, considered as a branch of mechanics, would 
be incomplete, unless extended to all possible laws of central force. 


SECTION I.—GENERAL EQUATIONS. 


The formula of virtual velocities, which contains, as shown by LAGRANGE, 
the conditions necessary to be fulfilled in the interior and at the boundaries of 
a continuous body, is the proper starting point for a deductive theory of the 
mechanical structure of bodies. Every hypothesis which may be made, and 
every fact which experience has discovered, respecting the molecular consti- 
tution of bodies, may be expressed in its most simple form by the aid of this 
formula ; which, by its flexibility, and the facility it affords for deducing theo- 
retic results, becomes of more importance in questions of this nature than in 
other mechanical problems. In order to express by means of it the condi- 
tions of equilibrium of a continuous body, it is necessary to distinguish the 
forces acting at each point into two classes, molecular and external forces ; in- 
cluding among the external forces the resultants of the attractions of the other 
points of the body, since these attractions arise from gravitation, and must not 
be confounded with the molecular forces. The formula of virtual velocities 
must also be stated in such a manner as not to involve any hypothesis as to 
the nature of molecular forces, so as to possess the requisite degree of generality. 
If the problem be dynamical, we must then add accelerating forces equal and 
opposite to those actually employed, so as to destroy the motion at each point, 
and consider the problem as one of equilibrium of forces. These negative accele- 
rating forces must be considered as external forces. 


and the Laws of Plane Waves propagated through them. 99 


The forces being thus divided into two classes, the formula will consist of 

two parts, 
= (Pip + Pip’ + &e.) + E (Qég + Vig’ + &e.) = 0. 

P, P’, &c., denoting the external forces, and Q, Q’, &c., denoting the molecular 
forces. If (a, y, z) denote the co-ordinates of a point at any instant of the mo- 
tion, and a virtual displacement (éz, ey, 6z) be conceived, these quantities will 
be functions of four independent variables, which will be the initial values of 
(2, y,2),and the time. Let (w’, v’, w’) denote the accelerating forces; hence 


= (Pip + Pp’ + &e.) = fff{(X—w') te +( Y—v') ty+(Z—w’) oz} din. 
I shall assume that the virtual moments of the molecular forces depend upon 


the differential coefficients of (é, ey, &), by means of the following linear 
equation,* 


= igo see: dix dia déa 
Qéq + Qeq + &e. = ge ae ae 
dey déy dey 

+ @ G+ Q aie: Qs = 

déz déz diz 

toot oe dy elas 


Inserting these values into the equation of virtual velocities, and integrating by 
parts, we find 
0 = [Illp (X — uv’) && + p(Y—v') y + p(Z—w’) bz} dadydz 
dP, dP, ak; , dQ, dQ) dQ; ie dR, dR, dR; ny ori 
-(f (Gee ee amet ag a ce sai ae tz | dadyd: 
+ (\( Pree + Qéy + Riz) dydz, (1) 
+ {j( Pie + Qéy + Rbz) dedz, 
+ fi(Pséa + Qyey + Ritz) dxdy. 
The equations of motion being determined by the triple integrals, and the con- 


ditions at the limits by the double integrals. ‘The equations of motion formed 
from this equation will be 


* The ground of this assumption is the fact, that molecular forces depend upon the relative dis- 
placements of the particles, and not on their absolute displacements. 


02 


100 The Rev. S. Haucuton on a Classification of Elastic Media, 
i aR? dP; GP; 
pt) ae saa “ae 
dQ dQ , dQ, 
U = _—— os 
p(Y-v') => ap ae (2) 
adh, dk, dk 
AV aed Ace Peet 
Pl aA ge dy dz 


These equations are the same as those deduced by a totally different method 
(which will be given presently), and involve no restriction as to the extent of 
the deviation of (a, y, z) from their original values (a, 8, ¢). 

If we suppose a =a+é y=b+y, z=c+{, the expression for the mo- 
ments of the molecular forces will become 


Qéq + Q’eq’ + &e. = Piéa, + Pyéa, + Pa, 


+ Qe; aa Q, eB. + Q:88s 
+ Ren a= Ryby. + Rey, ; 


where 
Eas Cee ce 
NS a aaa SS Feu 
_ dy _dy _ dy. 
BL aes eS dg B= 3.5 
d. d d 
nes 2a a =o. 


If we restrict the molecular forces by the condition 
Qég + Qeq’ + &e. = aV, 


we shall have the relations 


dV dV dV 

er ae Serna? 

dV dV dV 

Q= aa ene Q= ie 

dV dV dV 

hE Fae eye ° dys’ 
Vai (aq, a, a3, fi, Ba, Bs, Yio Y2 Ys): 


and the Laws of Plane Waves propagated through them. 101 


The kind of motion which it is the object of this paper to investigate is of 
the kind commonly called small oscillations ; and for this kind of motion it is 
not necessary to use the most general equations, or to consider the unknown 
quantities of the problem as functions of («, y, z, f). We may use, instead of 
(2, y, z), the co-ordinates (a, b, c) of the position of rest of the molecules. In 
fact, any differential coefficient of a function ¢, taken with respect to (a, 6, c), 
will be expressed by the equation, 


dp _ dd de, de dy , de de 
da” dx da’ dy da“ dz da’ 


but, smce r=a+é y=b+y, z=c+, we obtain 


da _ 1 d&é dy dy dz dg 
da da’ da da’ da da’ 


Hence, neglecting quantities of the second order, we find 


dp _ do 


da dz’ 


and similarly for the other differential coefficients. 

In the remaining part of this memoir (unless the contrary be expressed), I 
shall, therefore, consider (a, y, z) as the co-ordinates of the position of equili- 
brium of the molecules, and (é, 7, ¢) as the small displacements of the molecule ; 
the element of the mass will be expressed by the equation dm = ededydz, 
where e denotes the density, not considered as a function of the time, since 
(dzdydz) denotes the original element of the volume. 

Two kinds of waves can pass through such a body as water; one, a surface 
wave, depending on the action of gravity for its propagation ; the other, such- 
a wave as propagates sound, and does not directly depend on external forces. 
This latter is the kind of wave described in this paper. The equations pecu- 
liar to it will be found by omitting (X, Y,Z) from the general equations; but 
though the external forces are not explicit in the formule, yet as they affect 
the density and structure of the body differently at different points, though they 
do not directly affect the wave, we must introduce them implicitly by rendering 
e and the coefficients of V functions of (X, Y, Z), and therefore of (z, Y, 2) 


102 The Rev. S. Haucuton on a Classification of Elastic Media, 


The equation of virtual velocities thus modified will become, considering 
(x, y, z) as the positions of rest of the molecules, 


[fe (a sé + = yt 7 ae Eee) dxdydz = {lj Vdadydz. (3) 
As V isa function of the quantities (a, a:, a3, &c.) of a given form, we shall 


have 


iV. 
Oe aaa ep a a 
a) 


daz da; 
= dV dV 
aP ap, + ap, OBo+ aBs oBs 
dV dV dV 
EER LD oy. Sem 


Substituting this value in equation (3), and integrating by parts, we obtain 


{le (Fe eee coe d’ = | én + “ it) dadydz = (le Vdadydz 


AV en ad 0 Serie 
“4 BE te in + Ft) dydz 


V 26 
+((G BE + on" * Fe a ic) dedz 


LV 

+|] (= 8 + a én + ar =i) deedy (4) 

-{j d CL CNEL i _aV 
dx da, dy day dz da 


ei ah CN Gh GNA Gh 
— (Go So+ E e+ ae Gp) onto 


-(\($- +e te Seiod 
dx dy, dy d dz dys shee 


The double integrals, as usual, denote the conditions at the bounding surface, 
and the triple integrals give the general equations of motion in the interior. 
The laws of propagation depend upon the triple integrals, and the laws of re- 
flexion and refraction depend upon the double integrals. 


sédadydz 
3 


and the Laws of Plane Waves propagated through them. 103 


The equations of motion derived from (4) will be, 
GE Towed Lava “dV 


7 dé de” da,” dy” da,” de” day’ 
dn deg V ad) OV wd AV 

~ de de dp,” dy” dp, * de * ap,’ ys 
CELIA, a dV id av 

OS dE de dy,” dy dy, de yy 

These equations contain the laws of propagation of every variety of wave 
not depending on external forces ; and as the function has not been restricted 
by any hypothesis as to the law of molecular action, they will be the dynamical 
equations of propagation of sound in air, water, solids, and of light, if we adopt 
the undulatory hypothesis. In all these cases, the difficulty is to ascertain the 
correct form of V peculiar to the particular case ; the form being found, the 
coefficients must be determined by experiment for each body : so far as theory 
is concerned, the mechanical classification of bodies would be complete, if the 
form of V were known for all. 

The conditions to be satisfied at the limits will be different, according as 
the surface is fixed, free, acted on by special forces, or in contact with other 
bodies. As there is no difficulty in forming the equations for any of these 
cases, I shall here give only the conditions at the limiting surface in contact 
with other bodies. 

Let F(z, y, z) = 0 be the equation of the surface passing through the posi- 
tions of rest of the molecules which at any instant form the actual limiting 
surface f(z, y, z, t) = 0, hence 

dk dz + dF 
dz «dy 


and if A, w, v, be the angles which determine the position of the normal, we 


dF. 
dy + 7 dz=0; 


shall have 


cos A= a 
cos a 
= 1 SS5 

tod dy 

BF 


104 The Rev. S. Havcuton on a Classification of Elastie Media, 


If w be an element of the surface 


dydz = w cos N= kw = 
dzdz = w cos hM=kw 
dxdy = w cos v = kw S 


these equations will reduce the double integrals (4) to the form 


a=|| a ae oo dV dF 5 
= aa, ae ae ae aaa 
i dV dF dV dF adV dF : 
7 gai de aes dy dpe cde) 
+) dV dF dV dF dV dF : 
| dy, dx dy, dy dy; dz eS 


These will be the double integrals resulting from 


one body, and from them 


must be subtracted similar terms derived from the body which bounds the one 
under consideration. (2x, y, 7) =0 is common to both bodies when at rest, 
also , y, ¢, will be the same for all the bounding surface, f(a, 7, 2, t)=0, during 
the motion ; also 8, én, é¢, are independent ; hence the condition at the limits 


will be 
A’ Bat A” = 0, 


which is equivalent to three equations, 


dV3_aVi\ dF | (dVi_aVs\aF | (dVe_aVi\aF _ 
‘da, da )/d« '\da da )/dy  \da,. das/dz 


0, (6) 


avs iV ak dV, dVo\dF | (dVo_ dVo\dF _ 
api “dB, dx dp. dp, / dy Ups tbs) dean 
dV, adVi\dF : dV, dV,\dF ie dV, _ dVo\dF _ 
dy, dy, ) dx dy,  dy2 } dy dy; dy; /dz 


? 


V’, V" denoting the functions proper to the first and second body, and J’, 
denoting that the values of (, y,z), deduced from F(z, y, 2) = 0, have been 


substituted in V. 


To the three equations (6) must be added the self-evident geometrical 


and the Laws of Plane Waves propagated through them. 105 


equations, which denote that the vibrating molecules at the bounding surface 
may be considered as belonging to either body ; they are three in number, 
£28, man, Cad (7) 

Equations (6) and (7) contain the laws of reflexion and refraction of vibra- 
tions for all bodies, and are completely determinate when the form of V js 
given for each of the bodies in contact, 

Equations (5), (6), (7), are necessary and sufficient to determine the propa- 
gation and reflexion of waves, so fur as they are connected with each other ; 
and no mechanical theory of vibrations is correct which does not exhibit this 
connexion, or which assumes such laws of reflexion and refraction as contra- 
dict the laws of propagation ; the connexion between these laws is no proof of 
the truth of any theory, but the want of a connexion would be a proof of the 
inconsistency of a theory. 

The reduction of the general equations by the omission of the external 
forces may require some explanation. There are two kinds of waves, as I have 
stated in making the reduction, one only of which is the subject of our present 
inquiry. Fluid bodies, such as the atmosphere and the ocean, can propagate tidal 
waves depending on external forces; they are also capable of propagating waves 
of sound which depend directly on the molecular forces ; solid bodies can only 
propagate the second species of waves. In considering this kind of vibration, 
we neglect the external forces, as they are of so much less intensity than the 
molecular forces, that they produce no effect on the motion ; but if we suppose 
the motion to cease, and inquire into the state of equilibrium of the body, we 
should then use the general formula, which includes external forces ; and, even 
in the case of motion, all the coefficients must be considered as variable, in con- 
sequence of the position of constrained equilibrium to which the body would 
return, if the motion ceased. 

It is evident from an inspection of equations (5) and (6) that the differen- 
tial coefficients of the function V, with respect to (a,, a>, &c.), occupy an impor- 
tant position in the theory of elastic media. Hitherto, I have only given to them 
a mathematical definition, I now proceed to explain their physical meaning, by 
the consideration of an elementary parallelepiped of the body. If we conceive a 
plane drawn in any direction in the interior of the body, and consider the parts 

VOL. XXIL P 


106 The Rev. S. Havcuton on a Classification of Elastic Media, 


of the body situated at opposite sides as acting upon any element of the plane ; 
in general, the effect of the particles at one side will be to produce a normal 
force, and tangential forces acting in the element ; these tangential forces may 
be resolved into two directions at right angles to each other. Let us now con- 
ceive an elementary parallelepiped, with one corner situated at the point (,y,z) 
(these co-ordinates here denote the actual position of the molecule at any in- 
stant); let the forces acting on the side (dydz) be denoted by (P,, Q,, R,), P, 
being normal and parallel to the axis of («), (Q,, &,) tangential and parallel to 
the axes of Y and Z; let the forces acting on the side (drdz) be (P2, Q:, R2), 
Q, being the normal force ; and let the forces at the side (dxdy) be (Ps, Qs,Rs), 
R, being the normal force. The forces acting on the opposite sides of the 
parallelepiped will be :—on the side opposite to (dydz), 


dP. dQ dR 
(2, + ae dz) dydz, (2 + a ae) dydz, (2, + aia. ae) dydz ; 


on the side opposite to (dzdz), 


(P+ ry) ded, (a+5 aes 


dy) dadz, (2. + e ay) dadz ; 
on the side opposite to (dady), 


dP. dQ dR 
(?, + a dz) dady, @ + ae az) dady, ( 3+ as az) dady. 


These forces, acting on the six sides of the parallelepiped, must equilibrate the 
forces (Xdm, Ydm, Zdm), applied at the centre of the parallelepiped, and 
arising from external causes ; hence, the equations of equilibrium will be 


dP, mee ges 

Xdm + (Et dy tit =) dadydz = 
dQ, AQ 4 2% 

Ydm + (e+ A ay Se 2) dadydz = 
dR, = ics 


or, since pdxdydz = dm, and the molecular forces must act in the direction op- 
posite to the applied forces, including negative accelerating forces, 


and the Laws of Plane Waves propagated through them. 107 
2 Ps dP sy 


ried eben dy Lor et 

’ dQ, dQ: Qs, 5 
Gomme ueribaig tap ae a (8) 
ie ey ith at dR; 


dy “dz” 


These are identical with equations (2), and are true for all kinds of mole- 
cular action. In the particular case of a rigid parallelepiped, we should intro- 
duce another set of conditions arising from the equilibrium of couples. Let 
(Ldm, Mdm, Ndm) be external couples applied to the parallelepiped; these 
must equilibrate the couples arising from the molecular action of the sur- 
rounding parts of the body; it is easy to see that, neglecting the small forces 
arising from the differential coefficients of P,, P:, &c., the couples round the 
axes of z, y, z, will be 


(R, + Q;) dydz, (P;+ R,) dzdz, (Q,+ P2) dady. 
Hence the required conditions will be 


eL = f,+Q;; 
eM = P; + R, ; 
N=Q,4+P2; e 


and, if no external couples be applied, the conditions will be, 


= (0h. 
(P= It 8 (9) 
(Oh = Jee 


since the couples (#,, Q;), &c., must act in opposite directions. 

These conditions (9) were given by M. Caucuy,* and afterwards adopted 
by M. Porsson.f¢ These writers seem to have considered them as necessary for 
all systems; but this is not true, as equations (8) exhibit all the relations which 
exist between the forces and the motions produced. Equations (9) are necessary 


* Exercices de Mathematiques, tom. ii. p. 47. 
+ Journal de l’Ecole Polytechnique, cahier xx. p. 84. 
P2 


108 The Rev. S. Haucuton on a Classification of Elastic Media, 


for the equilibrium ofa rigid parallelepiped, and will be shown in this memoir to 
be satisfied by the equations of equilibrium of bodies whose molecules attract and 
repel each other in the direction of the line joining them ; but if no supposition be 
made as to the nature of the molecular action,there will be no condition resulting 
from the equilibrium of couples; for we have no right to assume, in the equili- 
brium of a parallelepiped, whose elements may alter their relative position, and 
thus develope new forces, that the same equations hold as in the equilibrium of 
an isolated rigid parallelepiped, for which case six equations of condition are 
necessary, arising from the equilibrium of forces and of couples. 
Restoring the usual signification of (2, y, z) in equations (8), and omitting 
the external forces, we obtain 
_ @E APs , dP APs 
dP de. di, dey. 
dy dQ, dQ , dQ 
= aE ae, ag eles ™) 
= xx ah, _ ais 428 
ade dz dy ‘dz 


These equations correspond with (5), and by comparing them we may deduce 


the following relations : 


dV dV dV 
Dina mene ete 
dV dV dV 
dB, Q,, dp, = & ap, 33 
dV dV dV 

— Po he, ee 
dy, dy, ; dy, 


from which we obtain the following theorem : 

“ Tf through any point (2, y, 2), three elements of planes be drawn parallel 
to the co-ordinate planes, the total action of the part of the body lying at one 
side of these planes will consist of three normal and six tangential forces; and 
these forces may be expressed by the differential coefficients of the function V, 
with respect to (a,, a), a3, &c.).” This theorem is of importance in classifying 


and the Laws of Plane Waves propagated through them. 109 


bodies, as it enables us to pass directly from the resultant forces of the mole- 
cules to the form of the function which determines the laws of propagation 
and reflexion. Introducing these forces into the conditions at the limits (6), 


we obtain 
Pe Gat Po Gt Pos Ge = Pie + Page + PSE 
ae ye = OT + OT + OE: 
By G+ Binge + Bea Ge = Bese + Regge + RE, 


If the axis of z be made to coincide with the normal, we shall have 


aF _o, dF _o aFo, 
Gas eae ae ee 
Hence, 
Pu=Pu, %=&, 
os = Qs, No = No » (11) 
Res = Fi , 6 = fo. 


These equations at the limits are the mathematical statement of two facts, of 
which one is mechanical and the other geometrical. 

1. That the forces, normal and tangential (arising from molecular action), 
acting upon an element of the bounding surface, must be equal and opposite for 
the two bodies in contact. 

2. That the motion of the particles in the bounding surface may be con- 
sidered as common to both bodies. 

I shall now return to the general equation (4); let the function V be di- 
vided into homogeneous parts, so that 


Vaht+ot+oo+¢; + &e., 


where gy is constant, ¢, of the first degree with respect to (a,, a)), and so of the 
others ; then, neglecting ¢ and terms higher than the second, we obtain 


110 The Rey. S. Haucuton on a Classification of Elastie Media, 


V= g, + dr, 
$, = Aa, + Asa, + A,a; 
=F Bp, + BB» + B;B; 
+ Cm + Coys + Css . 


2 = (4,') a" + (a2?) an? + &e. 
+ (a,b2) + By + &e., + (Cy) + Ys@2 + Ke. ; 


the expressions within the brackets denoting the corresponding coefficients. 

¢, will contain nine coefficients, which will be constant, or functions of 
(x,y,z), according as there are no external forces, or vice versd; and ¢» will 
contain forty-five distinct coefficients. I shall consider these functions separately. 
Introducing ¢, for V in equation (4), we obtain, 


{lle (= Sb we in Si &; ic) dadydz = {j(A,8é + Bin + Cee) dydz, 
+ ff{(Aseé + Béy + C80) dady 


((dA, dA, dA, dB, dB, dB. dC, , dCr dC). : 
Uae ape ae + ae ap ae) +a ay ae) ete 


da dy ad 


whence we obtain 
res dA, dA, dA, 
* de = dy * dz’ 
No ote dB, re dB, ie dB, 
“de da dy dz’ 
pom dC, 144 HGn. Gr 
“de de dy dz~ 


(13) 


The terms on the right hand side of equation (13) must be added to the 
dynamical equations arising from ¢,, even in cases where (X, Y, Z) may be 
neglected on account of the intensity of the molecular forces. If we wish to 
take account of the external forces, we should use, instead of (13), the fol- 


lowing: 


and the Laws of Plane Waves propagated through them. 111 
RU dA, dA, i dA, _ 
fom eae en 
2 n dB, dB, dB, ms 
“de wae ' ay dy arr OS 


oe a: dC, , dC, 
°de de * dy ‘dz 


eX ; 


— &Z, 


If no external forces act, equations (13) disappear, in consequence of A,, A,, 
&c., becoming constants ; but the conditions at the limits (12) will still remain, 
unless the coefficients be not only constant, but zero. 

The part of the differential equations of motion depending on @, will be 
found by introducing é, in place of 6V in equation (3), and integrating by 
parts, according to the methods of the calculus of variations ; but it may be 
found more readily by introducing ¢, for V, in equation (4). Neglecting the 
equations of condition at the limits, we obtain for the equations of motion, 


7 oe = (at) £84 (a = pt (ae) os 


aE @é 
Het) a i ee da 08) ny 


he 
+ (ab) £24 (aba) 2 et (abs) 3 

(14) 
ay ad? 
+ (ab; + ab) To + (ab; + ash) Aas + (a,b. + anb,) aaa 


= (ae 


ad? aL 
») Get (aoe) a 


a? a? a 
+ (2¢3 + AsC2) = + (ay€3+ a3¢1) oan + (dies + C1) oie 


—e 47 =() pe as Lie (1) F fl On 2 


72 C7 ha 
+2(babs) = iii = + 2(bD,) 5 fs csonndt 


112 “ The Rev. S. Haventon on a Classification of Elastic Media, 


+ (b,¢, Us (br) 5 73 E+ a) oh 


ss 
+ (bees + b3¢2) dy iy* (be, + b,c, ) = - SF (bic. + bye) ef 
+ (a,b,) = + (a2b2) i Bis (a,b,) 2 


a? d? 
+ (d2bs+ abe dy ~ +(a,b,+4,), aa + (ab2 + a2b,) ea 


Fe =) Th + 2) 4) F 


+ 2(c2¢s) ia + 2(¢¢;) ie + 2(¢¢2) E 
+ (a,¢,) = ot (axes) a (a. fies 
+ (a2¢3 + a3C2) —_ (ae, + a,¢,) = + (Me, + a1) i 
dydsz = oF Tay 
+ (bye) Oe + (brea) 5 pt bes) G 
+ (bits + b3¢2) 5 See (6, 0, +b,0,) = n+ (bie. + b2¢1) - 4. 


By combining these Pete with (12), and comparing (4), we obtain from the 


function V = ¢, + ¢, the following equations of motion, 
Pt d (dd, d (dd, dd» 
eae isis) + daa ) nae (ae +4, 
dn dbs d (dd, dd» 
~<a at) ayant) + lant) 


Car dp» dds dds Y 
ap = eee c) t alee zs 0) +4 Hae Se ): 


(15) 


These are the equations of small oscillations of all media, for which the direct 


influence of the external forces may be neglected. 


In equations (14) it will be observed that nine of the coefficients are 


and the Laws of Plane Waves propagated through them. 113 


composed of two terms, coefficients of the original function , ; these compound 
coefficients will, in the equations of motion, be equivalent to simple coefficients, 
so that the total number of distinct constants in the equations of wave-motion 
will be reduced to thirty-six ; this reduction cannot, however, be introduced 
into the conditions at the fee: because each coefficient will at the limits be 
multiplied by a different function of (, y, z). Hence may be deduced an im- 
portant theorem, which I shall prove in a general manner. 

“ Two bodies, different in their molecular structure, may have the same 
laws of wave-propagation, but cannot have the same laws of reflexion and 
refraction.” 


The laws of wave-propagation (5) depend upon the differential coefficients 


of (se &e.), taken with respect to (, y, z); but the laws of reflexion and 


refraction (6) depend on the quantities (Fe &e,) themselves. Each of these 


quantities is of the form 


A 


dé = pin dy. pul d¢ dé dé 
sig siege aise dase aphid Onda dg de 


If, therefore, for example, in the first of the equations (5), there be in (=) 


7 
a term of the form (2 =) there will be in = a term of the form (4 al 
a2 


then, differentiating the first with respect to 2, and the second with respect to 


? 


y, we shall obtain, as part of the equations of motion, (Bb + A’) Ty , while 


the corresponding part of the conditions at the limits will be {2 i sédydz 


+{[4’s gas 7, tededz. If, now, we suppose another body such that (45) a 


(2 i) are terms in (5) and (=) the part resulting from these quan- 
a ay 


oy 
tities in the equations of motion will be (A’+B) ar which is identical with 
eT 
the former value, while the corresponding portion of the conditions at the 
VOL. XXII. Q 


114 The Rev. S. Haveuron on a Classification of Elastic Media, 


limits will be {]4" Se tedyile + {2 © edd: ; which cannot be reduced to the 
former value, unless A’= B. 

It is sufficient here to establish the general theorem. JI shall return to it 
again, in comparing Professor Mac Cuniacu’s theory of light and that ad- 
vocated by M. Caucuy and Mr. Green, which give the same laws of wave- 
propagation, but differ in the laws of reflexion and refraction. 

I shall now integrate the equations of motion (14), for the particular case 
of plane waves and rectilinear vibrations. Let (/, m,n) be the direction cosines 
of the wave-normal, (a, 8, y) the direction of molecular vibration, and (v) the 


velocity of the wave ; then the integral will be 
Qa 
& = cos af\< (lz + my + nz — mu, 
Qa 
4 = COS Bf (da + my + nz — ut) |, 


G=Tcos rf\ z+ my + nz — ot) } 


Introducing these values into the equations (14), we obtain 


ev cos a= P’ cosa+ H’ cos B+ G’ cos y, 
ev cos B= Q cos B+ F” cos y + H’ cos a, (16) 
ev’ cos y = FR’ cos y + G’ cos a + F’ cos B; 
where 
P! = (a") P + (ay?) m? + (a3?) n? + 2(asa3) mn + 2(a,a3) In + 2(a,a,) lm; 
Q! = (b,°) P + (bs") m? + (bs?) n? + 2(bob3) mn + 2(bb;) In + 2(bib2) ln; 
RY = (¢,7) P + (e:") m? + (¢37) n? + 2(coc3) mn + 2(exes) In + 2(ere2) ln; 
ji! = (161) P+ (boe2) m? + (baes) 0? + (bees + bar) mnt (bie3+03¢1) + (Die, +boc; lm : 
G' = (a6) P+ (re) mM? +(dses) 0? + (A2C3+AsC2) MN+(Ayes+ AC; ) N+ (ay,er-Ha2¢, lm; 
i= (ab, ) P+ (Gabo) m?+ (dsbs) + (dabst dsb) min+ (aybstagb,) N+ (aybo+-asb, lm. 


Equations (16) are the well-known equations for determining the axes of 
the ellipsoid whose equation is 


P+ Up + hs 4+ 2F yz +2G/ez + 2H’ zy =1. (17) 


and the Laws of Plane Waves propagated through them. 115 


There are, therefore, three possible directions of molecular vibration for a 
given direction of wave plane; and there will be three parallel waves moving 
with velocities determined by the magnitude of the axes of the ellipsoid, the 
direction of vibration in each wave being parallel to one of the axef& The 
theorem involved in equation (16) was first proved by M. Caucuy,* for bodies 
whose molecules act by attractions and repulsions in the line joining them. It 
is here extended to every kind of molecular action, and shown to be a funda- 
mental property in molecular dynamics. It may be worth while to examine 
the reason of its truth. It arises from the homogeneity of equations (14) 
resulting from the absence of external forces. The right hand member of each of 
the three equations of motion consists of eighteen terms ; there will, therefore, 
be in all fifty-four terms; if each of these were supposed to have different and 
independent coefficients, equations (16) would cease to be true, and the coefli- 
cients of (cos a, cos B, cos y) would be nine distinct quantities, so that the 
theorem which represents the direction and magnitude of the molecular vibra- 
tion by means of an ellipsoid whose coefficients are functions of the direction 
of the wave, would no longer be applicable. Equations (14) contain only 
thirty-six distinct constants, and this reduction in the number of constants arises 
from the assumption that the virtual moments of the system may be repre- 
sented by {\jé Vdadydz; which is equivalent to assuming that the virtual mo- 
ments of the molecular forces applied at any poimt may be represented by the 
variation of a single function: 


Qeq + Qed + &. = 8V. 


The cubic equation whose roots are the squares of the reciprocals of the 
axes of the ellipsoid (17) is 


(P’—s)(Q'—s) (FR —s)—F? (P’—s)—G?(Q'-s) —H” (R'—s) 42h" H=0; 
where s=ev*. Hence, if (P, Q, R, F, G, H) denote the same functions of (a, y, z) 


that (P’, Q’, RB’, F’, G’, H’) are of (1, m,n), it may be shown, in a manner similar 


* Exercices de Mathematiques, tom. v. p. 32. 


Ow 


116 The Rev. S. Haucuton on a Classijication of Elastic Media, 


to the method for bodies whose molecules act in the line joining them, that the 
surface of wave-slowness* will be 


(P-1) (Q-1) (R-1) — F?(P-1)— G?(Q-1) —H?(R-1)+2FGH=0. (18) 


(P—1, Q—1, &c.) equated to zero, denoting the six fixed ellipsoids used in 
the memoir referred to ; these ellipsoids thus appear in the general theory of 
molecular dynamics, and will have the same use in interpreting the conditions 
at the limits in the general problem, as in the particular case of attracting and 
repelling molecules. As their use has been fully explained in my former me- 
moir, I shall only refer to it, and pass on to other subjects. 

I shall here state the general conditions necessary, in order that the mole- 
cular equilibrium of a body removed from the influence of external forces 
should be stable; this investigation will be found of use in the subsequent part 
of this memoir. The equation of virtual velocities, in the case supposed, will 
become 

{li Vdadydz = 0; 
or, as it may be more accurately stated, 
{Ji Vdadydz = 0, or < 0; 

this sum never becoming positive for possible displacements. The equa- 
tion of virtual velocities, as stated by M. Porsson and other writers, supposes 
no virtual displacements but those for which equal and opposite displace- 
ments are possible; the correct statement of the principle is, that the sum of 
the virtual moments of the system can never become positive for possible dis- 
placements. For the full development of this important correction of the equation 
of virtual velocities, as given by Lagrange, I shall refer to a memoir of M. 
OstTROGRADSKY, contained in the Memoires de 1 Academie de St. Petersbourg.+ 

The application of the principle to the present case will be evident upon 
the statement of the question. As the form of Vis given in terms of (a, a2, &c.), 
we shall have 


tV= dV Oa, ad, Ga, + &e.; 
da, day 


* Vide Transactions of the Royal Irish Academy, vol. xxi. part ii. p. 172. 
+ Tom. iii. p. 130. 


and the Laws of Plane Waves propagated through them. 117 


dV dV 
(Ge ePsg &e. 
which are functions of (2, y, z). The whole body may, therefore, be divided 
into couches by a series of surfaces whose equation will be 


a—C=0; 


(C} denoting the parameter of the system. Ina similar manner, the body may be 
conceived as divided into couches by other sets of surfaces corresponding to 
(4, a3, &c.). In any one of these couches the corresponding function 
(a, a, &c.) will have a constant value, which will vary from one couche to 
another. 

If L = 0 be the equation of a surface, we may conceive all space as divided 
into two portions, which will be distinguished by the property, that the portion 
lying at one side of the surface will have the function of (x, y, z) denoted by 
(L), positive; while for the rest of space, lying at the other side of the surface, 
the function (Z,) will be negative. Similarly, é£ will be positive for all dis- 
placements made at one side of the surface; negative for all displacements on 
the opposite side; and zero for displacements in the surface itself, 

Let us now resume the equation, a, —C=0, which denotes a surface drawn 


) denoting forces tending to alter the quantities (a), a),a;, &c.), 


in the interior of the body, along which the value of = remains constant. It is 


necessary for the stable equilibrium of the body, that if the particles composing 
this surface be displaced from it, the molecular forces developed by the dis- 
placement should tend to restore them to the surface; this condition will 
require that (i ; ay ; ke.) which are the forces developed by the displace- 
1 2 
ments (€a,, éa,, &c.), should have signs opposite to those of the displacements, 
If no forces are developed tending to restore the molecules, we shall have 
dV dV 
ia = 0, das = 0, &e.; 
and these equations will determine the dimits of stable and unstable equilibrium 
in the body. 


118 The Rev. S. Haucuton on a Classification of Elastic Media, 


SECTION Il.—LAWS OF NORMAL VIBRATIONS. 


It has been shown that the differential coefficients of the function V, taken 
with respect to (a,, a, &c.), denote the normal and tangential actions of the 
surrounding body on an elementary parallelepiped. I shall now suppose that 
the body is so constituted that the tangential forces vanish, and so deduce the 
laws of a body capable of transmitting pressure in a normal direction only. 
The condition that the tangential forces vanish will give the equations, 


dV dV dV 
dats 0, Gia ia 
dV dV dV 
ae aan a, 


which will reduce the function to the form 
2V = Aa? + BBY + Cy? + 2Ppoy,+ 2Qay,+ 2Ra,p. 


At first sight, it might appear that we might assume this or any other form 
of function to define a body, and proceed to deduce the laws of motion ; but, 
as it is possible that an assumed form of the function may be only true for par- 
ticular axes of co-ordinates, it is always necessary to examine whether a trans- 
formation of co-ordinates will introduce any new terms ; if this be the case, 
then the assumed function will not represent completely the molecular structure 
of the body, as it will be merely a simplification of a more complex function, 
produced by assuming particular axes of co-ordinates, which are connected 
with the crystalline structure of the body. I shall examine the function just 
given for normal pressures by this method, and determine it so as to be inde- 
pendent of the axes of co-ordinates. The relations between the two systems 


of variables are 
z= aa’ + by + cz, 
y & aa! + bly! + cz, 


if Its 


z=ala + bMy' + c%2; 
also (&, 9, ¢) will satisfy these equations. Let us now assume 


U=B,+92, VENT 4 w=a,+B,, 


and the Laws of Plane Waves propagated through them. 119 


we may immediately deduce, by the formule for transformation of the indepen- 
dent variables, the following values for the nine quantities (a,, a), &c.), 


a,=@a, + bp, +e ee + av’ + abu’, 
Po = aa, + 08) + cy + Ulu! + a'e'e! + a's’, 
= =— aa / 2b leisy +¢ naary, / s+ Olu! + ae Wat t- Vee, 


[+0 (ay, + bys + ev) + (aly +b’, + ey) 
a (aa, + b'a, + cas) a’ (aa, + ba’, + cas) 
a, = 4 +b (a’B, + a, + ¢'B5) B, = 4+05' (ap; + bB; + ¢B)) 
[+ e (ain + U'y2 + ey) ee e (ay, + bys + ox) | 


kes a! (aa, + ba, + a ” (ala, + b'a, + eas) 
B,= ++ 0! (ap, + OB, + | weft bY (a’ Bi + o'B, +e a) 
L+ of (aly, + Boy + cys) +0! (aly + Uy, + e'y)} 
[ a” (aa, + ba, + cas) 1 wl a (aay + ba, + 6a) 
= +0" (api + UB + Bs) “ne b (ap +0"B, + ep)! (19) 
[ 


It is plain from the first three equations that the change of the co-ordinate 
axes will introduce into the function V three new variables (u,v, w). Hence, 
the function which I have assumed is only admissible for particular axes, and 
the true form of the function from which it is derived will be that of a function 
of the six variables used in my former memoir. 

It is, however, possible to obtain such a function of (=. ma 4) as shall 
not change its form with the transformation of co-ordinates. For, adding toge- 
ther the values of these quantities, we shall banish (w’, v’, w’), on account of the 
relations, 

be + b'c' + bc’ = 0, 
ac +a'c +a"c"’=0, 
ab +a + ab’ = 0. 


The result of the addition will be 
dé dn, d¢_ dé’ di «= 


da * dy dz dx!" dy/' 


=w. 


This quantity (w) will retain its value, independent of the directions of the 


120 The Rev. S. Havcuton on a Classification of Elastic Media, 


co-ordinates, and consequently the proper form of the function V, for bodies 
which transmit only normal pressure in every direction, will be 


VE Fa): (20) 


There are two other forms of the function V (considered as containing the 
nine differential coefficients) which possess this property of reproducing them- 
selves by transformation of co-ordinates. Let (X, Y, Z) be determined by the 
following equations, 

X=—R-Y, Y=en—-aw, Z=m—f. 


It appears immediately from equations (19) that (X, Y, Z) are expressed by the 
following relations in terms of (X’, Y’, 2’), 


X = aX'+ bY’ 4+ cZ, 
Y=aX'+0Y'+ eZ, 
Zaa'X +0'Y' +02. 


These formule are well known, and prove that another self-producing form of 


the function V will be 
Vi Xe ay (21) 


I have proved in my former memoir that if (a, B, y, w, v, w) denote the co- 


efficients { = Zz ; = (Z <), (3 + =) (F + =) \ they will become, 
by transformation of co-ordinates, linear functions of (a’, 6’, 7, uw’, v', w’) ; and 
that the formule of tranformation are the same as for (2”), (y’), (2°), (2yz), 
(2xz), (2vy). Hence, a function of these six quantities will reproduce itself, 
by transformation of axes of co-ordinates. The third form of V which possesses 
this property is, therefore, 


V=F (a, B, 7, u,v, wv). (22) 


The forms of the function V, which have just been determined, are perfectly 
general, and do not merely express properties of the body with reference to 
particular axes, but general properties of its molecular structure, independent 
of the directions of the co-ordinates. 

I shall consider in the present section the function (20),which is peculiar 


and the Laws of Plane Waves propagated through them. 121 


to bodies which transmit normal pressure in every direction. Before deducing 
the equations of motion, it may be useful to show, in another manner, the neces- 
sity for reducing the function of (a, 8,7) to a function of (a+B+y¥). By the 
theorem proved in my former memoir, (a, 8, y) are transformed by the same 
equations as (2, y*, 2?) ; hence, V= F(a, B, y) may be represented by a surface 
whose equation contains only the squares of the co-ordinates. It is evident 
that such a surface will be symmetrical with respect to the co-ordinate planes ; 
and if this condition be satisfied for every system of co-ordinates, the surface 
must be a sphere ; hence, 


V = F(a,B,y) =F (a+ 644). 


The equations of motion deduced from (20) will be the equations commonly 
used in hydrodynamics, and for this reason it may be useful to state them in 


their most general form. Let (x, y, z) denote, as in equations (1) and (2), the 
actual positions of the molecules ; then, since 


st p{dee , diy diz 
Va Fee Gls 2), 


we shall obtain from equations (2) 


1 dp _ du du du du 

Ree dees dee. dy eas 

1 dp dv dv dv dv 

St pe lta Os ee dS At 23, 
Ath nr e Ee Oa He? Gea) 
1 dp dw dw dw dw 

Ren a ae a ae 


: dV . : ‘ 
assuming p = ae and recollecting that (u’, v’, w’) are the total differential co- 
w 


efficients of (u,v, w), taken with respect to (¢t). These are the mechanical 
equations of the problem, and, combined with the equation of continuity, 


dp, d(gu) , d(gr) , (pw) 
CO oa teat roman e 7 roplan) eee) 
VOL. XXII. R 


122 The Rev. S. Haucuton on a Classijication of Elastic Media, 


contain all that is requisite to determine the motion of points situated in the 
interior of the mass. The mechanical conditions to be satisfied at the limits 
are contained in the double integrals, which become, by the substitution of the 
element of the bounding surface, 


{[pdS (a cos X + &y Cos p + éz Cos v), 
(A, », v) denoting the direction of the normal. It may be easily shown from 
this expression, that if P denote a function of (2, y, z, t), expressing the normal 


forces applied at each point of the surface, the mechanical condition at the limits 
will be expressed by the equation, 


p-P=0. (23, b) 


To which must be added the equation of the bounding surface, deduced from 
geometrical considerations, 


es) (24, b) 


It is unnecessary to enter further into this subject, as it is fully treated by 
LaGRANGE, in the second volume of the Mecanique Analytique, and is indeed 
the only example given by him of the application of his formule to the problem 
of bodies composed of continuous points. 

Resuming the former signification of («, y, z, €, n, ¢), we find from equations 


(5) or (15), since 2V = 2pw + Av’, and on =p + Ao, 


Pe = dp dw 
S  igprds.. dx? 

dn _ dp dw 
Se de dy + dy b] 
Gee 4 de 

thie tke dz 


If no external forces act, p and A will be constants ; and, in this case, these 
equations become, assuming a negative sign for A, so that the equilibrium may 
be stable, 


and the Laws of Plane Waves propagated through them. 123 


PE , dw 
Sage de’ 
dy = dw 25 
«ae 4 ay’ aie 
ag _ 4 de 
“dt ~~ dz 


and, by differentiating with respect to (z, y, z), we obtain 


Co A/@wo dw dw 
d@ ¢ é 55 dy? i =| ; (26) 


which determines the cubical compression as a function of (2, y, z, t). 

The equations (25) and (26) are applicable to the propagation of sound in 
gases, and to the longitudinal vibrations of elastic solids ; but there will be an 
essential difference between the two cases. If the gas were freed from the 
action of external forces, and unconfined at its limits, its molecules would sepa- 
rate, and a displacement would develope no force tending to restore them to 
their original positions ; hence, (7. %) would become positive, which is in- 


consistent with stable equilibrium, and the velocity of wave propagation 


( y =) would become imaginary. In order, therefore, that the equilibrium of 
€ 


the gas be stable, we must suppose a constant pressure exerted at the limits, 
sufficient to keep the molecules together, and restore them to their original 
positions, if displaced. No such condition is requisite in the elastic solid, for 


aVi : F : : : 
(a ia) will be negative, without the assistance of forces applied at the bound- 
iw 
ing surface. 
SECTION Ill. LAWS OF TRANSVERSE VIBRATIONS. 


In order to obtain the form of the function V peculiar to transverse vibra- 
tions, we must suppose that, if a plane be drawn through the body in any 
direction, the molecular forces exerted on any element of the plane will be 
altogether tangential. Hence we obtain 

R2 


124 The Rev. S. Haucuton on a Classification of Elastic Media, 


dV os Ve 


ja ’ dp, ’ Tis 


and the function V will become 
V= F(a, a3, Pi, Bs, Yu 2): 


But, as I have already shown, such a form must be assumed, as will reproduce 
itself by transformation of co-ordinates. The only function which satisfies this 
condition is the function (21), 

V Se (Ae 2). 


This function, deduced in a different manner, has been used by Professor 
Mac Cuttacu in his mechanical theory of light; and for the discussion of its 
properties and the laws of propagation, reflection, and refraction, deduced from 
it, I shall refer to his memoir in the Transactions of the Royal Irish Academy.* 
As, however, I shall have occasion to use them hereafter, I shall here state the 
differential equations of motion, and the conditions at the limits. On account 
of the form of the function, the following relations exist : 


AS ae 

aX i dB, |. dry,’ 

BVipe OM OMe 

GY ay, ~ das 

DN NE sess 

aZ day 0 GBy 
Hence equations (5) will become 


a Si a Ai 

“dé ~ dy dZ~ dz dY’ 

ahi th Gh GR 2G 
~ Get de OX da dZ' (CO) 
_.f_4 av _d av 

d@ dz dY dy dX’ 


and the Laws of Plane Waves propagated through them. 125 


These are the equations of motion; also equations (6) will become 


(= 2) dF Ge: “) aS 


a, faz dy Lay mare) de g 

(aFs ave ah (a0 AV) ar 9g 
AX dX } dz dZ aZ } dz ¢ 

(aY5_ av ab (a0s_ ave) ar 
Ye RY | lee EXO EX) die 


These are the conditions to be fulfilled at the limiting surface F(a, y,z) =0. 
They are equivalent to two conditions only, as the third equation may be de- 
duced from the first two. The reason of this is evident @ priori; for the con- 
ditions at the limits express in general, that the normal and two tangential 
pressures arising from the molecular forces in each body equilibrate each other 
for every point of the separating surface; but in the present case there are no 
normal pressures ; hence there can be only two mechanical conditions at the 
limits. To these conditions at the limits, arising from the mechanical equa- 
tions, should be added the three geometrical conditions resulting from the equi- 
valence of vibrations; these conditions are 


/ 
& = £5 MN = 5 & = ¢ . 


These, together with the mechanical conditions, will be equivalent to five equa- 
tions, which Professor Mac Cutiacu reduces to four by the hypothesis that the 
density of the luminiferous medium is the same in all transparent bodies; this 
hypothesis is necessary in order to reduce the number of equations to the num- 
ber of unknown quantities in the problem. 

If no external forces act upon the system, the function V will be reduced 
to a homogeneous function of the second order, 


2V = PX’? + QY? + R27? 4+ 2FYZ + 2GXZ + 2HXY; 


and since (X, Y, Z) are transformed by a change of co-ordinates, in the same 
manner as (2, y, 2), it is evident that the coefficients of the rectangles will 
vanish for axes of co-ordinates which coincide with the axes of the ellipsoid, 


Pa? + Qy? + Re + 2Fyz + 2Gaz + 2Hay = 1. 


126 The Rev. S. HAucuton on a Classification of Elastic Media, 


Hence the simplest form of the function will be 
2V = PAP OY? + RZ 


The axes of co-ordinates are in this formula the axes of elasticity. 


SECTION IV. EQUATIONS OF A SYSTEM WHOSE MOLECULES ATTRACT AND REPEL 
EACH OTHER. 


The third form of the function V, which possesses the property of repro- 
ducing itself by a transformation of co-ordinates, is given by equation (22), 


V=F (a, p, 7, u,v, w)- 


The six variables contained in this function are the quantities upon which a 
change in the distance between the molecules depends; hence the variation of 
this function will express the virtual moments of a system of forces tending to 
alter this distance. In my former communication* I have made use of this func- 
tion, using definite integrals to represent the coefficients ; the equations thus 
found contain a smaller number of constants, than if the coefficients had been 
assumed to be arbitrary, without any relation expressed by definite integrals. I 
shall here use the function in its most general form, as the use of definite inte- 
grals may, perhaps, involve an hypothesis which would be too restricted to 
represent all the bodies whose molecular forces act in the line joining the 
molecules. 

The following relations will exist, in consequence of the form of the function, 


av av _av. 
du dp; dy.’ 


GINS ChE GNA 
aay a 
dw da, dp, 


These equations will reduce the equations of motion (5) to the following : 


* Transactions of the Royal Irish Academy, vol. xxi. p. 151. 


We 12 d dV d dV ane ee 
“d@ dz’ da ‘dy dw dz dv’ 
dy a aoe d ' diViieed aV 
di dy dp dz du + Te dw? 
Pe ad ae d dV da dV 
d? dz dy ‘dx dv tay ‘du’ 


(30) 


These are equivalent to equations (24) of my former paper, and are an imme- 
diate consequence of (29), which express the relations among the resultants of 
the molecular forces consequent upon the restricted form of the function. Equa- 
tions (29), or the corresponding equations (9), 


Q, — Rk, = 0, Rk, — P;=0, P,-—Q,=0, 


are analogous to a statical theorem given by Fresne in his Memoir on double 
Refraction. If no external forces act upon the system, or if their influence may 
be assumed to be constant at all points of the body, then the coefficients of V 
will become constants, and the linear part of V will introduce no terms into 
the differential equations, which will in this case depend upon a homogeneous 
function of the second order. There will be, therefore, in general, twenty-one 
constants, viz., the coefficients of the function 


2V = (a’)a’ + (B°)B + (yo? + (u?)w? + (v?)v* + (ww? 
+ 2} (By)By + (ay)ay + (a8) aB} + 2} (vw )ow + (uw)uw + (uv)uv} 
+ 2u|(au)a + (Bu)B + (yu)y} + 2v{(av)a + (Bv)6 + (yw) 
+ 2w} (aw)a + (Bw)B + (yw)7}. 

The equations of motion deduced from this form of the function V are 
identical with the equations used by M. Caucuy in his theory of light.* They 
are deduced by M. Caucny directly from the consideration of attractive and re- 
pulsive forces between the molecules. These equations have been used also 
by Mr. Green, who seems to have considered them as more general than M. 
Caucuy’s equations. 

The function (22) is not altered in form by an alteration of the co-ordinate 


* Exercices de Mathematiques, tom. v., p. 19. 
ft Cambridge Philosophical Society’s Transactions, vol. vii. p. 121. 


128 The Rev. S. Haueuton on a Classification of Elastie Media, 


axes, and is the most general which can be used for the case considered in the 
present section. The direction of the molecular vibration will not be either 
normal or transversal, but will be determined by the axes of an ellipsoid first 
noticed by M. Caucuy in treating of bodies whose molecules attract and repel 
each other. It may be worth while to examine whether there are any subordi- 
nate functions which possess the property of not being changed in form by the 
change of co-ordinates ; as such functions, if they exist, will contain the laws 
of classes of bodies contained under the general function (22). I have already 
discussed one such function (20), which is evidently a particular case of (22). 
I shall now determine another remarkable subordinate function, which, while it 
is much less general than (22), yet contains most of the bodies whose proper- 
ties are at all interesting. The following formule of transformation may be 
easily demonstrated.* 


a=a?a + DB! + cy! + bew' + acr’ + abu’; 

B = aa! fe bp! 4 c!9/ Bt be'u! ae a’e'v' et a’b’'w' ; 

y= a’? a’ i b'?p' + ery! ae 6 e'u' ib a el'y! ae ab!'w'; 

“u= Qa'a a! +20'bB 4260 +(b'c! +b" )u' + (a'e" +a" Ju’ + (a/b + ab’) wu’; 
vy = 2Qad‘a'+ 2bb'B! + 2ee!y' + (be +6"c)u' + (ac + a!c)v' + (ab" + ab) w'; 
w= 2aa'a’ + 2bb'B’ + 2ce'y! + (be + b'e)ul + (ac + a’c)v' + (ab! + a’b) wv’. 


If we now assume six functions of (a, 8, y, u,v, w), defined by the following 


equations : 
A=w—A4ABy, pa=v—4ay, v=w? —4af; 
@=2au—vw, x=2bv—uw, = 2yw—w, 
it may be shown without much difficulty, that these new functions are trans- 
formed by the following equations : 
A= aN + Bp! + cv’ + Ahed! + 2acy’ + 2abw’; 
waar + bu! +c? + Q'e'g' + 2a'e'y! + 2a'l'Y’; 
v= ant + dT + fy + 2c’ + 2a"c">' + 2a"'b" Ww; (31) 
p= aa N40 pW tec +(e +b"c') b' +(ale’ +a") x/ + (ab +-a"b) V'; 
x = aan’ + bb ul + ec!’ + (bel + be) gp! + (ac! + ae) x’ + (ab! + a/b) WV; 
v= aan + bb’! + cel’ + (be! + ce) b' + (ac + a’c) x! + (ab’ + a’b) Y’. 


* Transactions of the Royal Irish Academy, vol, xxi. p. 160. 


and the Laws of Plane Waves propagated through them. 129 


Hence a function of (A, p, v, , x, ¥) will reproduce itself by transformation 
of co-ordinates; let the function be 
2V = PrA+ Qut Rv + 2Po + 2Gy + 2H 


I shall first prove the existence of three rectangular axes, for which this 
function reduces to its first three terms. If the axes of co-ordinates be trans- 
formed, and the coeflicients of (¢’, x’, ¥) equated to zero, we obtain 


Phe +°Qb'c! + Bbc! + FC" + 0") + G(be" + be) + H(be + bce) = 0; 
Pac + Qa'e’ + Rae” + F(a'c’ + a) + G(ae" + ac) + H(ac’ + a’'ce) =0; 
Pab + Qa’b! + Rab" + F(ab" + ab’) + G(ab" + ab) + Hab’ + ab) = 0. 
These equations will be satisfied by assuming for axes of co-ordinates the axes 


of the ellipsoid 
Pa? + Qy + R2 + Wyz + 2Gaz + 2Hary =1. 


Hence, for these particular axes, 
2V = P(w — 4By) + Q(v’ — 4ay) + R(w* — 4a). (32) 
Using this value of V in equations (30), we obtain for the equations of motion, 


CEL dZ ay 


Pe Tt dy oe: 
Pe Waxes aZ,: 
EO Ta dX - 
(X, Y, Z) denoting the same functions as in (27). If the function were 
, 
2V=PX*?+ QY?+ RZ’, (34) 


equations (27) would be the same as (33). 

These equations are those used by Professor Mac Cutiacu and by Mr. Green. 
They denote transverse vibrations, and will give FresneL’s wave-surface for 
plane waves, and also the vibrations parallel to the plane of polarization. Mr. 
Green has deduced his equations from a homogeneous function of the second 
order of (a, B, y, u, v, w), by restricting it so as to be capable of propagating only 

VOL. XXII. s 


130 The Rev. S. Haveuron on a Classification of Elastic Media, 


normal and transverse vibrations; this restriction will reduce the constants 
from twenty-one to seven; six of which belong to the transverse vibrations, 
and the seventh to the normal vibration. It is to be remarked, however, that 
a function of (A, #, », @, x, +) will represent only a part of the properties of 
bodies whose molecules attract and repel each other. Such a body is always 
capable of transmitting normal vibrations, and though it may transmit trans- 
verse vibrations following the laws of FREsNEL’s wave-surface, yet the normal 
vibration cannot be supposed to vanish. If we include normal vibrations, the 
most general form of the subordinate function will be 


= F(a, Vy Hs %) Ps Xs y). (35) 


The manner in which I have obtained equation (35) is not so direct as 
Mr. Green’s method, and I have only used it for the sake of the intermediate 
equations (31), which exhibit a remarkable property of the quantities (A, 4, », 
¢,xX,¥)- The direct method of deducing it is the following. Let M. Caucuy’s 
ellipsoid (17) be constructed for the function V, which is homogeneous and of 
the second order with respect to (a, B, y, U, v, wv). 

Equations (16) determine the directions of molecular vibration ; in these 
equations, if (J, m,) be substituted for (cos a, cos B, cos y), we shall obtain 
the following: 


i 
(Q'— PR’) mn + EF" (n? — m?) + H'In — G'im = 0, 
(Rh — P’) nl + G! (P — nr?) + F’'ml — H'mn = 0, 
(P’— Q') ln + H! (m?— 2) + G’nm — F'nl = 0. 


These equations express that one of the axes of the ellipsoid is normal to the 
wave-plane, and consequently that the other two axes are contained in the wave- 
plane: by stating analytically that these conditions are true, independent of the 
position of the wave-plane, we obtain the following relations among the coeffi- 
cients of V, 
(pa)'= 0, (ev) =0,. (aw) = 0, 
(yu) =0, (yw) =0, (Bw) =0, 
(au) +2(vw)=0, (pv) + 2(uw)=0, (yw) + 2(uv) = 0, 
(a?) = (8°) = (7°) = 2(w’) + (By) = 2(e*) + (ay) = 2(w*) + (a8). 


These fourteen equations will reduce the function V to the form 


and the Laws of Plane Waves propagated through tnem. 131 
2V = Aw? + PA+ Qu + Ry + 2F ob + 2Gy + QM y. (35, a) 


This is the function used by Mr. Gruen, and is a particular case of equation 
(35). The first term of this function will determine the normal vibration, and 
the last six will represent, as we have seen, transverse vibrations propagated 
according to the laws of Fresnet’s wave-surface. 

If the body be homogeneous and uncrystalline, we shall have the relations, 


dy Sees 
B=0,) G=0; H=0, 


which will reduce the function V to the form 
2V = Aw’ + P(A + +4»). (36) 


This function will represent homogeneous solids, liquids, and gases, and will 
be the complete function for these bodies, provided there be neither external 
forces nor pressures at the limits. If there be such forces, however, it 
will be necessary to add to the function (36), which is of the second order, 
other terms of the first order, as in equations (15). If the function (36) be 
assumed to represent all the forces engaged, the equations derived from it 
will represent the motion of a body abandoned to its own molecular actions, 
and freed from all external influence, such as gravitation, pressure of an atmos- 
phere, &c. The known properties of solids, liquids, and gases, enable us to 
determine the form of the function (36), and thus lead to the terms to be added 
in the general case for each species of body. 

It is generally admitted that a solid body, if abandoned to itself, would be 
capable of vibratory motion, and that its molecules, if displaced, would tend to 
return to their former position. A gas, if abandoned to itself, would be dissi- 
pated by the repulsive force of its molecules, so that in this case the function 
(36) should lead to an impossible result, as vibratory motion is impossible 
without the addition of pressures at the limits, or some equivalent forces. A 
liquid occupies a position intermediate between a solid and a gas ; and if we 
assume that a liquid abandoned to itself will be in a state of unstable equili- 
brium (i. e. its molecules, if displaced, will not return to their original position, 
while, if undisturbed, they will not be dissipated), we shall obtain from (36) 

s2 


132 The Rev. S. Haueuton on a Classification of Elastic Media, 


the equations of liquid motion, including friction, which have been deduced 
by various writers from different considerations. 

A liquid need not be supposed to be exactly in this state at all times; a 
slight cohesive or a slight repulsive force may be supposed to exist among 
its molecules, according to the quantity of caloric contained in it, or other phy- 
sical circumstances, which may modify the intensity of the molecular actions. 
If such cohesive or repulsive forces be considered very small, as compared with 
the cohesive forces in a perfect solid, or the repulsive forces in a perfect gas, 
the equations deduced from the hypothesis, that these forces are zero, may still 
be used. 

We obtain from equation (36) the following: 


dV dV 

=F = Aw —-2P(w-a), Age 
dV 

Gyn de 2P (w~ 8) Age 

dV dV 

PRaae A Cm: Ane: 


It is necessary and sufficient for stable equilibrium that these six forces 
should have signs contrary to the signs of (éa, 0B, éy, bu, &, éw). If these be 
made positive, then the forces must have negative signs, and vice versd. 

Hence, for stable equilibrium, it is necessary that A and P be both negative, 
which will reduce the function (36) to the following, 


—~2V=Ae’?+P(A+ n+). (36, a) 


Also the first three equations (changing the signs of A and P), added together, 
must be negative; hence the condition, 


(- 34447) «<0. (36, b) 


If the equilibrium be stable, A cannot be less than = and if it be exactly 


equal to this value, we shall obtain the equations peculiar to liquids, because a 


displacement will produce no molecular force; andif A < = a molecular force 


and the Laws of Plane Waves propagated through them. 133 


will be developed which will tend to increase the displacement. The func- 
tion (36, a) will, therefore, represent solids, liquids, or gases, according as 
A>,= 2 . 

J ? B} 

I shall consider, first, the equations of homogeneous solids. The function 
(36, a), substituted in equations (30), leads to the following equations of 


motion. 


oF =(A ~P) + PG tS), 


dz dy? dz 
ay _ dw dy dy dy 
ee ~ PT P(e os = {37 


ae dw Ge. GEO fhe 
re - Py F+P(S apt 7): 
These equations of motion of solid bodies were first given by M. Cavcny ;* 
equations identical in form, but with the relation A = 3P between the coeffi- 
cients, had been previously obtained by M. Navier.t M. Potsson deduced 
equations identical with those of M.Navier. Mr. Green has used the equa- 
tions (37), with two independent constants, in his theory of light ;t and Mr. 
Sroxss has recently called attention to the importance of retaining the two coeffi- 
cients (leaving their ratio to be determined by experiment for each solid), in a 
memoir published in the Cambridge Philosophical Society’s Transactions.§ 

The relation A = 3P is a consequence of the use of definite integrals for 
the coefficients of the function V, and only represents a particular elastic solid; 
its introduction does not alter the form of equations (37), nor does it render 
them more simple than they are in their present state. 

The additions necessary to be made to the equations of hydrodynamics, in 
order to take into account the friction of the fluid particles, have been given by 
many writers. M. Navrer first stated the equations in their corrected form 
for incompressible fluids.|| M. Poisson has treated of the subject in a me- 


* Exercices des Mathematiques, tom. iii. p- 180. 

T Memoires de l’Institut., tom. vii. p- 389. 

} Transactions of Cambridge Philosophical Society, tom. vii. p- 11. 
§ Vol. viii. part 3. || Memoires de l'Institut., tom. vi. p: 414. 


134 The Rev. S. Haveuton on a Classification of Elastic Media, 


moir published in the Journal de [Ecole Polytechnique ;* and, more recently, 
M. Barre DE Saint VENANTY and Mr. Stoxesf have written on the friction of 


fluids in motion. 
The quantities to be added to the ordinary equations of hydrodynamics are 


the right hand members of equations (37), introducing the relation (4 = =), 


which expresses that a displacement produces no molecular force. 

The equations of the motion of gases have been already given, on the sup- 
position that there is no tangential action, which is equivalent to assuming that 
the vibrations are normal, and therefore (P=0). If we wish to take account 
of the friction of gases, we should use the equations which have just been indi- 
cated for liquid motion. 


SECTION V. COMPARISON OF MECHANICAL THEORIES OF LIGHT. 


It is well known that different mechanical theories have been proposed to 
account for the phenomena of the movement of light in crystalline bodies, and 
that, although these theories differ in their fundamental hypotheses, yet, to some 
extent, they agree in representing the most obvious phenomena of double re- 
fraction. The laws of wave-propagation in crystals, are geometrical conse- 
quences of the properties of FrEsNEL’s wave-surface; and no mechanical theory 
of light can be considered as even an approximation to the truth, unless it con- 
tains, as a deduction from its hypotheses, the wave-surface of FresneL. But 
it would be an error to conclude that any theory is correct, which satisfies this 
condition. There are, in fact, three different theories which satisfy this funda- 
mental condition, and it is evident that they cannot all be true. The first of 
these theories was propounded by Fresvet himself, in his memoir on Double 
Refraction.§ It is based on the hypothesis, that the luminiferous ether is com- 
posed of attracting and repelling molecules. The form of wave-surface known 
as FresNet’s is deduced by its author from this hypothesis, with the peculiarity 
that the vibrations of the molecules are perpendicular to the plane of polarization. 


* Cahier xx. p. 139. + Comptes Rendus, tom. xvii. p. 1240. 
t Transactions of Cambridge Philosophical Society, vol. viii. part 3. 
§ Memoires de l'Institut, tom. vii., p. 45. 


and the Laws of Plane Waves propagated through them. 135 


M. Caucny afterwards gave the general equations peculiar to such a system, 
and deduced from them Fresnxt’s wave-surface, asa first approximation to what 
he considered as the more accurate laws of Wwave-propagation.* 

In the year 1839, Mr. Green presented to the Cambridge Philosophical 
Society a memoir, in which, by a modification of M. Caucny’s equations, he 
obtained Fresnet’'s wave-surface as an exact deduction from the theory. 
This modification consists, as I have already stated, in restricting the system to 
propagate normal and transverse vibrations. In M. Cavcny’s or Mr. Green’s 
theory, the vibration of the molecules is parallel to the plane of polarization. 
In the same year Professor Mac Cutacu presented to this Academy a mecha- 
nical theory of light, not founded on the hypothesis of attracting and repelling 
molecules. The vibrations in this theory also are parallel to the plane of pola- 
rization, and the form of the wave-surface is that given by Fresnet. These 
three theories of light, therefore, agree, so far as the laws of wave-propagation 
are concerned ; and, excluding FresNet’s theory from the comparison (as the 
vibrations perpendicular to the plane of polarization make it distinct from the 
other two theories), there remain the mechanical theories of Mr. GREEN and Pro- 
fessor Mac Cutan, which are identical so far as the laws of Wave-propagation 
are concerned. The two theories are, however, really different in their funda- 
mental assumptions ; and this remarkable agreement in the laws of wave-propa- 
gation deduced from them admits of a simple explanation. I propose to account 
for the agreement, and to suggest the direction in which we should look for a 
true experimentum crucis between them. 

The function V used by Mr. GREEN, when reduced to its simplest form, 


will be 
—2V=Ao?+ PA+ Qut Rb; (38) 


and the simplest form of Professor Mac Curtacu’s equations will be derived 


from the function 
—2V = PX? + QY?+ RZ (39) 


It is evident from what I have stated in the first section, that (A, y, v) will 


* Memoires de |’Institut. tom. x., 1830. 
t Transactions of Cambridge Philosophical Society, vol. vii. p. 121. - 


136 The Rev. S. Haueuton on a Classification of Elastic Media, 


2 


produce the same terms in the differential equations of motion, as X*, Y°, 2°; 
for the squares will be the same in each, and the rectangles will be 


(2Bsy2 — ABoy3, 2103 — Aayys, 2ao8, — 4a,B,), and (- 2BsY2, —2y103, — 2aP). 


These two sets of rectangles will produce the same terms in the equations of mo- 
tion, since we may transpose the differentiations without affecting the result, so 
far as the laws of propagation are concerned. The surfaces of wave-slowness de- 
duced from (38) and (39) may be obtained immediately from equation (18), 
Equation (38) will give the following: 


P=AP + Rm? + Qn; EF’ = (A —P)mn; 
Q'= Am? + Pn? + RP; G=(A— OQ); (40) 
R= An? + QP + Pn’; H'=(A — R) Im. 


And similarly from equations (39) will be found 


P’ = Rm? + Qn’; FF’ =— Pmn; 
Q' = Pn? + RP; G’ =— Qin; (41) 
R= QP? + Pm’; H =— Rim. 


These equations differ from the former only by not containing A. 
The equation of wave-slowness (18) derived from (40) is 


{A (2° +y4+2)-1} 


42 
x { (a+apP-+2")( QRa?+PRiy?+PQ2)—(Q+R)a’—(P+R)y’—(P+Q)2+1}=0. Cy 
The first factor of this equation represents a sphere whose radius is a and 


belongs to the normal vibration ; the second factor is the equation of FRESNEL's 
wave-surface, and in it the vibrations are transversal. The equation of wave- 
slowness deduced from Professor Mac Cutiaau’s function (39) will be the last 
factor of (42). So far, therefore, as the laws of wave-propagation are concerned, 
the functions (38) and (39) are equivalent, with this difference, that the func- 
tion (38) introduces a normal wave, which does not enter into the equations 
derived from (39). It might be thought at first sight that we are at liberty to 
make A =0, and thus reduce the function (38) to a function representing 
nothing but transverse vibrations ; this, however, cannot be admitted, for as 


and the Laws of Plane Waves propagated through them. 137 


(38) represents a body whose molecules act in the line joining them, a wave of 
normal compression is always possible. This will be rendered more evident by 
considering the conditions at the limits. 

Let the limiting surface separating two bodies be the plane (7, ), then the 
equations of condition (11) will become, for the function (388), 


Qu = Q"e4'; & = &; 
Tigh TTY 2el AE No = 10 5 (43) 
A’) + ‘ay + PB, = a 4 Q’ ail’ au IEG a = Ge 


These equations are equal in number to the unknown quantities, provided nor- 
mal waves be included, because the unknown quantities of the problem are the 
intensities of the reflected and refracted waves ; it is impossible, therefore, for 
exclusively transverse waves to be produced by reflexion or refraction in such 
a body as (38) defines: in order to obtain unknown quantities whose number 
shall be equal that of the necessary conditions of the mechanical problem, we must 
introduce normal vibrations. The conditions at the limits deduced from (89) are 


OXF = Or. ee 
XG =P OX No = 05 (44) 
Ge Gi 


The additional hypothesis made by Professor Mac Cuxxacu, that the density 
of the medium is the same in the two bodies, reduces these equations to four, 
Accordingly, with this hypothesis, there is no necessity to have recourse to normal 
waves, as there will be four intensities to be determined in the transverse waves. 

From these considerations it appears, that the eaperimenta erucis between 
the rival theories of light must be sought for among the laws of reflexion and 
refraction ; but unfortunately these laws are not known with sufficient accuracy 
to enable us to decide the question. Mr. Green's theory contains the common 
laws of reflexion at the surfaces of ordinary media as first approximations, while 
Professor Mac Curiacu’s system has the advantage of giving these laws as exact 
results ; nothing, however, but more accurate experiments can decide whether 
the approximation or the exact result be most in accordance with the truth; and 
as these experiments involve considerations of the intensity of light, it would be 

VOL. XXII. az, 


138 The Rey. S. Hauauron on a Classification of Elastic Media, §c. 


difficult to make them with sufficient accuracy. The present state of the wave 
theory of light certainly suggests grave doubts as to the nature of the foundation 
on which the whole system is based. We first assume the existence of an un- 
known medium, whose existence must remain unproved and unprovable by us; 
then, from supposed properties of this unknown medium, we deduce the laws of 
propagation,&c. Here a new difficulty arises; for we find several different theories 
capable of explaining the laws of propagation, and explaining with more or less 
exactness the most obvious of the laws of reflexion and refraction. How are we 
to decide among these conflicting theories ? Are we to assume, with M. Caucuy, 
that the observed laws of polarized light occupy, with respect to the mathematical 
laws deduced from his theory, the same position that the laws of Kepter stand in 
with respect to the more accurate laws of planetary motion? or are we to assume 
that theory to be correct which agrees accurately with the common formulz 
for reflected light, when it is well known that these formule themselves are 
doubtful for highly refracting substances? It appears certain, that we do 
not yet possess experimental knowledge sufficient to enable us to determine 
which of the theories of light is correct, or whether any of them be so. Ina 
general point of view Professor Mac CuLLacn’s theory possesses an important 
advantage, as compared with other theories. It contains no inexplicable normal 
wave, and does not render this difficult subject still more intricate, by the in- 
troduction of a useless vibration. It is greatly to be desired, that the attention 
of experimentalists were directed to the necessity which exists for more accurate 
and general researches into the laws of crystalline reflexion and refraction, and 
that the surface of FrEsNEL were placed upon a purely experimental basis. From 
such researches, carefully conducted, might be deduced the geometrical laws of 
double refraction, and a foundation be laid for a complete and positive theory 
of the laws of polarized light. 


VI—On the Rotation of a Solid Bod y round a fixed Point ; being an Account of 
the late Professor Mac Curtacn’s Lectures on that Subject. Compiled by the 
Rev. Samurt Haventon, Fellow and Tutor of Trinity College, Dublin. 


Read April 23, 1849. 


Tue following Essay, on the Rotation of a Solid Body round a fixed Point, has 
been compiled from my notes of Professor Mac Cutracu’s lectures, delivered in 
the Hilary Term of the yeur 1844, in Trinity College. A short account of some 
of the results contained in it was published by Professor Mac Cuntacu him- 
self, in the Proceedings of the Royal Irish Academy.* As it has appeared to 
many of Mr. Mac Cutzaen’s friends desirable that a somewhat more detailed 
account of his researches in this subject should be published, I have, in ac- 
cordance with this desire, drawn up and presented to the Academy the following 
account of his lectures on Rotation. I have endeavoured to arrange the subject 
in a systematic order, and to give the results proved by him during the course 
of the lectures, carefully excluding all theorems and proofs of theorems, which 
were not originally given by him, as here stated. 


SamuzrL Haucuron. 


* Vol. ii. pp. 520, 542. 


140 The Rev. Samurt Havcuton’s Account of 


1.— Composition of Rotations. 


Let O be the intersection of two axes of rotation, OR, OR’; and let the 
magnitudes of the rotations be represented by o, »; then the motion impressed 
upon the body by these two rotations will be the same as the motion produced 
by a single rotation round an axis, which is represented in magnitude and po- 
sition by the diagonal of the parallelogram formed by , w’. For, draw through 
any point I of the body a plane perpendicular to the line OI, and project upon 
this plane the parallelogram formed by @, o’;—the sides of this parallelogram will 
be wsin ROL and o’ sin ROI. Now the velocities impressed upon the point I 
by the rotations and w’, are Ol.w sin ROJ, and OI.’ sin R’OL; and the di- 
rections of these velocities are perpendicular to the sides of the projected paral- 
lelogram. Hence, if this parallelogram be turned in its plane through 90’, its sides 
will represent in magnitude and direction the actual velocities ; the resultant 
of these velocities is perpendicular to the projection of the diagonal of the 
parallelogram («, w’); this projection, turned round through 90’, will represent 
the actual velocity, which is therefore the same in magnitude and direction as 
would be produced by a single rotation represented by the diagonal of (, w’). 
Hence rotations may be resolved along three rectangular axes by the same laws 
as couples, and they must be counted positive when the motion produced is from 
z toa, x to y, y to z, and vice versd. 


Il.—Linear Velocities produced by a given Rotation. 


Let the origin of co-ordinates be assumed on the axis of rotation, and let the 
magnitude of the rotation and of its components be represented by (, p,q, 7): 
the velocity of any point (7, y, z) is in a direction perpendicular to the plane 
containing the axis of rotation and the point (,,z); and its magnitude is re- 
presented by the area of the triangle whose angles are situated at the origin, 
the point (a, 7, z), and the point (p,q,7). Hence, the components of the linear 
velocity are represented by the projections of this triangle on the co-ordinate 
planes. These projections are 


Professor Mac Cutiacu’s Lectures on Rotation. 141 


uU=qz—TY; 
V=TL — pz; (1) 
w= py — qe. 


Il.—To represent geometrically the Moments of Inertia of a Body with respect to 
Axes drawn through a jived Point. 


The moment of inertia of a body with respect to any axis (a, 6,7) is 
M= A’ cos’ a + B’ cos’ B + C’ cos?y — 2L’ cos B cosy — 2M’ cosa cos y 
—2N'cos a cos B ; 
where 
A’ =((y? + 2) dm, L! = fyzdm ; 
B = {(a + 2) dm, M' = jxzdm ; 
C= \(a +) dm, N’ = faydm. 


Assume Af =5 ; « being the mass of the body, and r a distance measured on 


the line (a, B, y) and construct the ellipsoid whose equation is 

Ale? + Ba + C2 — 2L'yz — 2M'az — 2N’ zy = ps; (2) 
then it is evident that the moments of inertia of the body with respect to axes 
passing through the fixed point are represented by the squares of the reciprocals 


of the radii vectores of this ellipsoid. Assume A = pa®, B= pb’, C= uc’, and let 
the axes of co-ordinates be the axes of the ellipsoid; its equation will thus become 


ax? + by? + 2? = 1; (3) 


and the equation of the reciprocal ellipsoid will be 
Ger iene 
stat aL (4) 


This latter ellipsoid may be called the ellipsoid of gyration, as the perpendi- 
culars on its tangent planes represent the radii of gyration; this is evident from 
the consideration, that these perpendiculars are reciprocal to the radii vectores 
of the ellipsoid (3). In fact, the moment of inertia with respect to any axis will 
be represented by the formula 


142 The Rev. Samuet Haucuron’s Account of 


lid = 


M = (@ cosa + & cose B+ ec? cos’ y) w= wE = Fr; (5) 
uv 


(R,P) denoting the radius vector and perpendicular on tangent plane of the 
ellipsoid (4); and (2’P’), the corresponding lines in the ellipsoid (3). 


IV. —To jind the Magnitude, Position, and Direction of the Statical Couple produced 
by the Centrifugal Forces. 


If from any point (2, y, z) of the body, a perpendicular be let fall on the 
axis of rotation (a, 6, y), the centrifugal force will be represented by the pro- 
duct of the square of the angular velocity and this perpendicular; the corres- 
ponding elementary statical couple will be found by multiplying the centrifugal 
force by the distance from the foot of the perpendicular to the origin, which is 
represented by the quantity (« cos a+ y cos 8 + z cosy). The components of 
the elementary couple will be proportional to the projections of the triangle 
formed by the lines before mentioned. The components’ of the elementary 
couples must be integrated for the entire extent of the body, and the integrals 
thus found will be the components of the couple produced by centrifugal force : 
the expressions are as follows: 


w (7 cosa+ycosB+zcos y) (2 cos B—¥ cos y) dm; 
w (xv cos a+ y cos B + Zz Cos ¥) (x cos y —z cosa) dm; 
w (x cos a+ y cos B+ 2 cos y) (y cos a — x cos B) dm. 


If the axes of co-ordinates be principal axes, these expressions, when integrated, 
will become 
w’ cos Bcos y (B— C) = qr (B-C); 
w cos acosy(C—A)=pr(C—A); (6) 
w* cos a cos B (A —B) = pq (A — B): 


p, q,7 being the components of the angular velocity ». The position of the 
resultant couple may be expressed by means of the ellipsoid (4). If a tangent 
plane be drawn to this ellipsoid at the point (z, y, z), and perpendicular to the 
line (a, f,y), it may be easily shown that the projections of the triangle formed 
by the radius vector and perpendicular are represented by the quantities 


Professor Mac CuitiaGu’s Lectures on Rotation. 143 
cos 6 cos y (b° —¢’), cos acos y (¢?—a’), cos acos Bp (a? — 8); 


these three expressions multiplied by pw° will produce the quantities used in 
(6). Hence it appears, that the couple produced by the centrifugal forces lies 
in the plane of the radius vector and perpendicular to a tangent plane of the 
ellipsoid (4); the tangent plane being perpendicular to the axis of rotation. Also, 
the magnitude of the resultant couple is proportional to the triangle formed by 
the radius vector and perpendicular. 

The differential equations of motion commonly used in the solution of this 
problem may be deduced immediately from equations (6). In fact, as the axes 
of co-ordinates are axes of permanent rotation, the increment of angular velocity 
round each axis will be equal to the statical couple of the applied forces (in- 
cluding centrifugal forces), divided by the moment of inertia round that axis ; 
the statement of this fact, in analytical language, will give the equations of 
motion: 


he ER SE) eee 


dt 

Be OA ea (7) 
dt 7 

an : : Be 

é a= (A- B) pg t+ N: 


(LZ, M, NV) being the components of the applied statical couple. 

The position and magnitude of the couple produced by the centrifugal 
forces are easily found by the method which has been just given; but the 
direction will be found more readily by taking more particular axes of co-ordi- 
nates. Let the axis of rotation be the axis OZ, and 


the plane of radius vector and perpendicular be the iz 

co-ordinate plane XOZ. In the accompanying figure RN 

OR’ and OP’ are the radius vector and perpendicular Si aye 

of the ellipsoid (2), and OR, OP the radius vector and Bie oh 
perpendicular of the ellipsoid (4), which is reciprocal / 

to the former ; the rotation is positive, in the direction 9 x 


Sioa nee a 
indicated by the arrow. As the rotation is round the 


axis of z, it is easy to see that the statical couple produced by centrifugal force 


144 The Rey. SAmurL Haucurton’s Account of 


will have for components, round the axes of # and y respectively, the quantities 
w’{yzdm, w°*\xzdm taken with their proper sign; i. e. the components are + w*L’, 
+ wM’; L/W, being coeficients in the equation of the ellipsoid 
A’? + By + C2 — 2L'yz — 2M" az — 2N’ xy = p. 
The tangent plane to this ellipsoid, applied at the point (, y, z) will be 
(A’a — Wz—N'y) 2 + (By — Na — L'z) y+ (Cz—-L’y—- M2) 2 =p. 

At the point R’ the tangent plane will be perpendicular to the plane XOZ, and 
will be found by making « = 0, y= 0, and destroying the coefficient of y/ in 
the preceding equation. These conditions give us L’= 0, which proves that 
the statical couple produced by centrifugal force lies altogether in the plane 
XOZ. The equation of the tangent plane is the same as the equation of the 
line R’P’, and is 

Cz/—-Ma'=—. 

Hence we obtain 
on MW 
ang@=——. 
co) (Gz 


The value of the centrifugal couple is *J/’, which is found from the pre- 
ceding equation by replacing C” and tan @ by their values pP”, and es ; Q being 
the line RP. 

We thus obtain finally the centrifugal couple lying in the plane XOZ, and 
expressed by the equation 

w\xzdm = — po PQ. (8) 
It thus appears that the centrifugal couple lies in the plane of radius vector 
and perpendicular, is proportional to the area of the triangle ROP, and has a 
direction opposite to the direction of rotation. 


V.—To find the Relation between the Plane of principal Moments and the Axis of 
Rotation at any Instant. 


The motion of the body at any instant consists of a rotation of a certain 
magnitude round a certain axis; this rotation might be produced by an im- 


Professor Mac Cuttacu’s Lectures on Rotation. 145 


pulsive couple ofa determinate magnitude and direction, The statical impulsive 
couple thus conceived is the couple of principal moments. Let this couple be re- 
presented by G, and act round the axisOR (fig. 1, p.148); then the corresponding 
axis of rotation will be the perpendicular OP, and the relation between G and 
w may be thus found. Let the axes of co-ordinates be the axes of the ellipsoid 
(4), the radius vector being determined by the angles (A, , v), and the axis of 
rotation by the angles (a, 8, y). From mechanical considerations we obtain the 
equations 
G cos X= Ap = pw a’ cos a; 
G cos p= Bg = pw b? cos B; 
G cos v = Cr = pw c’ cos ¥. 
Hence we obtain 
cosA_a@cosa cosp Jb? cosp 
cosy cosy’ cosy ¢ cosy’ 
G G cos (9) 
pe cae a 


The first two of these equations prove that the axis of rotation is the per- 
pendicular on tangent plane of the ellipsoid, and the last equation gives the mag- 
nitude of the rotation in terms of the impressed couple and quantities determined 
by the nature of the body itself. Equations (9) are true, whatever be the forces 
acting on the body; if no forces act, @ will be fixed in magnitude and posi- 
tion in space, by the principle of conservation of areas, but will change its 
position in the body, the axis of rotation accompanying it, and changing its 
position both in the body and in space. 


V1—Rotation produced by Centrifugal Force ; particular Properties of the Motion 
when no Forces act. 


The axis of rotation produced by the centrifugal couple always lies in the 
plane of principal moments. This theorem may be thus proved: Let the 
radius vector and perpendicular be drawn, which coincide with the axis of 
principal moment and axis of rotation at any instant; a line perpendicular to 
the plane of radius vector and perpendicular is the axis of centrifugal couple ; 

VoL. XXII. U 


146 The Rev. SAmueL Haucuton’s Account of 


this line and the original radius vector are axes of the section of the ellipsoid 
made by their plane; at the point where the axis of the centrifugal couple pierces 
the ellipsoid let a tangent plane be applied; the perpendicular let fall on this 
tangent plane is the axis of rotation produced by centrifugal forces. From the 
construction it is evident that the plane of the second radius vector and per- 
pendicular is perpendicular to the axis of G; hence the axis of the centrifugal 
couple and the axis of rotation produced by it, always lie in the plane of prin- 
cipal moment. Two important corollaries follow from the theorem just de- 
monstrated, in the case where no forces act :—First, the component of angular 
velocity round the axis of primitive impulse is constant during the motion. 
Secondly, the radius vector which coincides with the axis of Gis of constant 
length during the motion. The first theorem is obvious; for as the axis of 
rotation produced by centrifugal force is always perpendicular to the axis of G, 
it cannot alter the rotation round that axis. The second theorem follows from 
equation (9), from which we deduce 


G 


cos = SS 
w ) ule 


(10) 
The left hand member of this equation is constant by the preceding theorem ; 
and G is constant, since there is no external force; therefore & is constant. 

As the axis of G is fixed in space, and the line £ is constant, it is evident 
that the axis of G will describe in the body the cone of the second degree, de- 
termined by the intersection of the ellipsoid (4) with the sphere whose radius 
is R. The equation of this cone is 


—= 2 =0. (11) 


As the axis of principal moments describes this cone in the body, it is accom- 
panied by the axis of rotation, which is always the corresponding perpendicular 
on tangent plane of the ellipsoid. The cone described by the axis of rotation 
might be found thus. Let tangent planes be applied to the ellipsoid along the 
spherical conic in which the cone (11) cuts the ellipsoid. From the centre let fall 
perpendiculars on these tangent planes; the locus of these perpendiculars is 
the required cone. 


Professor Mac Curtiacu’s Lectures on Rotation. 147 


VUL—The Axis of principal Moments is fixed in Space. 


This is evident from D’Atemzert's principle, but may be shown by geome- 
trical considerations in the particular case under consideration. The axis varies 
in position in the body, in consequence of the centrifugal couple, which must be 
compounded with the impressed couple at each instant. Referring to equa- 
tion (8), the value of the centrifugal couple is — yw*PQdt, the principal mo- 
ment being G = pwPR (vid. 9). Hence the angle through which the axis 
of principal moment shifts in an element of time is — ag ; this angle, mul- 
tiplied by the constant radius vector, will give the elementary motion on 
the spherical conic traced by the axis of principal moment on the surface of the 
ellipsoid ; this motion is therefore — wQdt; but in the same time the point 
of the body which coincides with the point where the axis of moments pierces 
the spherical conic will describe the angle + wQdt in consequence of the an- 
gular rotation. Hence the axis of moments will remain fixed in space, and will 
move in the body with a velocity proportional to the tangent of the angle be- 
tween the radius vector and perpendicular, the motion being in a direction 
opposite to the direction of the rotation; this is evident from the consideration 


that Qu = Pw tan ¢, Pw being constant and equal to “h (vid. 9). 


VUI.—To jind the Motion of the principal Avis in the Body. 


First Method. 


The point of the principal axis of moments, which is situated at the distance R 
from the centre, moves on the spherical conic which has been determined. Let 
this point be projected on the three co-ordinate planes; then, since the spherical 
conic is projected into a conic section, the movement of the axis of moments is 
reduced to the movement of a point on a conic section, according to a law 
which must be determined. The radius vector describes an elementary triangle 
in the surface of the cone (11); let the projections of this triangle on the co- 
ordinate planes be (dA,, dA, dA;); we obtain easily 

U2 


148 The Rev. Samuet Haventon’s Account of 


aA, _dz_ dy dAy_,de_ dz ddy_ dy de 
di dt, de! dts es ae dpe dia’ ai 
Substituting in these equations the values of the velocities given by (1), we 


obtain 


AMAR NGE ve ELS ul 
Tei a La Ga ee 

dA, RB 

ap = Poe = (Ba: (12) 
dA, P-— ¢ 


Tat Bt ete oa) 

These equations prove, that the areolar velocity of the projection on a co-ordinate 
plane varies at the ordinate to that plane. By means of the method of quadra- 
tures, we may determine from equations (12) the position of the projections of . 
the principal axis at any instant, and hence deduce the position of the axis 
itself. 


Second Method. . 


Ifthe spherical conic be projected on a cyclic plane of the ellipsoid of gyra- 
tion, by lines parallel to z and z,the projections will be two concentric circles, and 
the corresponding projections will lie on the same or- Fic. 2. 
dinate SII’ (fig. 2). The inner circle will belong to 
the projection parallel to 2, if R be greater than 6, 
and will belong to the projection parallel to z if Rk 
be less than b; and if & be equal to d, the two circles 
will coincide with each other and with the spherical 
conic, which in this case becomes the circular section 
of the ellipsoid. The projected point will revolve 
round the circumference of the inner circle, and will vibrate on the circum- 
ference of the outer circle, between the dotted lines. It is evident that the 
mean axis of the ellipsoid OY lis in the plane of the figure. Let SI and SI’ be 
equal to p, p’, and let C, C’ denote the radii of the two circles: the velocities 
of the projections in the circles will evidently be 


Professor Mac. Cutiacu’s Lectures on Rotation. 149 


Oly a, iChdy. 
p dt’ 72 dt’ 


C and C’ having the values 
ae 5 dy RP 
Cato (Sa -) (=o (F=S). 
The value of , deduced from (1) is, 
d Ma al al 
oe = Po (3-3) ve =Pa(5-<) pp’ sin 0 cos 6; 
6 being the angle made by the plane of the circular section with the plane (z, y). 


ind= 5 /(S—7 = a) eos 0=F o/ (Gao =). 


¥ dy. : G 
Introducing these values of m sin @ and cos @, and for Pw its value = we 
B 


obtain finally for the velocities 


rol {(e-2-B) eam 
r= BVA (e-DG-Bpeom 


The velocity of each projection, therefore, varies as the ordinate of the other. 
This theorem enables us to find a simple expression for the time. Using the 
angle (¢) marked in fig. 2, we obtain 


(13) 


=, =Kv(C?-C sin’ 9); 


(¢, C, K) belonging to the projection parallel to axis of z. If (¥, C’, K’) be 
the corresponding quantities for the other projection, we obtain also 


= KE NG C? sin? v); 


oe : 
or, since it is easily seen that we obtain finally 


me 
a6: ? 


150 The Rev. Samuet Havueuton’s Account of 
Kd= Lee 


(14) 
Kdt= 


J (1- Gey). 


The motion of the principal axis of moments is, therefore, expressed by an el- 
liptic function of the first kind. 

The motion of the axis of moments is determined by the magnitude of the 
radius vector of the ellipsoid, which is the axis of the original couple impressed 
upon the body; if this radius vector be greater than the mean axis of the ellip- 
soid, the corresponding spherical conic will have the axis of # for its internal 
axis; and if the radius be less than the mean axis, the axis of z will be the internal 
axis of the conic; in no case will the mean axis be the internal axis of the 
spherical conic. If the radius & be nearly equal to either the greatest or least 
semi-axis, the expression (14) for the time may be integrated, Let & be nearly 
equal to the greatest semi-axis. The first of the equations (14) belongs to 
the interior circle, which is of small dimensions in the case sapposed; the 
second equation expresses the vibratory motion of the projection, through a 
small are of the outer circle, which will have a radius much greater than the 
inner circle; we may, therefore, suppose the angle y to be equal to its sine. 


} 
Multiplying both sides of the equation by = we obtain 


(GH 

1 7 FAl dy 
ee dt = K'dt = i, 6 

C CP 
TF) 

C? 

Hence 
CX sin (K't + A). (15) 


If T, denote the time of a complete oscillation or revolution of axis of moments 
about the axis of z, and 7, the time of a revolution of the body round the 


Professor Mac Cutiacnu’s Lectures on Rotation. 151 


axis of x, the following relation between these two periods may be readily de- 
duced from (15): 
be 


T= et Vi(@ — 0) (@ — ec)’ (16) 


If the axis of moments, and consequently the axis of revolution, be situated near 
the axis of greatest or least inertia, it will always continue near this axis ; if, 
however, it be situated near the mean axis, the movement of the body will be 
determined by the following construction. Let the two cyclic planes of the 
ellipsoid be drawn through the mean axis; they will divide the ellipsoid into 
two regions, in one of which is situated the axis of maximum inertia, and in the 
other the axis of minimum inertia. The spherical conic described by the axis 
of principal moments will have the first or second of these axes for its internal 
axis, according as / is greater or less than the mean axis. If the axis of prin- 
cipal moments lie in one of the cyclic planes, the spherical conic becomes a 
circle, and its two projections become identical with itself (fig. 2, p. 148); the 
expressions (14) are reduced to the form 


Kaa 


‘a cos @ 
which when integrated gives 


z= BP) 
Kt + A = log cot ¢ aE 


cot G-§) = cot G-$)e (17) 


> being the value of @ corresponding to t = 0, and K being expressed by the 
following quantity: 


or, 


_ GVi(@ —¥) (Pe) 


2 ma bac 


It is evident from the equation (17), that the axis of moments will coincide with 
the mean axis of inertia at the end of an infinite time. 


152 The Rey. Samuet Haucuton’s Account of 


IX.—To find the Position of the Body in Space at the End of any given Time. 


First Method. 

The radius vector of the ellipsoid, which is perpendicular to the plane con- 
taining the axes of principal moment and of rotation, always lies in the plane of 
principal moment, and describes in that plane areas proportional to the time. 

Let OG, OO be the axes of principal moment and Ae 3. 
of rotation; OR’, OM’, the axes of centrifugal couple 
and of corresponding rotation; the plane YOO’ will 
contain the two successive positions of the axis of 
rotation. Let OI be the position of the axis of ro- 
tation at the end of the time é; then éw will be 
equal to the angle described in the fixed plane by i / 
the line OR’. Let #’ and J” be the radius vector ae) 
and perpendicular corresponding to the centrifugal 4, 
couple and its axis of rotation. The following relations are evident from the 


figure 
» sinQ/OI_ cos@’ os ¢’ sin peu 
=— =- ; because sin Q/OI = ——— ae Ec 
wv sinQOl © sin diu’ wv sin 0’ ain 201 sin 0 ’ 
but from mechanical considerations, 
w IER ee tise G F Gow sin Pit 
7 ae o= vo = - oF 
wo PRo sin L pat 3 4 pPR? pPR’ 


Hence, by equating the geometrical and mechanical expressions, we obtain 
— Ru = wo PRet = Ct (18) 


The position of the body in space is thus reduced to quadratures ; but the 
problem may be solved more readily in the following manner. 


Second Method. 


The axis of principal moments, appearing to move in a direction opposite to 
the rotation, describes in the body the cone whose equation has been given (11). 


Professor Mac Cutzacn’s Lectures on Rotation. 153 


If the cone reciprocal to this cone be described, one of its sides will lie in the 
fixed plane, and the whole motion of the body in space will be the same as the 
motion of this cone, which partly slides and partly rolls on the fixed plane, the 
sliding motion being uniform. This theorem is evident by resolving the an- 
gular velocity w into two components, one round the axis of principal moments, 
and the other in a direction perpendicular to this, round the side of the reci- 
procal cone, which is in contact with the fixed plane. These components are 
» cos @ and w sing; w cos @ being constant and producing the sliding motion, 
while w sin @ represents the angular velocity round the side of the cone in contact 
with the fixed plane. The angle described by the side of the reciprocal cone 
in the fixed plane at the end of a given time, is, therefore, the algebraic sum of 
two angles, one of which is proportional to the time, and the other is the angle 
described in the cone in consequence of the rotation w sing, and is, therefore, 
measured by the are of a spherical conic. The position of the body at the end 
of the time ¢ is thus found :—determine by equation (14) the position of the 
axis of principal moments in the cone (11); the corresponding position of the 
component axis of rotation in the reciprocal cone is therefore known. Hence 
the angle described in the time ¢ in the fixed plane is 


ds 8 
© =u cos gat + |= wcosg.t+ (IS) 
The equation of the reciprocal cone is . 
ax by? Cow 
Po@ tpt Re —p=?. 2) 


In (19) the positive or negative sign must be used according as R is less 
or greater than the mean axis of the ellipsoid; this is evident from the com- 
position of rotations, and from the consideration that in the former case the 
axis of rotation falls inside the cone (11), while in the latter case it falls outside. 


X.—To find a Point in a given Axis of Rotation, which being fixed, the Axis will 
be permanent. 


Let R’R” (fig. 4) be the given axis, round which the body revolves with a ro- 


tation expressed by w; describe the ellipsoid of gyration round the centre of 
VOL. XXII. Ks 


154 Rev. S. Haucuton’s Account 9f Professor Mac Cuiiacu’s Lectures, &e. 


gravity O, and draw OP’ parallel to RR”. The centrifugal force w*rdim at any 


point (2, y, 2), may be resolved into two components, igh 4: 
w°pdm and «”.R/P’.dm; rand p denoting the distances jl) Da WEY 

_ of the point from the axes R’R” and OP’ respectively ; aia 
the effect of the rotation round R’R” is therefore the pen. / 
same as an equal rotation round OP’, together with a _~ * JZ SR 
number of parallel constant forces applied to each point | 34 ww 5) 


of the body. The rotation round OP’ produces a cen-  ~__ SUL 
trifugal couple represented by — po*.OP.PR ( vid. 8); 
or, determining the point R’ by thecondition OP. PR= 
OP’. P’R’, the centrifugal couple is — po.OP’.P’R’. The resultant of the 
parallel forces is a force applied at the centre of gravity, acting in the direction 
parallel to R’P’, and equal to po”. RP’. Comparing this with the centri- 
fugal couple, it is evident that the forces at O destroy each other, and, therefore, 
the total result of the rotation round R’R” is to produce a force acting at the 
point R’, which has been just determined. If this point be fixed, the axis R’R” 
will be a permanent axis of rotation. The condition by which the point R’ is 
found is, that the triangle OR’P’ is equal to the triangle ORP; hence, if an 
ellipsoid confocal to the ellipsoid of gyration be described through the point R’, 
it will be perpendicular to the line R’R’. The general construction for per- 
manent axes is, therefore, the following. Let the ellipsoid of gyration be des- 
cribed, and confocal ellipsoids; any line which pierces one of these ellipsoids 
at right angles is a permanent axis of rotation for the point of intersection. 


R" 


‘ 
, 
a 
4 
, a 
j 
Sigua i 
‘ Pa’ 7 Hp bhas v 
r =" ’ » 
‘ie 
7 
P 
: 7 
a 
- a i yo 


TRANS. R.I. A. Vor. XXII. SCIENCE, p. 178. 


Prats IV. Prats V, 


Fig. 1. 


Puate VI. 


MMMIDEN ESE R PAPER EVENT ERSS INT y iii 


E 


155 


VII—Deseription of an improved Anemometer for registering the Direction of the 
Wind, and the space which it traverses in given intervals of Time. By the Rev. 
T. R. Rozrnson, D.D., Member of the Royal Irish Academy, and of other 
Scientific Societies. 


Read June 10, 1850. 


Amon G the various branches of meteorology, none has been less successfully 
cultivated than anemometry. As a necessary consequence, we are almost to- 
tally ignorant of the causes which originate and the laws which govern the 
currents of the atmosphere, notwithstanding their interesting character as ob- 
jects of physical research, and their importance as cosmical agents. This, how- 
ever, is not to be attributed to neglect; we find Hooxe and Deruam pursuing 
the inquiry almost at the first dawn of physical science; and a variety of 
subsequent inventions connected with it shew that its importance was never 
forgotten. But a wrong path of observation was followed: the data which 
anemology requires are the direction and velocity of the wind at a given time; 
those which (with few exceptions) were sought, are its direction and pressure. 
Of the many ingenious machines which have been contrived for this purpose, 
those which are not mere anemoscopes may be reduced to three classes. In 
the first, originally devised by Hooxy, the wind acted on a set of vertical wind- 
mill-vanes, which are kept facing it by a vane, or some equivalent contrivance, 
giving them motion round a vertical axis. They turn till the pressure on them 
equilibrates a graduated resistance of some kind, whose amount measures it. 
In the second, a square plane receives the impulse of the wind perpendicularly, 
and thus compresses a spiral spring which is connected with it. This, which 
was invented about a century ago by the celebrated Boucurr, has been lately 
brought into general use by Mr. Osster, who has much improved it, and made 
VOL. XXII. Y 


156 The Rev. T. R. Rosinson’s Description of an improved Anemometer. 


it self-registering.* In the third class, of which Linn’s is the type, the pres- 
sure of the wind is measured by the column of water, or some other fluid, which 
it is able to support in an inverted siphon. 

All these are liable to the following objections. First, wind fluctuates, both 
in velocity and direction, to an extent of which I had no conception till I en- 
tered on these researches. Instead of being a uniform flow of air, it may be 
likened to an assemblage of filaments moving with very unequal speed, and 
contorted in every direction ; being in fact analogous to a river in flood, but 
with its eddies and counter-currents considerably exaggerated. Now, assuming 
the common equation V?=mP, we find a = or the relative variations of 
pressure are twice as great as those of velocity; a record of the latter will 
therefore, be far less irregular. But the evil goes further ; for in the fluctua- 
tions both of pressure and direction, the inertia of the moving parts of the 
anemometer carries them far beyond the point of balance, and makes the mea- 
sure of pressure inaccurate, partly by exaggerating the amount of its changes, 
partly by the surface which receives the wind’s impulse being at times wrongly 
placed with respect to its direction. The magnitude of this cause of error may 
be appreciated from these two facts, that I have seen Linn (the only pressure- 
gauge which I possess) range in a few seconds from 0 to 2°6 inches; and that in 
some winds a free vane will oscillate through ares even of 120°. 

2. The velocity can only be deduced from the pressure by experiment : if 
the relation between them be constant, this necessity is of little importance ; 
but the fact is the reverse. In the case of the windmill-vanes, we have no in- 
formation ; and it is evident that the law which connects these variables must 
be very complex, in consequence of the wind which glances off the anterior 
surface modifying the minus pressure. In Boucuer’s instrument it is com- 
monly assumed that the pressure is the weight of the column whose height is 
that due to the velocity: there is, however, experimental ground for believing 
that it is nearly twice as great.} The excess is caused by the minus pressure, 


* An anemometer of this kind, acting against a series of weights instead of a spring, was long 
used by the late Mr. Kirway, and is described in vol. xi. of the Academy’s Transactions. 

+ See D’Ausursson, Hydraulique, p. 295. From De Buat’s investigations it is not unlikely 
that the velocities deduced from the records of OssLER’s gauge are about one-third too great. 


The Rev. T. R. Rozrnson’s Description of an improved Anemometer. 157 


which, I may add, seems to follow a different law of velocity from the plus one. 
In Linp a similar uncertainty is produced by the negative action of the wind 
on the remote aperture of the gauge. 

3. It has been well observed by Forpzs, in his Second Report of the British 
Association on Meteorology, that little progress can be made in anemometry, 
except by the employment of self-registering instruments. If these record pres- 
sure, we cannot thence readily deduce the mean velocity, even admitting the 
law V?=mP. Let V’and P be their mean values; V’+ v, P’+ 7, any others; 
n their number, then 

nV? 42V'x S(v) + S(v’) =n mP + mS(z), 
or as S(v) and S(7) = 0, sel, a S(v’) 


n 


in which the last term is often of very great magnitude ; or if we take 


Vi+v=Ymx VP, 
S(VP) 
n 


we have 


? 


Vi=Vmx 


but I have found the trouble of computing the sums of the square roots, even 
for a few minutes, an insuperable objection. 

These seem to me sufficient reasons for absolutely rejecting the pressure- 
gauge, and adopting instead of it one which gives directly the velocity, or 
rather its equivalent, the space traversed in a given time. Instruments fulfilling 
this object are by no means of recent date.. One was described in 1749 by the 
Russian Lomonosorr ; it consisted of a vertical wheel with float-boards like an 
undershot, half of which was screened, and which was kept in the plane of the 
wind’s direction by a vane. This, by a train of wheel-work, indicated on a dial 
the revolutions of the wheel ; there was no provision for recording these in 
connexion with time, but a very ingenious one for noting the quantities of 
wind which blow from each point of the compass. A much neater one was 
constructed in 1783, by the late Mr. Epcrwortu, and used by him to measure 
the velocity of air currents, though designed for a different purpose.* It con- 


* For measuring the ascent of a balloon; two years later it was used by our countryman 
Crosse in his perilous ascent, and was preserved by him when the rest of his apparatus was lost 


y¥2 


158 The Rev. T. R. Ropison’s Description of an improved Anemometer. 


sisted of four light windmill-vanes, delicately mounted, the arbor of which 
had an endless screw, that recorded its revolutions by means of the elegant 
arrangement now called the cotton-counter. This, the invention of which is 
attributed by WixxIs to the late Dr. WoLLAsTON (who, I believe, learned it from 
Mr. Epcrworts), consists of two wheels of n and + 1 teeth, driven by the 
same screw ; a tooth of the first passes a fixed index for each revolution of the 
vanes, and an index borne by it passes a tooth of the second for every n revo- 
lutions.* In 1790, the hydrometric fly of WoLTMAN was proposed by its inventor 
as an anemometer; but Dr. WHEWELL is the first who appreciated in its full ex- 
tent the importance of the space-measure, especially in its giving an integral in- 
stead of a differential result. His memoir, published in the sixth volume of the 
Cambridge Transactions, marks an era in the science, and, in my opinion, indi- 
cates the only path of its progress. The instrument described by him has been 
used by several observers, but most extensively by one whose energy and 
talents were well adapted to establish its character, Sir Wi~iiAm Snow 
Harris. The results which he exhibited to the British Association in 1841, 
while they fully proved the value of the principle, shewed, at the same time, 
that the mechanical details were not sufficiently perfect to carry out the views 
of the inventor: in particular, the space traversed by the recording pencil is 
(at least in moderate winds) not as the velocity, but rather as its square. 
Harris proposed to investigate corrections for this, which, however, would be 
different in each anemometer, and probably variable even in the same one. 
This error arises from the small size of the vanes, which have, therefore, too 
little power compared to the friction; while that is greatly increased by the 
same cause, as, from their great angular velocity, a complicated train of wheel- 
work is required to bring down the speed of the recording point to a manage- 
able amount. This report induced me to consider the subject carefully; and 
as it seemed possible to correct the defect in question, and some others which 
I had observed in a similar instrument used by Captain Larcom, R.E., at 


in the sea. The wheels have seventy-two and seventy-three teeth, and the revolution of the second 
wheel measures a mile. 

* A very convenient portable anemometer is made by furnishing a set of my hemispherical 
vanes with such a counter. In that exhibited to the Academy, the radius of the circle described by 
their centres = 5°6 inches, and the diameter of the hemispheres = 3°] inches. If the number of re- 
volutions which it makes in a minute be divided by 10, the quotient is the velocity in miles per hour. 


The Rev. T. R. Rogrson’s Description of an improved Anemometer. 159 


Mountjoy Barracks, I obtained permission from the governors of the Armagh 
Observatory (who had already directed me to erect an anemometer) to carry 
into effect my views. After some preliminary experiments, I constructed in 
1843 the essential parts of the machine, a description of which I now submit 
to the Academy, and I added in subsequent years such improvements as were 
indicated by experience. It was complete in 1846, when I described it to the 
British Association at Southampton; so that I have had sufficient opportunity 
to ascertain its efficacy. 

In contriving it, I was guided by the following principles : 

1. The moving power should be so great in comparison of the friction, that 
the correction due to the latter may be inconsiderable. It should also be easily 
applied. 

2. One means of effecting this is to have surfaces which receive the wind’s 
impulse as far from their axis of motion as is consistent with strength. This 
satisfies the second condition, namely, that they shall be acted on by a large 
section of the current, and thus give an average result. When the vanes are " 
as small as those used by WunweExt, they may give measures far different from 
the general velocity, if met by those partial streams to which I have referred. 

3. The movement of those surfaces should be as slow, relatively to that of 
the wind, as may be consistent with a sufficiency of moving power: this lessens 
the train required to bring down the speed of the recording point, and also 
diminishes the wear and tear of the whole machine. 

4. It seems desirable that it should act without requiring any special pro- 
vision for turning it in the direction of the wind. 

5. The structure should be such, that all made after the same type will 
give identical results. 

The third, fourth, and probably the fifth of these conditions, are against the 
vertical windmill as a measure. Its vanes never move slower than the wind, often 
three or four times as fast at their outer extremities.* With the best guiding ap- 


* This must generate a considerable centrifugal motion in the air dragged round with the 
vanes, which will complicate the direct impulse of the wind. Its effect in large windmills is illus- 
trated by a remarkable fact, observed in Holland by the late Mr. Nimmo, that in some of the best 
of them, the weathering at the extremity of the sail is negative. This can only act by preventing 
the escape of the air. An effect of this kind must be difficult to calculate. 


160 The Rev. T. R. Rozinson’s Description of an improved Anemometer. 


paratus, its motions round the vertical axis will not exactly correspond with the 
oscillations of the wind; and very trifling variations in the angle of the vanes 
will make a great variation in their speed. The fourth condition excludes those 
horizontal windmills which act by a moveable screen. Of the remainder, in one 
class the vanes are made to turn during the revolution, so as to present a dimi- 
nished surface to the wind while returning against it ; these are objectionable, 
because the necessary machinery is liable to derangement, and involves much 
friction, which will vary during a long period of working, and change the space 
unit. There remain then those only in which the vanes are curved, so as to be un- 
equally resisted on their opposite surfaces. Of these, the most elegant in prin- 
ciple and definite in action that I know, was suggested to me many years ago 
by Mr. Epcrworrtu. Its vanes are hollow hemispheres, whose diameters coin- 
cide with the arms that support them ; the action on their concave surfaces ex- 
ceeds that on the convex so much, that the machine is capable of being used as 
a motive power with considerable advantage; its simplicity of form is such 
that, without very great exactness of workmanship, similarity of action can be 
attained; and it combines great lightness with strength sufficient to resist very 
severe gales.* 

The relation between the velocity of its vanes and that of the wind can be 
determined satisfactorily, in the actual state of hydrodynamics, only by experi- 
ment. In this instance, however, the problem is so modified by the antagonism 
of the returning vanes, that theory gives not merely the law which connects 
them, but a close approximation to their ratio, and the correction due to 
friction. 

Let AH be an arm of the machine, bearing the hemispheres AIB, DKH, and 
revolving in the direction of the arrows, so that the velocity of their centres =v. 


* In the gale of December 15, 1848 (the anemometer diagrams of which are among the speci- 
mens exhibited to the Academy), the space recorded during the hour 2"*3"=61°5 miles, but during 
24 minutes it is = 4-27, which gives 102°5 miles per hour for the velocity of that squall. Short as 
it was, it did much damage in the neighbourhood, but the instrument was unhurt. A still heavier 
gust is recorded in the diagram of the cyclone of March 29, 1850, where the velocity is nearly 130 
miles per hour for 3 minutes. 

+ At least this point is assigned as the centre of effect by the common theory; it may, per- 
haps, be a little further out in the concave. 


The Rev. T. R. Rosryson’s Description of an improved Anemometer. 161 


This rotation in quiescent air, will cause a resis- 
tance to the convex surface of each hemisphere 
=a'v’; a’ being a coefficient depending on its 
diameter. To this the wind, supposed to act 
in the direction WE, adds another resistance on 
the convex of AIB; but it also acts on the con- 
cave of DKH, with a force which tends to in- 
crease v; and as its coefficient @ is considerably 
greater than a’, v will increase. In consequence 
of this, the concave surface recedes from the Bie, Tk 

wind, and the convex meets it more rapidly; the impelling force, therefore, 
diminishes, and the retarding forces increase. To the latter must also be 
added the centrifugal force expended in producing an outward current in the 
air that is dragged with the convex surfaces, and the effect of friction. Evi- 
dently, therefore, a speed will soon be attained, at which these forces balance 
each other. If 6=the angle WEH, V the wind’s velocity, we have, by the 
theory of Borpa for the undershot wheel, 


Force on DEKH = a JV? sin? 6 — a Vv sin 0. 


Force on AIB =a’ V? sin? 6 + a’ Vv sin 0. 


The force due to the rotation alone = 2a’v’, and the centrifugal force being as 


v? may be assumed = 20’. Let f also = the moment of friction at C, then the 
actual impelling force 


F= (a—a’)V* sin’ 0—(a+a’) Vvsin 0— 2v’ (a +b') —f. 
We must, however, take the mean value of this through the semicircle. It is 


Fido _a-a'y, ata’ 
0 7 FO y 7 


x 2Vv—2v? (a' +b’) + f-* (1) 


* This reasoning supposes a and a/ to retain the same value through the semicircle. Experi- 
ment shows that they vary; but as the change is greatest when their influence on the velocity is 
least, the error of this assumption cannot have much influence. The centrifugal force cannot act 


on the concaye, as there is no tendency in the air which it holds to escape in the direction of the 
arm. 


162 The Rev. T. R. Ropison’s Description of an improved Anemometer. 


As their mean force vanishes when the condition of permanent rotation is at- 
tained, if we equate it to cypher, we deduce 


V a+a 2 (a—a’ 
<== = (+ ae 6) i+ Vf 147 (ate FZ) 1] (2) 
This shows that if we neglect the term introduced by friction, the ratio of the 
velocities V and v depends on the ratio of a and a’ alone, being independent 
of their absolute magnitudes and also of v. It is, therefore, independent of the 
speed of the wind and the size of the machine. 

Calling this ratio m, and making the instrument register mv =V, the true 
velocity of the wind =V + uw, wu being the correction due to friction, we have 
from (1) 


+uy—22(a-4a') (V+u) — 20" (a! +0) -f=0, 


“5 ses =" (ata) V —2v° (a’ +b’) =0; 
whence 
2 ji) 2 
wun] 1 (FEE) | ie (3) 
ma \a—a a—a 


the positive root of which may be tabulated for a series of values of V. 

The constants of these equations must be given by experiment, and it is 
not easy to obtain them satisfactorily, especially the most important of them, a 
and a’. But for the unsteadiness of the wind,* both in force and direction, 
we might attach hemispheres to some weighing apparatus, with theseoncave 
and convex surfaces turned to the wind, and thus obtain absolute measures of 
them. This, however, could only be done by connecting the two with a pair 
of registers like those of OssEr’s instrument, which would give the mean pres- 
sure for a considerable period ; and such an apparatus is not at my command. 

As, however, m depends on their ratio only, I found a method, which, though 
disturbed by the same cause, is tolerably successful. Two hemispheres, similar 


* In illustration of this I may mention, that having placed two hemispheres on the arm, so 
that both concaves faced the wind (when, of course, they might be expected to remain in equi- 
hbrium), they oscillated with considerable force through ares of 90°; the distance between their 
centres was 48-5 inches, 


The Rev. T. R. Rosinson’s Description of an improved Anemometer. 163 


to those of the actual anemometer, are fixed on an arm in which, by means of 
along slit, the axis of rotation can be shifted to any position; this axis causes a 
graduated circle to measure 0, the zero of which is determined by a vane above. 
The axis is shifted till the two pressures are equal, when, of course, a and a’ 
are inversely as its distances from the two centres. In reducing this to prac- 
tice, however, I found a difficulty which I had not anticipated. Since the forces 
on the hemispheres are as V* sin? 0, I concluded they would be at the maximum 
at 90°, and vanish at 0° or 180°; and began by observing them in the first of 
these positions. To my great surprise, I found that the equilibrium there is un- 
stable, so that if the angle be changed the least either way, the concave predo- 
minates. This makes it hard to ascertain the true point of balance, as the 
direction of the wind is ever changing ; but nevertheless I think I am war- 
ranted in concluding, with some confidence, from sixteen experiments made in 
four days with winds from a moderate breeze to a hard gale, 


one 
a 


or, in round numbers, the action on the concave is four times that on the 
convex. 

I was the more surprised at this predominance of the concave when the 
arm is inclined to the wind, because then the part HK of its convex acts 
against it. 

From some other angles I obtained, though by fewer observations, 


Gf Sephe BN) So arog. 
a 

75h eM ne AATS. 

608 6, |. A710, 

ACR ses anal an: 

Op we Kia Tt LOD? 


Beyond this it is impossible to go, as there the convex surface apparently ceases 
to act. In fact, on removing the hemisphere DK, the other remains as in the 
wood-cut, making @ = 210° nearly, and oscillating as the direction of the wind 
changes. Whether this arises from the minus-pressure at the segment IA, or 
from the wind which passes at B eddying into the concave, I cannot decide; 

VOL. XXII. Z 


164 The Rev. T. R. Roprson’s Description of an improved Anemometer. 


but it is a striking illustration of the imperfect state of this branch of hydro- 
dynamics. * 

As to the coefficient 0’, its limits at least may be obtained by a process 
which I at first thought might give a and a’,—the same which EpGEworts, 
Hutton, Borpa, and Vice, employed in their experiments on resistance. The 
resisting surface is placed at the extremity of a horizontal arm made to revolve 
round a vertical axis by a weight attached to a cord wound on the latter, and 
passing over a pulley. When the rotation becomes uniform,f the resistance 
must equal the accelerating force, and if this be constant, all the resistances 
must be equal, and, therefore, can be compared with the velocities. With this 
hope the apparatus described in the preceding section was placed in a tower 
of the Observatory, and alternately driven with its concave and convex sur- 
faces foremost. Twenty revolutions were made before the time was noted ; 
and then thirty were taken, giving S= 381 feet. The mean velocities varied 


* From this it follows, that, if the friction do not prevent it, an anemometer of this kind should 
revolve even when its axis is in the direction of the wind. The small one already described does 
so, but this may be owing to the oscillation of direction. 

; I fear the physicists just mentioned took the fulfilment of this condition for granted. This 
does not necessarily happen. Let F’= the impelling power, K the moment of inertia of the appa- 
ratus, S the space described, 7 the time, V the velocity of the centre of the resistance. 

F- av 
K 


v= x V (1-e*). 
T= Rp x log (4). 
EK 0 


Square of mean yelocit: a =—-—x—; 
q TTS eG EGE 


Accelerating force = 


mean square of velocity = 


From these expressions it is manifest, that v cannot be uniform till Sis infinite. In my trials 
it continued to increase even till SS was the largest I could command, 1143 feet. Hence also, the 
mean square of velocity (which ought to be used in computing the resistance) must differ from the 
square of the mean velocity; the latter, however, has always been used. As, moreover, no esti- 
mation has been made of the air’s centrifugal force in the results which have hitherto been 
obtained in this way (and in fact it cannot be separated from the resistance), I am compelled to 
think they require revision, though they are at present received as standard facts. 


The Rev. T. R. Rosryson’s Description of an improved Anemometer. 165 


from 2:23 to 8:50 feet. The values of F' were determined by attaching to the 
centre of a hemisphere a fine thread perpendicular to its diameter, and passing 
over a delicate pulley (whose friction is known), to which weights were sus- 
pended, such that the driving weight just moved the apparatus when slightly 
jarred. These weights, divided by the mean squares of the velocities, give 
a+banda’'+b'* The result is 

a+b 


arp = 2°019, 


and assuming a=a’ x 4-011, we have 
b’ =a’ x 0-9866 +6 x 0:4953. 


No means of determining the ratio of } to b’ occurs to me; I could only 
satisfy myself that it is considerably less, by suspending a light body two feet 
outside the circle, and estimating the resultant ofits deflection from the vertical 
in the direction of the radius. This made it evident that comparatively little 
air is thrown outwards by the concaves, the hollow, I suppose, carrying it round, 
and preventing its escape. We may, therefore, safely assume, that it is between 
the limits b = b’, b= 0, and much nearer the latter. These suppositions giving 
the limits 6’ = a’ x 1:9866; b’=a' x 0:9866. 


If now we substitute these values and that of 5 in (2), we obtain 
7 
= 3°306, if 6’= b; rT. 2:999, if b=0. 


It must, from what precedes, be much nearer the second ; and if we also 
. a cil BR cs 
consider that the mean value of 7 through the semicircle is a little greater than 


that at 90°, we shall be justified in assuming the theoretic value of m = 3-000. 

It is in very unexpected (by me) agreement with that given by experiment. 
The most obvious mode of determining this constant—placing the instru- 

ment on a carriage, and comparing its record with the space actually traversed — 


* Tt is assumed in this, that a and a/ are the same as in a current of air, which, however, may 
not be the fact. Especially it is possible, that the air of the apartment may be dragged round with 
the cups, and thus offer less resistance. 


AP 


166 The Rev. T. 8. Rostyson’s Description of an improved Anemometer. 


I found to fail, partly from the difficulty of eliminating the action of the wind, 
but still more from the fact, that a carriage drags with it a quantity of air, 
so that for many feet from it the anemometer does not feel the full effect of 
the motion. At low speeds, and on days of calm, I have got results which 
agree with that given by other methods, but more frequently the discord- 
ance destroys all confidence in it. The aerial log proposed by Sir W. S. 
Harris in the report at Plymouth, could not be applied, on account of the 
lofty position of my instrument ; but I tried one far more delicate, by ex- 
ploding small charges of powder at it, while my assistant noted the time re- 
quired by the little globes of smoke (which in dry weather are not dissipated 
for many seconds) to traverse 150 feet. But the irregularity of the wind’s 
motion makes all such trials unsatisfactory, and I got the most discordant 
results, the reason of which was evident by watching the track of the smoke , 
it rose, descended, twisted in eddies, and even occasionally came back many 
feet against a strong breeze. But in addition it can only give the movement 
of that one part of the current which it occupies, while the anemometer shows 
those of all that pass it in the same time, which are essentially distinct. I may 
add, that the impossibility of obtaining accurate measures of velocity by such 
means, was long since pointed out by Mr. Brice.* 

The plan which succeeded consists in applying the whirling apparatus to 
carry the anemometer, as in the annexed figure. The anemometer has four hemi- 
spheres; it is similar to at 
the actual one, and about S : 
a fourth of its dimensions: j- 
the distance AB is 45°6 a 
inches, and as the diame- 
ter of the hemispheres is 
only 3 inches, we may as- 
sume the velocity of their 
centres to represent that 
of the wind. C is acoun- 


terpoise. I found that in Fic. 2. 
this case the rotation produced no important outward current. The machine 


* Phil. Tra ns., 1766. 


The Rev. T. R. Roprnson’s Description of an improved Anemometer. 167 


was permitted to make a few revolutions to come to its speed; and then the 
counter was put in action for a certain number of revolutions of the arm AC, 
generally 96. The time was also taken to give the mean velocity. I found 


Driving i i No. of 
Weight. ov _| Observations. 


I did not venture higher velocities, as the apparatus was not strong enough ; 
but the above are sufficient to show that, after allowing for friction, the value 
of m= 3:000.* 


* Some facts observed during these experiments may be deserving a record. 
1. The mouths of the hemispheres being covered with paper, so that planes were substituted 
for concaves, I found, with V = 12°80 feet, m= 5-041. 
2. Cutting away the central paper, so as to leave merely a ring 0'°2 broad, which (from what 
has been observed with Piror’s tube) I thought might increase the effect, proved very disad- 
vantageous, 
3. Making the cups segments of 220° was also hurtful, for, with 
V=13°87, m=5°'220. 

4. A single hemisphere with a flat counterpoise presenting its edge to the air, gives 
V=7:30, m=3°700. 

5. With three arms, two carrying entire spheres, and one a hemisphere, 
V=10-30, m=7-900. 

6. Five vertical windmill-vanes (the best number), of the same outer diameter, but heavier, 
and set at 45°, give, in 96 revolutions of the arm, 

V=763. No. rev. = 497°5. 

V=12-29. No. rev. = 516°0. 
The four hemispheres at the same time, 

V=1361. No. rev. = 141:2. 


The tips of the vanes here move about 3:4 times as fast as the wind. 


168 The Rev. T. R. Rosryson’s Description of an improved Anemometer. 


That this ratio holds for the large anemometer, as well as the small, is ex- 
perimentally shown by placing the latter beside the other, and counting the 
revolutions made by it during eighty-eight of that. Fourteen such trials give, 
with a mean velocity of wind = 15°6 feet, the ratio of the revolutions = 4°12, 
the inverse of their dimensions being 4:29. The difference is due to the large one 
being above the other, and therefore getting the wind more freely. 

As this relation does not depend on the elasticity of the impelling fluid, it 
should hold when the instrument is acted on by a stream of water, with the 
advantage of being much less affected by friction. I tried this in a large mill- 
course near Armagh, placing the small instrument in the central part of the 
current, where the velocity was found by floats = 1613 feet. I obtained, 


: With four hemispheres, . . . m= 2972. 
WVulinOs “Goo 8 "SB Wo oe o Sah 
With three, equidistant,. . . . =3:041. 


The trial with two was made rather from curiosity than from any depend- 
ance on the result which might be obtained, as, when passing the line of centres, 
the impelling force is so slight, that any eddy will produce a disturbance of the 
motion. It would not change the mean much, but I think should be rejected. 
That of the other two is 3:006, still probably a trifle too large, as the four are 
preferable on the same grounds to the three. 

From all this I think we are warranted in laying down this law, that in a 
horizontal windmill of this description, the centres of the hemispheres move 
with one-third of the wind’s velocity, except so far as they are retarded by 
friction. 

This principle once established, its application is easy. Plate IV., fig. 1, shows 
the external appearance of my anemometer, as it stands on the flat roof of the 
dwelling-house. Its frame consists of four uprights, 3’ by 2", and 15/ 4* long ; 
6! 5' asunder below, 2/ 4' above. They support the strong frame B, in which 
a diagonal carries the bearings of the axles C and D. The part H is sheathed 
and roofed with plank (the roof covered with painted canvass); and it forms 
a very convenient room for the self-registering apparatus. The copper funnel 
F is attached to each axle, to prevent the entrance of wet. The great height 
of this frame is necessary to clear the dome of the west equatorial, which rises 


The Rev. T. R. Rosrnson’s Description of an improved Anemometer. 169 


S.E. of it; but it has the double disadvantage of causing additional friction by 
the weight of the long axles, and making the whole less stable. To obviate 
this last defect, about 3cwt. of pig ballast is disposed round the floor of H ; 
notwithstanding which, the machine was blown down in March, 1845. After 
this it was further secured by three iron shrouds attached to the walls in the 
directions S.E., S.W., and N.W.; and it has since withstood still heavier 
gales. The axle C bears the mill G for space; the axle D the vane V for 
direction. 

The dimensions which I chose for the first of these are, 12 inches for the dia- 
meter of the hemispheres, and 23 inches for the distance of their centres from that 
of the axle. The latter might, perhaps, have been increased with advantage; but I 
was afraid of weakening the arms too much. The hemispheres are made of sheet 
zinc, strengthened by a wire rim ; each weighs 1°31 1bs., but might have been 
lighter if made of thin copper. The arms which carry them are iron, 1*5 inches 
broad, and 0:1 thick, but feathered off to a sharp edge at each side, and kept 
from bending downwards by stays of wire. The hemispheres are four ; for I 
found, by trials with the small anemometer, that this number is better than 
either five or three. Six is inferior to any lower number, not excepting two ; 
probably because some eddy from the concaves reaches the convex surfaces. 
The iron tubes T, 8 and 18-5 inches long, are secured to the diagonal of the 
top frame, and carry boxes of bronze, in which are bronze balls, on and be- 
tween which the axles C and D turn. This arrangement is the result of many 
experiments. At first they turned above in common brass journals, and their 
hardened points rested below on surfaces of hard steel. As, however, C with 
its appendages weighs 20°691bs., and makes, on an average, 1500 revolutions 
per hour,* the bearing surfaces were soon abraded ; the friction also was far 
too great, being equivalent to 104 grains acting at the centre of a hemisphere. 
I then refashioned the pivot very carefully, and set it in an agate cup ; but, 
though this was kept full of oil, after a year’s work, I found that a hole of some 
depth had been drilled in it. I substituted for it one of sapphire, but even this 
failed after two years; and the friction was not so much lessened as I expected, 


* Of this 6°69 is due to a piece of iron tube composing C, which I have recently replaced 
by a shaft of deal; this has reduced the weight to 16-23lbs. The average velocity of the wind is 
about 10 miles per hour. 


170 The Rev. T. R. Rosrnson’s Description of an improved Anemometer. 


being 73 grains. This was finally replaced by the present mounting in May, 
1849. It is shown in Plate V., figs. 2 and 3, where C is the axle, 0°82 inches 
diameter, D the box of bronze (8 copper to 1 tin); B, five balls of the same, 
1:12 diameter; I a disc of iron truly turned on the axle; H an aperture for in- 
troducing occasionally a few drops of oil, which I find necessary for the lateral 
action of the balls. They bear both the lateral pressure and the weight ; and, 
therefore, require only a slight lateral support below, which is given by the 
arbor of the endless screw. This arrangement shews no trace of wear after 
more than a year’s work, and the total friction is but 53 grains :* the coeffi- 
cient of that part of it which belongs to the balls, I find to be +, of the load. As 
in high winds there is added to this a lateral pressure, in respect to which the 
balls do not act quite so advantageously, we may take it. From this value 
of the friction, the correction of V is easily computed;f but it is in some 


* Of this I find that 20:36 belong to the mill, and 32°64 to the registering apparatus: with 
the new shaft the total friction will be 48°61. 
+ For this it is also necessary to know the constant a—a’. I approximated to this as follows: 
a spring-balance is attached to a cord wound on the axle C, which, as v =0, measures with four 
cups the foree V?(a—a’). Its slide moves a pencil parallel to the axis of a cylinder covered with 
paper, and made to revolve by clock-work, on which it traces the curve of time and force. The 
small anemometer already described gives V by comparison with the time. This V is reduced to 
that of the large instrument by comparative trials at the time of experiment. It must, however, be 
remembered, that it is a mean velocity, and that, therefore, the value of a—a’' thus obtained, is too 
small if the fluctuations be considerable. As Vis affected by friction, the first values of a—a’ are 
used to correct it, and thus a more exact result is given bya second computation. By six diagrams 
I find, 
Time = 126°2; V* (a—a’')= 828'6grs.;5 V=4"99a — a! = 33:28 ers. 


98:8; 17606; 10:40 16°22 
966; 11681; 6:27 29°71 
184:2; 6851; 2°85 51:57 
101-2); 555°8 ; 5:04 21:04 
98-0; 1698-7; 681 36°03 


The second and fourth were marked as doubtful from excessive fluctuations; but as the mean of 
them and the fifth differs little from that of the other three which were considered satisfactory at 
the time of experiment, I retain them, and take a — a’ = 31-997, or 32 in round numbers. The 


: 3 3 3 a 
equation (3) becomes, with the values previously given for ai and m, 


The Rev. T. R. Rozinson’s Description of an improved Anemometer. 171 


respects preferable to correct mechanically by applying to C an auxiliary force 
equivalent to the friction. Besides the saving of labour, it extends the action 
of the instrument ; as, from the data in the preceding note, it cannot move with 
less than 1-29 mile per hour. The dynamic effect of such a force, while the wind 
53 grs. x 5280 x 100 
3 x 7000 
therefore, require a weight of 37\bs. falling 36 feet. The locality does not 
permit this; and I, therefore, purpose to use a remontoir, wound up by a small 
mill similar to the anemometer itself. Perhaps an electro-magnetic machine 
might be simpler; the expenditure of zinc and acid would be trifling, and their 
consumption proportionate to the work done. The chief difficulty would be the 
inconstancy of the current. 

The vane V is three feet long by one and a half extreme breadth; it also is 
made of sheet zinc. From a wish to give it as little momentum as possible, it 
was at first a light wooden frame covered with varnished calico, which the wind 
soon destroyed. This axle turns also on balls. 

It remains to describe the self-registering apparatus; and first, that for the 


= 1332Ibs x 1 foot; it would, 


traverses 100 miles, = 


space. 

My first intention was to adopt a form resembling the charts of wind- 
paths given by Dr. WuEweEtt in his memoir, but in which the curves should 
be drawn by the wind itself. The arrangement I proposed was to make the 


w= Vx 060637 { /(14+-2, x SE) 1}, (4) 


which, with the above values of f and (a — a’) is 


u=V x 064637 {/( aS) =! }. (5) 


From this the following table is computed: 


Via a = 1285 V =6"u=0"-068 
2 0°469 7 0:050 
3 0240 8 0-039 
4 0:144 9 0-031 
5 0:095 10 0:025 


It is evident that above 5” per hour the correction is insensible. 
VOL. XXII. 2A 


172 The Rev. T. R. Rosmson’s Description of an improved Anemometer. 


plane which holds the paper move by means of two slides at right angles to 
each other. Its motion should be given by a rack, travelling proportionally 
to the space, but revolving so as to be always in the direction of the wind. 
A pencil placed over the centre of its revolution would describe on the 
paper a track perfectly similar to that of the wind. At each hour and quarter 
hour, a clock was to print by punches a series of marks, which would repre- 
sent the time.* The mechanical arrangements were planned, and certainly this 
method would have the great advantage of showing at one view the three vari- 
ables, and speaking most distinctly to the eye; but I gave it up, from a convie- 
tion that it is much less adapted to give periodical means than the method 
of co-ordinates. 

Of these I prefer the polar to the rectangular, for the following reasons. 
In the first place, the direction, being an angle, is at once recorded ; secondly, 
a movement of rotation can be given to the paper-holder with much less fric- 
tion than a rectilinear one ; thirdly, this movement may be continued through 
many circumferences without inconvenience, while the other is limited by the 
length of the rack, or other contrivance for producing it. In the rectilinear 
direction-register there is also the inconvenience that, if the wind veer several 
times in the same direction round the horizon, a new series of graduations must 
commence. I may add, that there is, perhaps, a want of graphic propriety in re- 
presenting angular veering by a right line, but none in measuring miles by a 
graduated arc. Fourthly, one form of printed paper serves for both. The only 
objection to the polar form, of which I am aware, is, that the scale is less near 
the centre than at the circumference; this, however, may be obviated in any case, 
when it is desired, by winding up the apparatus at shorter intervals, so as 
to keep the pencil near the latter. 

First, then, as to the space: the dimensions which I have adopted for the 
windmill are such that, in 440 revolutions, the hemispheres travel one mile, 


* August 16th. This, I find, has been applied by Mr. Osstrr, who showed me at the late meeting 
of the British Association, some beautiful wind-curves, where the time is thus expressed. He checks 
the excursions in direction by using a windmill, and with great success. The « of his curves is 
the space, the y the direction. The time is shown by dots, single and multiple, struck in pairs at 
each side of the paper, and its record is very complete. 


The Rev. T. R. Rozrnson’s Description of an improved Anemometer. 173 


and the wind three. If degrees on the paper be miles of wind, the number of 
the former must be 440 x 120 for one of the paper-holder. A train which 
effects this very simply was arranged for me, by one whose recent loss I lament, 
not merely from personal regard, but from regret that science is deprived of 
aid so powerful as that of his high mechanical talents,—the late Mr. Ricnarp 
Suarp. It is shown in Plate VL, fig. 4, where A is an arbor held loosely in 
the lower extremity of the axle, and carried round with it by the screwe. An 
endless screw on this drives the wheel B, of 88 teeth; a second endless screw S 
drives C, of 100; its pinion D, of 16, drives E of 96. On this the brass 
plate P, 14 inches in diameter, is fastened by a steady-pin and the nut H, which 
also assists in holding down the paper. The speed of the train is therefore 
= 88 x 100 x 6 = 440 x 120. . 

The arrangement for direction is shown in Plate VI., fig.5. The arbor F 
(which is also loose in the hollow of the vane axle) bears the wheel G of 96, 
which drives K of 96. On this the paper-holder P’ is secured by H’; its angular 
movement is therefore equal to that of the vane, while the paper can be more 
easily removed than if it were immediately carried by the vane-axle. 

That axle is connected with the arbor F, not by any rigid attachment, but 
by the spiral spring L. This is necessary, not merely to prevent the destruc- 
tion of the machinery in violent oscillations of the vanes, but still more to 
lessen their extent on the register-paper. Though Dr. WHEweELt had pointed 
out the magnitude of these oscillations, andthe impossibility of preventing 
them, I was not at all prepared for what I found. It may be that these 
waverings of the wind are of greater amount at Armagh than elsewhere, owing 
to the exposed situation, and the undulating surface of the country; but, with- 
out some contrivance to check them, the direction-papers would be very un- 
sightly objects. It must, however, be remembered, that they cannot be avoided 
entirely, nor is it desirable that they should be too much diminished ; for I find 
that this is a distinctive character of some winds, independent of their velocity, 
and, therefore, implying some peculiarity in the origin or progress of the cur- 
rent. In particular I have remarked, that when excessive, it is connected with 
a roaring sound, that gives an exaggerated impression of their force. This was 
strikingly exemplified in the destructive tempest of February last, whose highest 
velocity did not exceed 40 miles per hour. On another occasion, when the 

2a2 


174 The Rev. T.R. Rosryson’s Description of an improved Anemometer. 


velocity was of nearly the same amount, the sudden diminution of roar led me 
to suppose the gale was abating; but, on going to the instrument, I found the 
velocity had increased to 52, while the range of direction was only half its pre- 
vious extent. 

The contrivances which I have applied as checks on the direction-fluctua- 
tions seem to work well. In the first place, such as are completed in a second 
or two are chiefly expended in bending the spring L, being past before its ten- 
sion can overcome the inertia of the paper-holder and its machinery. Secondly, 
the wheel G drives a regulator attached to the arbor of the pinion I, but not 
shown in the drawing. This consists of four vanes, 
shown in plan, Fig. 3, made of light deal frames covered 
with paper. Each is 37 inches high and 15 broad. As 
the whole is very light and turns on an agate, it yields 
to the slightest impulse of the vane, if time be given, but 
presents a very great resistance to rapid motion. Its 
speed is 24 times that of the vane,* and this, combined ic. 3. 
with the action of the spring, will often reduce the oscillations to one-third of 
their absolute magnitude. As at first applied, the regulator was much smaller 
and immersed in water; but I was obliged to abandon that plan, in consequence 
of its action being interrupted during frost. 


Lastly, Plate V., fig. 6, shows the method of connecting these two registers 
with that of time. N is a cast iron plate which bears the whole machinery, 40 
inches by 14. P and P’ are the paper-holders ; each has three spring-clips at 
its circumference, to hold the paper, which is further secured by the screw H 
passing through a hole punched in its centre; this screw serves also to centre it, 
being of the same size as one of its circles. One of these clips bears a fiducial 
line, with which the zero of graduation is made to coincide when a new paper 
is applied. M isacommon clock movement, the weight and pendulum of 
which pass through openings in N. Its barrel carries a second wheel, which 
moves, by a rack, the bar pp’ through six inches in twelve hours. This 


* I have since added an intermediate wheel and pinion, which makes the speed 2 x £2 = 28:8, 


which is a considerable improvement. 24 might be immediately obtained, and would be, perhaps, 
the best. 


The Rev. T. R. Rogryson’s Description of an improved Anemometer. 175 


bar slides in a dovetail on the front plate, and carries adjustable tubes at its 
extremities, in which pencil-holders are placed, and made to act by weights 
placed in their cups. Since, however, in the direction-register, the pencil, as at 
first arranged, and shown in the figures, travels from the circumference, I have 
found that in damp weather it occasionally has pulled the paper from the clips 
and torn it. I have, therefore, lately carried it by an additional piece, one end 
running in a guide at O, the other provided with a stud which fits in p’: this 
complicates it a little, but remedies the inconvenience, and makes the time- 
reading the same in both registers. 

The paper used is printed in red, from a plate engraved with a graduation 
of degrees and half degrees. Within this are a series of concentric circles, 
which represent portions of time. Those which correspond to hours are 
stronger than the rest, and half an inch apart ; the intermediates show decimals 
of the hour. The mode of using it is this: the pencil p’ being removed, the 
date is written on P near its pencil; the clock is then wound up, and p draws 
a line from the circumference to the centre. The paper on P’ is then removed 
or shifted, and if another be placed, it is similarly dated, with the addition of 
the degree, which is set at the fiducial line; and the pencil p’ is replaced. 
Then, during the ensuing twelve hours, the action of the clock carries the 
pencils from the centre to the circumference. If there were no wind they 
would merely draw radial lines; but in general p traces a spiral, and p’ shades 
an regular sector. The clock should be adjusted so that the twelve hour 
circles should be exactly traversed. In general, a space-paper may contain 
four or six spirals, dating each winding line ; and a direction one, two, or three 
sectors, shifting the zero point for each. This zero in my practice repre- 
sents a wind from the south, and the graduation goes round from west to north. 
The papers are finally fixed with a weak solution of mastic in common whiskey, 
and preserved for reference. 

In reducing these diagrams to a form available for computation, I have 
found no system preferable to the method pointed out by Dr. WHEWELL in his 
memoir. In the first instance, the centres of the papers are restored; in the 
space-papers, drawing radii through the intersections of the spirals with the 
hour-circles, the graduation gives the hourly spaces, which, if necessary, are 
corrected for friction: these are tabulated. In a second column is entered the 


176 The Rev. T. R. Rosrnson’s Description of an improved Anemometer. 


direction at each hour. This is found by bisecting the arc of the hour-circle, 
which is shaded by the pencil.* The mean direction during each hour will, 
in general, not differ from the mean of those at its beginning and end; but if the 
eye perceives that this is not the case, those for the decimals of the hour may 
be taken. From this are computed two rectangular co-ordinates, which are 
given in the third and fourth columns ; w the motion of the wind from the west, 
s that from the south. These are obtained by multiplying the hourly spaces into 
the sine and cosine of the mean direction. I have found it easiest to do this bya 
large sliding rule, having arranged a table of sines and cosines for each deci- 
mal of the degree. They need only be to three places of decimals, but should 
have a quadruple argument; its first column from 0° to 90°, its second from 180° 
to 270° (these on the left): its third from 360° to 270°; its fourth from 180° to 
90° (these on the right): and over each column the appropriate signs. Details 
of this kind may seem trifling, but the waste of labour which they avoid is of 
great consequence when so great a mass of work has to be performed, as even 
one year of such a registry involves. 

From these co-ordinates any final results may be obtained, as hourly, 
daily, monthly, or yearly means. Let W be such a mean of w, S of s, attending 
to the signs ; then D, the mean direction for that time, and =, the mean space, 
are given by the equations 
S W 


cosD~ sinD’ 


tan D = = 


Ww 
Ss? 
remembering that sinD has the same sign as W, and cosD as S, from which 
the quadrant of D is known. 

As an example I annex the reductions of the twelve hours during which the 
centre of the cyclone already referred to passed the Observatory, as one which 
will illustrate the process in an extreme case. 


* This is most rapidly performed by a plan explained in the 
figure. Let BC be the arc of the hour circle H; lay an edge of 
the ruler RT through C, and the centre I, so that its extreme 
point is on the hour circle. Then lay the parallel-ruler PL through 
that point and B; remove TR, and move the half of PL till it 
passes through I; the point G is in the line bisecting BC. 


The Rev. T. R. Rosryson’s Description of an improved Anemometer. 177 


March 29, 10 p.m. 
11 


~ 
in] 


1 
2 
3 
4 
5 
6 
7 
8 
9 
0 


The means for the two irregular hours are taken from the reading for 


46°3 : hee : 
each tenth. We have tan D — saz» Which, as both are positive, must be in 


83° 
first quadrant, therefore, 
" ee Eg 
D.= 28° 95, and > — sin 28°57" =o 65. 


It appears, therefore, that during these twelve hours, the real movement of 
the air was only 95-6 miles, from a point 29° west of south. 


For all purposes of physical investigation, this method of exhibiting the 
results is fully efficient ; at the same time it is much to be desired, that some 
graphic method could be devised which would exhibit to the eye the relation 


* At 3-30" the wind veered suddenly 217° +5, against the order of graduation, which is shown 
by the sign —. The mean direction for the hour = 219°*2. There also was at 7” exactly another 
veer, in the same direction, of 210°-5. The mean direction for the hour = 132°-0, 


178 The Rev. T. R. Rosrson’s Description of an improved Anemometer. 


of the space, direction, and time at one view. This might in some degree be per- 
formed by a delineation of the actual trajectory of the wind, either drawn by 
itself, or laid down from the co-ordinates w and s, on which the corresponding 
times are marked ; but the analogy of curves described on a plane, and expressing 
the relation between two variables, naturally leads to the notion of a solid whose 
three dimensions would afford a triple representation. It would involve the 
construction of a model, or at least a contoured plan. For, in fact, if we con- 
ceive perpendiculars to be raised on one of my direction-papers, at each point of 
the shading, proportioned to the velocity at the corresponding instant, their 
totality would be limited by a relieved surface which would show by its undu- 
lations the state of the aerial movements, and might be contoured. Unfortu- 
nately, the changes of direction are so abrupt and large, that it is absolutely 
impossible to exhibit in this way the conditions of any short period ; but it is 
probable that it may be different with the hourly or even annual mean of a 
considerable number of years; and I venture to recommend it, or some equiva- 
lent, as an object worth the attention of meteorological inquirers. 


T. R. Ropryson. 


ARMAGH OBSERVATORY, 
June 8, 1850. 


VIIL.—On the Equilibrium and Motion of an Elastic Solid. By the Rev. Joun 
H. Jeter, Fellow of Trinity College, and Professor of Natural Philosophy 
in the University of Dublin. 


Read January 28, 1850. 


1c THe problem which forms the subject of the present Memoir has already, at 
various times, occupied the attention of mathematicians. Although much of the 
interest which it has excited is due to its connexion with the undulatory theory 
of light, the importance of the problem itself, considered as a branch of rational 
mechanics, is fully admitted; and more than one writer has treated of it without 
regard to the real or supposed existence of a luminous ether. Nor can it, I 
think, be doubted, that such a distinction between the rational and the physical 
science, is in accordance with the dictates of just philosophy. The rational 
science would still be real, even though the existence of the ether were (if that 
were possible) disproved ; and the admitted reality of the several solid and fluid 
bodies which are found in nature gives us, in such cases, the means of testing 
by experiment the accuracy of the laws arrived at. ‘“ Whatever theoretic ob- 
jections,” says Mr. Havcutoy, “ may be made to the application of the theory 
of elastic media to optics, none such exist as to its application to solid and fluid 
bodies. The mathematical investigations which, in the case of light, must be 
hypothetical, are, in the case of solid and fluid bodies, essentially positive, and 
may be made the subject of direct experiment. A general inquiry into the 
laws of elastic media is an interesting application of rational mechanics; and 
although it must necessarily include cases purely hypothetical, it is not, there- 
fore, to be considered unimportant.” * 


* Transactions of the Royal Irish Academy, Vol. xxii. Part i. p. 97. 
VOL. XXII. 2B 


180 The Rev. J. H. Jetxrerr on the Equilibrium and Motion of an Elastic Solid. 


2. Two general methods have been adopted by the various authors who have 
treated of this problem. Of these, the one consists in forming expressions for 
the forces which act upon each particle in the medium under consideration, 
and then determining the laws of its equilibrium, or motion, by the general sta- 
tical or dynamical equations. This method is followed by Porsson and Cav- 
cuy. It is also adopted by Navier in the commencement of his Memoir, but 
soon abandoned, as being less complete than the second method. This latter, 
which is the method of LaGrancs, and is followed by Mr. Grern, Professor 
Mac Curnaca, and Mr. Haucuton,* takes as its basis the equation derived 
from the combination of D’ALEMBERT’s principle with that of virtual velocities, 
and is distinguished by the greater completeness of the solution which it affords; 
the same analysis giving both the general equations of equilibrium, or motion, 
and the particular conditions which must be satisfied at the bounding surface 
of the body or medium under consideration.t This is the method which I pro- 
pose to adopt in the present Memoir. The discussion of a problem like the 
present must, of course, rest upon principles more or less hypothetical, mas- 
much as the nature of molecular action cannot (at least in the present state of 
physical knowledge) be ascertained by direct experiment. The classification, 
however, with which the present investigation commences, cannot be considered 
as other than positive, inasmuch as the two kinds of force, upon the distinction 
between which it is founded, are known to exist in nature, and cannot, without 
a hypothesis, be reduced to one. The principle of this classification I shall 
now proceed to state. 


* All these writers commence with the assumption that the sum of the internal moments of a 
medium may be represented by the variation of a single function. To this method it may, per- 
haps, be objected that it takes, as the foundation of a physical theory, a principle which is almost 
purely mathematical, and to which it appears difficult to give a definite physical meaning. This 
hypothesis, moreover, does not give to the equations of motion all the generality of which they 
are susceptible. I have, therefore, preferred taking, as the basis of the present Memoir, a prin- 
ciple essentially physical; more especially as the equations of motion derived from this principle 
are, in the case of homogeneous bodies, possessed of the full number of constants, and have, there- 
fore, the greatest amount of generality which their form admits. 

+ The investigation of these conditions, according to the method ordinarily adopted, is, how- 
ever, open to serious objections. These the reader will find noticed in a subsequent part of the 
present Memoir. 


The Rev. J. H. Jectert on the Equilibrium and Motion of an Elastic Soild. 181 


GENERAL CLASSIFICATION OF BopIEs. 


L—Hypothesis of Independent Action. 
IL— A ypothesis of Modified Action. 


3. The classification which I propose here to adopt, and which forms the 
basis of the present Memoir, is founded upon the following very obvious prin- 
ciple. The force, or influence, which one particle or molecule exerts on 
another, may show its effect either by causing a change in its state, or by 
causing a change in its position. Either or both of these changes may affect 
the influence which this particle in its turn exerts upon any of those around 
it. Thus, for example, if m, m’, m’’, be three particles acting upon each other 
by the ordinary attraction of gravitation, the action of m’ upon m” will be mo- 
dified by the action of m only so far as their distance from each other is 
changed by it. The attraction of m has no power to change the attraction of 
m/ upon any other particle, except by altering its distance from that particle. 
But the case would be altogether different if we supposed m, m’, m’’, to be elec- 
trified particles. In this case the action of m upon m’ would modify the action 
of that particle upon m’’, not only by changing the distance between them, but 
also by changing their electrical state, and, therefore, the force which each ex- 
erts upon the other. In the former case, if m’ and m’’ maintain the same relative 
position, the force which they mutually exert remains unchanged. In the se- 
cond, even though the relative position of the two particles remains unaltered, 
their mutual action will be modified by the presence of a third particle.* 
From this distinction an obvious classification follows. In the first class we 
place all bodies whose particles exert upon each other a force which is inde- 
pendent of the surrounding particles; a force, therefore, which can be changed 
only by a displacement of one or both of the particles under consideration. In 
the second class, which includes all other bodies, the mutual action of two par- 
ticles is supposed to be affected by that of the surrounding particles. 


* T donot, of course, mean to say, that in a case like that of electrified particles, change of state 
in the particle itself may not be caused by change of position in the particles of some fluid which 
pervades it. It is sufficient for my purpose, that in such a case the force which two particles 
exert upon each other may be changed without a displacement of the particles themselves. 


2B ‘ 


182 The Rev. J.H Jettert on the Equilibrium and Motion of an Elastic Solid. 


We shall now proceed to investigate the equations of equilibrium and mo- 
tion, for bodies of the first class. 


J.—Hyportuesis oF INDEPENDENT ACTION. 


4. Let the several particles of a body, which satisfies the hypothesis of inde- 
pendent action, be displaced from their original position of free equilibrium, 
this displacement being supposed to follow some regular law. Let it be re- 
quired to determine the conditions of equilibrium of these particles in their 
new position, or, in other words, to assign the forces which should be applied 
to each of them in order to keep them at rest. Again, if the particles be left 
to themselves after the displacement, let it be required to determine the law of 
their motion. 

In applying the method of Lagranex to any problem of equilibrium or 
motion, it is plainly necessary to commence with two assumptions, namely :— 
1. An assumed expression for the intensity of each of the acting forces. 2. An 
assumed expression for the effect which this force tends to produce; the effect 
of a force being defined by the quantity which it tends to change. 

Let m, m’ be two particles of the body under consideration, and let F’ be 
the force which, in their displaced position, they exert upon each other. 

Let z, y, z be the co-ordinates of m in its original position, and &, », ¢ its 
resolved displacements. Let also 2’, y’, 2’, &,1/, ¢’ be the co-ordinates and 
displacements of m’ .Then, since, by the hypothesis of independent action, #’ 
does not depend upon the displacement of any of the other particles, and since, 
if the body have a regular constitution, the state of each particle must be a 
function of its position, 

F=f (2, Ys 2 a’, y' Coen ¢ E0; oy; 
or, as it may be otherwise written, 


1h = if (z, Y, 2; x, y's Z, é, y) & i &, yf y; iG ae ¢)- 


But in all media with which we* are acquainted, no internal force appears 
to be generated by a mere transference of the entire system from one position 
in space to another, the relative positions of the several particles remaining un- 


changed. 


The Rev. J. H. Jeter on the Equilibrium and Motion of an Elastic Solid. 183 


This being supposed universally true, we shall have, as is easily seen, 
LF ia, yyy ef oR B uy —n, C —%). 
Let p, 0, @ be the polar co-ordinates of m’ with regard to m; then since 
a =x+psinOcosg, y/=y+psind sing, 2’=z+pcosée; 
it is plain that the foregoing expression for may be written 


= F(a; 4,2, p, 9, d, & —§, 7" — 4%, Goa: 


Hitherto no assumption has been made either with respect to the magnitude 
of the distance between the particles m, m’, or with respect to that of the dis- 
placements é, », ¢ &, 1, ¢. But previously to proceeding further, it is neces- 
sary to make the following suppositions: 

(1.) That the greatest distance between two particles which are capable 
of acting upon one another, or, as it is ordinarily termed, the radius of mole- 
cular activity, is indefinitely small compared with the intensity of the force 
generated. 

(2.) That the sphere of molecular activity contains, nevertheless, an inde- 
finitely great number of particles. 

From the first of these assumptions, combined with the supposition that 
the displacements follow some regular law, we have 


f=64+F an+% ays % ae, 


dy dz 
r_ , ay dn dn 
PY ap tt Gg, Ot a, oe (A) 


poopy oS dg dg 


quantities of higher orders being neglected. 
For the same reason, 


BaF, +A (f-£) 4B (—) +0 (¢-9). (B) 


This expression consists, as will be seen, of two distinct parts, namely F,, 


184 The Rev. J. H. Jevtert on the Equilibrium and Motion of an Elastic Solid. 


which represents the force which m’ exerts upon m in the original position of 
these particles, and 


A (#—&) + By -n)+C (U-8), 


the force generated by the displacement. 

The supposition that the original state of the body was one of free equili- 
brium permits us to disregard the former of these parts. For it follows from 
that supposition, that if the several particles of the body receive equal displace- 
ments, the new position is also a position of equilibrium. Hence the suppositions, 


gv=8 w=u C=, 
must satisfy the general equation of equilibrium. But these suppositions give 
[elite 


Hence the terms depending upon /, will disappear of themselves. We have, 
therefore, for the effective part of the force, 


P= AiG = £) PB =n) OC =); 
where A, 6, C are in general of the form 


S(t Y % ps ). 


Let a, 6, y be the angles which the direction of p makes with the axes, so 


that 
cosa=sin@cos¢, cosB=siné sing, cos y = cosé. 


Then since 
dz =pcosa, dy=pcosp, dz=p cosy, 


we shall have from equations (A), 


ae Bi eon Peas Ue 
i — £= p (cos « 7: + 0088 5 + cos 77), 


oe dy dy dy 
n= p (cos a Tt + cos pT + cosy (C) 


Jase dg dg dg 
(é ~ ¢=p (cos « TE + cos p FE + cos 45 ; 


and therefore, 


The Rev. J. H. Jexert on the Equilibrium and Motion of an Elastic Solid. 185 


F=Ap (cos « FE + 008 aT 5 e087 52) 


dy | dy 
+ Bp (cos « 9! + 00s 8 5" + c0s y 2) (D) 


dé dé d¢ 
+ Cp (cos « SE + 008 8 5! + 0057 3 : 
Let a’, p’, y' be the angles which the direction of this force makes with the 
axes, and X, Y, Z its components. Then 
dé dé # 


X=F cosa’ = p cosa’ {4 (reson tome ra 


+B (cos a 2 + cos oo Ba cos ¥ 2) 


Co (ae teed sna) (E) 


¥ = Feos pf = p cos p'| 4 (cos « 5 + Ge.) + c.f, 


d 
=F cos7=p cos y/| A (cos a até.) + &e, \. 

We have next to consider the effect which this force tends to produce ; and 
on this point the assumption here made is, that the forces developed by the displace- 
ments of the several particles tend to change their relative positions only. ence 
it is evident, that the moments of the forces X, Y, 7 will be 


X5(é'—£), Vi(n'—m), 26 (¢'—9), 


respectively, or 


pX (cos a — cos B ze + cos ¥ Ze) 
dén din déy 
wr om ut 087 Ge) (F) 


pZ (cos « = + cos B a + cos ¥ a): 


186 The Rev. J. H. Jexerr on the Equilibrium and Motion of an Elastic Solid. 


Substituting for X its value from (E), we find the following expression for 
the moment of that force: 


dé die dbé. 
d dz 


p* cos a’ (cos a i + 0088 G+ e084 Ge 
dé dé dé 

x{4 (cos a $e + e08 BT +0084) (G) 
dy dy __ ay 
+B (cos a i + cos B+ 008 4 72 


dé d¢ d¢ 
+0 (cos a 4 00s 8 56 + cosy) 


This expression denoting the moment of that part of the force acting on m, 
which results from the relative displacement of m’, it is evident that the com- 
plete moment of the forces X, which act upon m, will be found by multiplying 
(G) by the element of the mass, and integrating through the entire sphere of 
molecular action. Let ¢ be the density at the point 2’, y’, 2’, and a the radius 
of the sphere of molecular activity. Then the element of the mass will be 


du = ep’ sin 0 dp dé dd; 
and the limits of integration with respect to p, 0, @, will be 0 and a, 0 and z, 0 
and 2n, respectively. If then we assume, 


(2 


A, = {if Ap cos’ a cos a’ du =e i. Aep* cos a’ sin’ @ cos? d dp dé d®, 
A,,, ={\j Ap’ cosa cos B cosa’ dy, 
A,,.:={[ Ap’ cos a cos y cos a’ dy, 


&e. ; 

Bax, = {fj Bp’ cos’ a cosa’ du, 
&e. ; 

C2. =f Cp cos? a cosa’ dp, 
&e. ; 


we shall find for the complete moment of the forces X acting upon the particle 


m, the expression 
; 


The Rev. J. H. Jevtuerr on the Equilibrium and Motion of an Elastic Solid. 187 


BREE Sp SOO roy yt aE 

** dx dz ody dy Y©* dz dz 
thw age a) on ae =) Au ies iy * ay te 
shales 88) oe on, (ate 


Je 
4 (Cs dg ae PMS GEE ake dg det 

da dx "dy dy We dz dz 

dg déé dg déé d¢ dt&é de det : dé dé de doe) 

+ Cs Ge dz * de dy) * C= (7: de t da dz) + \ae dy + dy de 
Similar expressions are found for the moments of the forces Y and Z. 

5. Let X’, Y’, Z’ be the external forces necessary to keep the particle at rest. 
Then, the equation of virtual velocities being in general 


ff (XE + Ven + 26g) din + jij (LL +M +N) dxdydz = 0 


if we substitute for Z, W, N their values found as above, we shall have the 
equation 


= | I (ae + Yq ce aiedy dz 
offen 


ey (1) 


te : 
+Q or Q5 ea 


one 


? 
+h, i 


Where e is the density, and 
Poss a AL 


+h m +R, «) dzdy dz. 


+ ee" = 


a Cine E+ Cue = (K) 


aya’ dz 


ers Bia ay +B 
dy 


+ Cough 


VOL. XXII. 2 ae 


188 The Rev. J. H. Jevzert on the Equilibrium and Motion of an Elastic Solid. 


dé dé dé 
WA ee a A goa E +Azgy oF 
dy dy dy 


+ Bass 7 + Bea G+ Bow Ze 


d d d. 
+ Copa! oA 45 Cp291 = + Cayo’ = g 3 


dz 

¥) dé dé dé 
P= Ane i + Abe ay dy Sidi dz 
dy dy 

+ Boe ae + Bow Gy + By, Ts 
dg | i dg 
oF ee au CaF, yt Cire! dz’ 


the values of Q,, Q,, Q; being deduced ie these expressions by changing, 
in the suffixed letters, a’ into p’; and those of R,, R., R;, by changing a’ into /. 
Integrating by parts, and equating to zero the coefficients of &é, 6, 6¢, under 


the triple sign of integration, we find the equations of equilibrium to be 


QUES GME REE 


er de dy dz’ 
net HOR CKO 
eae Wade ees 
Ry © dikes, alle 

(fiaet ait 2 3 
— dz dy eas 


The corresponding dynamical equations will be 


. @\ dP, dP, aP, 
ce du * dy + de’ 
yr @ny _ dQ , dQ , AQ, 

dé dy, dest 
(a — \_ ah , Uy, aR, 
GO AG a ye de 


(L) 


(M) 


If now we suppose that no external forces act, and replace P,, P,, &c., by 
their values (K), we shall have the three general equations of small oscillations 


The Rev. J. H. Jetiert on the Equilibrium and Motion of an Elastic Solid. 189 


in a body whose particles have been displaced from their original position of 


free equilibrium. 


= 2 + Ape ate yee 

wo ERE, = Bane a + By, = 

+ Core = +C <a + Ca, = 

2A pe Wud 2A... = +24... 
dy ay 


2B, 


iipe ees 


b dyda + Co Gade 


(= FEO i eleres =) dé 


+ 2C 4. 


dx dy dz 


Ans, GAg,  dAga\ dé 
+( as dy ae 


dy 

DA wea! dA prot + dA ay dé 

ah Gras dy dz) dz 
ABay | CBise | TBayw\ Iq 
Pde) dy. de j\de 
ABiee EBay  ABga\ an 
+( dx dy de dy 
Bie , EBay , IBi2y\ dq 
+( de * dy ' dz ) dz 
AC uy | Wow » Ua IE 
+( da dy tae ) daz 
BC seu, Upra , UC pa\ UE 
+( ge dy + ae dy 
AC rat , Woe , Irv UE 
+(e + ay + de ) de 


dys * 2Bane Gags * Bate dady 


(N) 


190 The Rev. J. H. Jevzert on the Equilibrium and Motion of an Elastic Solid. 


dy, @é 
ap Ae de 


Te 


+ &e. ; 


ma WG we 
ae =Awy sat 3 + &e. 
Of these equations the second and third are deduced from the first by 
simply changing, in the suflixed letters, a’ into p’ and 7’ respectively. 
If the body be homogeneous, i. e. if all its points be absolutely similar, the 
quantities 


A. 


aa? 


&er, -#Bi2,7, wee (Clay, &c., 


will be evidently constant. The terms involving 


dé ie dy 


Ben TOTES 
da ; dn? © Fs &e., 


will, therefore, disappear, and the equations (N) will become homogeneous 
partial differential equations of the second order with constant coefficients.* 
The number of constants which these equations contain is the same as the 
number of terms in the right hand members, namely, eighteen for each equa- 
tion. Hence it is evident, that the equations which represent the small oscil- 
lations of a homogeneous medium satisfying the hypothesis of independent 
action, contain, in general, fifty-four constants. This is the greatest number of 
constants which these equations could be made to have without a change of form. 

6. The conditions to be fulfilled at the limits of integration are, of course, 
obtained from the terms which appear under a double sign of integration in 
the equation derived from (I). These terms will evidently give 


(J (Pisé + Qin + Rec) dydz 
+ fj (Pee + Qoéy + Kel) dzdx (N’) 
+ fj (Pscé + Q3éy + Ree) dady =0. 
Let p, g, r be the angles which the normal to the surface bounding the 


given medium makes with the axes, and let dS’ be the element of this surface. 
Then, if equation (N’) be transformed in the usual way by making 


* This conclusion does not hold for molecules situated at the surface of the body.—Vid. Art. 15. 


The Rev. J. H. Jetzert on the Equilibrium and Motion of an Elastie Solid. 191 
dydz = cospdS', dzdx =cosqdS', dady = cos rdS’; 


we shall have 
{[(P. cos p+ P, cosq + P; cos r) t&dS’ 


+ {[(Q, cosp + Q, cos g + Q; cos r) én dS’ 

+ {[( 2, cosp + R, cos g + PR, cos) &¢dS’ 

+ {[(X, 6 + VY, + Z, 6) a dS’ =0; 
where X,, Y,, Z, are forces acting solely at the surface of the medium. The 
mode of treating this equation in the several cases which may occur having 
been fully given by Mr. Haucuton, I do not think it necessary to pursue this 
part of the subject further. On the most important of these cases, namely, the 
transmission of motion from one medium to another, vid. Art. 15. 

7. We shall now proceed to integrate the equations (N), for the particu- 

lar case of plane waves and rectilinear vibrations in a homogeneous body. 


Assume, 
&=cosl.f (ax + by + cz — vt), 


n = cosm.f (ax + by + cz — vt), 
€=cosn.f (av + by + cz — vt); 
where a, b, ¢ are the cosines of the angles which the wave normal makes with 
the axes, and /, m, n are the angles made by the direction of vibration. 
Substituting these values in (N), we find 
— ev’ cos/=TI, cos/ + ®, cos m + W, cos n, 
— ev cosm= II, cos! + ®, cos m + W, cos n, (O) 
— ev’ cos n= TI; cos] + ®, cosm + W; cosn; 
where 
= Awa + Ags b+ Aw C+ 2A, be + 2AQ.. aC + 2A,5 ab, 
®, = Baye + Boy P+ Braye + 2Baw be + 2B, ac + 2B, ab, (O') 
Wi = Cy C+ Cory BP + Cy C+ 20,4: b¢ + 26.44 aC + 2C yp, ab ; 
the values of II,, ®., W,, I;, ®;,W, being deduced from those of TI,, ©, W,, 
by changing, as before, a’ into p’ and y’. Assuming 


s=— wv’, 


192 The Rev. J. H. Jetxerr on the Equilibrium and Motion of an Elastic Solid. 


and eliminating J, m, n between the equations (O), we find 


(s = II,) (s a ,) (s— Ws) aa 0, WV, (s—Ih)- wy, II, (s—®,) — II, ®, (s—W;) 
— fi, ©, VW, —Tl, &, v, = 0: (P) 


The value of s being determined by this equation, those of cos /, cos m, cos n 


are found at once from (O), combined with the condition 
cos’ + cos? m + cos*n = 1. 


Hence, the equation (P) being of the third degree, it appears that for each di- 
rection of wave plane there are in general three directions of molecular dis- 
placement ; of these directions one is necessarily real, while the remaining two 
may be either both real or both imaginary. The vibration will not, however, 
be necessarily real, because its direction is so, as it is further necessary that the 
corresponding velocity of wave propagation should be real. Hence, as 


$=— a’, 
it is plain that at least one value of s must be negative. We infer, therefore, 


generally, that no body will be capable of transmitting a plane wave propa- 


gated by parallel rectilinear vibrations, unless equation (P) have at least one 
real negative root. 


The surface of wave slowness, being the locus of a point upon the wave 


normal whose distance from the origin is inversely as the velocity of wave pro- 
pagation, will be found by putting 


in the general equation (P). It is evidently a surface of the sixth order. In 
fact, if we put 

PHAgyt + Apo y + Aye 2 + 2A gaye + 2A oye f2 + 2A gy BY, 

Q= Bax + &e., 

R= Ca 8? + &c., 
and denote by P’, Q, R’, P”, Q’, R” the expressions derived from these by 


replacing a’ by p’ and ¥/’ successively, we shall have, as the equation of the 
surface, 


The Rev. J. H. Jevtert on the Equilibrium and Motion of an Elastie Solid. 193 


(P—1) (@-1) (R’ -1)— RQ" (P-1) —P’*R(Q-1)- QP" (R"-1) 
+ PQ’R+ P'QK =0. (Q) 


We shall next proceed to consider the two hypotheses which have been 
most frequently made by writers upon this subject, namely:—1. That the sum 
of the internal moments may be represented by the variation of a single func- 
tion. 2. That the force which one molecule exerts upon another is a force of 
attraction or repulsion. 


Hypothesis of the Existence of a single Function V, by whose Variation the Sum 
of the internal Moments of the Body may be represented. 
8. This condition gives the equation 
L+M+N=8~d. 
The three expressions (H), p. 187, must, therefore, when added together, give 


a complete variation. Now if we examine the value of Z there given, we shall 
see that the first six terms, those, namely, which are multiplied by 


A 2 A par Avan, Aa A. 5 Aas; 


a*a’) 
form in themselves a complete variation, namely, 


5 | Pag + $A go, dy? + Ate +4 Pre! Ty dz 


dé dé dé ae 
aya’ dz dz aBa’ dz dy 2 


+A 


Sumilarly in the values of Mf and NW the terms multiplied by 
Byzp, B 26s &e., Cray; C245 &c., 


respectively, form complete variations in themselves. 
Let us now consider the term in the value of Z 


Corresponding to this term, we have in the value of 1/ 


dé déy ’ 
a8’ da dr ? 


194 The Rev. J. H. Jetrerr on the Equilibrium and Motion of an Elastic Solid. 


and, therefore, since no such term can occur in J, we shall have in 


E+ M +N, 
the group 
dy déé dé diy me 
Bast Te PP ie dn (Q’) 


Now if L + +N be a complete variation, it is plain that this expression 
must have been derived from a single term of the form 


dy dé 


dx dz” 


Taking the variation of this term by the ordinary rule, and comparing it with 


(Q’), we have the condition 
A wx = Bee . 


Proceeding in a similar way with the remaining terms, we find altogether 
eighteen equations of condition, namely, 
A 2p = Bie; A gp => 15 yar Ajy — Bae, 
y 
Bay = Cusp Bea — Craps Byy = Cys, 


Cie = A), Cara => A gry Cia => As, (R) 
Avge = Baga, Aa = Boys Apye = Boyar 
Bag = ape’? Boy = Vays Bory = Carats 


Cape! = A apy Capa! =A Caye’ ar Agy- 


These equations may be more briefly written as follows: 
{| (A cos p’ — B cos a’) (é — €) (4 — y) dm =0, 
i) (C cos a’ — A cos +) (¢/ — g) (2 — 8) dm =0, (S) 
{| (B cos 4 — C'cos ") (x/ — 1) ( —g) dm=0. 
For if we substitute for 
ESG0 ef mG 


their values (C), and perform the integrations with regard to dm, the first of 
the foregoing equations may be written 


The Rev. J. H. Jetnerr on the Equilibrium and Motion of an Elastic Solid. 195 


dé dy 
tie 


a = dé dy 


(Ang — Bo.) Fo + (Ape — Bru) = oo 


pt Ave ~ Bre) 5 


dé * a dy 
+ (Auge — Bene) (= dpa 7) 


dé dy. dé dy 
Baga a) (= Ta ada ae 


nial el ips 5 (G2 dy . dé =) AG 


dy dz * dz dy 

Since then these equations are supposed to hold for all possible displace- 

ments, we must have the six equations 
A se = Bow, App = Bes, Ape= Ba, 
A ji ee i EA, a Al Beep Dg 

Six equations being furnished by each of the remaining equations (S), we 
shall have in all eighteen equations which are obviously identical with (R). 

9. If the sum of the internal moments admit of being represented by the 
variation of a single function, the three directions of molecular displacement 
corresponding to a given wave plane will be at right angles to each other. 
This has been shown by Mr. Haucuroy. We shall now proceed to prove the 
converse of this theorem, namely, 

Tf the three directions of molecular displacement corresponding to the same 
wave plane be at right angles, and if this be true for every wave plane, the sum of 
the internal moments of the body may be represented by the variation of a single 


function. 
We have seen that the directions of molecular displacement corresponding 


to a given wave plane are determined by the equations 
— ev’ cos / = II, cos/ + ®, cosm + W, cosn, 
— ev? cosm= II, cos! + ®, cosm + W, cos n, 


— ev” cos n = II; cos] + ®, cosm + Wy; cos n. 


Eliminating ev* between the first two of these equations, we have 
II, cos7 cos m + ®, cos? m + W, cosm cosn 
= II, cos? /+ ®, cos / cosm + W, cos! cos n. 
VOL. XXII. 2D 


196 The Rev. J. H. Jetxerr on the Equilibrium and Motion of an Elastic Solid. 


Hence if J,, 7,7, 2, m2,%., ls, ms,%3 be the three systems of values of l, m, 7, 


we shall have 
II, cos J, cos m, + ®, cos? m, + Wi cos m, cos 2, 


= TI, cos? J, + ®, cos, cos m, + WV, cos /, cos n,, 
II, cos /, cos m, + ®, Cos”? My + Wy COS My COS Ny 
= TI, cos? /, + ®, cos 1, cos m, + VW, cosl, cos ny, 


fl, cos 1; cos ms + ®, cos? m3 + W COs m3 COS Ns 
= II, cos? /; + ®, cos J; cos ms + W, cos /; cos 3. 


Adding these equations, and recollecting that, as the three directions of vibra- 


tion are rectangular, 
cos? 7, + cos? /, + cos? J; = 1, 


cos? m, + Cos? mz + cos’? m; = 1, 
cos J, cos m, + cos I, cos mz + cos ls cos ms; = 0, 
cos J, cos”, + cos 1, cos nm; + cos l; cosn; = 0, 
COS Mm, COS 2, + COS Ms COS Ny + COS M3 COS; = 0; 


we have 
II, = ®,, 


and similarly 
9,=¥V,, VW, = 11, 


or, substituting for T1,, &c., their values from (0’), 
(Anp—Boy) @ + (App — Bora) b+ (Apy—Byrw) C+ 2(A pp — Boye) be 
+ 2(A 9 — Bia) aC + 2(Aase — Baga) ab = 0, 
(Bay aD Cuzp) a’ + (Bary oa Carp) er (Byy 7 C29) c 
ar 2( Bary! <= Cora) be st 2( Bay ai Cie) ae + 2( Bas, Tt Cupp’) =z 0, 
(Cha Ane ithe (Ope, Agee) Hal Ong) 
+ 2(Coya — A pyy) bC + 2( Oya — Aa) U6 + 2( Cigar — A apy) ab = 0. 


Bya! 
If these equations hold for all directions of wave plane, it is easily seen that 


the coefficients of 
a, b,c, ab, ae, be, 


must vanish of themselves. This condition will give eighteen equations which 


The Rev. J. H. Jezerr on the Equilibrium and Motion of an Elastie Solid. 197 


are evidently identical with the system of equations (R). The theorem, as 
stated above, is, therefore, true. 

10. The total number of constants in 1+ M+ N being fifty-four, it is evi- 
dent that the number of distinct constants contained in 6V, and, therefore, in 
V, will be 

54 — 18 = 36. 


Now V, which is, as we have seen, a homogeneous quadratic function of the 
nine quantities 


dé dé dé dyn dyn dy dg dé dg 
dz’ dy’ dz’ dz’ dy’ dz’ dz’ dy’ dz’ 


will contain in general forty-five terms, and therefore, if it be subjected to no 
restriction, forty-five distinct constants. The function at which we have arrived 
is not, therefore, in its most general form. In fact, if we examine the composi- 
tion of the terms in the yalue of Z(H), we see that the quantities 


dy déé dy déé 


dy dz’ dz dy’ 
have the same coefficient, namely 6,,,. Similarly, in the value of M/ we should 
have two terms 

dz dy’ dy dz’ 
with the common coefficient A,,,. These coefficients being, by the equations 
(R), identical, the four terms enumerated above may be written 


1, [1 a Os dn, dy as eae 
fre''\dy dz dz dy * dz dy ° dy dz/’ 
or. 


dy dé dy dé 
Bye (Ft Ae Fae 77 
Hence it is evident, that the terms in V containing 
dy de dy dé 
dy dz’ dz dy’ 
will be of the form 
2D2 


198 The Rev. J. H. Jeter on the Equilibrium and Motion of an Elastic Solid. 
(7 yn dé dy =) 


dy de* dz dy)’ 
Similar conclusions will be obtained for all terms of this form. These terms 
are distinguished by the technical rule, that, in the products which they seve- 
rally contain, the same letter does not occur twice. Thus the conclusion at 
which we have arrived does not apply to terms of the form 


where the same letter £ occurs twice; nor to terms of the form 


dé dy 
in which the letter « occurs twice. The preceding discussion gives us, there- 
fore, the following general theorem: 
If the constitution of a body, whose particles act independently, and whose ori- 
ginal position is one of free equilibrium, be such, that the sum of the internal mo- 
ments may be represented by the variation of a single function, this function must 


be of the form 
oe d? dé dé dé dy 
gee errr) ead 


Ij dé dy dé 

9 fl face D WecelP 

fies & dz* dz dy ) 
Each of the sums denoted by = will contain nine terms, thus giving thirty-six 
for the total number of distinct constants in V. 


11. Previously to proceeding further, it may be well to compare this result 
with the investigations of Professor Mac Curiacu and Mr. Green, in the un- 


dulatory theory of light. Both these writers assume the original state of the 
supposed luminous ether to be one of free equilibrium.* Both suppose also, 
that the sum of the internal moments may be represented by the variation of a 


* Mr. Green has also investigated the problem under the supposition that the original posi- 
tion is not one of free equilibrium, The remarks in the text are, of course, only meant to apply 
to the first supposition. 


The Rev. J. H. Jetzerr on the Equilibrium and Motion ofan Elastic Solid. 199 


single function. This function, in the system of Préfessor Mac CuLLaGu, is in 
its simplest form given by the equation 


= (i _ UY , yp (dé _ dey (1 _ EY 
~2V= 0 (E— )+a(S dx Te dz dy)” 


dz 
The function used by Mr. Green is given by the equation 


GRE aah dc? 
= 2V=4 (T+ dy de 


Lis | (G+) -4 dy =| 


dz dy dy dz 
dé dt dé d¢ 


dé dy? dé dy 
eG nce ees 

Comparing these successively with the general form (T), p. 198, we see 
that the function used by Professor Mac Curtacu cannot by any supposition 
be identified with (T), inasmuch as it contains the products 

dg dy dé dé dy dé 

dy dz’ dz dz’ dz dy’ 
without the corresponding products 

Ae dy dé dg dy ae 

dz dy’ dx dz’ dy dz 
To identify the function used by Mr. Green with (T), we should have, as is 
easily seen, 

L=M=N=\n 

These conditions would render the body uncrystalline, and therefore incapable 
of being generally identical with the luminous ether. 

Hence we infer, that if the supposed luminous ether be a medium such as 
either of these writers assume it to be, the mutual action of its particles cannot 
be independent. In other words, we must suppose that in such a medium the 
capacity which each particle possesses of exerting force on any other particle, 
is modified by the action-of the surrounding particles. 


200 The Rev. J. H. Jetrert on the Equilibrium and Motion of an Elastic Solid. 


” 


Bodies composed of attracting and repelling Molecules. 


12. Two conditions may be supposed to be included in the supposition, that 
the molecular force is a force of attraction or repulsion, namely: 

1. That the direction of the force is in the line joing the molecules. 2. That 
the intensity of this force, for each pair of molecules, is represented by a function 
of the distance. Retaining the former of these conditions, we may replace the 
second by the hypothesis made in the foregoing section, namely, that the sum of 
the internal moments may be represented by the variation of a single function. 
For as the effect of the force is in this case to change the distance between 
two molecules, if this force be represented by /’, and the distance between the 
particles by p, the moment of the force /’ will be 


F%p, 


or dividing the force F’as before into Fy and’/,, and putting p+ p’ for the dis- 
tance as changed by displacement, 


effective moment = /’,é)’, 
and therefore the complete moment is expressed by 
{If Piep’dm, 


which cannot be a complete variation, unless 


int. = Fp): 


Hence the proposition is evident. Instead, therefore, of defining the body to 
be one composed of attracting or repelling molecules, we shall define it to be 
“a body in which the molecular force acts in the direction of the line joining 
the molecules, and in which the sum of the internal moments is represented by 
the variation of a single function.” We shall consider successively the simplifica- 
tions which these two suppositions introduce into the general equations. 

The first hypothesis, that, namely, which regards the direction of the mole- 
cular force, is mathematically represented by making 


a=a p=B 7 =7. 


The Rev. J. H. Jetzert on the Equilibrium and Motion of an Elastic Solid. 201 


If these conditions be introduced into the general equations (N), it is easily seen 
that the number of distinct constants will be reduced to thirty, se., 
A,;, Ag, A,, Ag, A 2g, Aa: Ain, A.) A p2,; A 
Bs, &e. 
C3, &e. 


apy? 


The equations so reduced will refer to a system of attracting or repelling 
molecules, in the more enlarged sense of the term attraction or repulsion, the 
force being defined solely by its direction, without any hypothesis as to its in- 
tensity. Using the words in this sense, we may state the conclusion at which 
we have arrived as follows: 

The equations of equilibrium or motion in a system of attracting or repelling 
molecules, will in general contain thirty distinct constants. 

13. We shall next proceed to consider what further simplification is intro- 
duced into these equations by the supposition that the sum of the internal 


moments may be represented by the variation of a single function. Making 
. 


a’'=a, p'=8, v=” 
in the equations of condition (R), we shall find that their number will be re- 
duced to fifteen, the nine equations 


Any = Baw, Chaya’ = A ayy's Bary = Varp's 
Ang =Baay Care = Ags Basy = Copp, 
Ae = Tee. Cpa! = A py By, = C22, 


being obviously equivalent to but six. Hence we infer that 

The equations of equilibrium or motion of a body in which the molecular force 
acts in the line joining the molecules, and is represented by a function of the distance, 
will contain fifteen distinct constants. 

This agrees with the result obtained by Mr. Havenron, to whose Memoir 
the reader is referred for the further discussion of this case.* 


* Vid. note at the conclusion of this Memoir. 


202 The Rev. J. H. Jevzerr on the Equilibrium and Motion of an Elastic Solid. 


I].—Hyrortuesis or Moprrrep ACTION. 


14. Let m, m’ be two molecules of the medium under consideration, m being 
that whose equilibrium or motion is required. Then if, as before, we suppose 
the force which m’ exerts upon m to be composed of two parts, one depending 
upon the relative displacement of these two particles, and the other existing pre- 
viously to the displacement of either, we shall still have, as in p. 183, 


F=F,+A(#-—€) +B - 9) + C(e— ©). 


Now it is easily seen that the difference between this case and the preceding 
will show itself in the nature of the quantity /. In the former case, in which 
the action of m’ is independent of the other particles of the medium, /, must 
be of the form 


S (2, Y % p, % ); 


and may, as we have seen, be neglected in the case of a body whose original 
position is one of free equilibrium. But in the present casein which it is sup- 
posed that the displacement of the other particles has itself the power of deve- 
loping a force between m’ and m, the form of F’, is completely changed. Our first 
object, then, must be to determine the new form to be assigned to this quantity. 
Let m” be a third molecule of the given medium; 2”, x", ¢”, its displace- 
ments; and p;,;, 1, OF pi, %, Pi, Y1, its polar co-ordinates with regard to m. 
Then it will appear, by reasoning similar to that of p. 183, that the mathematical 
expression for its effect in developing a force between m and m’ will be 


F (Yr 2 POs bs Pas Ory Grr E”—&  — m OG BE, os SE); 
or, as it may be otherwise written, 
F(®I»2, HP Pir Osgrs EE 9 —m OG EE a — mH FO). 
Treating this expression as in p. 184, it becomes 


dé dé dé 
fa ap(cos a5, + 00s p 7 + 008747) 


dy dy dy 
+ bp (cosa + cos 8 + cosy : 


a 


The Rev. J. H. Jetxert on the Equilibrium and Motion of an Elastic Solid. 203 


dé pedi dé 
+ Cp (cos att + cos Pay + cos z) 


d d d. 
+ pi (cos a + cos p; = +cos 71 =) 


dy dy 
+ bps (008 01! +608 Bi 7a + 008 1 52) 


Sra 
+; pi em 


+ cos a, i cy cos y1 %)> 

where f, is the force which is independent of the displacements of any one of 
the three particles. First let it be supposed that f, is independent of the dis- 
placements of any other particle.* Then, as the foregoing expression represents 
that part of the modifying force which results from the relative displacement 
of m’’, it seems that the most general supposition which we can make as to the 
agoregate effect of all the particles is, that it is estimated by multiplying this 
expression by some function of the polar co-ordinates of m’’, as also by the ele- 
ment of the mass, and integrating through the whole sphere of molecular acti- 
vity. It is easily seen, that the result of this process will be an expression of 


the form 


dé dé dé 

£,+4,>— FET A,— 

+B + B,S Se 
dy 


rae} ae rs 
vA 


where Ey, A,, B,, &c., are definite integrals depénding upon the constitution 
of the medium, being in general of the form 

SG 4% ps % $)- 
Hence the general value of F’ ((D), p. 185) will become 


* Itis easily seen, that this supposition does not limit the generality of the result. 
VOL. XXII. 25 


204 The Rey. J. H. Jevterr on the Equilibrium and Motion of an Elastic Solid. 
d. 
Ey, +(Ap cosa + Ne + (Ap cos p +4) 5 + (Ap cosy +A) F 


+(Bpcosa+ B, sige Dy + (Bp cosy +B; 


i Fe 


+ (Cpcosa + C, £4 (Cp cos 8 + Cx) SE E+ (Cp cosy +0) 3. 


rz dx 
Resolving this force as before along the three axes, and proceeding as in p. 186, 
we find an expression for Z similar to (H). There is, however, one important 
difference. In the value of L, which is derived from the principle of indepen- 
dent action, the quantities 
dé dé dé dté 
dz dy’ = dy dz’ 
have the’same coefficient ; and the same is true of the quantities 
dé déé dz dot 
dz dz’ dz da’ 
dé dté dé dé 
dy dz’ dx dy” 
dy déé dy deé 
FE aE CONTE 
dy deé dy dot 
de dz’ dz dx’ 
dy dbé dy det 
dy dx’ dx dy’ 
dé det dg déé 
dz dy’ dy dz’ 
d¢ ds — dg dt& 
dz dz’ dz dx’ 
d¢ déé dg déé 
dy da’ dx dy’ 
Now it is easy to see that in general this restriction has no effect in L- 
miting the generality of the equations of motion of a homogeneous body. For 
whether the coefficients be equal or not, each of the foregoing pairs of quan- 


» 


The Rev. J. H. Jevxert on the Equilibrium and Motion of an Elastie Solid. 205 


tities will furnish but one term to the equations of motion. Thus, if the 
quantities 


dé dé dé dé 
dz dy’ dy dz’ 


enter into Z in the form 
dé déé dé dé 
the equations of motion will derive from them the single term 


aN as 
(A+B) dydz* 


A 


It is evident, therefore, that the supposition 
i =a, 

will not restrict in any way the generality of these equations. We have seen 
accordingly, that the principle of independent action gives to these equations 
the greatest number of independent constants which they can have, without a 
change of form. But the restriction may show itself in other ways. Thus, when 
we assume that the sum of the internal moments may be represented by the 
variation of a single function V, we find that in order to reconcile this suppo- 
sition with the principle of independent action, it is necessary to assume further, 
that the coefficients of V are connected by nine equations of condition, and that, 
therefore, that principle does not admit of the existence of a function V in its 
most general form. This restriction has evidently been removed by supposing 
the state of each molecule to be modified by the action of the surrounding 
molecules. For, as we have just seen, this supposition enables us to obtain values 
for L, M, N in which the coefficients are completely independent of each other ; 
and, with regard to the particular case of physical optics, we infer, as before, 
that if a luminous ether exist, whose constitution agrees with either of the hy- 
potheses advanced by Professor Mac Curnacu and Mr. Green respectively, 
each of the particles of that medium must be supposed to be capable of modi- 
Fying the force exerted by any other particle within its sphere of action. 

It is unnecessary to pursue the consequences of this principle further; 
for, as we have already seen, all the varieties of the general equations of mo- 
tion, to the consideration of which the present Memoir is specially devoted, 
may be obtained from the more limited principle of independent action. + 

252 


206 The Rev. J. H. Jentert on the Equilibrium and Motion of an Elastic Solid. 


15. It is usual with writers upon the subject which has been here discussed, 
to consider the problem of the transmission of undulations from one body to 
another with which it is in mathematical contact. This problem, which, by an 
extension of the phraseology of optics, has been denominated the problem of re- 
fraction, has been investigated with special reference to a luminous ether, by 
Professor Mac CuttaGu, Caucuy, GREEN, and others; and has been discussed 
by Mr. Haucuron for the case of solid bodies in general. But all these inves- 
tigations appear to me to be liable to an objection to which I am unable to con- 
ceive any satisfactory answer. The nature of this objection, which has deterred 
me from following in this particular the steps of the writers in question, I shall 
now proceed to state. 

On referring to p. 189 it will be seen, that the form of the senses equations 
of motion, upon which the whole theory of undulation is based, depends upon 
the fact, that the coefficients are constant quantities, a fact which is, as we have 
seen, a result of the homogeneity of the medium, and the conclusions of p. 192 
are evidently true, so long as the molecule under consideration is situated at a 
finite distance from the bounding surface of the medium. The functions to be 
integrated retaining the same form, and the limits of integration being the 
same, it is evident that the definite integrals will have the same value for every 
point. 

Let us now consider the case of two media in contact. For the sake of 
simplicity, let the common surface of contact be an indefinite plane, which we 
shall take for the plane of zy. Let a, a’ be the radii of molecular activity for 
the two media, and suppose that the molecule under consideration is situated 
at a distance from the plane of zy less than the greater of these. If now two* 


* Instead of two spheres we may (as is easily seen) substitute a single sphere described with 
a radius not less than the greater radius of molecular activity. This substitution does not, how- 
ever, in any way affect the reasoning in the text. The single definite integral 

{iJ A cos? a cos a/dm 
will still be replaced by 
{IJ A cos? a cos a! dm + fff A, cos? a, cos a,/dm; 

the first being extended through the upper segment of the sphere, and the second through the 
lower segment. The value of the sum of these two quantities will evidently depend upon the dis- 
tance ef the point from the surface of separation. 


The Rev. J. H. Jecterr on the Equilibrium and Motion of an Elastic Solid. 207 


spheres be described, with this molecule as their common centre, and with 
the radii a, a’ respectively, each of the definite integrals of p. 186 will con- 
sist of two parts, the first being extended through all that portion of the first 
sphere which lies within the first medium; and the second through all that 
portion of the second sphere which lies in the second medium. Thus, instead 


of the definite integral 
{JA cos? a cos a’ dm, 


taken through the entire of a sphere whose radius is a, we should have 
{JA cos? a cos a’ dm + {ij A, cos? a, cos a; dm, 


the limits of integration in each of these being determined as above stated. The 
limits of integration, and therefore the value of each of these integrals, depending 
upon the distance of the molecule from the plane of separation, it is evident 
that the coefficients in the general equations (N) will be functions of z, whose 
form will depend upon the constitutions of the two media, and will be, therefore, 
in general, unknown. The form of the equations of motion will therefore be 
completely altered, not only by the change of constant into variable coefficients. 
but by the introduction of terms of the first order, 

dé dé dy d. 

an dy’ &e. Tn? &e. e, &e. 
The integral which represents wave motion will, therefore, be no longer appli- 
cable, nor will it be possible to give any integral of these equations without 
forming a number of additional hypotheses as to the constitution of the medium. 

From these mathematical considerations, the following physical conclusions 
appear to be legitimately inferred: 

(1.) That in the case of a single medium of limited extent, the molecules 
which are situated at a distance from the bounding surface less than the radius 
of molecular activity, move according to a law altogether different from that 
which regulates the motion of the particles in the interior. 

(2.) That it is impossible to assign this law without forming one or more 
hypotheses as to the nature of the medium. 

(3.) That ifa plane wave pass through a homogeneous medium, it will not in 
general reach the surface ; that is to say, the motion of the particles in and im- 


208 The Rev. J. H. Jenxert on the Equilibrium and Motion of an Elastic Solid. 


mediately adjoining the surface will not be a wave motion composed of recti- 
linear vibrations. 

(4.) That if two media be in contact, there will be a stratum of particles ex- 
tending on each side of the surface of separation to a distance equal to the 
sreatest radius of molecular activity; and that the motion of the particles in 
this stratum is altogether different from that of the particles in the interior of 
either medium. 

(5.) That, therefore, two media which are thus in contact, may be each per- 
fectly capable of transmitting plane waves through them in all directions, and 
yet incapable of transmitting such a motion from one to the other; and that 
even in the case of reflexion, in which the motion is transmitted back again 
through the same medium, the vibrations may cease to be rectilinear. The 
phenomenon of total reflexion affords an instance of this. 

Now in the investigation of the problem of refraction, it is supposed that 
the integral which represents plane waves is applicable to the motion of the 
molecules which are actually situated in the surface of separation, a supposition 
which the foregoing considerations prove to be generally untrue. Nor does the 
truth of this conclusion depend upon the method employed in the previous dis- 
cussion. On whatever principle we investigate the motion of the particles of a me- 
dium, it is easily seen, that for all points situated in the stratum described above, 
the medium cannot be considered homogeneous, inasmuch as the force to which 
each molecule is subject varies with its distance from the surface of separation. 
Within this stratum, therefore, the molecules must be considered as forming a 
heterogeneous medium, whose constitution varies rapidly according to some un- 
known law. It is difficult to see what modification is thus introduced into the dis- 
cussion of the problem of refraction, in which the two media are supposed to be 
homogeneous. But it appears to me, that the supposition of plane wave motion 
extending to the mathematical limits of a medium is in general untenable. Nor 
shall we remove the difficulty in question by the supposition, that the molecules 
of one medium are incapable of influencing those of another. The only effect 
of such a supposition, which is, besides, wholly gratuitous, would be the substi- 
tution of one integral such as 

{JA cos* a cos a’ dm, 
for the sum of two, 


The Rev. J. H. Jetzert on the Equilibrium and Motion of an Elastic Solid. 209 


{JA cos* a cos a’dm + fj A, cos? a, cos a,/dm,. 


But as the limits of integration are still variable, the form of the general equa- 
tions of motion will still be that described in p. 207. These equations do not, 
as we have seen, admit of an integral representing plane wave motion. It is 
easily shown that the difficulty here alluded to does not affect that part of the 
theory of light or sound in which the direction of the reflected or refracted ray 
is derived from the consideration of wave motion. 

16. Before concluding the present Memoir, I think it necessary to say a few 
words on the applicability of the integral calculus to problems like the present, 
or more generally to any problems in which bodies are considered, not as con- 
tinuous masses, but as assemblages of distinct molecules. 

I may remark, in the first place, that the method and results of the present 
Paper would be in no wise affected by the rejection of the molecular hypothesis; 
all that is essential to the validity of the method here given being attained 
by defining a molecule to be a particle so small, that the motion of the system may 
be fully represented by the motions of all these particles considered as units; and 
without such a supposition no equations of motion of a continuous body appear 
to have a perfectly definite meaning. 

But as the constitution of the bodies which we find in nature appears to fa- 
vour the supposition of separate molecules, rather than that of perfect conti- 
nuity, it becomes an important question to determine how far the methods of 
the integral calculus are applicable to such cases. This is the more necessary, 
as M. Poisson denies the applicability of these methods to any problems con- 
nected with molecular force; and, more generally, to any problems in which the 
force varies with extreme rapidity within the limits of integration:—“ Au reste 
la formule d’Euter qui sert 4 transformer les sommes en intégrales, contient une 
série ordonnée suivant les puissances de la difference finie de la variable, qui 
n’est pas toujours convergente, quoique cette difference soit supposée tres petite. 
L’exception a lieu surtout dans le cas des fonctions comme /(r) qui varient 
trés rapidement.”* 

It is quite true, that the methods of the integral calculus are in strictness 
applicable only to continuous masses, and that it is in such cases only that the 


* Mem. de I’Inst. tom. viii. p. 399. 


210 The Rev. J. H. Jewtert on the Equilibrium and Motion of an Elastic Solid. 


results which it furnishes are mathematically accurate. When the mass ceases 
to be continuous, these results become approximate, and would of course be 
valueless, unless we had some means of testing the degree of approximation at- 
tained. This we shall now proceed to consider. 

Let m be the mass of any one of the separate molecules of which the body 
is composed, and let a, y, z be its co-ordinates. Let m/f(x, y,z) be the mathe- 
matical expression of some quality or power belonging to this molecule, of 
such a nature, that the corresponding quality of the entire body is mathemati- 
cally expressed by the swm of the expressions which refer to the several mole- 
cules. Let also m’, x’, y’, 2’, m’, x’, y’, 2’, &c., be the masses and co-ordinates 
of the other molecules. Then, if we assume 


u =f (2, yY z), ul =/) (2’, y', 2), &e., 
the accurate expression sought for will be 


mu + mu! + mul’ + &e. = Smu. 


Now let dv be the element of the volume geometrically considered, and e the 
mean density of the matter which occupies it, so that its weight may be repre- 


sented by 
gedv. 


Then the approximate equation furnished by the integral calculus will be 
=mu = fuedv. 


In order to estimate the amount of the error which is involved in the use of 
the integral sign instead of the symbol of finite summation, we shall consider 
successively the several suppositions which are made in the interchange of 
these symbols, and the amount of the error introduced by each. 

The object of this investigation being to determine, not the actual magnitude 
of the error, but merely its order, it is in the first place necessary to establish a 
notation to represent the respective orders of the several small quantities with 
which we are concerned. 

Let e be an indefinitely small quantity which we take as the standard. Let 
the distance w, between two consecutive molecules, be of the order 2, or in other 


words let 4 
w= ke; 


The Rev. J. H. Jeviert on the Equilibrium and Motion of an Elastic Solid. 211 


where & isa finite magnitude. Let 7’ denote the degree of rapidity with which 
the function w varies, i.e. let it be supposed that w receives a finite increment 
in passing from one to another of two molecules, whose mutual distance w’ is 
given by the equation 

wo = Ke’. 

Suppose now the entire geometrical space which is occupied by the sys- 
tem of molecules, including also the small intervals or pores which separate 
them, to be divided into an indefinite number of equal portions, v, the linear 
dimension of each of which is a quantity of the order 7’. We shall then 


have 
v = ke", 


Let ©, mz denote a finite summation extended to all the molecules contained 
in the first of these elements, 2,mu a similar summation for the molecules of 
the second element, 2;mzw for the third, &e. Then 


Snu = mu + Domu + Tamu + &e. 


This equation is evidently exact. 
Now let the following suppositions be made: 
(1.) That w retains the same value for every molecule within the ele- 
ment v. 
(2.) That the coefficient «, which represents the mean density, is indepen- 
dent of the magnitude of the element. 
These suppositions will give the following equations: 
LMU = UM = Uy, 4%}, 
LyMU = Uy DVoM = Uy €yVq, 


&e. &c.; 
and, therefore, 
Du = Uy. VU; + UpeV. + &c. = Duev. 


Finally, instead of the symbol of finite summation ©, let us substitute the 
symbol of integration {, and we shall have 
mu = fuedv = fudp. 


VOL. XXII. QF 


212 The Rev. J. H. Jetxerr on the Equilibrium and Motion of an Elastic Solid. 


Let us now consider the order of the error introduced by each of these sup- 
positions. 

(1.) The supposition that u remains the same for all molecules situated within 
the element v, will introduce an error whose order is the same with that of the 
actual variation of u within that space. We assume here, that the function wu 
varies continuously within the space w’; in other words, that if w be divided 
into any number of equal parts, the variations which w receives in each of these 
parts are quantities of the same order of magnitude. Hence it is easily seen, 
that the variation of w within the space ke” will be represented by an ex- 
pression of the form 

he pa 
For if w’ be divided into a number of parts, each equal to ke", the variations 
in these segments may be represented by 


aye”, a6", &C, 
the exponent m being, in conformity with the foregoing assumption, the same 
for all. Hence we shall have for the complete variation of wu, 


(a, + a + &e.) e”. 
Now since aj, a, &c., are finite quantities, 
a,+a,+ &e., 


will be a quantity of the same order as their number. Denoting this number 
by n, we shall have 


w aS 
n= Ke = ru é hi 
Hence it is evident, that the complete variation of wu is of the order 
m+t—w. 
Since, therefore, this variation is by hypothesis finite, we must have 


m+ —t’= 0, 
or 
m= t = a! 
Hence the expression for the partial variation of w is 


eae 
Kees: 


The Rev. J. H. Jetxert on the Equilibrium and Motion of an Elastic Solid. 213 


A 


Let «, be the least value of w within the element v, and w, + ke’—* the 
greatest, and let it be supposed, as the most unfavourable case, that w has 
throughout the value Dap 

Uy, + [I 
Substituting this expression in 2,muw we have 
Vmu = uy Tym + ke" —" Sm. 


Hence the error in the equation 


mu =uy=,m 
is at most 
ke —-* Sim; 
and, therefore, the error in 


Umu =u Tm + uy Zm + &e., 


is, at most, a quantity of the form 
La zaate 


This equation will, therefore, be free from sensible error if 


(2.) In estimating the error produced by the second supposition, we shall 
assume that the densities and magnitudes of the molecules vary with a /inite 
degree of rapidity; and that, therefore, at any one point in the body, the sum 
of the masses of the molecules contained in an element is proportional to their 
number. Hence the equation 


=m = €U, 


is equivalent to an assumption, that the number of molecules contained in the 
element v is proportional to its volume. 

To estimate the error involved in this assumption, let us compare, for the 
sake of greater generality, two elements whose bounding surfaces are wholly 
different in form. Suppose these elements to be similarly divided into rec- 
tangular prisms with the same transverse section, whose linear dimension is 
of the same order with the molecular distance. The error involved in such 

2¥2 


214 The Rev. J. H. Jetxerrt on the Equilibrium and Motion of an Elastie Solid. 


a supposition will be, for each of the prisms, represented by the expression 
Ae; 
and therefore, for the whole element, by 
Ae* x number of prisms. 


But the number of these prisms, being directly as the volume of the element and 
inversely as the volume of each prism, will be represented by the expression 
Bee 
Hence the error in the foregoing division will be for each element 
Corrs 
Now since the bounding planes of these prisms, taken two and two, are sym- 
metrically situated with regard to the molecules which they contain, if the extre- 
mities of the prisms were symmetrically situated with regard to the extreme 
molecules, the number of such molecules contained in these two prisms would 
evidently be as their lengths. But these extremities can always be made sym- 
metrical by adding to one of the prisms a portion whose length is of the same 
order as the molecular distance. Hence the error involved in the assumption, 
that the number of molecules in each prism is proportional to its length, is re- 
presented by an expression similar to 
BES 
The total error for each element is, therefore, expressed by a quantity similar 
to Ce" +* Let 0,1, l’, &c., be the lengths of the several prisms into which the 
element v is divided, and let A, A’, A”, &c., denote the corresponding quantities 
for v’. Let also w be the common transverse section. Then it follows from 
the assumptions which we have made, that 
Ym =L (14+ 4+1'+ &.), 
Dem = E'(N+ N+ A"+ &e.). 
We have also 
v=o(l+l4l'+ &e.), 
v=wu (A+ Ne A &e.), 
and therefore, 
=m E v 


Som EH 


The Rev. J. H. Jecterr on the Equilibrium and Motion ofan Elastic Solid. 215 


Hence, in general, 
>) = €&v. 

Now we have seen that the error involved in the supposition from which 
this equation is derived, is for each element represented by an expression of 
the form ie. 

Cert 
The order of the total error will be found by multiplying this expression by 
the number of the elements. Now 


totalmass MW ._. 
Number of elements = aa 7 Car 
Hence the order of the total error will be 
4—1". 
The equation 
=m = €U 
will, therefore, be free from sensible error if 


jets 


(3.) Lastly, it is easily shown, by reasoning similar to that of (1) and (2) 
that the error in the equation 
Duev = {juedv, 


is at most of the order 7”. The method here employed will, therefore, be free 
from sensible error if the three following equations hold: 
0 ge as! a@) ails, 0) 

Hence we infer that 

The methods of the integral calculus are applicable to questions of molecular 
mechanics, provided that the molecular force varies continuously within its sphere of 
action ; and provided also that the sphere of molecular action is of such a magni- 
tude as to admit of being subdivided into an indefinite number of elements, each 
element containing an indefinite number of molecules. 


216 The Rev. J. H. Jeter on the Equilibrium and Motion of an Elastic Solid. 


NOTE ON ARTICLE 12. 


On a reperusal of Article 12, it appears to me that I have not stated with sufficient 
accuracy the distinguishing characteristic of a system of attracting and repelling mole- 
cules, and I think it, therefore, necessary to add a few words in explanation of what I have 
there said. 

The supposition that the molecular force is a function of the distance may have one 
of two meanings, namely:—1. That all molecules situated at the same distance from m 
exert upon it a force of the same intensity. 2. That the force which any one molecule 
m exerts upon m cannot be changed, except by altering the distance between these two 
molecules. If we recollect that the symbol d denotes a passage from one molecule to 
another, and 6 the displacement of the same molecule; and if we use the latter in its most 
general sense, as applied to any displacement, virtual or real, we may represent the first 
hypothesis by the equations 


dF dF 

ST rene ae 
and the second by 

BE aon ee! 

ey) op 


It is in the latter of these significations that the second hypothesis made in Article 12 is to 
be understood. 

Now it has been shown in the text, that if the sum of the internal moments be capable 
of being represented by the variation of a single function, we must have 


Fi =f(p) = 9, 


since p’is indefinitely small. If then we use the symbol 6 to denote an increment pro- 
duced by a real displacement, we shall have 


P= 8Fy p= 8p, 
and, therefore, 


oF = aép. 
Hence 
oF oF 
iy) = 0, op = 0, 


The Rev. J. H. Jetterr on the Equilibrium and Motion of an Elastic Solid. 217 


denoting, as we have seen, that the molecular force is, in the sense above defined, a force 
of attraction or repulsion. If, however, we confine ourselves to the strict sense of the 
terms attraction and repulsion, we ought to define the force solely by its direction, without 
any regard to its intensity. Properly speaking, therefore, the equations of motion of a 
system of attracting or repelling molecules will, in their most general form, contain thirty 
distinct constants. 


: ih . 


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wo AN scuggtod.) 
dyiiel 


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ceaenn 


» 
i = » 4 * 
AMY faa! ddva¥ yleo elitet are Oft wt i 4 
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219 


IX.—Account of Experiments made on a New Friction Sledge for stopping 
Railway Trains. By the Rey. Samug Haveuton, Fellow of Trinity College, 
Dublin. 


Read June 4, 1850. 


Tue instrument which is here described, and with which the following ex- 
periments were made, is the invention of Mr. S. Witrrep Haveuton, Engineer, 
and Superintendent of the Dublin and Kingstown Railway Engine Factory at 
Ringsend Docks. It is intended to be used at the termini of railways, instead 
of the spring buffer usually employed to stop the train, in case it should happen, 
through the carelessness of the engine-driver or guards, to enter the terminus 
with too great speed. The objection to the use of the spring-buffer is two- 
fold: the space through which the recoil can take place is too short, and the 
second recoil of the spring produces effects which are only less dangerous than 
those of the first shock; this latter inconvenience is sometimes remedied by 
the use of ratchets, which prevent the recoil of the spring after it has been 
compressed by the shock. But the first objection is founded on the use of the 
spring itself, and cannot be removed. A careful consideration of these ob- 
Jections led Mr. S. W. Havcuron to the invention of his Friction Sledge, as a 
substitute for the spring buffer. 

The Friction Sledge consists of two strong wooden frames, shod with iron, 
and shaped as in the annexed diagram, which represents a side view of the 
sledge in action ; these two frames are provided with iron flanges on the 
inside (so as to prevent them from slipping off the rails), and being placed pa- 
rallel to each other at a distance equal to the interval between the rails, are 
strongly tied together by iron braces. The sledge, being placed upon the rails, 

VOL. XXII. 26 


220 The Rev. Samugt Havenron’s Account of Hapervments made 


is ready to perform its office of stopping a train moving with any moderate 
degree of velocity. The engine or foremost carriage of the train runs forward 
upon the sledge, and, striking against its curved front, receives a shock, which, 
if the sledge were immoveable, would be as fatal as the shock caused by im- 
pinging upon a stone wall; but the sledge, having sustained a portion of the 
shock, slides forward, and the remainder of the momentum is gradually de- 
stroyed by its friction against the rails. 


Si Sea | Bl! | iS en ips ele Elst tel [Sitar it) 228 a 


The first time I had an opportunity of seeing the Friction Sledge in action 
was upon the 20th of April, 1849, on which occasion no accurate record was 
kept of its performance ; it appeared, however, so completely successful in a 
practical point of view, that I was induced to attempt a few experiments, with 
a view of obtaining a correct knowledge, theoretical and practical, of its mode 
of action. I take this opportunity of acknowledging the kindness of the Board 
of Directors of the Dublin and Kingstown Railway, in allowing the use of wag- 
gons and a portion of the rails suited to the experiments ; and of stating the 
obligations I am under to Mr. Witrrep Haveuton and the Rev. Josrrn A. 
GALBRAITH, without whose assistance in conducting the experiments, and after- 
wards in calculating their results, I should have been unable to complete this 
account. 

Our first experiments were performed on the 27th of April, 1849, with an 
engine and train of five empty passenger carriages, in the presence of the Rev. 
T. Romyey Rosryson, D.D., of Armagh Observatory, and Mr. Brreiy, Secretary 
to the Dublin and Kingstown Railway. On this occasion our mode of measuring 


* The velocity of the train on this occasion was determined by counting with a chronograph 
the time occupied in performing the last four or five revolutions of the driving wheels of the 
engine; this determination, however, was rendered uncertain by the occasional slipping of the 
wheels on the damp rails. 


on a new Friction Sledge for stopping Railay Trains. 221 


the velocity of the train was so imperfect, that I shall merely state the general 
results, without attempting to deduce any accurate conclusions from them. 


Number of 
Experiment. 


13°66 feet. 
14-75 
12°58 
16°33 
15°50 
18:16 


Velocity of Impact. Length of Slide. 
| 


8:6 miles per hour. 
9-4 


The weight of the engine and train was about 32 tons, and the sledge 
7cwt. The results of this trial are sufficient to prove the great efficiency of 
the Friction Sledge as a means of stopping a train in motion. 

In order to obtain more accurate results, I determined to experiment with 
a single loaded waggon; and to measure the velocity with precision, I used a 
portion of the rails inclined to the horizon, and measured, by means ofa pair 
of chronographs reading to the fifth of a second, the time of describing a given 
space, when the waggon was made to enter upon the inclined plane with an 
unknown velocity ; or measured the space traversed by the waggon, when its 
whole motion took place on the inclined plane. 

The subsequent experiments on the Friction Sledge were conducted as fol- 
lows :—An inclined plane of about 160 feet, on the rails at the Engine Factory, 
Ringsend Docks, was selected, at the lower extremity of which the friction 
sledge was placed, and a loaded waggon was either pushed or allowed to run 
down the inclined plane, so as to impinge upon the sledge at the bottom. The 
velocity of impact and the length of the slide were the quantities to be mea- 
sured, from which all others could be inferred by calculation ; the velocity of 
impact was measured by noting the time taken by the loaded waggon to pass 
over a measured space on the inclined plane, or by allowing the waggon to start 
from fixed points on the inclined plane. 

0" 


Let O00! be a portion of the inclined plane, / the inclination of the plane 
262 


222 The Rev. Samuet Haveuton’s Account of Experiments made 


to the horizon, 7 the angle which the axis of the waggon makes with the in- 
clined plane when the front wheel is at the point Z. The line OY is horizontal ; 
X is the point of bisection of OO’; and XZ is also horizontal. The velocity of 
the waggon at O’ is its velocity at the commencement of the shock; the velocity 
at O is equal (neglecting the friction of the wheels) to its velocity at Y; i. e., 
its velocity at the end of the shock. 

I shall assume that the shock consists of a single blow given at the point Z 
with the velocity which animates the waggon at the point X. 

If v’ represent this velocity, then the velocity of impact actually imparted 
to the sledge will be 


m denoting the weight of the waggon, 
/ 


TO ies ty ek a ae oes 


If V represent the velocity with which the sledge and waggon begin to 
move, and pu, k, represent the coefficients of friction of rest and motion respec- 
tively, we easily obtain (neglecting the loss of momentum caused by imperfect 
elasticity) the following equations : 


V=v cosi—p(gcos J —vsinz); (1) 

?— 29s (k cos J — sin J); (2) 

the first of which expresses the fact, that the momentum with which the sledge 
begins to move is equal to thedifference between the original momentum and that 
destroyed by the friction of rest ; the second equation is true on the hypothesis, 
that the friction of motion is a constant retarding force ; eliminating V between 


these equations we obtain 
v=AYs + pu seci; (3) 


A and wu being defined by the following equations: 
A cost = (2g [k cos I — sin J), 
u=gcosI—vsini. 


Each experiment tried with the Friction Sledge, should give particular 
values for s and v; which, substituted in (3), would afford a relation between 


on a new Friction Sledge for stopping Railway Trains. 223 


A and ». A few trials soon convinced me that , was not a constant, and that 
equation (3) did not represent the experiments ; this result might have been 
foreseen, as the loss of motion arising from the shock of imperfectly elastic 
bodies was neglected in finding equation (3). I could not discover any di- 
rect method of introducing the loss of motion due to the shock, and therefore 
sought to modify equation (3) by experiment, so as to make it represent what 
actually occurred in each trial. After many failures I was induced to assume 


OS IT 


K being a constant. Introducing this value of » into (3), and dividing by vs, 


we obtain 
v 


. uv 

—=A+Kseci—. 

vs i V/s 

I hope to be able to show that this equation represents faithfully the whole 

series of experiments, and that, too, with a degree of accuracy which seems to 
prove that it is the true expression of the facts which were observed. 

The numerical values of the constants in the above equations were deter- 


mined with care, and are as follows: 


OO’= 22°5 feet, sin 7 =-0146, sinz=-050; 
O’X=11-25 feet, cosT=-999,  cosi=-998. 


(4) 


The force down the inclined plane, allowing 10lbs. per ton for friction, resist- 
ance of air, &c., is consequently, 


f= 4651 ft. 


The original measurements and calculated results are all given in the fol- 
lowing tables, in which I have not suppressed a single experiment, although one 
of them is undoubtedly erroneous. The evidence on which I was induced to 
adopt the form (4) is completely given, and an opportunity thus offered for 
another interpretation of the experiments, although the accuracy with which 
equation (4) represents the results seems to preclude the possibility of an 
interpretation differing much from that which is here given. 


224 The Rev. Samuet Haucuton’s Account of Experiments made 


First SERIEs. 


January 25, 1850.—Day damp and wet. 
ewt. qrs. Ibs. 
Weight of waggon=99 0 0. 


Weight of sledge, = 4 3 91. 


Taste (1).—Ortcrnat Measurements. 


1A 
2 


Observations. 


First explosion off hind wheel. In- 
terval between wheels, 7ft. 6in. 


Explosion off hind wheel. 


BIDAR WNe 


The first and second of these experiments were performed by placing two 
fog signals on the rails at O and O”, distant from each other 100 feet, and mea- 
suring with a chronograph the interval of time between the explosions, as re- 
gistered in the first column; the remaining experiments were performed with 
one fog signal placed at O, the time of the front wheel passing O” being ob- 
served by sight. The waggon was impelled by a number of men, who ceased 
pushing it before its arrival at O”. 


Taste (2).—Catcuratep Resurts. 


146°954 
147-689 
146-734 
1527121 
156-070 
158379 
159°101 
152°851 


1 
2 
3 
4 
5 
6 
7 
8 


on a new Friction Sledge for stopping Railway Trains. 225 


In this Table v’ denotes the velocity of the waggon at the point X, situated 
11 feet above the sledge; i.e. it is the mean of the initial and final velocities 
of the shock ; it is computed from the velocity at O, by adding to its square the 
square of the velocity due to the space OX, and extracting the square root of 
the sum. The velocity at O is found from the formula 
_ 200 +4651 #? 
te Qt , 
in which ¢ denotes the time of describing OO”, in Table (1). In Exp. (2) we 
must substitute 185 for 200 in the formula ; and in Exp. (6), 215 instead of 200, 
adding, in the latter case, in order to compute v’, the square of the velocity due 
to 4 feet instead of 11-25 feet 

In the second column, sis found from the second column of Table (1). 

In the third column, v = +9525 v’; the numerical coefficient being deduced 
from the weights of the waggon and sledge. 

In the fourth column, w=827134—-05 v; the coefficients being deduced 
from the equation which defines w (p. 222). 


pl 


SECOND SERIES. - 
January 26, 1850.— Wet day. 
Weights of waggon and sledge same as before. 


Tasxe (1).—Oricivat MEASUREMENTS. 


Observations. 


A 
2 


Explosion off hind wheel. 


1 
2 
3 
4 
5 
6 
7 
8 
9 
10 


a) 
Ne 
—a 


SCKHOWWWWWRhADD 


These experiments were tried in a manner similar to the last six experi- 
ments of the first series. 


226 The Rev. Samus, Havcuton’s Account of Experiments made 


Taste (2).—Catcuratep Resvtts. 


12°112 31558 : 145°157 
11-685 31578 | 4:48 139914 
11-012 SI610" | || 4: 141-268 
10°344 31641 | 4°85 152-733 
10:256 31-646 ; 155-430 
10°325 31643 | 4: 156843 
10-290 31-644 “36 169662 
10°325 | 31643 e 173-454 
10°249 31-646 55% 175°727 
13°803 | 31477 i 137393 
14-238 31-456 : 125-463 
14-238 | 31-456 ; 1307132 


1 
2 
3 
4 
5 
6 
us 
8 
9 


The quantities here tabulated are the same as in the first series of experi- 
-ments; and in calculating v’ for Exp. 5, the same method was followed as in 
Exp. 6 of first series. 


Turrp SERIES. 


February 23, 1850.—Fine day. 
Weights of waggon and sledge same as before. 


The mode of estimating the velocity on this day was to allow the waggon 
to run down the inclined plane a measured distance, and thence compute the 
velocity of the impact. 


Tas ie (1).—Onricinat MEasuREMENTS. 


on a new Friction Sledge for stopping Railway Trains. 227 


Tasre (2).—Catcuratep Resutts. 


191°349 


166-208 
3 163-097 
49288 | 155-994 


The velocity v’ at the point X is found from the formula 


u? = fs = -9302 s, 
s denoting OO”; and from v’ and s the remaining quantities are calculated as 


before. 


Fourtu SERI&s. 


March 5, 1850.—Fine day. 


tons. cwts. qrs. Ibs. 


Weight of waggon = 2 4 38 8. 
Weight of sledge = 4 3 21. 


The velocity of impact was determined as in third series. 


Tasre (1).—Orternat MrasurEMENTS. 


1 
2 
3 
4 


aol 
tal 
moO De 


Note.—The point O in these experiments is 20 feet above the sledge. 
VOL. XXII. 24 


228 The Rev. Samugt Haucuton’s Account of Experiments made 


TasiE (2).—Catcunatep Resvutts. 


233°164 


188-488 
179°437 
182-746 


In this Table v is calculated by the formula 
i= See 


the other quantities are deduced in the same manner as in the other experiments. 
Having obtained the results calculated from the foregoing series of experi- 
ments, I had recourse to equation (4), 
v Uv 
—— = A kK eee S=- 
vs sf _ vs 
which contains two unknown quantities, A and K sec7. Having found ap- 
proximate values of these quantities in each of the four series of experiments, 
I then, by trial of successive numbers extending to the fourth decimal place, 
obtained finally the following results, which give the values of K sec 7 and 4 
which best satisfy all the experiments. 


First SERIES. 


K sec t = :0313. 


Mean = ‘0644 


Rejecting the second experiment, which is manifestly erroneous. 


on a new Friction Sledge for stopping Railway Trains. 


SECOND SERIES. 


K seci = '0311. A= | 7 
ge 

| go 

pie 
i 12° 


| . | 10° 


0851 
0873 
0879 
0920 
0867 


0900 


Mean = ‘0835 


Tuirp SERIES. 


K sec zt = 0305. 


Fourtu SERIES. 


K sec t = *0307. 1° 1555 
2° 1379 
3e 1451 
4° “1580 


Mean = ‘1491 


Referring to p. 222, we find 


A cosi= ¥{29(k cos [—sin J)}. 
Hence, 


+sinJ=kcos J; 
or, 


k=:0154 A? + -0146. 
2H2 


230 The Rev. Samurt Haucuton’s Account of Experiments made 


Computing the four values of & from this formula, we obtain finally, for the 


two coefficients, 


(1) K =-0313 (1) k= 0147 
(2) K =-0311 (2) k =-0147 
(3) K = -0305 (3) k = "0150 (5) 
(4) K = -0307 (4) k=-0149 


In order to appreciate the degree of accuracy obtained in these experiments, 
let us transform equation (4) into the following: 


v > . Ww 
——A-—K seci —=0; 


V/s VAS 


and substitute in its left hand side the values of K sec 7 and mean values of A found 
above. The results of this substitution for the four series of experiments are 
as follows, in which ® denotes the left hand side of the equation just given. 


SECOND SERIEs. 


First SERIES. 


It is evident, on inspection of the foregoing results, that ® = 0 is true to 
two places of decimals; and it is not difficult to prove, that it may be inferred 
from this, that the values of K and k (5) are true to three places of decimals. 


on a new Friction Sledge for stopping Railway Trains. 231 


From the remarkable agreement of all these results, I think we are entitled to 
assume, that equation (4), or its equivalent ® = 0, is fully established. 

In order to determine the lowest velocities for which equation (4) might 
be considered proved, I added to the third and fourth series of experiments a 
set of experiments, the object of which was to ascertain the point from which 
the waggon should be allowed to descend, so as just to move the Friction Sledge. 
The result of these trials was as follows: 


mS ee eee 


Third day, 142 | 3:078 | 31:88 | 21-6760 | 691-0308 
Fourth day, ‘110 | 2885 | 31:99 | 26-2273 | 839-0017 


Substituting these expressions in equation (4), and replacing A by 1681 
and ‘1491 on the third and fourth days respectively, we obtain 


Ki 308i 1, KS = 0310) 


The agreement of these results with (5) is sufficient to prove, that the equation 
from which they are deduced is true for velocities as low as 3 feet per second. 

The experimental truth of equation (4) being thus established, the results 
obtained from the foregoing series of experiments may be briefly summed up as 
follows: 

Ist. The momentum possessed by the waggon at the moment of impact on 
the Sledge is destroyed by two causes, which may be considered separately: first, 
the loss of momentum occasioned by the shock itself, and the adhesion of the 
Sledge to the rails; this I have called the Friction of Rest : secondly, the loss 
of momentum which takes place after the Sledge is set in motion, caused by 
friction against the rails; this is the Friction of Motion. 

2nd. The friction of rest is directly proportional to the pressure against the 
rails, and to the velocity of impact, jointly. 

3rd. The friction of motion is directly proportional to the pressure against 
the rails, and is independent of the velocity. 


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233 


X.—On certain Improvements in the Construction of Galvanometers: on Galva- 
nometers in general :; and on a new Instrument for measuring the relative Force 
of Magnetism in compound Needles intended to be nearly Astatic. By MicHaE 
Donovan, Esq. 

Read May 22, 1848. 


Tue galvanometer, in the present day, has become a most important instru- 
ment of research, whether it be considered as a measure of electricity or of heat. 
In the latter capacity, it exceeds all others in sensibility and the promptness of 
its indications; and when it is recollected that by its aid facts have been ascer- 
tained which had been erroneously represented by the thermometer, that de- 
grees of heat have been estimated to which the thermometer was in some cases 
almost insensible, and in others inapplicable, its value and capabilities need no 
encomium. But it is necessary that, for delicate purposes, we should have the 
instrument in its utmost attainable state of perfection. Under such impres- 
sions, I have made some efforts to improve it; and believe I have succeeded 
in rendering it more certain and accurate in its results, as well as more sensible 
in its indications. 

The sensibility of a galvanometer is increased when its construction is such, 
that the two layers of the wire coil, between which the compound or double 
needle lies, are as near as possible to each other, the consequence being that the 
lower bar of the compound needle will be very close to both. The upper bar 
should be equally near the upper layer of the coil. The proximity of the bars 
to the coil is one of the great sources of sensibility; but, to permit this, many 
things must be attended to. 

In the first place, however carefully the wire of the coil may have been 
covered with silk or cotton, there will always be a number of fibres projecting 


234 Mr. Micnart Donovan on certain Improvements in 


from the material. They are short it is true; but when the bars of the needle 
are very close to the three acting faces of the coil, these fibres are sometimes 
sufficiently long, resisting, and numerous, to obstruct the motions of the com- 
pound needle when in a state of great sensibility. The following plan succeeded 
in removing this source of uncertainty. 

The wire, well covered with silk, is wound on a brass frame, each round 
so tight and close to the adjoining one, that the first layer may lie perfectly flat, 
without springing or bellying in any part. When the first layer has been wound 
from the beginning to the end of the frame, it is to be wound back again; and 
if the rounds of the first layer have been put on very compactly against each 
other, they will support the second layer without allowing the wire to force 
itself between any two which lie underneath. The flatness of the first layer 
will insure the same perfection for the second; and equal attention to tightness 
and flatness in winding the third layer, or fourth, if there be one, will produce 
a coil of great regularity and closeness, and of equal thickness,—qualities of the 
sreatest utility. 

Under these circumstances, it is obvious that the frame must be strong 
enough to sustain the collective tension of such a number of coils ; and there- 
fore brass, well covered in the touching parts with hard varnish, is to be preferred 
to ivory; although the latter is often used on account of its being a non-conductor. 
The four sides, which constitute the parallelogram on which the coil is wound, 
would not, without being inconveniently clumsy, afford sufficient resistance to 
this tension, but that the two end pieces of the frame, instead of being mere 
bars like the side pieces, constitute portions of a circle at the inner side, and 
are flat at the outer. 

From what has been described, it is evident that the vacancy between the 
layers of the coil being but one-eighth of an inch, the numerous filaments pro- 
jecting from the silk or cotton must be even more likely than in ordinary cases 
to obstruct the needle: and the very means adopted for securing sensibility 
would also react against that result, but for the following construction. Two 
plates of very thin, well-hammered brass are soldered to the two arches in such 
a manner as to connect them, and constitute what may be called a floor and a 
ceiling to the narrow chamber in which the lower bar of the compound needle 
rotates, thus effectually removing all possibility of obstruction by filaments, and 


the Construction of Galvanometers, Sc. 235 


greatly adding to the strength of the frame. The coil is wound round the out- 
side of the frame and its brass plates, leaving the internal circular chamber of 
brass for the uninterrupted oscillations of the enclosed needle. Its vertical width 
is reduced by the two brass plates to one-eighth of an inch. 

But the upper bar of the needle would still be liable to obstructions from 
filaments of the upper layer of coil, were it not that a circular plate of well- 
hammered silvered brass lies loosely on it, and exactly fills up the interior of 
the circle on which the graduation is engraved. 

In order to permit the compound needle to be placed within, and removed 
from its berth in the chamber, as occasion may require, there is a slit along the 
middle of what I have (for want of a better name) called its ceiling, so narrow 
as barely to admit the lower bar of the needle. ‘To keep the wire of the coil 
and its filaments in situation, without encroaching on this slit, its edges are 
guarded all round by an elevated margin* of very thin sheet brass, which 
stands exactly as high as the thickness of the coil. The circular silvered brass 
plate above mentioned, although described as one piece, really consists of two 
semicircles, the diametrical junction of which is so accurately fitted, that it ap- 
pears as a straight engraved line upon one circular plate: it represents the 
magnetic meridian of the galvanometer. When the needle is to be removed, the 
semicircles are easily pushed up from below. Between the semicircles, and in 
their common centre, there is a small hole, which permits the spindle or con- 
necting axis of the two bars of the compound needle to play freely. In the top 
of this spindle is a very small hole, barely large enough to receive the silk fibre 
which sustains the compound needle. Thus the two bars, which constitute the 
compound needle, are brought as near as possible to the three faces of the coil, 
without risk of obstruction. The chamber in which one bar of the needle rotates 
may be as vertically narrow as will allow free motion ; one-eighth of an inch will 
be sufficient. In so narrow a space, it is obvious that any deviation from the 
horizontal position of the coil and frame would cause obstruction to the move- 
ments of the needle: the same would happen also if the needle were not accurately 
balanced on its spindle, and therefore on the suspending fibre of silk. The 


* The coil must be wound as closely as possible against this margin on both sides; for here the 
energy of a voltaic current is most required to overcome the inertia of the needle. 


VOL. XXII. OT 


236 Mr. Micuart Donovan on certain Improvements in 


horizontal portion is attainable by means of a detached spirit level and levelling 
screws; and the balance of the needle is regulated by a very small slider made 
of brass foil. It will be often found necessary to have a slider even on each 
member of the compound needle; for as the intensity of its magnetism is some- 
times stronger, sometimes weaker, in consequence of spontaneous or induced 
changes, the dip will affect it more or less; and hence the necessity of the 
sliding equipoise to maintain the horizontal position in so narrow a chamber. 
The second slider becomes necessary when the poles are reversed in the man- 
ner hereafter described. 

The level and levelling screws afford the means not only of rendering the 
plane of the chamber perfectly horizontal, but of giving true verticity to the 
pillar from the cross-bar of which the needle hangs. Without such a precaution 
the spindle of the needle would not freely rotate in the small hole made for it 
in the meridian line of the circular plate, or rather between the two semicircu- 
lar plates. 

To give greater precision to the centrality of this spindle, the hole in its 
top is made exceedingly small, and through it is looped the suspending silk 
fibre, the other end of which is looped through an equally small hole in a pin 
which may be secured by a thumb-screw, in the cleft end of a horizontal cross- 
bar, moveable in every direction at the top of the pillar. The use of having 
the holes so small is to secure the silk from shifting, and thus altering the ba- 
lance or position of the needle. The length of silk fibre which I conceive to 
be sufficient is 74 inches, exclusive of what is looped above and below. 

When occasion requires the compound needle to be removed from the gal- 
vanometer, the thumb-screw which screws against the pin in the cleft of the 
cross-bar at the top of the pillar is to be loosed; the pin with the silk fibre is 
to be drawn out; the two semicircular plates which lie within the graduated 
circle are to be pushed up from below, and the needle withdrawn. This faci- 
lity of removing and replacing the needle is a great advantage when its mag- 
netism requires regulation; and beside this the silk fibre often becomes twisted 
by the rapid spinning of the needle which certain experiments occasion and even 
require: it is prevented from untwisting by the polarity of the needle; but if 
the needle be held between the fingers while the pin hangs down by its fibre of 
silk, the latter will untwist itself; and when the pin ceases to spin, the whole 


the Construction of Galvanometers, §c. 237 


may be replaced. Torsion, even of so slender a fibre, has more effect in im- 
pairing sensibility than might be supposed. 

The frame of the coil is screwed on a strong circular plate of brass, sur- 
rounded by a hoop sufficient to secure the French shade which covers the 
whole. The solid vertical axis of this plate turns smoothly and slowly in 
a ground socket, by means of a crown wheel fixed to the plate, acted on 
by a pinion and thumb-screw attached to the tripod on which the whole in- 
strument stands. The levelling screws pass through the tripod, and rest in so 
many holes in a circle of brass screwed to a mahogany stand, in the bottom of 
which should be a drawer to contain various necessaries. On the stand fits a ma- 
hogany cover or box, with fastenings. The ends of the coil pass down through 
two holes in the circular brass plate, bushed with ivory, and are soldered under- 
neath the plate, each to an insulated binding screw, situated one on each side of 
the meridian line. Between the binding screws, and affixed to the circular brass 
plate, is a horizontal, hollow, square trunk, three inches in length: each side of 
the interior measures about three-sixteenths of an inch: it is fixed in the di- 
rection of the magnetic meridian line of the galvanometer, and has a continu- 
ation of this line engraved on its upper surface. At the end of the trunk, and 
on the meridian line, is erected a short, sharp brass point, on which may be oc- 
casionally placed a common compass needle. When the galvanometer is to be 
used, the compass needle is to be placed on the brass point, and the thumb- 
screw underneath turned until the point of the compass needle and the meridian 
line coincide precisely. The instrument is now set; the compass needle is to 
be removed, lest it interfere with the astatic needle: the latter should also have 
been previously removed, as it would equally interfere with the compass needle. 
The necessity of thus setting the instrument by a detached compass needle, 
and of not depending for this service on the astatic needle, although the latter 
is usually relied on, will abundantly appear hereafter. 

The trunk is made hollow, because it has other duties to perform. It is 
intended to contain one prong of a magnet made exactly in the shape of what 
musicians call a “tuning fork,” except that the prongs are nearer together, 
being just the distance that the two needles are from each other on their 
spindle. ‘This magnet slides in and out of the trunk, which it exactly fits; it 
is so placed, that one prong is always vertical over the other when it is in use. 

212 


238 Mr. Micuart Donovan on certain Improvements in 


Its duty is occasionally to assist the directive power of the terrestrial magnetic 
meridian, and thus to lessen the influence of deflective forces on the needle. 
With needles of very great sensibility, very weak deflective forces will often 
produce deflection = 90°, and then the galvanometer is incapable of indicating 
any greater effect. The magnet is graduated in inches and tenths, on both 
prongs, in order to regulate its proximity to the astatic needle, and therefore its 
influence in experiments which require repetition or correspondence. The 
prongs are square, as well as the trunk in which one or the other slides; and 
one side of the trunk has a spring which presses on the magnet and enables it 
to slide evenly. Were the prongs cylindrical as well as the trunk, the magnet 
might turn to one side or the other, and then the other prong would ex- 
ercise an undue influence on the astatic needle. When the magnet is not re- 
quired in an experiment, it should be drawn out and put aside at a considerable 
distance. One prong is marked N, the other $; sometimes one must be upper- 
most, sometimes the other. It is easy to see how it should be placed in order 
to moderate the effect of a deflective force on the needle. 

It is usual to graduate the circle from 0 to 90°, on each side of the magnetic 
meridian line. There is an inconvenience in thismode: in some experiments, 
the voltaic action, which is the cause of the deflection, exists but for an instant; 
there is no permanent effect to measure, nor any effect beyond one sudden start 
of the needle, and its immediate return. Yet sometimes the momentum is such 
as to carry the needle far beyond 90°, and even to whirl it round several times. 
I think it more convenient that the graduation should be carried to 180°. 

The next thing to be considered in the construction of a galvanometer is 
the compound or so-called astatic needle, a subject of great importance and 
curious interest. A needle may be defective in two chief points: it may have 
too little sensibility, by having a strong directive tendency; or it may have too 
much, by having been brought too near the state of perfect astaticism: in the 
latter case, a weak deflecting force will produce a maximum deflection, and the 
needle will be insensible to all higher degrees of energy. 

To avoid these imperfections, I employ the following construction, having 
discarded the common compound needle, which consists of two bars permanently 
fixed to one spindle. The lower bar of the needle is secured, in the usual man- 
ner, to the lower end of the spindle; but the upper one is moveable on the 


the Construction of Galvanometers, &c. 239 


upper end of the spindle, and turns round on it as on an axis: it may be 
secured in any position by means of a minute nut which screws it against a 
shoulder on the spindle. Yet the total weight is trifling. One of my compound 
needles, thus constructed, weighs but 24 grains, including the nut; its bars 
are distant from each other + of an inch; each is 24 inches in length, and 
o; inch in width; their sides are parallel. The best material for the bars is 
the mainspring of a small Geneva watch; it is very thin, and retains magnetism 
along time. When saturated with magnetism, it no doubt dissipates a portion 
in a few days; but it retains about one-third for any length of time, and this is 
sufficient for ordinary purposes. It is obvious that the bars must be filed per- 
fectly straight, and placed parallel to each other. 

The following is the process which I employ for magnetizing the compound 
needle when great sensibility is not required. I caused a horse-shoe magnet of 
considerable power to be made, the limbs of which, from one extremity of the two 
polar faces to the other, are of such extent and thickness that the compound 
needle intended to be magnetized can rest its whole length on the faces. The 
limbs of the horse-shoe should approach each other within half an inch. In 
this way the compound needle will rest one edge of each bar on the terminal 
faces of the magnet, being placed exactly between the two limbs, and in the 
same situation that its keeper generally occupies. The compound needle will 
become saturated with magnetism in four hours. Before it is removed, the 
keeper of the horse-shoe should be put on laterally, close to the extremities, to 
facilitate the removal. 

The needle is now capable of two different applications. If it be intended 
to measure powerful deflective forces, it is ready for that purpose, so far as its 
state of magnetism is concerned. But as the two north poles are together, the 
needle has acquired a dip, and it is necessary to balance this exactly by the 
counterpoise sliders already mentioned. The needle, when properly placed in 
the galvanometer, being not astatic, it will give short, quick oscillations, will 
require no small voltaic energy to deflect it to 90°, and will return to zero with 
great precision and promptitude. It is now in its least sensible form. 

Should greater sensibility be required, we have only to turn the upper bar 
round on its axis until it be precisely reversed, and to remove the counterpoise 
towards the centre. To reverse the bars with precision is no easy matter, as 
will be seen hereafter. 


240 Mr. Micuaet Donovan on certain Improvements in 


It will be found very convenient thus to have a needle susceptible of a 
strong directive tendency by causing the poles to act in concert, or of greater 
sensibility by their acting in opposition; for in this way, and with the occasional 
aid of the forked magnet, a great range of voltaic forces may be measured. 
With ordinary galvanometers, if the sensibility be great, a very feeble deflecting 
foree carries the needle to its maximum, and no greater force can be estimated. 

When the bars have been reversed, as described above, the instrument will 
be found to possess the usual sensibility of astatic needles ; but not a sufficiency 
for all purposes, especially when it is intended as a measure of heat. In this 
case, other proceedings must be resorted to, which, after a few preliminary ob- 
servations, I will describe. 

During some experiments on different modes of communicating magnetism 
to needles, results were obtained which J am not aware have been observed by 
others, or made the subject of inquiry. I sometimes produced a compound needle 
which found its position directly across the magnetic meridian, instead of coin- 
ciding with it. As often-as it was moved into the right position, it would re- 
turn to the wrong one; and the more care I took to insure an equally distri- 
buted magnetism, the more certainly would this perplexing anomaly recur. It 
would be useless to trouble the Academy with all the particulars; it will suf- 
fice to say that, m order to investigate the cause of these failures, and provide 
a remedy, I was obliged to contrive a new instrument. As it would be difficult 
to refer to its employment without giving it a name, I will here call it a volta- 
magnetometer, the prefix being sufficient to distinguish it from the magnetometer 
used for a different purpose. 

The volta-magnetometer consists of a horizontal brass graduated circle, or 
ring, fixed directly over and parallel to a circular brass plate of the same total 
diameter. Their distance from each other, maintained by three stout brass 
studs, is a quarter of an inch, sufficient to allow free space for the oscillation of 
the compound needle of the galvanometer, which is to be transferred to it as 
occasion may require, one bar of the needle lying above the graduated ring, 
and the other between the latter and the circular brass plate. On the circular 
brass plate is engraved a circle, corresponding with that of the upper graduated 
ring: both circles are graduated and numbered with such precision, that each 
degree on the upper circle is exactly vertical to the corresponding one under- 
neath. The degrees on the lower circle are carried a little farther in towards 


the Construction of Galvanometers, Se. 241 


the centre than those on the upper circle, to enable the observer to take the 
two corresponding degrees in his view, along with the interposed points of the 
needle, when his eye is directed vertically over the four objects, so that they 
shall all coincide. As a further facility, the numbers are engraved inside the 
circle. The instrument stands on levelling screws, which are received in holes 
in a brass ring screwed to a wooden stand; and the whole is covered by a 
French shade. A stop which acts underneath the stand checks tedious oscil- 
lations. 

From one of the three studs which support the upper circle, proceed 
horizontally two long brass blades hinged to it in such a manner that they can 
be made to approach towards or recede from each other. When brought toge- 
ther, they fit closely by their straight edges, and constitute a kind of forceps 
capable, by its long handles, of firmly grasping the spindle of the compound 
needle when it is suspended in the centre of the graduated circles. By means 
of a sliding clip, they can be retained in this position. The silk fibre, which 
sustains the compound needle, is suspended from a pin in across bar at the top 
of a pillar, in the same manner as in the galvanometer, and is similarly circum- 
stanced in all respects with regard to the adjustments which have been already 
mentioned. A compound needle, with its silk fibre and pin, may thus be trans- 
ferred from one instrument to the other, and will fit exactly in either. 

Experiments made with the volta-magnetometer soon convinced me that the 
apparently anomalous position assumed by the needle, which I had taken so 
much pains to render astatic, and which nevertheless stood perpendicularly to 
the magnetic meridian, was in strict accordance with the circumstances under 
which it was placed. To explain the matter, it is necessary to advert to what 
the properties of a compound needle would be, if, as its name expresses, it were 
really astatic. If the four poles of the needle, supposed to be perfectly similar 
in magnetic power, be placed in the same vertical plane, with the synonymous 
poles contiguous to each other, the directive power will be at its maximum. If 
in this state of things the bars be opened out, no matter what the angles sub- 
tended by them may be, the law of the parallelogram of forces comes into ope- 
ration: the compound needle will take such a direction, that the resultants of 
the parallelograms, two sides of which are the intersecting magnetic axes, will bi- 
sect the vertical angles which include the magnetic meridian, and will, therefore, 


242 Mr. Micuart Donovan on certain Improvements in 


coincide with it. The resultants will represent the intensity of the directive 
forces of the compound needle, and in reasoning on the subject may be substi- 
tuted for them. In proportion as the bars of the needle are opened, and the 
vertical angles which include the magnetic meridian are enlarged in conse- 
quence, the resultants or directive forces diminish in energy, until at length 
the bars are entirely opened and lie with their dissimilar poles contiguous, 
exactly in the same vertical plane: the resultants then vanish; there is no 
longer any directive force; and consequently the needle will remain in any 
position. 

This state of indifference depends on the condition laid down, that the four 
poles possess exactly the same intensity and distribution of magnetism, and that 
the bars lie precisely in the same vertical plane with the synonymous poles con- 
tiguous to each other. If this position of the bars be ever so little disturbed, 
by turning one of them on the common axis away from the other, even to the 
amount of one or two degrees, the resultants begin to exert their influence, 
weakly, it is true, but sufficiently to cause the compound needle, previously indif- 
ferent, to take up a position at right angles with the magnetic meridian, because 
the resultants coincide with it. In that position the needle will permanently 
remain, and if disturbed, will, after a few oscillations, return to it. Thus the 
apparently anomalous phenomenon, which surprised me because it had never 
been previously observed, is very easily understood. 

If, instead of equal distribution of magnetism, the power of one bar of the 
compound needle exceed that of the other, the needle, instead of becoming in- 
different when both bars are brought into the same vertical plane, will obey the 
predominant power of the stronger bar, and pass at once into the magnetic me- 
ridian. Indeed the tendency to doso may be exhibited before the two bars are 
brought into the same vertical plane; the resultants, still feebly in operation, 
may more or less antagonize the predominant power of the stronger bar; a ba- 
lance of the two forces will take place; the compound needle will take up a 
position nearer to or farther from the magnetic meridian, according to the de- 
gree of resistance which the resultants offer: but if the bars be brought into 
the same vertical plane, the resultants will be eventually overpowered. 

In order to bring the compound needle to a right angle with the magnetic 
meridian, the deviation of its bars from the vertical plane must be more or less 


the Construction of Galvanometers, Se. 243 


according to the greater or less predominance of magnetism in one of them: 
and the more equal the distribution of magnetism is amongst the four poles, 
the nearer to the same vertical plane may the bars be brought without causing 
them to swerve from the right angle at which they stand with thie magnetic 
meridian; although, when they are precisely in the same vertical plane, the needle 
loses all tendency to that or any other position. 

The condition of greatest sensibility is that in which the resultant is barely 
so far overpowered by the predominant magnetism of one bar, that the needle 
turns very slowly into the magnetic meridian from being at right angles with 
it, and in passing through 180° oceupies from 30 to 36 seconds, 

There is sometimes great difficulty in obtaining the results described: the 
magnetic axes may not coincide with the metrical axes, so that when the bars 
appear to be in the same vertical plane, the magnetic axes are not so: the true 
poles may not be equidistant from the centres of the bars: the magnetism may 
he irregularly distributed, owing to peculiarities in the steel; and all these cir- 
cumstances may combine. Empirical trials are, in such cases, the only resources; 
and patience will insure success. 

The volta-magnetometer is capable of imparting sensibility to galvanometer 
needles in two ways: first, by affording means of distributing the total quantity 
of magnetism between the four poles in a degree so nearly equal, that the 
feeblest directive power only will remain, and thus the least resistance will be 
offered to weak deflecting forces. Secondly, by causing the needle to assume 
a true position with regard to the magnetic meridian, and thus enabling it to 
give a just estimate of a deflecting force acting on it, which, as we have seen, 
it does not always present. By means of this instrument, we can prepare needles 
of any degree of directive power, and can describe that degree in giving an 
account of experiments. Results obtained by persons at a distance from each 
other may be compared, when the sensibility of the compound needle made use of 
is expressed numerically: it may be so expressed by stating the number of de- 
grees by which the magnetism of the two bars of the compound needle differ, 
when tested on the graduated circles of the volta-magnetometer: this will very 
nearly give the sensibility, but absolute precision cannot be attained. 

Thave already described the process of magnetization by which the compound 
needle acquires sufficient sensibility for ordinary purposes; but if required to 

VOL. XXII. 2K 


244 Mr. Micuart Donovan on certain Improvements in 


be in its condition of greatest sensibility, we must proceed as follows. It is to 
be transferred to the volta-magnetometer, and its spindle or common axis is to 
be confined between the blades of the forceps. The upper bar is to be turned | 
on the common axis until it form any angle with the lower one, suppose 80°: 
the forceps being opened, the needle will oscillate, and finally settle in such a 
position, as will show the relative intensity of the poles by the degrees pointed 
to on the graduated circles. If the magnetism be equal, the four poles will 
stand at 40°. But it has been already shown, that this equality may be but 
apparent, owing to the want of coincidence between the magnetic and metrical 
axes. In order to test this, the bars are to be closed until they fall into the same 
vertical plane, the poles being reversed. If the compound needle, when libe- 
rated, after oscillating a while, turn very slowly into the magnetic meridian, no 
more need be done; for although some little irregularity in the distribution of 
the magnetism is thus manifested, the desired effect is obtained. If the needle 
do not turn into the magnetic meridian, the bars are to be again opened to an 
angle of 80°, one of the poles is to be touched with the opposite pole of a strongly 
magnetized steel wire, or sewing needle, until there be a difference of 1° on the 
indications of the bars. This, or less, will be sufficient difference, when the 
bars are closed, to carry the compound needle into the magnetic meridian. 
Should the difference be more than 1°, that bar nearer the magnetic meridian 
line should be touched with the similar pole of the magnetized wire, and by 
lessening or increasing its power, the difference of 1° may be attained. The 
spindle being then caught in the forceps, the upper bar of the needle is to be 
turned round on the common axis, until the reversed poles appear in the same 
vertical plane. But a want of precise coincidence in this respect, between the 
reversed poles of the bars, to an amount often undiscoverable by the eye, will 
cause the compound needle to lie at right angles with the magnetic meridian. 
Hence, to produce perfect coincidence, the eye must be assisted by a magnifier, 
and the compound needle must be executed with great precision so that the 
bars shall be straight, and identical in all their dimensions. The mode of 
viewing the needle is of great consequence. The eye must be placed in such 
a situation that the four objects concerned shall be seen in the same vertical 
line; namely, the degree on the lower ciréle, the point of the lower bar, the 
corresponding degree on the upper circle, and the point of the upper bar. The 


the Construction of Galvanometers, Se. 245 


needle being adjusted, the spindle is to be disengaged from the forceps. If the 
reversed poles precisely coincide in the same vertical plane, the needle will 
oscillate, and finally settle in the magnetic meridian, provided that it retains 
sufficient directive tendency. If the needle do not lie directly north and south, 
other trials must be made, and generally the process of perfect adjustment is 
tedious and troublesome. 

It sometimes happens, as already observed, that the magnetism of the bars 
is equal, and the needle has no directive power. In such a case, the slightest 
touch of a magnetized wire to any one of the poles of the compound needle 
will increase or lessen its power, and thus alter the balance: the slighter the al- 
teration the better. 

The predominant magnetism should be so feeble, that the needle will very 
slowly fall into the magnetic meridian; but the predominance should be ade- 
quate to produce that effect. If the bars be not precisely in the same vertical 
plane, they will have a weak tendency to cross the magnetic meridian: but 
having also a directive power, they will be acted upon by the two forces, and 
will point at the degree on the graduated circles which expresses the balance of 
forces. In this state the needle is unfit for service; for although the deflec- 
tion from the magnetic meridian thus produced may amount to a few degrees 
only, it will resist a weak tendency to deflection in the opposite direction, when 
the galvanometer is employed to measure voltaic action, and may modify even a 
stronger one. Thus the condition of the needle most conducive to sensibility is 
that of being retained precisely in the magnetic meridian, with the feeblest pre- 
dominance of magnetism in one bar, which is adequate to this effect. 

A needle is frequently found to lie in the magnetic meridian, not because 
its bars coincide with precision in the same vertical plane, for perhaps they do 
not at the time, but because the magnetism of one or the other bar is so strong 
as to overpower the great error which would have arisen in consequence. The 
volta-magnetometer will detect the offending bar, by the inequality of the 
angles to which the poles will point on the graduated circles when the bars are 
opened out, and it may be weakened to the necessary degree by the similar 
pole of the magnetized wire. Needles which point truly north and south, on 
account of this inordinate predominance of power in one bar, are deficient in 
sensibility ; and when a needle has extreme sensibility, it may be that it points 
erroneously for want of sufficient predominance. 

2K 2 


246 Mr. Micuart Donovan on certain Improvements in 


In this state of extreme sensibility the needle is subject to making unac- 
countable excursions, amounting to 5°, 10°, or 12° east or west. On one occa- 
sion, when I had suspended a needle by a new silk fibre, it hung for that day 
exactly north and south. Next morning, at five o’clock, it was found 8°; at nine 
o'clock it was 0, and so remained all day. These changes recurred every day, 
about the same hours, during the month of April. On some days, the excursion 
and return took place twice. About the fifth week, the needle stood constantly 
at 8° for two days; it then shifted to 10° in the opposite direction, but returned 
to 0 in the middle of the day. I endeavoured to trace these changes to torsion 
by an hygrometric quality of the silk, or to alterations of temperature, but 
could not come to any certain conclusion, although I still attribute them to 
either or both of these causes, knowing no other that could operate. 

Be this as it may, these variations in the direction of the needle would be a 
source of false estimation of any deflective force, were the galvanometer planted 
according to the indications ofa needle thus in error: and variations will more 
certainly occur, the greater the sensibility of the needle. The remedy, however, 
is easy: the pin which sustains the silk fibre may be turned round ever until 
the needle point accurately; but this mode of rectification is only admissible on 
the condition that the position of the galvanometer has been rectified by its 
independent compass needle, and its magnetic meridian line: and here is 
another use of this needle and line; without them, what errors might in such 
cases be committed. 

I have frequently found, that when the compound needle was adjusted ex- 
actly north and south by the volta-magnetometer, it pointed 10° or 12° diffe- 
rently when carried to a different room where the galvanometer was stationed 
to receive it: hence the rectification of the needle by the volta-magnetometer 
should be effected beside the galvanometer. 

From what has been said, it is evident that the volta-magnetometer is only 
necessary when needles of exceeding sensibility are required. In ordinary 
cases, the method of magnetizing already described, or that commonly practised, 
is sufficient. 

Having now brought under notice the erroneous bearing which the com- 
pound needle is apt to assume, and the possibility of its being in error, even to 
the amount of 90°, when the deviation of one bar from the vertical plane of the 
other is so small as to be undiscoverable by the eye, it is obvious how bad a 


® 


the Construction of Galvanometers, Sc. 247 


guide such a needle is for determining the position of the galvanometer in order 
to render it fit for use. Yet, as hitherto made, we have no other means of setting 
the instrument in the magnetic meridian than to turn it round on its axis until 
the compound needle point north and south on the graduated circle. It is true 
that so great an error will only be possible when the needle is brought unusu- 
ally near the astatic state; but it will be considerable in proportion to the sensi- 
bility attained. The magnetic meridian line and compass needle, which I have 
added to the galvanometer, afford a protection against this source of fallacy. 

One immediate ill consequence of the error of the needle, should it exist 
undiscovered and uncorrected, is, that it affects those degrees of the circle 
which are of most value in delicate galvanometry. The first twenty degrees are 
in the direct ratio of the deflecting force, which no other degrees on the circle 
are. The effect of terrestrial magnetism is as the sine of the angle comprised 
between the magnetic meridian and the magnetic axis of the needle on which 
it acts. The sine of 20° is as nearly as possible double the sine of 10°; but 
beyond 20° the virtual ratio cannot be determined without submitting each 
particular galvanometer to an experimental investigation. A nd more than this, 
if the experimenter shall have taken the trouble of ascertaining the value of 
the degrees above the twentieth, by Mrttonr’s, or any other method, it will 
prove unavailing; for the whole scale of ratios of deflecting forces to angular 
deflections becomes deceptive if the magnetic meridian line of the galvanometer 
do not correspond with the terrestrial magnetic meridian. When the instru- 
ment is used as a galvanoscope, a small error is perhaps of little consequence, 
except that it causes the needle to represent deflecting forces weaker or stronger 
than they really are; but when it is used as a measure of heat, and for some 
other nice purposes, a want of coincidence between the magnetic meridian of 
the instrument and the terrestrial magnetic meridian would be productive 
of serious error. It is therefore evident how useful is the addition of the 
magnetic meridian line, with its point and compass needle, for setting the gal- 
vanometer due north and south: it at once detects the error of the astatic needle, 
if such exist. 

On the subject of the coil, it may be proper to mention that, although it is 
often made of copper wire covered with cotton, such a covering is altogether 
unfit. I have observed that one of my galvanometers, which is furnished 


* 


248 Mr. Micuart Donovan on certain Improvements in 


with a cotton-covered coil, although sometimes as sensible as most others, 
often becomes singularly otherwise. On such occasions, it will not be affected 
by a thermo-electric current generated by the heat of the fingers on two wires, 
bismuth and antimony, soldered together, which at another time would move 
the same needle 60° or 80°. I have not been able to connect these failures 
with any particular states of the weather, although such states may be the cause, 
acting perhaps on the hygrometric properties of the cotton. Coils covered with 
silk are not subject to this uncertainty in their action. 

As silver is said to be the best of all conductors of electricity, it might be 
supposed that the wire of the coil should be of that metal. I made compara- 
tive trials of silver and copper coils, each resembling the other in every respect 
except the metal. JI could perceive no decided difference in their effects, but 
imagined the copper to have some little advantage, and therefore adopted it. 
The difficulty of covering pure silver wire with silk is, as lam informed, great; 
and this, along with the cost of the silver, made a difference in the total cost of 
the galvanometer of more than £3. The advantage, if there be any, is certainly 
not commensurate. 

I conceive that, in the generality of galvanometers, the coil and its frame are 
too narrow: there is certainly an advantage in having them so broad that they 
extend on each side nearly to the whole diameter of the graduated circle which 
covers them. 

To conclude:—the improvements in the construction of galvanometers, 
here suggested, may be summed up as follow:—1. The addition of means, in- 
dependent of the astatic needle (which may greatly err), for setting the instru- 
ment in the magnetic meridian. 2. The close approximation of the needles to the 
coil. 3. The removal of obstructions to the rotation of the needle. 4. The 
means of inducing in the bars of the needle the least difference of polarity that 
is consistent with their function. 5. A method of detecting and preventing 
derangement of the needle arising from forces which cause in it a tendency 
to stand transversely to its true position. 6. A construction of the needle 
which renders available the operation of a strong or a weak directive force, as 
may be required. 7. The introduction of a controlling graduated magnetic 
power for increasing or diminishing the deflecting influence of voltaic forces on 
the needles. 


the Construction of Galvanometers, §c. 249 


I venture to hope that these improvements, along with the several adjust- 
ments and facilities added, will render the instrument more convenient, will 
increase its sensibility, and contribute to the accuracy of its indications. 

Some persons may conceive that the sensibility, to attain which I have taken 
so much trouble, is practically redundant. I can only say that I have expe- 
rienced the absolute necessity of the arrangement described, during my late 
investigation of the laws of tribothermo-electricity, some of which would have 
remained unknown but for the excellence of the galvanometer made use of. I 
need not again refer to the delicacy required for thermometrical experiments. 


NOME: 


I extract from the Proceedings of the Academy the following observations on this com- 
munication, made by the Rey. Dr. Luoyn, President: 

‘“« The President observed, that all the facts respecting the position of equilibrium of 
the astatic needle, to which Mr. Donovan had directed the attention of the Academy, and 
which (as far as he was aware) he has been the first to notice, were immediate consequences 
of theoretical laws. 

“ When two magnetic needles are united by a fixed vertical axis passing through 
their centres, and perpendicular to both, the moment of the force exerted by the earth 
upon them is the sum of the moments which it exerts upon each needle separately, and is, 
therefore, 

X (Msinu+ M' sin v’); 
in which M and M’ denote the magnetic moments of the two needles, u and w the angles 
which their magnetic axes make with the magnetic meridian, and X the horizontal compo- 
nent of the earth’s magnetic force. In the state of equilibrium this moment is nothing; so 
that if w) and uw’ denote the corresponding values of u and w’, there is 


M sin uy + M’ sin uy = 0. (1) 


Consequently, if two lines be taken from any point of the vertical axis, parallel to the 
magnetic axes of the two needles, and proportional to their magnetic moments, JJ and MW’, 
the diagonal of the parallelogram constructed upon them must lie in the magnetic meridian, 
when the compound needle is at rest. 

“« Again, if we substitute w= uo+v, w =u + v, in the general expression of the statical 
moment, it becomes, in virtue of (1), 


X (I cos uo + M’ cos up) sin v 


250 Mr. Micuaret Donovan on Improvements in Galvanometers, Se. 


Hence the compound needle is acted upon as a single needle, whose magnetic awis lies in 
the direction of the diagonal of the parallelogram above mentioned, and whose magnetic 
moment is 

w= cos up + M’ cos uy. (2) 
Accordingly, the diagonal of the parallelogram already referred to will represent in mag- 
nitude the magnetic moment of the compound needle. For, if the equations (1) and (2) be 
squared, and added together, and the angle contained by the magnetic axes of the two 
needles, w — uo, be denoted by a, we have 


w= MP + 2MM cos a+ M”. (3) 


“Tn the case of the astatic needle, a = 180 - 6, 6 being a very small angle, and 
cos a= — cos 0=—1+ 40%, g.p. whence 


w2 = (M- MV)? + MM'®. (4) 


Accordingly, whem M = M’is not a very small quantity, the second term may be neglected 
in comparison with the first, and «= M—- M’, nearly. On the other hand, when M- W=0, 
we have pp = Mo. 
“ Returning to (1), and substituting for w, its value, up + a, we have 
—sina 
tan Uo = em | (5) 
— + cos 
Te og 
by which the position of the needle with respect to the magnetic meridian, when at rest, 
is determined. In the case of the astatic needle the preceding equation becomes 


tan Up = a ésin lL’. (6) 
From this we learn, 

“1. That the tangent of the angle of deviation of the astatic needle from the magnetic 
meridian varies, ceteris paribus, as the angle 6, contained by the magnetic axes of the two 
component needles. 

«2. That, however small that angle be, provided it be of finite magnitude, the tangent 
of the deviation may be rendered as great as we please, and therefore the deviation be 
made to approach to 90°as nearly as we please, by diminishing the difference of the moments 


of the two needles.” 


251 


XI.—On the Original and Actual Fluidity of the Earth and Planets. By the 
Rev. Samuet Havucuton, M. A., Fellow of Trinity College, and Professor 
of Geology in the University of Dublin. 


Read May 12, 1851. 


THE communication which is here offered to the Academy contains a brief 
examination of the three following questions: 

1st. Whether the nebular hypothesis of Lapnace affords an explanation 
of the equality of the mean movements of rotation and revolution of the moon 
and other satellites. 

2nd. Whether the evidence of the original fluidity of the earth and 
planets, afforded by their observed figures, is satisfactory with respect to all the 
planets. 

3rd. Whether we possess, from the data afforded by astronomy, sufficient 
knowledge of the structure of the interior of the earth to enable us to draw 
conclusions respecting it, which are of geological value. 

The answer which I have given to each of these questions is in the nega- 
tive, and the object I have had in view in offering this communication will be 
accomplished, if it should in any way assist inquirers in estimating at their 
just value speculations relating to the original condition of the earth. The im- 
portance of such speculations has been, I believe, greatly overrated, and they 
have been too readily applied to the explanation of some geological facts, for 
which other and more probable causes can be assigned; such as the changes 
of climate which have taken place on the surface of the earth, and the increase 
of temperature as we descend below its surface. I have, therefore, examined 
these questions with the view of proving that, if we confine ourselves to the 
facts which we certainly know respecting the earth and planets, neither the ne- 
bular hypothesis, nor the hypothesis of the internal fluidity of the earth, is 
entitled to take a place in the list of positive facts. 

VOL. XXII. 21L 


252 The Rev. SamurL Haucuton on the 


I.—On the Physical Cause of the Equality of the Mean Angular Movement of 
Revolution and Rotation of the Moon and other Satellites. 


The exact equality which exists between the mean angular motion of revo- 
lution and rotation of the moon has given rise to many investigations and specu- 
lations as to its physical cause. The French Academy of Sciences proposed as 
the subject for a prize essay, in 1764, the theory of the Libration of the 
Moon. This prize was obtained by Lacrancr, who showed, that if there 
were in the beginning a very small difference between the movements of revolu- 
tion and rotation of the moon, the attraction of the earth would be sufficient to 
establish a rigorous equality between these motions. Lapxacg, in his Systeme 
du Monde, p. 472,* has made some remarks on the physical cause of this re- 
markable phenomenon, which is not peculiar to the moon, but has been proved to 
exist in the case of the four satellites of Jupiter, and the eighth satellite of Saturn; 
according to him, there must have been some physical cause which first brought 
the difference between the angular motions of revolution and rotation of the 
satellites within the narrow limits, in which the attraction of the planet could 
establish their perfect equality; and subsequently the libration caused by the 
establishment of this exact equality must have been destroyed by the operation 
of the same cause, at least in the case of the moon, since the observations of 
Mayer, Bouvarp, and Nicotter have proved that no such libration now ex- 
ists in that satellite. A physical cause capable of producing both these effects, 
Laptace believed might be found in the nebular hypothesis proposed by him- 
self to account for other remarkable phenomena of the planetary system, such 
as the movement of the planets in the same direction, and nearly in the same 
plane; the movement of the satellites in the same direction as that of the 
planets; the movement of rotation of these different bodies, and of the sun, 
in the same direction as their movement of revolution, and in planes nearly 
the same; and the small eccentricity of the orbits of the planets and satellites. 
According to this hypothesis, the moon, when existing in a gaseous condition, 


* Vid. note. 


Original and Actual Fluidity of the Earth and Planets. 253 


would, by the powerful attraction of the earth, be forced to assume the 
form of an ellipsoid of unequal axes, having its longest diameter directed 
towards the earth; the terrestrial attraction continuing to operate in the same 
direction, must, according to the theory, have at length, by approximating the 
movements of revolution and rotation, brought their difference within the limits 
in which an exact equality would begin to be established; the libration pro- 
duced in the greatest axis of the moon in this manner must have been subse- 
quently destroyed by the internal friction of its particles, and thus the singular ap- 
pearance produced of an exact equality between the angular motions of revolution 
and rotation. The illustrious author of the nebular hypothesis having thus ex- 
plained by means of his theory this remarkable fact, proceeds to apply it to the 
explanation of the relation which exists between the mean motions of revolution 
of the first three satellites of Jupiter. Into this further application of the 
theory it is not my intention to inquire, as the facts may be accounted for by 
friction ab eatra, acting on the satellites, the existence of which may be readily 
admitted without adopting the nebular hypothesis. But with reference to the 
explanation offered by Lapxace, of the equality of the movements of revolution 
and rotation of the six satellites whose time of rotation has been observed, it ap- 
pears to be natural to inquire, whether the explanation does not prove too much, 
and whether it would not apply equally well to establish the equality of the 
motions of revolution and rotation of the planets. Unless, in fact, it.can be 
shown, that the physical cause assigned for the explanation of the fact relating 
to the satellites operated upon those bodies more powerfully than upon the 
planets, the explanation cannot be admitted; for it will be granted, that the 
attraction of the sun must, on the nebular hypothesis, have operated in the same 
manner on the planets, as the attraction of the latter on their satellites. The 
question is therefore one of degree, and not of kind, for the same cause operated 
in both cases. With the view of ascertaining whether the cause assigned by 
Lapiace acted more powerfully on the satellites than on the planets, I have 
made the following calculations. 

I shall commence by investigating the figure of a planet, supposed homo- 
geneous and gaseous, revolving on its axis and round the central body in the 
same time and in the same plane; it is easy to prove that the conditions of 
equilibrium are satisfied by its surface assuming the figure of an ellipsoid with 

2L 2 


254 The Rev. Samurt Haucuton on the 


three unequal diameters, the least being the axis of revolution, and the greatest 
being directed towards the central body. 
The components of attraction of the fluid mass upon a particle at its sur- 
face* are 
Ag Dy. azrs 
where 


_ 3Mf PRE HID. aM el I. fay GIP 
Sa oni a oi elcome aE ce 


M denoting the mass of the fluid, a the least semi-axis of the ellipsoid, f the 
dynamical measure of attraction of two units of mass at the unit-distance, 

ae { udu 
a V1 +r 1 + ru?’ 


2 2 2 
wa va4 n? C—a 
a a ’ a 


? 


the equation of the ellipsoid being 


2 2 2 
Let the axis of rotation be the axis of x, and the axis of y be directed towards 
the central body ; if w denote the distance from the centre of the sun to any 
particle of the planet, 6 the distance between the centres of the sun and planet, 
E the mass of the central body, and » the angular velocity; it is easy to see that 
the equation of the surface, deduced from hydrostatical principles, will be 


(4 +5) ada + (By AY _ ay) dy + (c- 044) ede=0; 


but, neglecting small quantities, 


BAF (14%), oa 220-0 2) 


3 33 = 


uw 6 e uw ae 


therefore, the equation of the surface becomes 


* Vid. Dunamet, “Cours de Mecanique,” Tom. t. p. 198. 


Original and Actual Fluidity of the Earth and Planets. 255 


(4 +4) ode + (B— = = o) ydy + (c —s o) zdz=0. 


Combining this with the assumed equation, 


ada, ydy , zdz _ ; 


aoe 7 


we find the following equations of condition, 
EH E 
A a = (1+A") (+5 - w); 


Vig Lea gia (p- 4 -«). 


e 
Substituting in these the values of A, B, C, and making 


E a wae 
36 =a 3s jl’ 
we obtain 
oe 
L+p=(1tn) (“RA ag-2); 


(1) 
L+g=(1 +n) (SS — 26-2). 


But since @ = 8, by the third law of Keprer, equations (1) become simply 


d.NL 


L+go=(1 +r"), 


(4) 
L+o=(1+%') (“<- 39). 


If the definite integral Z be expanded, it becomes 


laafd ASAE (lind MENA +0 BANA 
L=5-(G. 5 ) Ga Ti vit 222 +) ~ &e., 


substituting this value in (2), and neglecting quantities higher than A’, A’, we 
find, 
ABO ies so A= Aas 


256 The Rev. Samuret Haucuton on the 


or if e, e, denote the ellipticities of the principal sections, passing through the 
greatest and least diameter, and mean and least, respectively; since A’ = 2e, 
A” = 2e, we obtain finally for the ellipticities of the principal sections 

e=5 oS, ps ahs (3) 

M® 4° M8 

from which it appears that the ellipticity of the section passing through the 
greatest and least diameters is four times greater than the ellipticity of the sec- 
tion passing through the mean and least diameters. 

If the planet be supposed to revolve on its axis with an angular rotation 
different from that of its revolution round the central body, the equality @ = 
will no longer subsist, and we should therefore use equations (1) to determine 
the ellipticities of the principal sections. The result is 


cal (Bpts) catia (4) 


@ and g being the quantities already defined, and depending on the central 
body and rotation of the planet respectively. If the central body be supposed 
so remote as to produce no effect on the figure of the planet, then ¢=0, which 
renders the ellipticities equal, and corresponds to the figure of revolution as- 
sumed by the planet, if acted on only by its own attraction, and the centrifugal 
force caused by its rotation.* If, therefore, we suppose the spheroid of revolution, 
whose ellipticity is e=14,° 2, described, having the axis of rotation for its least 
diameter, the effect produced by the attraction of the central body will be 
measured by the shape and magnitude of the couche included between this 
spheroid of rotation and the ellipsoid which forms the actual surface of the 
planet. The friction between this couche and the interior spheroid, which 
would constitute the surface of the planet, if the central body ceased to exist, 
will tend to render the motions of rotation and revolution of the planet equal 
to each other, and when the difference of these motions has fallen within the 
narrow limits indicated by analysis, will destroy the libration produced by 
the action of the central body in rendering those motions exactly equal. It 
may be proved by simple geometrical considerations, that if the planet separates 
from the central body, as a nodular or annular mass, without much friction, that 


* Vid. Potsson, ‘‘ Traité de Mecanique,” Tom. 1. p. 544. 


Original and Actual Fluidity of the Earth and Planets. 257 


its times of rotation and revolution at the period of separation will be nearly 
equal; and since we have no reason to assume any difference in the mode 
in which the planets and satellites were thrown off from the central mass, we 
may suppose, in order to render our calculations possible, that at the period 
of separation, the movements of rotation and revolution were so nearly equal 
as to justify us in using equations (3) instead of (4). Equations (4) might be 
used as well as (3), but require an additional hypothesis as to the time of ro- 
tation of the planet; but as this hypothesis should be the same for the planets 
and satellites, the generality of the reasoning is not affected by the use of equa- 
tions (3). In these equations, the only quantity which is unknown is a, the 
radius of the planet or satellite at the time of its separation. We may obtain a 
value for a, in terms of the actual radius of the planet and its past and present 
moments of inertia, by the ordinary principles of mechanics; andif we as- 
sume as the measure of contraction of each planet the ratio which its original 
time of rotation bears to its actual time of rotation, we can calculate the value 
of e and é’ for each planet and satellite. It will be shown afterwards, that the 
amount of contraction thus assumed is much too small for the planets which 
are attended with satellites, and probably for all the planets; but it will be 
useful to make the calculation upon this supposition in the first instance. 

Let 7, J denote the former and present moment of inertia of the planet, sup- 
posed homogeneous; a, a, its former and present radius, and m the number of 
rotations contained in one revolution; then 


TS CSRs E377) Sle 
therefore, 
SEVER AD Ole 


or, 


a te), n: 
and substituting this value in (3), we find 
La . : 
c= 5705 Ne (5) 


The data from which I have calculated the values of ¢ corresponding to each 
planet and satellite are contained in the following Tables. 


The Rey. Samuget Havcuton on the 


Taste I.* 
SATELLITES. n a:d E:M € 
2153 1 
Moon,.....-- 1:00 7926 x 59-964 87-73 24524 
2508 1000000000 1 
Ist, . | 1:00 87 x 6048 17328 32-00 
2068 1000000000 1 
Satellites of 22% - | 1°00 87 x 9623 23235 308 32 
Fd 3377 1000000000 1 
Bee aE | Sedencsjele00 87 x 15350 38497 1094-5 
2890 1000000000 1 
4th, .| 1:00 87 x 26998 42659 45803 


PLANETS. 


Taste II.* 


Mercury, 


Venus, 


Jupiter, 


Saturn, 


Uranus, 


3140 
190 x 387098 
7800 
190 x 723331 
7926 
190000000 
4100 
190 x 1523692 
87000 
190 x 5202776 
79160 
190 x 9538786 
34500 


190 x 19182590 


4865751 


401839 


389551 


2680337 


1047871 


3501-600 


24905 


1 
36082 
1 
103970 
1 
205121 
1 
529573 
1 
1084480 
1 
1589015 
1 


11029750 


* The figures contained in the first three columns of Table I. are taken from the third edition 
of Sir Joun F. W. Herscuev’s Astronomy, pp. 331, 649, 650. The corresponding figures of 
Table II. are calculated from the Tables of the same book, pp. 647, 648. 


Original and Actual F. luidity of the Earth and Planets. 259 


From the foregoing Tables, it would appear that the effect of the planets in 
elongating the figures of their satellites was greater than the effect of the Sun 
upon the planets; and so far the conclusion to be drawn from the calculation 
accords with the idea of Larracr. But a slight consideration will show that 
the amount of contraction assigned to the planets is much too small. In fact, 
we are entitled by the nebular hypothesis to assume that each planet, at the 
time of its separation, extended at least as far as the orbit of its most distant 
satellite; this consideration supplies us with another and safer measure of the 
contraction of those planets which have satellites. 

The following Table contains the values of ,/n, which express the amount 
of contraction used in Tables L and II., and also the value of the ellipticity of 
each planet, supposed homogeneous and extending to the orbit of its outermost 
satellite. 

Taste III. 


7926 x 59-964 
190000000 


87000 x 26-998 
— es 
190 x 5202776 
79160 x 64-359 
190 x 9538786 
34500 x 22-8* 
190 x 19182390 


Uranus, . .. 


From the first column of this Table, it appears that the original radius of 
the planets used in Tables I. and IL. in no case exceeded ten times the present 
radius, which is too small for the planets with satellites, especially the Earth and 
Saturn, and probably too small for all the other planets. From a comparison 


* These figures refer to the fourth satellite. 
VOL. XXII. 2M 


260 The Rev. Samuret Haucuron on the 


of the ellipticities in Tables I., II., III., we are led to infer that the action of 
the Sun in elongating Jupiter, and so by internal friction causing his move- 
ments of rotation and revolution to become equal, was much less powerful than 
the corresponding action of Jupiter upon his satellites ; hence the physical cause 
assigned by Larace for this equality may be admitted in the case of Jupiter’s 
satellites. But this conclusion will not apply to the Earth. From Table IL. it 
appears, that the elongating action of the Earth upon the Moon is represented 
by the fraction g¢45y; while Table III. shows that the similar action of the 
Sun upon the Earth is represented by the fraction 35-494 - 

Before quitting this subject it may be useful to consider the various expla- 
nations which might be offered to explain the difficulty which undoubtedly 
exists in the case of the Earth and Moon. 

We are not at liberty to assume that the planets separated from the central 
mass as annuli, and the satellites as nodules, which would give to the planets a 
quicker rotation than to the satellites. In this case s >, and therefore e < 4’; 
hence the couche, on the friction of which the effect in question depends, would 
be less for the planets, ceteris paribus, than for the satellites. But this assump- 
tion is not admissible, since the only annuli with which we are acquainted 
in the solar system occur among the satellites. Neither are we at liberty to 
assume greater friction among the particles of the satellites than of the planets, 
for, according to the nebular hypothesis, they are probably composed of the same 
materials. It is possible to explain the difficulty by assuming a sufficient amount 
of contraction in the Moon. It is, in fact, easy to prove that the effect of the 
Earth upon the Moon would be equal to that of the Sun upon the Earth and 
Moon, supposed to extend as far as the orbit of the Moon, provided the Moon 
extended to a distance represented by the equation 


é a 
== 24;322;, OF, == 9:076; 
a a 


and this amount of contraction is physically possible, since it is less than the 
distance from the Moon at which a particle would be equally attracted by 
the Moon and Earth. But how are we to reconcile this amount of contraction 
with the observed facts, without tacitly assuming that the internal friction of the 
Moon, supposed fluid, was greater than that of the Earth ; an assumption which 
is purely arbitrary, and made to explain the difficulty. 


Original and Actual Fluidity of the Earth and Planets. 261 


There remains one real difference between the case of the planets and satel- 
lites, which, so far as it operates, is a vera causa, and acts in the direction required. 
The effect of the internal friction in destroying the increment of angular velo- 
city must be greater in proportion as the mass of the planet or satellite is less; 
as we observe small rivers more retarded by the friction of their bed than large 
rivers. But it may be doubted whether this cause is sufficient to account for 
the remarkable difference which exists between the planets and satellites. 

The conclusion which the foregoing calculations appear to warrant us in 
drawing is the following: that the nebular hypothesis does not explain the 
equality of the mean movements of revolution and rotation of the satellites, 
although it cannot be said to be absolutely inconsistent with it. 


Il.—Fiigqure of the Earth and Planets. 


It is well known that on the hypothesis of the original fluidity of the planets, 
it is necessary that the ellipticity of each planet should lie between two limits, 
which are, respectively, five-fourths and one-half of the fraction which expresses 
the ratio of centrifugal force to gravity at the surface of each planet ;* the first 
or major limit corresponding to the case of homogeneity, and the second or 
minor limit corresponding to the case of infinite density at the centre. It is 
possible to compare this theory with observation in the case of five planets and 
the Moon. In the following Table, m denotes the ratio of centrifugal force to 
gravity at the surface of each planet, gravity being expressed in feet, and cal- 
culated from the formula 

2 
G= es : (6) 
in which G',g, denote gravity on the surface of the planet and Earth respectively; 
P, E, the masses of the planet and Earth; £,r, the radii of the Earth and planet. 
The centrifugal force at the equator of each planet is calculated from the ordinary 
formula 


fe 
f= 4 i 


in which r is expressed in feet, and 7, the time of rotation, in seconds. 


* CiairauT, Figure de la Terre, p. 294, 


2m 2 


262 The Rev. Samuet Haucuron on the 


Taste IV. 


Observed Ellipticity. 
Centrifugal | Minor Limit, | Major Limit, Sere Te aeny: 


Force. gm 


PLANETS. 
Observer. 


Earth, ... say Bessel. 

W. Herschel.* 
Mars,... 
Arago.t 


Jupiter, . . ; 5 Arago.} 


Saturn,... | : —— — “—— W. Herschel. § 


Uranus, . . <> <i> — Midler. 


On comparing the observed ellipticities with the limits calculated in the 
preceding Table, it appears that the ellipticity of Mars exceeds the major limit 
admissible on the fluid hypothesis; the inference from which fact is, either 
that gravity is not perpendicular to the surface of Mars, or that his interior 
structure is not that which would be assumed bya fluid body. The first of these 
suppositions appears inadmissible from the fact, that there is reason to believe, 
that there are degrading and disintegrating forces at work on the surface of that 
planet, similar to those now in operation on the Earth, and which would render 
the surface perpendicular to gravity, if not so originally. The second suppo- 
sition would appear to be inconsistent with the idea that Mars derived his pre- 
sent figure from having been originally fluid; at least, we are scarcely justified 


* Transactions of Royal Society of London, for the year 1784. The ratio of the axes of the 
planet Mars, deduced from observation, is 1355 : 1272. 

+ Exposition du Systeme du Monde, p. 37. The ratio of axes deduced from observation by 
AraGo is 194: 189. 

+ Exposition du Systeme du Monde, p. 39. ‘The ratio of axes is 177: 167. 

§ Transactions of Royal Society of London, for the year 1790. The ratio of axes is 2281 : 2061. 


Original and Actual Fluidity of the Earth and Planets. 263 


in assuming the original fluidity of all the planets, when there exists so re- 
markable an exception in the case of the planet Mars.* 


III.—On the Structure of the Earth, supposed partly Fluid and partly Solid. 


In the following investigation I shall suppose the Earth composed of ellip- 
tical couches of small ellipticity, the density of each couche being constant and 
a function of its distance from the centre. The surfaces bounding the couches 
’ must be perpendicular to the resultant of the forces acting upon the particles 
composing them, in the parts of the Earth which are supposed fluid, and also 
at the boundary between the solid and fluid parts, since the friction of the fluid 
would render the bounding surface perpendicular to the resultant, if not so ori- 
ginally. The only external forces supposed to act upon the particles are the 
centrifugal forces arising from the earth’s rotation. 

The condition that any surface bounding one of the couches of equal density 
should be perpendicular to gravity is contained in the following equation : 


const = V + N, (7) 
in which V is the potential of the earth, and 
i N= zo? —_ Swe ; (8) 


r denoting the radius of the surface, w the angular velocity, and g = cos’@ — - 
@ being the angle contained between the radius vector and the axis of rotation.t 
The potential contained in (7) is composed of two parts, one relating to the 
couches inside the surface considered, and the other to the couches outside the 
same surface. The value of the potential of a body constituted as we have 
supposed the earth, on an external point, is, 


* It has been remarked by Larrace (Mec. Cel. Tom. 1. p. 370, and Tom. v. p. 287), that the 
ellipticities of the principal sections of the Moon, deduced from the moments of inertia obtained by 
the observations of Topras Mayer and Nicoter, are nearly ;,>, and ;;+,, and that both these 
ellipticities are greater than those of the figure of the Moon, if supposed fluid and homogeneous, 
which would give the maximum ellipticity. We have, therefore, in the Moon a case similar to 
Mars, viz., the actual ellipticity is greater than the major limit of the fluid hypothesis; but it is 
easier to admit that gravity is not perpendicular to the surface in the case of the Moon. 

+ Mec. Celeste, Tom. 1. p. 66. 


264 The Rev. SamurL HaucGutTon on the 


v= 


milli Sho (9) 
r br da 
in which p is the density of any couche, a the radius of its equi-capacious sphere, 
and ¢ its ellipticity. 
The potential of a shell composed of couches arranged in the manner sup- 
posed, on an internal point, is, 


A4nr’s( de 

_ at | | eal 
V=4nfpa 5 Jea- (10) 
The radius vector of the surface of each couche is given by the following equation, 
r=a(l—es); (11) 


from which may be deduced the values of the equatorial and polar axes, viz., 
a(1 +e), and a(1- 2). Substituting from the foregoing equations in (7), 
we find 


d.ae 
const = = (14+ es) p 3 «(oS 
14 fi F, 4na* e|" de Ana? fi de 
” AP 5 Pda Dae if da 
4na?m i o Sram. (eg 
* 3a° ~~ gas :| y 


a denoting the mean radius of the external surface, a, the mean radius of the 
internal surface of the shell supposed solid, and m the ratio of centrifugal force 
to gravity at the equator. This equation consists of two parts, one independent 
of s, which is satisfied by means of the constant; the second, which is the coef- 
ficient of s, gives the condition, 

Grn i (doa oP ae oan j 

= ag — —— —. — — —_—- — ar == (0) 12 

cl vale da 5 fe da  2a° Ai (=) 
This equation expresses the fact, that each fluid surface is perpendicular to the 
resultant of all the forces acting upon the particles composing it. 

Differentiating this equation, so as to banish the integrals, we obtain, 


2 9 2 3 
ae ee eo (1- Be )=0. (13) 


da je pa? da a 3 ("pa 
0 0 


Original and Actual Fluidity of the Earth and Planets. 265 


This equation is identical with that derived from the supposition that the 
Earth is completely fluid, and is therefore independent of the law of density and 
ellipticity of the solid parts of the Earth; it determines the relation which neces- 
sarily exists between the law of density and ellipticity of the fluid portions of the 
Earth. If the law of density of the fluid parts be given, the integral of this dif- 
ferential equation will give the law of ellipticity, involving two constants, one 
of which is determined by the condition that the density does not become infi- 
nite at the centre, and the other constant may be expressed in terms of the 
ellipticity of the surface which bounds the fluid. If we suppose that there is 
a fluid nucleus inside the Earth, whose radius is a,, and ellipticity 4, equation 
(12) will give for the bounding surface of the nucleus the following, 


14 
Pda 2a A She 
If, also, we assume, as we may in the case of the Earth, that the external 
surface is perpendicular to gravity, equation (12) may be applied to this sur- 
face, although not fluid. Hence we obtain, 


[ee = (2e—m) a pat (15) 


Equations (14) and (15) assert, respectively, that the inner and outer sur- 
faces of the solid shell are perpendicular to gravity. 

In the case of the Earth, the integral at the right-hand side of these equa- 
tions is known, because the mean density of the Earth is known. The integral 
at the left-hand side of equation (15) is also known; since it may be expressed in 
terms of the difference of the moments of inertia with respect to the polar and 
equatorial axes, which is given by the inequalities of the Moon’s motion pro- 
duced by the structure of the Earth, or by the phenomena of precession and 
nutation, which are produced by the same cause. In fact, if C, A denote the 
moments of inertia with respect to the polar and equatorial axis respectively, 


& fp ; 1 ir d.a’e - Fle de_ ma , 
a, Jo 5a} ts da | 


8x (* d.ave 
ae . 6 
Jom (16) 
Also the first and second integrals, on the left-hand side of equation (14) are 
known from the differential equation (13), if we assume the law of density 
of the fluid parts to be known. 


266 The Rey. Samuget HauGutTon on the 


There remains, however, the third imtegral on the left-hand side of (14), 
which cannot be known without assuming a law of density and also of ellipti- 
city for the solid portion of the Earth. 

We are thus led to the conclusion, that it is necessary to assume three hy- 
potheses with respect to the internal structure of the Earth, before we can be in 
a position to assert how far it is solid and how far fluid. The three necessary 
hypotheses are: —Ist. The law of density of the fluid parts. 2nd. The law of 
density of the solid parts. 3rd. The law of ellipticity of the solid parts. 

If we suppose that these are given, then equations (14), (15) will become, 


F'(a,a,, 64, m)=0; 


J (a, a, & 41, m) = 0; 


(17) 


in which F, f denote known functions. In these equations a, e, m are known, 
and a, «|, are determined by the equations themselves. 

If we suppose that the fluid parts of the earth are bounded on both surfaces 
by solids, we should then have three equations, analogous to (14) and (15). be- 
longing to the two surfaces of the fluid, and to the external surface respectively. 
From these, assuming the law of density of the fluid, and of density and ellipti- 
city of the solid parts, we should obtain 


@M (A, 2, Ao, & &, &, m) ='0!- 
Exe (a, 4, Bo, € &, &, m) =e (18) 
W (a, 1, Ao, €, &, €, m) =e 


a,, « being the radius and ellipticity of the second surface of the fluid. In 
equations (18), as before, a, e, m are known; but the number of unknown 
quantities is greater than the number of equations, the unknown quantities 
being four, viz., @, &, &, €, while there are only three equations. The pro- 
blem is therefore not so definite as the last, and requires an additional hypo- 
thesis. 

Confining our attention to the simplest case (17), we see that before a 
single step can be made towards using equations (14) and (15), we must as- 
sume three laws, respecting facts of which we have no certain knowledge, 
and probably never shall. The subject would thus appear to be excluded 


Original and Actual Fluidity of the Earth and Planets. 267 


from the domain of positive science, and to possess an interest for the mathe- 
matician alone. 

I shall conclude this investigation by examining the structure of the Earth 
on the simple but improbable hypothesis of homogeneity, and by determining 
how far the density belonging to the rocks of the surface may extend to the 
materials composing the interior of the Earth. 

If the Earth be supposed to be composed of a solid shell, having the density 
of the rocks at its surface, and of a fluid homogeneous nucleus, equations (14) 
and (15) will become 


2 3 m 
pa — om (ea) = A™, (19) 
and 
6 
: |Poe® + (p—p,) 48} = (2e—m) Aa’; (20) 


5 
in which p, signifies the density of the rocks of the shell, p the density of the 
nucleus, and A the mean density of the whole Earth. To equations (19) and 


(20) must be added the following, which expresses that the mass of the Earth 
is equal to the sum of the masses of its shell and nucleus. 


a’ 
P — Po = (A—p) 55- (21) 
1 
Eliminating p from (19) and (20) by means of (21), they become respectively 
% a’ 3 m 
F{m+(A—p)apa-ga(e-a=a (22) 
and 
6 a? a? 
Bncmt (Anat =(e—mas (23) 


In the case of the Earth A = 2p,; substituting this value of the mean den- 
sity, and solving equations (22) and (23) with respect to ¢, we find 
_ 5m + 3e_ 
~ 5 + 29%’ 


€ 


(24) 


7Je— 5m 
ES pr aa wee (25) 


: Le a 
¢ being used to denote the fraction z 
1 


VOL. XXII. 2N 


268 The Rev. SamurL Haucuton on the 


These are the equations which correspond, on the supposition of homoge- 
neity, to the equations (17). Equating the values of ¢,, we obtain the following 


equation to determine ¢: 
5m + de 


5 te 
AD eRe 


(26) 
Substituting in this equation for m and e their values in the case of the Earth, 
viz., seo and s50) we find, 

2h? + 5p? = 1357743. (27) 


Applying Sturm’s theorem to this equation, it is easy to prove that it has only 
one real root, which lies between @=1 and @=2. The numerical value of 
this root is 
Hee 1:2407 
are OS PG 
Hence, since a = 3958 miles; a,= 3190 miles, and 
a — a, = 768 miles. (28) 


This is the thickness of the earth’s crust, on the hypothesis that both the crust 
and nucleus are homogeneous, and the surfaces of both perpendicular to gravity. 
I shall now prove that this thickness of crust is a major limit to the depth 
to which the density of the rocks at the surface can extend into the interior ; 
the density being supposed heterogeneous. 
The difference of the moments of inertia of the nucleus with respect to its 
polar and equatorial axis may be expressed as follows: 


C-A= 


Sapt:d.a°e 8 «G 
poe ==. pa 29 
isl? dz i5ee < C3) 


o denoting an unknown number, depending on the structure of the nucleus, and 
which, if the nucleus be supposed fluid, is greater than unity. 
Substituting from (29) in equations (14) and (15) we find 


Jalna 1 1 : 
a($- gx) mt (A=n)o—Zm(e—a)=z ams (80) 
and, 


Or] bo 


[r» (ed — 4) + {p+ (A—p.) ON] = 5A (2e—m) g (31) 


Original and Actual Fluidity of the Earth and Planets. 269 


Solving these equations with respect to ¢,, and making A= 2p, we find 


3 
m+re 


_ (te— 5m) 


Eliminating ¢, and solving for o, we find, 
1 _ (3¢°+ A) + 59" (¢' +1) (34) 
o (3¢°+A)(g> +1) ’ i 


: ; 5m + 3 
in which A = 3 oUF 
Te — 5m 


But the nucleus being supposed fluid, the denominator of the right-hand mem- 
ber of (34) is greater than its numerator; consequently we have the inequality 


. BD AoW BE - 
2¢? + 5b REI (35) 

The value @ = 1°2407 renders the left-hand member of (35) equal to the 
right, and therefore @ must be less than 1°2407, and, consequently, the depth 
to which the density of the surface extends is less than 768 miles. 

The results which have just been obtained are to be regarded merely as ex- 
amples of the manner in which equations (14) and (15) should be used, if we 
were acquainted with the laws of density and ellipticity of the fluid and solid 
parts of the Earth. So long as we are ignorant of these laws, we cannot calcu- 
late numerical values, and indeed the chief use of the investigation I have just 
given appears to be, to enable us to estimate at their just value speculations 
relating to the interior of the Earth, of whose real structure we are, and must 


remain, hopelessly ignorant. 


2n2 


270 The Rey. SamuEL Haucuton on the 


NOTES. 


No. L, referred to in page 252.—‘ Un des phénomenes les plus singuliers du systéme solaire, 
est Pégalité rigoureuse que l’on observe entre les mouvemens angulaires de rotation et de révo- 
lution de chaque satellite. Il y a l’infini contre un a parier qu’il n’est point l’effet du hasard. 
La théorie de la pesanteur universelle fait disparaitre l’infini, de cette invraisemblance, en nous 
montrant qu’il suffit pour l’existence du phénoméne, qu’a Vorigine, ces mouvemens aient été tres 
peu différens. Alors V’attraction de la planéte a établi entre eux, une parfaite égalité; mais en 
méme temps, elle a donné naissance a une oscillation périodique dans l’axe du satellite, dirigé 
vers la planéte, oscillation dont l’étendue dépend de la différence primitive des deux mouvemens. 
Les observations de Mayer sur la libration de la lune, et celles que MM. Bouvarp et NicoLLer 
viennent de faire sur le méme objet, 4 ma priére, n’ayant point fait reconnaitre cette oscillation, 
la différence dont elle dépend, doit étre trés petite; ce qui indique avec une extréme vraisem- 
blance, une cause spéciale qui d’abord a renfermé cette différence dans les limites fort resserrées 
ou Vattraction de la planéte a pu établir entre les mouvemens moyens de rotation et de révolution, 
une égalité rigoureuse, et qui ensuite a fini par détruire Voscillation que cette égalité a fait 
naitre. L’un et autre de ces effets résultent de notre hypothése; car on congoit que la lune a 
Pétat de vapeurs, formait par l’attraction puissante de la terre, un sphéroide allongé dont le grand 
axe devait étre dirigé sans cesse vers cette planéte, par la facilité avec laquelle les vapeurs cédent 
aux plus petites forces qui les animent. L’attraction terrestre continuant d’agir de la méme 
maniére, tant que la lune a été dans un état fluide, a da a la longue, en rapprochant sans cesse 
les deux mouvemens de ce satellite, faire tomber leur différence, dans les limites oX commence 4 
s’établir leur égalité rigoureuse. Ensuite, cette attraction a di anéantir peu a peu Voscillation 
que cette égalité a produite dans le grand axe du sphéroide, dirigé vers la terre. C’est ainsi que 
les fluides qui recouvrent cette planéte, ont détruit par leur frottement et par leur résistance, les 
oscillations primitives de son axe de rotation, qui maintenant n’est plus assujetti qu’a la nutation 
résultante des actions du soleil et de la lune. I] est facile de se convaincre que l’égalité des mouve- 
mens de rotation et de révolution des satellites a di mettre obstacle a la formation d’anneaux et de 
satellites secondaires, par les atmosphéres de ces corps. Aussi l’observation n’a-t-elle jusqu’a 
présent, rien indiqué de semblable.”—Lapiace, Eaposition du Systeme du Monde, pp. 472, 473. 


No. IL, added March 25, 1852.—Since the foregoing communication was offered to the 
Academy, I have become acquainted with Mr. HEnnEssey’s Researches in Terrestrial Physics, 
published by the Royal Society of London in the Philosophical Transactions, Part I]., for 1851. 
In these Researches, pp. 544, 545, Mr. HENNEssEY obtains numerical values for the major and 
minor limit of the thickness of the Earth’s crust, the interior being supposed fluid. These limits 
are 600 miles and 18 miles respectively. The first limit is obtained by assuming Lapnace’s law 
of density for the fluid nucleus of the Earth, and the same law for the solid shell, with an alteration 


Original and Actual Fluidity of the Earth and Planets. 271 


of the constants to correspond with the supposed alteration of density of the shell in passing from 
the fluid to the solid condition. As the hypotheses used to obtain this limit are arbitrary, the 
limit itself must be considered only as of the same value as the limit in equation (28), deduced 
from the improbable hypothesis of homogeneity in the shell and nucleus. The other limit is more 
interesting, being assumed to be a minor limit to the thickness of the Earth’s crust, and independent 
of the law of density of the interior. 

On a careful examination of the hypotheses on which the determination of this limit depends, 
I believe that it will be found, that one of them is inadmissible, and others arbitrary. If I under- 
stand Mr. Hennessey aright, the following are the statements from which he deduces his minor limit 
of the thickness of the Earth’s crust: 

Ist. The shell is homogeneous and of the density of the rocks at the surface. 


2nd. The shell is bounded by similar surfaces, whose ellipticity is a0 : 
3rd. The internal surface of the shell is perpendicular to gravity. 
4th. The external surface of the shell is not perpendicular to gravity, and its ellipticity, if it 
1 
were so, would be say 
The fourth of these statements appears to me to be inadmissible for the following reasons: the 


ellipticity of the surface perpendicular to gravity is assumed by Mr. Hennessey to be se which 


3 aires eli | 1 : she 
is a mean between the ellipticities pan and Bone deduced from the pendulum, and lunar inequalities,* 


but the ellipticity deduced from the lunar observations, 30° is identical with that deduced from the 


measurement of meridian arcs, and although there may be some chance in this agreement, yet it is 
sufficient to suggest the idea, that the surface of the Earth is rigorously perpendicular to gravity, 
and that the pendulum experiments are influenced by variations of local attraction, arising from 
variable density in the rocks, or from the position of land and water. Such are the usual explana- 
tions of the difference between the ellipticity obtained from the pendulum and that deduced from 
lunar observations; and unless some explanation be offered of the agreement between the ellip- 
ticity of the actual surface obtained from meridian arcs, and the ellipticity of the surface perpen- 
dicular to gravity deduced from the lunar inequalities, it is not allowable to assume, that the mean 
of the results of the pendulum and lunar observations gives the surface perpendicular to gravity. 
In fact, the observations of the pendulum and of the Moon should give exactly the same ellip- 
ticity, and would do so, were it not that the pendulum is liable to local variations, from which the 
other method is exempt; the result of the latter is, therefore, more trustworthy, and this result 
is almost identical with the ellipticity of the actual surface. It is certainly unphilosophic to take the 
mean of observations which differ more from each other than they differ from the quantity with 


* The figures here given are those adopted by Mr. Hennessey, and are probably as near the truth as any others which 


have been deduced. The ellipticity deducible from Saprve’s pendulum experiments is 


1 
304°1° 


1 
——j; and from Bouvagp, 
283°7 


Burcknarpt, aud Bure’s lunar observations, is 


(Mec. Cel., Tom. v. p. 45.) 


272 The Rev. SAMUEL HauGuHTon on the 


which we wish to compare them, and then to assume that the difference between the mean so found 


and that quantity is a real difference. 
Adopting the four hypotheses above mentioned, Mr. Hennessey has deduced from his formule 


the following value for the ratio of the radius of the nucleus to the radius of the exterior surface, 
p. 545; 


5 
2 147-O 
Gems ae : (1) 
qi ae 


In this equation a, denotes the ratio of the radius of the nucleus to the radius of the external sur- 
face, which is assumed equal to unity; m= >= 1s the ratio of centrifugal force to gravity at equa- 


= 0 is the ellipticity of the actual surface of the Earth; and (e) = saz(the mean of the frac- 
tions = and a , obtained from the pendulum and lunar observations), is theellipticity of thesurface, 
if perpendicular to gravity. Substituting these values in equation (1), Mr. Hennessey obtains 
a,*= 0°97714, and a, = 0:99539, 1 — a, = 0:00461, from which he infers, that ‘ consistently with 
observation, the least thickness of the Earth’s erust cannot be less than 18 miles.” It is very easy 
to prove, that if the shell be bounded by similar surfaces, both of which are perpendicular to gra- 


vity, that its thickness is zero; this I believe to be the true minor limit of the thickness of the 


tor; € 


crust. 
But even admitting Mr. Hennessey’s assumption, that the outer surface of the Earth is not 


perpendicular to gravity, I am unable to agree with him as to the formula from which its thick- 
ness should be calculated. In equation (1), which is deduced from the previous equations, @, is 
the reciprocal of the quantity I have called ¢. This equation contains only the fifth power of a, or 
@, whereas, the equation deducible from the investigation which I have given contains both the 
fifth and third powers of @, and gives a numerical result which differs materially from Mr. Hen- 
NESSEY’s. The investigation is as follows. Assuming «¢=e=e in equation (30), which asserts that 
gravity is perpendicular to the inner surface of the crust and is deduced from (14), and solving 
for o, we find, making A= 2p,, at 
g+lye—m 

SoS (@+]je @) 
In equation (15), the external surface is supposed perpendicular to gravity, and, therefore, the 
ellipticity « of its right-hand member must be replaced by (¢); the integral at the left-hand 
side of this equation is proportional to the difference of the moments of inertia of the Earth with 
respect to its polar and equatorial axes (16), and does not require the surface to be perpendicular to 
gravity; in fact, the left-hand side of this equation may be supposed to belong to any body having 
the same difference of moments of inertia as that belonging to the Earth. Separating the integral 
into two parts, belonging respectively to the shell and nucleus of the Earth, the external surface 
being supposed similar to the inner, and not perpendicular to gravity, we find, 


3G — 1) e+ 3(G +1) <= 5 [2(€)- m) Bs 


Original and Actual Fluidity of the Earth and Planets. 273 


which might have been deduced directly from (31), by making ¢ = e, = ¢ on the left-hand side, 
e=(e) on theright, and A=2p,°. Solving this equation for o, we find, 
3 {10(e) — 3¢ — 5m} $° + 3e z 
= 5e(@ + 1) (3) 
Eliminating o from equations (2) and (3), we obtain finally, 


5m — 2e be 
aie 10(e)— 3e-—5m 10(e) — 3e—5m 


p. (4) 


In this equation ¢ is the reciprocal of a,, and the other letters are the same as the corresponding 
letters’ used in equation (1). Equation (4) differs widely from the equation (1) obtained by Mr. 
HeEnnEssEY; the hypotheses used in obtaining it are the four hypotheses used by him; and yet I 


am unable to perceive any error in the process by which (4) is found. 


Aas ; ih 1 “ 
Substituting for m, e, (e); their values Se and agua We find, 


@ + 1:58425 = 2°48290 ¢*. (5) 


Applying Srurm’s theorem to this equation, I find that it has three real roots, one negative and 
two positive; the latter lying between @=1 and @=2. These roots are 


% = 10436; ¢ = 1°3626. 


Rejecting the negative root, as being not applicable to the question in hand, it would appear at 
first sight as if there were two solutions, corresponding to the two real positive roots just found; 
but it is evident, by referring to equation (28), that the second value of ¢, being greater than 
1-2407, is to be rejected as well as the negative root; in fact, the second value of @ would give a 
thickness to the crust of the Earth greater than the depth to which the density of the rocks at the 
surface can extend; and such a thickness, as has been already shown, is inconsistent with the 
supposition of a fluid nucleus. Calculating the thickness of crust corresponding to the least 
positive root of equation (5), we find, 

a — a, = 166 miles. (6) 
This result differs materially from that obtained from the same data by Mr. Hennessey, but as the 
hypothesis on which it is founded is untenable, the result itself is of little value, except so far as it 
illustrates the use of the equations already given. As I have before stated, the thickness of the 
crust would be zero, if we were to admit the first three statements, and combine with them an 
assertion that the surface of the Earth is perpendicular to gravity. This I believe to be the true 
minor limit of the thickness of the Earth’s crust; and the major limit appears to me to require for 
its numerical calculation a knowledge of facts, respecting which we must be content to remain in 
ignorance. 


ean tal ent gilgowea petit), af = 


Hephsuiett tr Aisi w 


Sh bolt Wnytaal 
are unl a2 


275 


XIL— On the Homology of the Organs of the Tunicata and the Polyzoa.* By Grorcr 
James Attmay, M.D., F.R.C.S.1, M.R.I. A., Professor of Botany in the 
University of Dublin. 


Read January 26, 1852. 


THOUGH the close affinity between the Tunicata and the Polyzoa has been 
generally acknowledged, yet the full extent to which the organization of the one 
is represented by that of the other does not appear to have been hitherto re- 
cognised by the zoologist. I propose in the present communication to point out 
some apparently unnoticed instances of homological identity, while I shall en- 
deavour to show that almost every modification of form in the organization of 
the one is, by the easiest transition, convertible into a corresponding form in 
the other; that they are both, therefore, constructed on precisely the same type, 
and must constitute one and the same great natural group. 

In order to render this subject intelligible, it will be necessary in the first 
place to fix the terms indicative of the various aspects of the Tunicata and the 
Polyzoa, terms which are so vaguely used by different authors as to give rise 
to great confusion in description. In the determination of the anterior and 
posterior aspects, there would seem to be no difficulty, as the former must ma- 
nifestly be assumed as that to which the mouth is directed, while the posterior 
will then of course be the aspect directly opposed to this. The determination 
of the dorsal, or superior, and of the ventral, or inferior aspects, is not so easy. 
I believe, however, that the cephalic ganglion, or its homologue, must be here 
our true guide, and that its position will always correspond with the dorsal, or 
superior aspect of the animal, to which the ventral will then consequently be 
diametrically opposed. Mr. Huxtey, in his admirable memoir on Salpa and 


* Polyzoa THompson, synonymous with Bryozoa EnRENBERG. THompson’s name has priority 
of date over that of Enrenzerc, and should, therefore, in justice to its founder, and in obedience 
to the laws of Natural History nomenclature, be adopted. : 

VOL. XXII. 20 


276 Dr. G. J. Attman on the Homology of the Organs 


Pyrosoma, assumes the heart as indicating the dorsal aspect of the Tunicata ;* 
the cephalic ganglion, however, in those inferior members of the animal king- 
dom in which the dor- 
sal and ventral aspects 
are already indicated 
by other characters, is 
invariably placed on 
the dorsal side of the 
alimentary canal, and 
though it be admitted 
that the almost uni- 
versal position of the 
heart among inverte- 
brate animals is also 
dorsal; yet where, as 
in the Tunicata, we 
find the ganglion and 
heart placed on oppo- 


Fic. 1. Diagramatic view of Clavelina. 
Fic. 2. Diagramatic transverse section of 
Clavelina.t 

a, external tunic; 6, middle tunic ; 
¢, internal tunic ; a d,d, sinus system ; 


e, respiratory orifice; f, cloacal orifice ; 
9,g, transverse respiratory bars; A, h, longi- 
] 7 o i iratory bars; 2, b hial sinus ; 
site sides, the superior taudinal respinatory Rams; f brani 

k, k, proper membrane of respiratory sac ; 
importance of the gan- 1, languets; m, mouth; n, cesophagus; 


glion will, I think, jus- o, stomach; p, intestine; g, anus; 7, cloaca; s, tentacula; ¢, muscular fibres in 
middle tunic; w, heart ; v, nervous ganglion ; w, gemma. 


tify us in assuming its 
position as the constant one, and concluding that it is the heart therefore and 
not the ganglion that has changed place. The only apparent difficulty in as- 
suming the ganglion as the index of the back results from its not being always 
obvious that the nervous mass before us is homologous with a true cephalic, 
or supra-esophageal ganglion; there will, however, I think, always be found 
marks sufficient to decide this point ; we shall subsequently see that the gan- 
glion, both in the Tunicata and the Polyzoa, undoubtedly contains a supra- 
esophageal element, which from its pre-eminent importance will determine the 


* “ Observations upon the Anatomy and Physiology of Salpa and Pyrosoma, together with Re- 
marks on Doliolum and Appendicularia.”” By Thomas Henry Huxley. Phil. Trans., 1851. 

{ In all the figures accompanying this paper, the same letters are used with the homologous 
organs. 


of the Tunicata and the Polyzoa. 277 


dorsal position of the ganglionic mass, even though the latter should also perform 
functions usually devolving on ganglia situated below the alimentary canal. 
1. Respiratory Sys- 


tem.—As it is in the 


Fic. 4. 


respiratory organs of 
the two groups that 
the leading peculiari- 
ties of their structure 
are to be found, our’ 
attention must be first 
directed to this por- 
tion of the organiza- 
tion, with the view of 
determining how far 
the respiratory appa- 
ratus in the one has 
its homologue in the 
other. Now two dis- 


Fic. 3. Diagramatic view of a hippo- 
crepian Polyzoon(retracted). Fic.4. Dia- 
gramatic transverse section of a hippocre- 
pian Polyzoon. 

a, ectocyst; b, endocyst; c, tentacular 
sheath; d,d, d, perigastric space; f+ e, 
external orifice of cell; g,g, tentacula; 


tinct notions have pre- i, lophophore ; 4, 2, caliciform membrane ; 

vailed on this point, 1, oral valve-like organ; m, mouth; 7, ceso- 
5 - h 3 0, st h; p, intestine; g, anus; 

some zoologists* main- Be atid Sie ghee eo 


at T, cavity of tentacular sheath ; ¢, muscular fibres in endocyst; », nervous ganglion . 
taining that the res- — w, gemma. 


piratory sac of the Ascidian has its representative in the pharynx of the 
Polyzoon, and that the rudimental tentacula at the orifice of this sac are ho- 
mologous with the tentacula of the Polyzoon; while others} assert, that the 
branchial sac of the Ascidiw is homologous with the tentacular crown of the 
Polyzoa, the longitudinal bars of the sac corresponding to the tentacula of the 
Polyzoa, and the transverse bars becoming extinct. Now, neither of these views 
appears to me to represent the exact truth, for, while I conceive that the tenta- 
cular crown of the Polyzoa has undoubtedly its true homologue in the respi- 


* See Dr. A. Farre, “ Observations on the Minute Structure of some of the higher Forms of 
Polypi.” Phil. Trans. 1837. 
+ See Van Benepen, ‘“ Sur les Ascidies Simples.” Mem. de l’Acad. Roy de Belgique, Tome 
xx., 1847. 
202 


278 Dr. G. J. Attman on the Homology of the Organs 


ratory sac of the Ascidic, I believe that it is to the transverse, and not to the 
longitudinal bars of this sac that the tentacula of the Polyzoa are homologous ; 
and this is a very important distinction, the non-recognition of which has ren- 
dered all previous attempts at comparison between the tentacular crown of the 
Polyzoa and the respiratory sac of the Ascidie untenable. 

On this subject much light is thrown by the hippocrepian Polyzoa, or those 
fresh-water genera which, like Plumatella, have their tentacula arranged on a 
erescentic “lophophore ;’* and we shall best perceive the relations in question 
by comparing an ascidian Tunicate with one of these Polyzoa, a Clavelina (Figs. 
land 2), for example, with a Plumatella (Figs. 3 and 4). In Clavelina, the great 
“ branchial sinus” of Mmnre-Epwarps,} from each side of which the transverse 
bars or vessels of the respiratory sac are given off, will correspond to the elongated 
lophophore in Plumatella, and the richly ciliated transverse bars to the ciliated 
tentacula, while the delicate membranous sac, to the interior of which the respira- 
tory bars are adherent, and which Mitnz-Epwarps has shown to be perforated in 
the intervals of these bars by the “ respiratory stigmata,” will have its homologue 
in the calyx-like membrane adherent to the base of the tentacular plume in F’rede- 
ricella and the hippocrepian Polyzoa. This correspondence will be rendered more 
obvious by imagining the branchial sinus to be rotated round its oral extremity in 
a vertical plane through an angle of 90°, towards the superior or anal side of 
the Tunicate ; its position from longitudinal will thus be changed to transverse, 
while the transverse bars will become longitudinal, and the branchial sinus and 
its bars will then have the same direction as the exserted lophophore and ten- 
tacula of Plumatella ; while it is interesting to observe that, during the retracted 
state of the Polyzoon, the lophophore assumes the normal direction of the bran- 
chial sinus in the Tunicate. 

That the tentacula of the Polyzoa are not homologous with the unciliated 


* In a Report on the Fresh-Water Polyzoa, read before the Edinburgh Meeting of the British 
Association for 1850, I found that our increased knowledge of the structure of the Polyzoa ren- 
dered it necessary to make some change in the terminology hitherto employed in their description; 
and the terms used in that Report are also adopted in the present memoir. The Polypide is the 
retractile portion of the Polyzoon as distinguished from its cell; the Hetocyst is the external tunic 
of the cell; the Endocyst is the internal tunic; the Lophophore is the kind of disc or stage which 
surrounds the mouth and bears the tentacula. 

+ See M. Mitne-Epwarps’s beautiful memoir, ‘‘ Sur les Ascidies Composeés.” 


of the Tunicata and the Polyzoa. 279 


rudimentary tentacula at the entrance of the respiratory sac in the Ascidiw 
is also apparent, not only from the difference of structure, but from the fact, 
that while the tentacula of the Polyzoa are in immediate relation with the 
digestive tube, those of the Ascidiw are evidently mere appendages of the 
internal tunic. It is true, that in accordance with this view, we can find no 
homologue in the Polyzoa for the tentacula of the A scidiw ; we must therefore 
conclude, that these organs have absolutely died out in the Polyzoa, a circum- 
stance for which we have been already prepared by their disappearance in Salpa 
and other Tunicates. 

In connexion with the tentacular crown, there is another part of the orga- 
nization of the Polyzoa for which we have still to find an equivalent, and which, 
without comparison with the Tunicata, would remain inexplicable, namely, the 
curious valve-like organ which overhangs the mouth in F’redericella and the 
hippocrepian Polyzoa. Now this is plainly homologous with the tongue-like 
bodies, the “ languets” of Mitne-Epwarps, which are attached along the bran- 
chial sinus in Clavelina and certain other Tunicates, and thence project into the 
interior of the branchial sac, and which in Salpa are represented by a single 
one. The languet in Salpa is connected with a peculiar ciliated cavity lying 
immediately at its base, and which seems also to have its representative in the 
excavation of the lophophore at the base of the oral appendage in Plumatella 
and the allied forms; and through which the cavity of this appendage appears 
to communicate with the perigastric space. Further observation will, in all pro- 
bability, prove that the interior of the languets in the Tunicata communicate 
in these with the great “ sinus system,’* which is equivalent with the perigastric 
space of the Polyzoa. Mine-Epwarps believes the languets in Clavelina to 
exhibit a kind of erection, a phenomenon which would suggest as its expla- 
nation such a communication as that here supposed, and which, at all events, ren- 
ders still more striking the resemblance between the languets of the Tunicata 
and the oral appendage of the Polyzoa, an organ which seems to present an 
analogous phenomenon. In both groups the bodies in question would seem to 
be organs of special sense, probably of taste. 


* This name has been given by Huxtey to the whole of the space included between the inter- 
nal and middle tunics in the T'wnicata, and through which the blood, uninclosed in proper vessels, 
vaguely circulates. See Huxcey, loc. cit. 


280 Dr. G. J. Atiman on the Homology of the Organs 


We now need only a few unimportant modifications in order to complete the 
resemblance between the branchial sac of Clavelina and the tentacular crown 
of Plumatella; we have only to imagine the oral extremity of the branchial 
sinus to be prolonged with its bars for a short distance downwards, so as to 
surround the mouth, the transverse bars to become free at their extremities, 
where, opposite to the branchial sinus, they communicate with the “ thoracic 
sinus,” the longitudinal bars to be suppressed, and the “ languets” to be re- 
duced to one situated in the immediate vicinity of the mouth; a series of changes 
involving no essential modification of structure; and we shall then have an 
organ only wanting in a deep crescentic depression of the distal extremity of 
the branchial sinus, to resemble, even in minute details, the tentacular crown 
of Plumatella. 

Now nearly all the changes which we have thus hypothetically supposed to 
take place in Clavelina, in order to convert its branchial sac into the tentacular 
crown of Plumatella, do actually occur in other genera of Tunicata, some in 
one, and some in another. The predominant importance of the transverse over 
the longitudinal bars of the branchial apparatus in the Twnicata is sufficiently 
manifest; in most cases they are larger and more evident than the longitudinal; 
in Pyrosoma, as appears from Mr. Huxzey’s account of this genus,* they are 
not only the better developed, but they alone carry cilia; the transverse bars, 
moreover, are constant in all the genera, while the longitudinal actually disap- 
pear in Salpa and in Doliolum, unless, indeed, we adopt the ingenious view of 
Mr. Huxtzy, who supposes that the lower division (“‘ Epipharyngeal Band” of 
Huxtey) of the gill in Doliolum is homologous with the longitudinal bars in 
Pyrosoma and other tunicates ; an opinion, however, which is surely opposed 
by the fact, that in two species of Sa/pa examined by Savieny, this naturalist 
has pointed out the existence of a small inferior gill, maintained by Mr. 
Houxtey to be the homologue of the inferior division of the gill in Doliolum; 
and yet the superior or constant gill in one of these Salpa shows at the same 
time traces of longitudinal bars as in Pyrosoma. In Doliolum, as it would ap- 
pear from Mr. Huxtey’s short but interesting account, the superior and inferior 
divisions of the gill are directly continuous with one another behind; indeed 
they are evidently one and the same organ carried across the thoracic chamber 


* Loe. cit. 


of the Tunicata and the Polyzoa. 281 


(Fig. 5); the gill in Doliolum then plainly consists of a great branchial sinus, car- 
rying its respiratory bars on each side as in Clavelina, but differing from the 
disposition of parts in the latter genus by having its posterior extremity pro- 
longed downwards till it reaches the inferior wall of the thoracic chamber, along 
which it then runs forwards parallel to the superior portion. The mouth per- 
forates this inferior prolongation of the sinus, and thus becomes related to the 
sinus and its bars exactly as the mouth in the Fic. 5. 

Polyzoa is to the lophophore and tentacula in 
these. Savieny informs us, that the mouth opens 
between the inferior and superior gill in the Salpe 
examined by him; butit is not easy to determine 
from his description whether these portions are 
directly continuous, as in Doliolum. In Doliolum, 
moreover, the remote extremities of the branchial 
bars of one side are quite separate from those of 
the other, and thus present the open condition 
which characterizes the tentacular crown in the 
Polyzoa, so that the gill of Doliolum constitutes 
the exact link by which the branchial sac of the 
Ascidie passes immediately into the tentacular 
crown of the Polyzoa. In Pyrosoma we have also 


an approach to the open condition of the tentacu- —_Fre. 5. Ideal longitudinal section of Do- 
lar crown, for the inferior extremities of the trans- 

5 a+b, external and middle tunic united: 
verse bars of one side are separated from those  ¢, internal tunic; d,d, sinus system: 
of the other by a considerable space, and, accord- — & respiratory orifice; f cloacal orifice; 
ing to Lesteur, even become free for some distance 2 “PAO barsi hb branchial sinus; 

; gs ; 3 : m, mouth; m, cesophagus; 0, stomach; 
from their extremities in the species which hep, intestine; , anus; 7, cloaca; v, ner- 
describes. yong ganelan. 

The structure and connexions, then, of the ascidian tentacula, together 
with the modifications actually experienced by the longitudinal and transverse 
bars in the different forms of Tunicata, and the fact that the tentacular crown 
in the hippocrepian Polyzoa will admit of a satisfactory explanation in accord- 
ance alone with the views here taken, afford evidence that the homologues of 


282 Dr. G. J. ALuMAN on the Homology of the Organs 


the tentacula in the Polyzoa are neither the rudimentary tentacula at the en- 
trance of the branchial sac of the Ascidie, nor the longitudinal bars of this 
sac, as maintained by those naturalists who have yet recognised in the branchial 
sac of the A scidia an organ homologous with the tentacular crown of the Polyzoa; 
but that their true equivalents must be sought for in the transverse bars, and 
this is further borne out by the observation’ of the ascidian embryo in which 
the longitudinal bars would seem to make their appearance subsequently to the 
transverse ones; the respiratory sac thus passing in the course of its development 
through a stage more nearly corresponding to the simpler condition which we 
meet with in the respiratory crown of the Polyzoa. 

In Salpa the languets are reduced to a single one, that, however, which re- 
mains in this genus is not, as we might be led to expect from the comparison 
we have made between these organs and the oral appendage of Plumatella, the 
languet nearest the mouth, but on the contrary (if we may judge from its po- 
sition), the most remote from this part of the animal. Itis, however, particularly 
worthy of attention, that both the existing languet of Salpa and the oral ap- 
pendage of Fredericella, and the hippocrepian Polyzoa, are quite similarly re- 
lated to the great nervous ganglion. This ganglion we shall presently see 
to be homologous in the Zwnicata and Polyzoa, and it is manifestly it, and not 
the mouth, that determines the place of the persistent languet. 

However interesting the hippocrepian Polyzoa may be in directly indi- 
cating the relations here dwelt on, the infundibulate genera present no diffi- 
culty, for they exhibit, after all, but an unimportant modification of the former, 
and are connected to them by a series of intermediate forms. The arms of the 
lophophore in Plumatella have only to become obsolete in order to transform this 
genus into a I’redericella, in which, however, the lophophore still retains a bilateral 
figure, which is rendered yet more decided by the presence of the oral valve- 
like organ. In Laguncula Van Brn., the oral appendage has disappeared, but the 
lophophore still presents a slight bilaterality. Finally, in the fresh-water genus, 
Paludicella, and most of the marine genera, not only has the oral appendage 
disappeared, but all trace of bilaterality has now vanished from the lophophore. 

2. Dermal System —M. Mutye-Epwarps has proved by the anatomy of Cla- 
velina, that there exist in this genus, and probably in all 7% unicata, three distinct 


—_———— 


of the Tunicata and the Polyzoa. 283 


envelopes, which, however, may be variously united with one another in the dif- 
ferent genera.* Now all these have their homologues in the Polyzoa ; the external 
sac or test of the Tunicata corresponds to the external investment, or ectocyst, of 
the Polyzoa ; the middle sac, or mantle, of the Tunicata,to the internal investment, 
or endocyst, of the Polyzoa ; and the internal tunic of the Tunicata, which sur- 
rounds the branchial sac, and forms the “ thoracic chamber” of MrtngE-Epwarps 
(and which is divided into two portions, one inferior, containing the proper 
branchial sac, and the other superior, constituting the cloacal chamber), will 
be equivalent with the tentacular sheath of the Polyzoa. The homology of the 
two outer tunics of the Zunicata with the ectocyst and endocyst of the Polyzoa 
is obvious, and need not here be further dwelt upon; but the homology of the 
third or innermost tunic of the Tunicata with the tentacular sheath of the Polyzoa 
is very important, and will require to be considered more in detail. If we ex- 
amine this tunic in Clavelina, we shall find that it is continuous with the mantle 
at the respiratory and cloacal orifices, and becomes attached to the alimentary 
canal, just behind the mouth and anus. It thus holds to the surrounding parts 
in the Tunicata exactly the same relation that the tentacular sheath or inverted 
tunic in the Polyzoa does to the corresponding parts of these during the retracted 
state of the animal. In the Polyzoa there is, properly speaking, but one external 
orifice, namely, that through which the tentacular crown is projected and re- 

‘tracted ; but this is equivalent to the respiratory and cloacal orifices of the Tu- 
nicata united, and the point where the rectum opens externally in the Polyzoa 
is not, therefore, as supposed by VAN Brnepen and others, the homologue of 
the cloacal orifice in the Twnicata, with the cloacal chamber itself become 
extinct,—a view which evidently originated in the too exclusive contemplation 
of the Polyzoon in its exserted state,— but rather corresponds to the point where 
the rectum penetrates the internal tunic in the Twnicata, and the cloaca in the 
latter will then be represented by the superior or dorsal portion of the space 
between the tentacular crown and sheath in the Polyzoa, this space becoming 
obliterated in the exserted state of the polypide.t 


* See Huxtey, loc. cit. 

} To the normal structure both of the Tunicata and the Polyzoa, Appendicularia presents a 
remarkable exception. In this singular little Tunicate, as described by Hux.ey, the branchiz are 
reduced to a mere rudiment, and while the thoracic chamber formed by the internal tunic is largely 


VOL. XXII. 2P 


284 Dr. G. J. AttmAN on the Homology of the Organs 


3. Digestive System.—The form, structure, and peculiar course of the ali- 
mentary canal in the Tunicata, closely resembles what we find in the Polyzoa. 
This canal in the Polyzoa consists of three distinct portions: cesophagus, sto- 
mach, and intestine; the esophagus communicates with the stomach by a well- 
defined cardiac orifice, and the cardiac extremity of the stomach frequently 
presents a cylindrical elongation, with the esophagus opening into its anterior 
end; the stomach is separated from the intestine by a well-marked pylorus. The 
alimentary canal in the Tunicata is also divided into esophagus, stomach, and 
intestine; in some instances these divisions are obscurely marked, but in others 
they are as well defined as in the Polyzoa. Now if, in accordance with the 
views attempted to be established in the present memoir, we consider the 
branchial sac of the Ascidian as the homologue of fhe tentacular crown of the 
Polyzoon, we shall have the three regions of the alimentary canal of the one 
exactly homologous respectively with the three regionsin the other. If, on the 
contrary, the branchial sac of the Ascidian be homologous with the first region 
—the pharynx or cesophagus—of the alimentary canal of the Polyzoon, then, in 
order to find a homologue in the Polyzoon for that portion of the canal which 
intervenes between the branchial sac and the stomach in the Ascidian, and which 
is without doubt a true esophagus, differing altogether in structure from the 
stomach, wherever in the 7unicata the alimentary canal acquires its proper de- 
velopment, we must take the cardiac prolongation of the stomach in the Polyzoa 
for an esophagus, a view not borne out either by its structure or its functions ; 
for independently of the fact that it is not always present, this prolongation ob- 
viously belongs to the proper stomach, having, it is true, special muscles some- 
times developed in it, so as to give it the structure and office of a gizzard ;* 
but more frequently being a simple prolongation of the gastric cavity, in no 
respect differing from the remainder of this cavity either in structure or func- 


developed, the intestine does not open into it, but passes forwards and downwards to perforate 
the middle and external tunics, and thus open directly outwards. There is consequently here no 
cloaca. Appendicularia at a first glance appears to afford the connecting link between the T'wnicata 
and the Polyzoa; but a little consideration will show that the most important point by which it 
differs from the normal T'unicata, namely, the absence of a cloaca, is that which also separates it at 
the greatest distance from the Polyzoa. 

* See ‘Report on Fresh-water Polyzoa.” Rep. Brit. Assoc., 1850, p. 310. 


of the Tunicata and the Polyzoa. 285 


tion. In both the Tunicata and the Polyzoa the intestine is invariably bent on 
the first portion of the alimentary tube as it passes forward to the anal outlet; 
but there is a curious difference between the two groups in this respect, namely, 
that while in the Twnicata the first bend of the intestine, as noticed by Mr. 
Hux ey, is always towards the lower side, or that opposite to the ganglion, its 
whole course in the Polyzoa is as invariably towards the upper, or ganglionic 
side, a difference, however, in no degree invalidating the homological identity 
of the parts. The structure of the walls of the alimentary canal in the Tunicata 
reminds us strongly of that in the Polyzoa. In some Tunicata there is a well- 
developed liver ; in others, however, this organ is entirely absent, or only repre- 
sented by a peculiar coloured layer on the interior of the walls of the alimentary 
canal, exactly as in the Polyzoa. 

4. Circulatory System.—The circulatory system of the Tunicata admits of a 
very interesting comparison with that of the Polyzoa. The degraded condition 
of the vascular system in the former, where the heart scarcely advanced be- 
yond the embryonic condition, is alternately branchial and systemic; and the 
undefined or extra-vascular circulation in the whole of the abdominal region 
conduct us at once to the complete absence of the heart in the Polyzoa, where 
the circulation—altogether extra-vascular, except so far as the tubular tentacula 
and lophophore represent a vascular system—is effected by the propulsive action 
of vibratile cilia. The condition of the circulatory system in the Polyzoa has al- 
ready been quite anticipated in the curious Tunicate genus Pelonaia,* where the 
heart itself has disappeared. The great “sinus system” of the T'unicata, filled 
with the vaguely circulating blood, has its exact homologue in the perigastric 
space of the Polyzoa, occupying, like the latter, the interval between the middle 
and internal tunics. 

5. Muscular System.—The muscles on which devolves the office of the re- 
traction of the polypide in the Polyzoa are of course absent in the Tunicata, 
but notwithstanding this, we have some interesting points of correspondence 
between the muscles of the two groups. In the middle tunic or mantle of the 
Ascidi@ there is, as is well-known, a large development of muscular tissue 
in the form of circular and longitudinal fibres, which give to this tunic its cha- 


* See Forzes and Goopsir in Edinburgh New Phil. Jour., vol. xxxu. p. 29. 
2P2 


286 Dr. G. J. Attman on the Homology of the Organs 


racteristic contractility. Now these muscles are exactly represented by 
equivalent fibres which are developed in the homologous tunic or endocyst of 
the Polyzoa, and constitute the “ parietal muscles” of these animals. The cir- 
cular bands of Salpé and Doliolum appear to be developed in the internal tunic, 
and have their representatives in the sphincters occurring in the inverted 
tunic of the Polyzoa. Striated muscular fibre exists in many, if not in all the 
Polyzoa, and a similar condition of this tissue has been detected by EscuricutT 
and Huxtey in Salpa. 

6. Nervous System.—Between the great nervous ganglion in the Tunicata 
and the Polyzoa there is apparently a marked difference in position, this gan- 
glion in the Tunicata being placed between the respiratory and cloacal orifice, 
while in the Polyzoa it is situated on the esophagus near its oral extremity, and 
this difference might at first lead to the belief, that the homological identity 
which we have witnessed between the other organs of the two groups fails to show 
itself in the nervous system; still, however, it can be rendered evident, that no 
exception is here offered to the unity of plan already demonstrated, and that 
the two ganglia are strictly homologous. The ganglion is manifestly iden- 
tical in function in the two groups, for in each we have nerves passing off from 
it both to the respiratory apparatus and to the ceesophagus and region of the 
mouth, a distribution in which it corresponds with that of both the branchial 
and cephalic ganglia of the higher Mollusca, whose offices it thus seems to 
combine. 

In several of the Tunicata, a well-defined otolithic capsule has been dis- 
covered in connexion with the ganglion; and Mr. Huxiry has suggested to 
me that this ganglion ought therefore to be considered as homologous with the 
pedal ganglion of the Lamellibranchiate Mollusca, since in these the otolithic cap- 
sule is always found in connexion with the pedal ganglion. To this view, how- 
ever, several objections appear to me to present themselves; the ganglion of the 
Tunicata and of the Polyzoa has functions devolving on it which we never see 
performed by the pedal ganglion of the Lamellibranchiata; the development 
of the pedal ganglion, moreover, bears a constant relation to that of the foot, 
and though the obliteration of the foot does not necessarily bring with it the 
absence of the ganglion—as in Teredo, for example, where the researches of 
QuaTrEFAGEs have shown the existence of a pair of minute ganglia, manifestly re- 


of the Tunicata and the Polyzoa. 287 


presenting the pedal ganglia of those Lamellibranchiata, in which the foot is not 
suppressed,—yet the pedal ganglion presents us under such circumstances with its 
lowest condition of development, and analogy will not permit us to suppose that in 
the absolutely footless Tunicate or Polyzoon this ganglion acquires its maximum, 
and even becomes here the only nervous centre present. It would, indeed, seem 
as if the solitary nervous centre of the Twnicata and Polyzoa combined the func- 
tions of the several separate centres of the Lamellibranchiata, while the superior 
importance of the cephalic element determines its supra-cesophageal position. 

If we now carefully consider the difference of position between the two 
ganglia, we shall find that this is, after all, unimportant ; in the Twnicata, while 
the ganglion is always placed between the two external orifices, it is at the 
same time situated in the interval between the internal and middle tunic, and 
is consequently in the midst of the sinus; in the Polyzoa, the two orifices co- 
alescing, the ganglion can no longer occupy the position it held in the Tunicata ; 
it is, therefore, carried backwards, and, still bathed in the fluid of the sinus, now 
becomes situated on the esophagus, a difference of position which, it will easily 
be seen, involves no important change of relations, and which is necessarily 
connected with the difference in the arrangement of the other organs in the 
respective groups. In the Polyzoa, from their constant motions of retraction 
and exsertion, the ganglion could not occupy the fixed position which it does in 
the Tunicata, and, therefore, comes to be situated upon the polypide itself, all 
whose motions it then necessarily follows. 

7. Generative System.—The construction of the generative’ system in the 
Tunicata and Polyzoa is also in conformity with the views of the present memoir. 
Both are hermaphrodite; in both we have, besides true sexual generation, 
generation by gemmation, the gemma in the Polyzoa being formed exactly 
as in the Zwnicata from a diverticulum of the sinus system. 

Though our knowledge of the developmental phenomena is in many re- 
spects so deficient as to afford much less assistance in the present inquiry than 
could be desired, yet if we compare the embryological development of an 
Ascidian as given by Mitne-Epwarps or VAN Benepen, with that of a Polyzoon, 
we shall still find the results in accordance with the views of the present paper. 
In the embryo-Ascidian, after the internal organs have begun to assume the 
definite form which is subsequently to characterize them, we find that the in- 


288 Dr. G. J. Attman on the Homology of the Organs 


terior of the body presents from behind forward four cavities, more or less dis- 
tinguishable from each other, and which there is no difficulty in recognising as 
the future intestine, stomach, cesophagus, and respiratory sac. As yet, how- 
ever, there is no trace of longitudinal or transverse bars in the respiratory sac, 
and it is only at a subsequent period that these bars come to line its walls. 
Observations are here deficient, but so far as they go it would seem that the 
transverse bars first make their appearance, that the longitudinal then show 
themselves; and lastly, that the sac becomes pierced by the respiratory stig- 
mata. The circumstances under which the minute tentacula within the orifice 
of the respiratory sac become developed have not yet been satisfactorily ob- 
served. So many difficulties oppose themselves to our observation of the de- 
velopment of the ovwm in the Polyzoa, that no facts of importance in the deter- 
mination of the present question can thence be derived; but if we examine the 
corresponding development of the bud of Paludicella, we shall find after a time, 
that the nascent Polyzoon presents three distinct cavities, which are to become 
intestine, stomach, and cesophagus, and which are manifestly homologous with 
the cavities to which we give the same names in the embryo-Ascidian. Instead, 
however, of the closed cavity which in the Ascidian lies anterior to the cesopha- 
cus, and is to constitute the respiratory sac, we have here the anterior extremity 
of the esophagus surrounded by a ring—the future lophophore—round whose 
outer margin a number of minute tubercles soon show themselves, and these 
then, becoming elongated, constitute the tentacula of the Polyzoon. Now be- 
tween the formation of these tentacula and that of the respiratory bars of the 
Ascidic, the resemblance appears quite complete; in Paludicella and most other 
Polyzoa, there is, it is true, nothing homologous with the proper membrane of 
the respiratory sac of the Ascidie (the caliciform membrane of Fredericella and 
the hippocrepian Polyzoa being here absent), and consequently the closed pre- 
buccal chamber of the Ascidie does not exist in them; but the essential part of 
the respiratory apparatus—the transverse bars of the Ascidian and the tentacula 
of the Polyzoon—entirely correspond in their order and mode of development, 
and so far the evidence derived from the phenomena of development coincides 
with that afforded by anatomy. In Fredericella and the hippocrepian Polyzoa, 
the proper membrane of the sac shows itself in the form of a delicate calyx, which 
surrounds the base of the tentacular plume; the difficulty of observing the deve- 


of the Tunicata and the Polyzoa. 289 


lopment of the bud through the more opaque tissues of these Polyzoa has ren- 
dered us here deficient in the class of facts now under discussion, and we are 
not, therefore, yet prepared to institute an actual comparison between the deve- 
lopment of the branchial membrane in the A scidie and the caliciform membrane 
in the hippocrepian Polyzoa ; so far, however, as our imperfect observations go, 
the facts are still in accordance with the views of the present paper ; and though 
we have but little positive evidence to assist us in our conclusions, yet there is 
not a single observation tending to disprove the position that the branchial 
membrane of the one, and the caliciform membrane of the other, present in the 
circumstances of their development the conditions of homologous organs. 

Among the other points of resemblance between the two groups, it is 
interesting to observe the frequent occurrence among the Tunicata of definite 
compound phytoidal forms resulting from gemmation, exactly as in the Polyzoa. 

From what has now been stated it must be manifest, that the Tunicata and 
the Polyzoa are more nearly related to one another than either to any other 
branch of the animal kingdom; that they really belong to one and the same 
great structural type; and that the differences between them are non-essen- 
tial modifications of this type, rendered for the most part necessary by the 
new power superadded upon the Polyzoa of alternately projecting and retracting 
the respiratory crown and anterior portion of the digestive organs through the 
external orifice of the cell. 

The homology of the organs in the Tunicata and the Polyzoa, which it has 
been the object of the present paper to demonstrate, will be rendered more | 
apparent by bringing together the equivalent organs of the two groups in the 
following two parallel series: 


TUNICATA. POLYZOA, 
External tunic, . . . . = Ectocyst. 
Muddletunic,-. 5." . 1! 6 "=" Endoeyst. 

Internal tunic,. . . . . = Tentacular sheath. 
Sinus system, . . . . . = Perigastric space, 
Respiratory orifice, . . . : 

P y : \ = External orifice of cell. 
Cloacal orifice, . 


Transverse respiratory bars, = Tentacula. 


290  Dr.G.J. Antaan on the Organs of the Tunicata and the Polyzoa. 


TUNICATA. POLYZOA. 
Branchial sinus, . . . =  Lophophore. 
Membrane of reaiateey' sac, = Caliciform membrane. 
Languet,. . . . - + - = Oral valve. 
Cloaca, . . - . . . - = Space between tentacular crown 
and sheath. 
(Esophagus, . . . . - = Césophagus. 
Stomieh, Og co. Aor = Stomach 
Intestine, . . : . = Intestme. 
Muscles of idle tunic, . = Parietal muscles. 
Muscles of internal tunic 
(Salpa, Caen . . =  Sphincters of internal tunic. 
Ganglion, . . . . . = Ganglion. 
Tentacula, 4. 2) -°'"- a) 


Longitudinal Rane bak, =e 
Hearn aoe ABE Ah 


THE 


TRANSACTIONS 


OF THE 


ROYAL IRISH ACADEMY. 


VOLUME XXII. 


PART V.—SCIENCE. 


DUBLIN: 
REN ED BY MS He Gi 1, 


PRINTER TO THE ROYAL IRISH ACADEMY. 


SOLD BY HODGES AND SMITH, DUBLIN, 
AND BY T. AND W. BOONE, LONDON. 


MDCCCLY. 


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Tae Acapemy desire to be understood, that they are not answerable for any 
opinion, representation of facts, or train of reasoning, that may appear in the 
following Papers. The Authors of the several Essays are alone responsible for 


their contents. 


CO NEE WTS: 


ART. 
XIII. Experimental Researches on the Lifting Power of the Electro-Magnet. 
Part I. By the Rev. T. R. Rosison, D. D., Member of the 
Royal Irish Academy, and of other Scientific Societies. Read 
June 14, 1852. 
XIV. Report on the Chemical Beamiviation of Agius ‘yrom the Mr 
seum of the Royal Irish Academy. By J. W. Mautrt, A. B., 
Ph. D. Presented April 11, 1853. . DUN Are Ss 
XV. On the Properties of Inextensible Surfaces. By the Rev. Joun 
H. Jevrert, Mellow of Trinity College, and Professor of Natural 
Philosophy in the University of Dublin. Read May 23, 1853. 


XVI. On the Attraction of Ellipsoids, with a new Demonstration of 


Clairaut’s Theorem ; being an Account of the late Professor 
Mac Cutacu’s Lectures on those Subjects. Compiled by GEorcE 
Jounston Atrman, LL. D., of solicke College, Dublin. Read 
June 13, 1853. Seek Me n> oat A sey 

XVII. Notice of the British Enptteruahe of November 9,1852. By Ropert 
Matter, C.L., M.R.[.A. Read February 13, 1854. . 

XVIII. Notes on the Meteorology of Ireland, deduced from the Observations 
made in the Year 1851, under the Direction of the Royal Irish 
Academy. By the Rev. Humpnrey Luoyp, D.D., F.R.S.; Hon. 
F.RS.E.; V.P.R.I.A.; Corresponding Member of the Royal 
Society of Sciences at Gottingen ; Honorary Member of the Ame- 
rican Philosophical Society, of the Batavian Society of Sciences, 
and of the Societe de Physique et d’ Histoire Naturelle of Geneva, 
Ge. §e. Read June 27 and December 12, 1853. 


VOL. XXII. b 


FAGE. 


291 


313 


343, 


379 


397 


411 


vi CONTENTS. 


ART. PAGE. 
XIX. Experimental Researches on the Lifting Power of the Electro-Magnet. 
Part II. Temperature Correction ; Effects of Spirals and Helices. 
By the Rev. T. R. Rosryson, D. D., President of the Royal Irish 
Academy, and Member of other Scientific Societies. Read June 26, 

fQhAS.” 3. Lae Merten ne es 
XX. Some Account of the Marine Botany of the Colony of Western Aus- 
tralia. By W. H. Harvey, M. D., M. RI. A., Keeper of the Her- 
barium of the University of Dublin, and Professor of Botany to the 

Royal Dublin Society, §e. Read December 11,1854... . . 525 


291 


XIII.—Laperimental Researches on the Lifting Power of the Electro-Magnet. 
Part I. By the Rev. T. R. Rosryson, D. D., Member of the Royal Irish 
Academy, and of other Scientific Societies. 


Read June 14, 1852. 


As soon as Oersted’s great discovery had led to the construction of electro- 
magnets, high expectations were formed that they might afford a motive power 
as energetic and more economical than the steam-engine. The prodigious force 
which they manifest when excited by even a feeble current, and the power of 
annulling or reversing it in an instant, might seem to justify the hope; and an 
immense amount of inventive talent has been expended in attempts to realize it. 
These attempts, however, have shown that electro-magnetic engines can scarcely 
ever be either a cheap or a very efficient source of power. Electricity is now 
known to have a definite mechanical equivalent ; the zine and acids required 
to produce it are more costly than the coal, which will evolve isodynamic heat ; 
and the hitherto contrived methods of converting electro-magnetism into moving 
force involve much more loss than the mechanism of the steam-engine does in 
respect of heat. I may add, that the great magnetic force which I have referred 
to exists only in contact ; on the least separation of the keeper it decreases ra- 
pidly, not merely because magnetic force follows the law of the inverse square 
of the distance, but because that separation destroys in a very great degree the 
actual magnetism of the magnet. It must, however, be kept in mind that there 
are many cases where economy and intensity are of less consequence than faci- 
lity of application and convenience ; in which, therefore, the electro-magnetic 
engine deserves a preference even for industrial purposes, and much more for 
the work of the experimental physicist, although its action may be more costly. 
In particular, the absence of all danger, and perfect quiescence when not put in 
VOL. XXII. 2a 


292 The Rev. T. R. Rosrnson’s Experimental Researches on the 


action, and the capability of being moved to any locality where a couple of 
wires can be led from its battery, deserve special consideration. Such views 
several years ago induced my friend, Mr. T. F. Brretn, to experiment on the 
construction of a machine suitable to the workshop of the amateur, or the labo- 
ratory of the philosopher ; and I hope he will at no distant period lay his in- 
vention before the Academy. In its progress he occasionally consulted me as 
to the form and mass of the magnets to be employed; the distribution and kind 
of wire in their helices ; and the intensity of the currents transmitted through 
them which might be expected to give the highest dynamic effect from a given 
consumption of materials. On all these points I was surprised to find that 
there was little or no exact information extant ; I therefore determined to look 
for it myself; and since the beginning of 1848 have given to this object such 
attention as was permitted by my other avocations. In carrying it out I have 
derived much valuable aid from Mr. Brrern, not merely in the contriving and 
constructing the necessary apparatus, but also in making many experiments 
which I had not the means of performing. During this period several German 
physicists have been engaged in similar investigations ;* but if I do not deceive 
myself, neither their results, nor those of Mr. Joutn,t go so far as to make the 
present communication unnecessary ; and I trust it will be found not merely 
useful to the practical magnetician, but also valuable, as affording data which 
have been carefully determined, to those, who like Dr. Wini1am THomsoy, are 
investigating the theory of magnetic induction. 

Before describing my methods of experimenting, a brief account of what 
occurs in the action of the electro-magnet may make their object more intel- 
ligible. If we conceive the cylindric core divided into thin sections perpendicu- 
lar to its axis, and confine ourselves to the uppermost of them; on passing a 
current through the helix, its two surfaces will possess opposite polarities, de- 
rived mainly from the inducing power of those spires which are in its plane, but 
also in a decreasing amount from those which are below it. The intensity of 
these polarities depends on that of the inducing forces and of those which op- 
pose them; the former is known to be proportional to the intensity of the 


* Translated by Dr. TyNDALL in the Philosophical Magazine, March, 1851. 
+ Philosophical Magazine, October, 1851. 


Lifting Power of the Electro-Magnet. 293 


electric current and a function of the number and diameters of the spires, but 
the other is almost totally unknown. It is admitted that these polarities com- 
port themselves as if they were two fluids, each repelling itself or attracting the 
other inversely as the square of the distance, and becoming latent when per- 
mitted to unite ; we might, therefore, suppose that under the influence of the 
excited helix, they will separate until the increasing repulsion of themselves, 
and attraction of each other, balance its influence. But there is yet another 
force which prevents this separation from proceeding quite so far ; it is called 
the coercive force, and may be described as a resistance which the molecules 
of iron present to any alteration of their polar condition, whether the change 
be union or separation of polarities. The first of these will be as the polarity, 
the last some function of it, of which, I believe, nothing is known. Let now a 
second section be placed below the first, and in contact with it; it will be 
excited to an equal intensity ; but the heteronymous polarities partially neu- 
tralize each other at the contact surface, and the remaining two being at twice 
the former distance have less power to oppose the induction of the helix. 
Therefore it will produce a still greater separation of the polarities, and so on, 
till the helix is filled with these sections. For this we may evidently substitute 
a solid bar; the intervals between its molecules being analogous to the surfaces 
of contact, and as evidently it can be shown that the extremities of the bar will 
exhibit opposite polarities, whose intensity gradually decreases towards the 
centre till it vanishes at that point. If now a keeper of the same section be 
placed on one extremity of the magnet, suppose the Boreal one, it will also be- 
come a magnet, and its Austral polarity will neutralize much of the Boreal of 
the other ; the action of the helix will therefore evolve a still higher degree of 
magnetism in the latter, till a new equilibrium of forces is attained. In this 
instance, however, we can measure the new polarity, for it is proportional to 
the force with which the keeper is attracted by the polar extremity of the 
magnet. On the same principles the development of the magnetism will be 
carried still higher if the remote extremity of the keeper be connected with the 
Austral extremity of another magnet ; and it will reach its maximum if the re- 
maining poles of the two magnets be united as in the ordinary horse-shoe, and 
thus a magnetic circuit be completed. In this case there would be scarcely any 
free magnetism evident, and the forces which oppose H, the action of the helix 
Ph (0) 72 


294 The Rev. T. R. Rozsiyson’s Experimental Researches on the 


on each molecule, are the coercive force C; and the differences of polar attrac- 
tions across the molecule itself J/, and across the intervals between it and those 
which adjoin it D. At the contact of the keeper this interval must be far 
greater than in the continuous iron ; and the constant of attraction may also be 
different, but I think the attractions will be in a constant, perhaps an assign- 
able, ratio.* Ifin this state of things the current in the helices be stopped, the 
polarities of the molecules tend to re-unite by the forces J/— D, and are pre- 
vented by the force C, which now maintains the magnetic state as it opposed 
its production. As M must be always greater than D, and, as I have said, pro- 
portional to it, the magnetism must sink until 1/—D=C, and then remain 
permanent. It has long been known that the keeper of an electro-magnet ad- 
heres to it with considerable force when the current ceases; but I am not 
aware that the meaning of this fact has been interpreted, or measures of it taken. 
Now lifting the keeper, D is destroyed at the polar surfaces, and the forces are 
M— C,so that the magnetism will decrease till I= C, but will not necessarily 
vanish even in this case. 

It is not my intention to go further into the theory of electro-magnetism, 
which I hope will be fully developed by the able geometrician to whom I have 
already referred ; and I merely call attention to these elementary principles of 
it for the purpose of indicating the sort of information which I have endea- 
voured to obtain, and the way in which it seems to bear on these molecular 
forces. 

The power of an electro-magnet may be examined either by measuring the 
force required to detach a keeper from its poles; secondly, by observing its 
attraction of a mass of iron at a small distance ; or thirdly, by its deflection of 
a magnetic needle. The second of these methods appears to me objectionable, 
from the complication introduced by the rapid curvature of the lines of mag- 
netic action near the poles, and from the great diminution of the forces by a very 
small interval ; this is even more felt in the third, as the needle must be placed 
at a very considerable distance from the magnet. In both the varying distri- 
bution of the magnetism must be taken into account, and neither of them seems 


* The contact will be closer when the attraction is powerful, and therefore the adhesion of 
the keeper something greater than what is due to the mere intensity of the magnetism, but I do 
not know whether this effect is appreciable. 


Lifting Power of the Electro-Magnet. 295 


to offer any mode of distinguishing between the forces M, D,andC. The first 
may be perhaps less accurate as to individual measures, or at least requires 
greater care and more numerous repetitions than the method of deflection ; but 
these are probably more than compensated by the magnitude of the quantity to 
be measured. In applying it I have examined— 

1. The relation between a magnet’s power and the intensity of the current 
passing through its helices. 

2. The effect of varying the number of spires in the helices and their dis- 
tribution on the magnet. 

3. The change produced by varying the unexcited portion of the magnetic 
circuit. 

4. The difference between electro-magnets of iron and those of steel; and 

5. The influence of the length and diameter of the magnet. 

The first of these is the subject of the present communication, reserving the 
others for another opportunity. 

The apparatus which I used in making these experiments consists of an 
electro-magnet, a weighing apparatus, and the instruments for measuring and 
regulating the exciting current, each of which requires some notice. 

1. The magnet consists of two cylinders of iron (the softest and most ho- 
mogeneous that I have ever seen), each twelve inches long and two in diameter. 
They were made hollow, as from Bartow’s experiments I had imagined that 
the central portion added little to the effect ; and I purposed to experiment at 
temperatures above boiling water, by introducing heaters in these cavities. I 
find that in this I was mistaken,* but the results are merely reduced in propor- 
tion to the transverse section, or as 3: 4, the cavity being one inch diameter. 
The cylinders are screwed, with their axes 6 inches apart, into a base of the 
same iron, 2 inches deep, and 2} broad; together they weigh 26 lbs. The 
keeper is a rectangular prism, the same size as the base, weighing 7 lbs. It was 
planed and fitted so carefully, by scraping, to the polar surfaces of the cylin- 
ders, that it all but adheres to them by atmospheric pressure ; and was then 
fitted with guides, so as always to insure uniformity of contact. 


* Mr. Beret, with my helices on a solid magnet of the same dimensions, obtained with a 
current = 1:U117, a lift of 670°8 lbs, This magnet, with the same current, gives 509°2; the num- 
bers are as 4: 3:03. 


296 The Rev. T. R. Roziyson’s Experimental Researches on the 


The helices are made of lapped copper wire, No. 12, or 4 inch diameter, 
coiled in four layers on mahogany bobbins, 2% diameter, and 10-9 long. The 
two have 638 spires, and 483 feet of wire; each layer being well soaked with 
lac varnish. I used wood for these bobbins, to prevent the magnet from being 
much heated when powerful currents are employed, but in all subsequent 
helices used copper, as the wires were sometimes so hot that I feared for their 
covering.* The external diameter of the helices is 33 inches. 

2. The weighing apparatus is shown in the wood-cut. It consists of a strong 


a(R) 


| 


NAMM 
4 


Le 


oak table, T, 32 by 16 inches, and 2 inches thick, in which are, inlaid and se- 
cured by strong wood screws, two pieces of % boiler-plate. On one of these is 
fixed the magnet by a strong bolt tapped into the centre of its base B, and set 


* On one occasion, with metal bobbins, the magnet and its keeper were heated 35° in 70 minutes. 


Lifting Power of the Electro-Magnet. 297 


vertical by adjusting screws not shown in the figure.* The same iron plate 
bears the pillar P, also iron, 27-5 inches high, 2 and 1} diameter at its extre- 
mities, firmly screwed below, and steadied by oblique braces of 3-inch round 
iron (not shown), bolted to the iron at the other end of the table. This bears 
in rings of hard steel the fulcrum knife-edge of the lever L, which is of spring- 
steel, 3 thick, 3 deep, tapering to 2 and 13. Its arms are 21 and 3:5. Its short 
arm carries by knife-edges the cylinder H, in which is tapped a strong steel 
screw passing through a hole in the centre of the keeper K, and bearing it by 
a hemispheric head fitted in a corresponding cavity. The other arm is similarly 
linked by EE’ to a second lever L’, whose fulcrum is in the pillar P’ 12 inches 
high. Its arms are 10 and 1 inches; and at its outer extremity it carries the 
scale dish S. A slit in the direction of its length enables it to act as a steel- 
yard, by shifting along it small weights suspended by a loop of fine iron wire ; 
and for this object it has a division from 1'.9 to 9.5. The whole apparatus 
(except the scale) is counterpoised by attaching to L a piece shown in plan, 
fig. 2, by the screw sand the steady pin ¢t. The box O contains shot, and the 
ball R, which is tapped on a fine screw, makes the adjustment exact. 


The mode of using this instrument is easily understood. When the magnet 
is excited, and weights nearly equivalent to its lift are placed in the scale, the 
screw of the keeper must be turned till a mark on L’ stands at the index I. 
This index, which is hinged to P, so that it can be turned out of the way, shows 
when the lower edge of the slit in L’ is horizontal. Then a check-nut on the 
screw must be turned into firm contact with H, to preserve this adjustment 


* This arrangement of the magnet did not admit of its being removed, and replaced with the 
requisite precision; and latterly it was changed for one which Mr. BErctn contrived to meet this 
difficulty. A very strong rectangular frame of brass is secured on the table, 2 inches deep, and 
able to receive within it the base of the magnet, with an inch play all round. The magnet is 
slightly excited, so that it may hang freely from its keeper in this space. Then steel screws tapped 
in the brass, one in front, two behind, and two at the ends of the frame, are brought up so as to 
pinch the base equally, and thus I am certain that the pull which separates the keeper from the 
magnet will always be direct. This I find acts most satisfactorily. 


298 The Rey. T. R. Rosrnson’s Experimental Researches on the 


during a series of measures. The least of the sliding weights is now hung to 
its loop and cautiously moved, till either it lifts the keeper, or arrives at the 
end of the division. In the latter case it is changed for aheavier. If none of 
them overcome the magnet, a scale weight, equivalent to the greatest moment 
of the last of the steelyard weights, is placed in the dish, and so on. Those 
which I use are 0:1 Ib., 0:2, and 0°6 for the steelyard ; the others are 0°5, 1, 2, 
4,7, and 14; the dish also = 0°5. They were carefully verified by a set of 
grain-weights belonging to me, and another of Professor Stevetty. The le- 
verage of the machine was determined with equal care. By means of the above 
weight and a balance, for the use of which Iam indebted to my friend Mr. 
Mattet,* two of 28]bs. and two of 56 were verified. Suspending them to 
the keeper, I found the weights required to counterpoise 56, 112, 168, and 199 
Ibs., and obtained their ratio = 59°730. In these trials additions to the load of 
0:031, 0°046, and 0:094 lb. were easily detected ; an error of about 1 Ib. in 
the ton. 

A machine of this kind is of course not expected to equal the accuracy of 
an ordinary balance ; but for the work which it has to do it is far preferable 
on two accounts. To lift the keeper by weights equal to its attraction would 
be very dangerous, for the sudden descent of 8 or 9 cwt. would cause a 
fearful concussion ; while the fall of its equivalent, 15 on the pad T’, is scarcely 
felt. Besides, when the separation is nearly attained, the most delicate mani- 
pulation is necessary ; and it is far easier to avoid jar in sliding a light weight, 
than in placing in a scale one sixty times as heavy. But in fact the force to be 
measured is itself fluctuating to an extent which far passes any errors of the 
weighing. 

3. I have measured the intensity of the voltaic current by a tangent 
rheometer; and this mention of it might suffice, were it not that even in an in- 
strument so well known the details of its use are not without value, and that its 
results cannot be duly compared to those of another without a distinct know- 
ledge of its individuality. I prefer it to the one described in a former commu- 


* It is the smallest of those mentioned in his Report to the British Association on the Corro- 
sion of Railway Bars; when loaded with 56 lbs. in each scale it turns decidedly with three grains. 
All these comparisons were made by the method of double weighing. 


Lifting Power of the Electro-Magnet. 299 


nication,* as including a wider range, and being independent of the intensity of 
its needle’s magnetism. Its circular conductor consists of five copper rings, 
each 0-5 broad and 0:05 thick, the innermost of which has 16 inches internal 
diameter. This is commonly used alone, but the others can be combined with 
it. The connectors descend from the nadir of the rings within the wooden 
stem which supports them, pass through its base (which is provided with 
levelling screws), and then, proceeding about 18 inches in the magnetic meri- 
dian, turn at right angles, and proceed parallel, and almost in contact, for three 
feet, to a commutator which connects them with the general circuit. By thus 
reversing the current, not merely in the rheometer, but also in so great a length 
of the connectors, I designed to eliminate their influence ; and experience shows 
that such a precaution is quite necessary. Concentric with the rings, and per- 
pendicular to their plane, is fixed a brass circle 9 inches diameter, divided to 
half degrees, at whose centre stands a point of hard steel, very carefully 
finished to an angle of 60°. On this turns a needle 1'.77 long, 0.25 deep, and 
0-05 thick ; it has a ruby cap, and pointers of palladium long enough to reach 
the divisions ; and it weighs altogether 75 grains. It has been shown by 
Wes:Er (Poggendorf, vol. lv.) that if the ratio of the ring’s diameter to the 
length of the needle be greater than 4 or 5, the tangent of deflection is propor- 
tional to the force. This ratio, however, is too low for high deflections. When 
it is 4 I find the law fails at 33°, and when 4°'8 at 50. In this rheometer it is 9. 
As, however, it was necessary to ascertain whether the influence of the con- 
nectors was injurious, I at the same time examined its sufficiency by the volta- 
meter, and found for 28 angles from 20° to 75°,} that the tangents are exactly as the 
quantities of mixed gases evolved in a given time, supposed dry, and at the nor- 
mal temperature and pressure. The factor by which the tangent gives the current 
force ’ depends on the unit assumed for that quantity. Weber, in the memoir 
referred to, uses one derived from the intensity of terrestrial magnetism at the 


* Transactions of the Royal Irish Academy, vol. xxi. p. 303. 

{ It was formed by traversing it while rapidly revolving in the drill apparatus of a slide-rest, 
inclined at 30° along the surface of a cylindric lap also rapidly revolving, and charged first with 
very fine emery, and then with crocus. It bears examining with a power of 120 diameters, and is 
far more perfect than any point which I have seen in a theodolite or compass. 

} The greatest which 18 Groves’ could produce with the voltameter. 


VoL. Xx. 2k 


300 The Rev. T. R. Rozrson’s Experimental Researches on the 


place of observation, a quantity variable in itself, and by no means easy to ascer- 
tain. Dr. W. Tuomson has more recently proposed* one expressed in terms 
of the mechanical effect to which the current is equivalent ; which, however, 
must be regarded as a scientific conception, rather than of practical use. A 
standard, to be available, must be of easy access and application, and in these 
respects I see no reason for preferring any to one which is in frequent use, the 
electrolysis of water. The most obvious current unit is that which can decom- 
pose a grain of water in a unit of time. It seems to me, however, that if a 
second, or even a minute, be taken as time unit, the values of current will be 
inconveniently fractional, if an hour, as much too large, and therefore I take 
five minutes. Adopting this, all that is required to make these rheometers 
speak a given language is, to note the seconds in which a known volume of the 
gases is evolved, and reduce it to that due to 300 seconds ; to compute its nor- 
mal volume G by means of the formule in treatises of Pneumatics, and measure 
carefully the deflection ¢’, then we have 

Gxcotang | FP 
log (0°89310)’ 
the experiments for which can be completed in a single day. 

Both ends of the needle are read with direct, and again with reversed cur- 
rent, to eliminate excentricity and zero errors; the readings are made with a 
prismatic microscope, and can be depended on to 2’. } 

The rheostat is used in these experiments merely to equalize the current, 
and therefore has no necessary connexion with their results; but as in a former 
communicationt I mentioned its peculiar construction, and promised further 
details, I take this opportunity of stating my conclusion as to its working. 
As exhibited to the Academy on that occasion, it consisted of a wire of pla- 
tinum, whose length was varied by raising it out of mercury, while it was 
cooled by being surrounded with distilled water ; and I expected that by mea- 
suring the temperature of this latter fluid I might apply the necessary correction 
for the change of resistance due to the heat evolved by the passage of the cur- 
rent. Unless this be attended to, I am satisfied that no measures can be made 


m= =m x tang; 


* Philosophical Magazine, 1851; p. 551. 
+ Transactions of the Royal Irish Academy, vol. xxi, p. 303. 


Lifting Power of the Electro-Magnet. 301 


deserving full confidence, and that it is necessary even with the feeblest transference 
of electricity. ‘This especially applies to those methods in which a current is 
divided between two conductors, and its respective quantities in them are esti- 
mated from their relative resistances, previously determined. That relation 
involves the temperature of each, and varies with the current. In many re- 
spects this rheostat was a great improvement on that which I previously used, 
these probable errors being 0'.16 and 0'.28 ; but I soon found it could not in- 
variably be trusted. Occasionally a film of water would adhere so obstinately to 
the platinum, that its contact with the mercury did not occur till two inches 
below the surface of the latter ; and this state would continue for several days. 
A little solution of potassa lessened this tendency, but made the water too good 
aconductor ; I therefore abandoned the mercury in that part of the instrument, 
and made the contact by a spring clip of platinum. This change enables me to 
use a wire of palladium instead of platinum ; the former resisting twice as much 
with the same section, and, what is more important, varying its resistance ten 
times less by a given change of temperature ; being, in this respect, the lowest of 
all the metals which I have examined. These alterations have improved the ac- 
curacy of the rheostat, its probable error being now only 01.06. The wire is 
qs diameter, and its range 15 inches, read to 0'.01, by a vernier.* If greater 
resistance be required, 19 equivalents of the same wire, also immersed in water, 
can be added to the circuit. I wish I could give some more definite statement 
of this wire’s resistance than is contained in the mention of its diameter, for that 
alone is not sufficient. Platinum wire I find, even when drawn in a gemmed 
hole, and heated white hot after its passages, resists unequally in different parts 
of the same piece,—much more may different specimens be expected to differ. 
A tolerable approximation to it, however, is given by the fact, that if we use 
the current unit just described, the intensity (or the electro-motive force of the 
contact theory) of a Groves’ cell, determined by the tangent rheometer, = 47°282 
inches of this wire. 

Another measure (which I hope may ultimately prove an accurate one) is 
afforded by the electrolytic intensity of water (the imaginary polarization of 


* Equal to 970 inches of ;1; copper wire. 
+ Mean of the last 20 I observed, the greatest being 48°675, the least 45°345. 
2R2 


302 The Rev. T. R. Rosinson’s Experimental Researches on the 


electrodes of the contact theory). As I have formerly shown, it varies by heat. 
I assigned 0:04986 as the change for 1° Fahr., but this value was obtained by 
dividing the current, and without means of correcting the rheostat for tempe- 
rature. I have since obtained by better methods— 


e at 60° = 62:229, change for 1°= 0:06735. 


It is not affected by the quantity of sulphuric acid mixed with the water to in- 
crease its conducting power, being almost identical whether this be 4 or ;, of 
the electrolyte. Nor is it (within very wide limits) by the size of the electrodes; 
being the same when they oppose surfaces of 19 square inches (the size of the 
platinum in the battery), of 3, or of 0°75, the intensity of the battery being 
given. 

But there is a change, real or apparent, depending on that intensity. The 
value above given was obtained with two Groves’; with three it is 69°137 at 
60°, and with four 75-052. It is my present belief that this seeming increase 
is caused by two things: by the internal resistance of the cells decreasing in 
consequence of being heated by the current, and by the rheostat wire being 
hotter within than at its surface. The thermometer immersed in the water 
gives merely the latter temperature, and therefore the resistance correction is 
too small.* This, however, I hope soon to be able to determine. 

After this long preface (which I hope will not be useless to any one who 
may engage in these or similar researches), I proceed to state in the following 


* Taking the equation 
# 

Rir 
and introducing a resistance p, which produces the deflection ¢’, 

_ _m(p+dk) 

~ cot @’ — cot d’ 
dR being any change of the cells’ resistance. Introduce now the voltameter, and a similar equa- 
tion gives H—e. Now if the wire be hotter than we reckon, we use a value of p less than the 
truth, E — ¢ is therefore too little, as we compute it; but H, as separately determined, is also too 
little, nay, even more so, because the current is stronger when the voltameter is not in circuit. 
Therefore e will be too great. To obtain access to the truth, it will be necessary, first, to deter- 
mine the law of the cell’s resistance as connected with its temperature; and secondly, to measure 
the wire’s temperature not by an immersed thermometer, dwt by its own expansion. 


mtan p= F= 


Lifting Power of the Electro-Magnet. 303 


Table my results, subjoining an explanation of each of its columns, and any 
miscellaneous facts which could not be easily tabulated. 


TABLE. 
; dL 
Obs. F 7 L at 60°. a | X A 
| 
ae eee ee ee 
10 6°8528 78°1 775°24 as 4-66 131°81 
10 5°2015 85°4 722-70 20) 4526 136°34 
10 4°6566 94-2 713-79 31 | 477 131-31 
10 3:9366 65:1 677-00 50 5°46 125°51 
15 3°5843 66-0 65928 42 || 4-79 131-74 
10 371303 724 645°14 32 || 5:52 131-07 
15 2:5496 67:9 632-72 45 5:60 128°31 
10 2-1769 65°5 61002 78 4°30 130°80 
10 1-8876 63:9 588:07 75 || 465 126°10 
19 15384 62-7 568°51 99 4:74 SO 
15 14107 61-5 553°81 102 4-56 13416 
20 1°2565 63:7 540°61 101 4-60 128750 
25 1:1071 62:9 521°12 128 4:87 131°41 
25 0°:9589 62:3 499°80 180 4-41 13039 
10 0-7909 62:3 462°53 264 5°17 13114 
15 0-6272 61°8 412°52 305 || 4:37 125°71 
10 05482 62-0 388742 340 4:59 12488 
10 0:4693 617 || 358-81 492 4:96 127:29 
10 0°3921 62-0 31204 638 4:38 116712 
10 0°3145 61-1 259°95 735 4°53 110710 
10 0:2340 61-1 195-49 799 5°06 90°78 
10 0:1565 62:2 13367 928 4°87 77:49 
| 10 0:1164 60-2 93°79 1028 4°36 62°37 
10 0:0794 59°2 54-61 1029 4:04 37°50 
10 0:0389 59°3 14:18 621 412 10:08 
50 0:0000 Cos 4-44 41 aval eiomike 
10 | — 0:0389 58°8 + 2:19 49 + 2°75 + 3°28 
5 | — 00798 59°5 -— 2°81 134 + 3-00 — 3°67 
5 |-—0:1162 62:8 — 29°30 1148 | - 1°81 -— 11°19 
5 |-0°1551 60:0 — 91:26 1503 - 3:79 - A777 
5 | — 0°2343 62:1 — 166-72 926 — 4:20 -— 7758 
4 |-—0°3140 62:1 | — 238-46 776 — 469 — 92°76 
5 | — 0°3925 64-7 — 289°81 735 4-4 lee cpeuens 
3 | — 04707 61-2 — 353°64 ae 6 — 6:49 -— 114:39 
5 | — 06243 60:2 — 404-64 teh Vo OA ats a felele 


The second column of this Table contains the number of experiments on 
which the value of Z given in the fifth is based. In general, two sets of five 
each were taken on separate days, and if they were in close agreement this was 


304 The Rev. T. R. Rosinson’s Laperimental Researches on the 


thought sufficient. But it sometimes happens that though each set is perfectly 
consistent, the two differ as much as 20 lbs., which occurs especially when the 
magnet’s lift is about half its maximum, at which point the coercive force of the 
iron seems to make some abrupt change. In these cases other sets were taken, 
till from the uniform spread of the differences I felt satisfied that I had obtained 
a fair average. 

The third column, headed F, contains the values of the currents expressed 
in the unit which has been described above. It must be remembered, however, 
that they act on 638 spires. I consider them true to 0:001 at least of their as- 
signed amount. The negative sign indicates that in these instances the direction 
of the current is reversed in the helices. 

The fourth column gives 7, the temperature of the magnet, as shown by a 
thermometer dipped in mercury, which filled the upper inch of the cavity in 
the northern cylinder of the magnet ; at first both cylinders were tried, but this 
was found useless. It is necessary to know the temperature, for the force of 
electro-magnets, as of common ones, varies with it. To investigate the correc- 
tion, 40 feet of leaden pipe, %-inch external, and } internal diameter, were 
coiled on helices, containing 316 spires of the same wire used in the others, but 
coiled on tin tubes. These worms had each 25 turns; they were covered 
with thick cloth, and connected by a tube of vulcanized caoutchouc with a 
small boiler, so that a current of steam could be passed through them, and the 
condensed water escaped from their open extremity.* As the keeper and base 
(which were also covered with cloth) presented much cooling surface, the 
temperature could not be maintained above 180°, but could be kept very steady. 
The lift of the magnet being then determined, the magnet was left to cool, 
and the observation was repeated at the ordinary temperature, and with the 
same current as nearly as could be managed. As I was not aware of any rea- 
son for supposing that the effect of temperature changes its law under that of 
boiling water, I assumed the change to be as the temperature, or, L being the 
lift at 60°, 

Ie lhisg {1+ 7(T'—60)}. 


* To the last it was turbid with sulphuret of lead, so that this material cannot be depended on 


as a conductor of steam. 


Lifting Power of the Electro-Magnet. 305 


Hence 


Bp aol i ge gt Uline 6:60? yar dec 
P=1P at) UT HT) 


Then I obtained 
1 ase viene. LS 6ie:0). «+. Less 830 


p=VA80;94e yW-u-ue Sue CONS eet 15868 
9 ie DSoiOAN aie tan cneles AGASSI eS 2°6198 
LUGO Sees tatters UO Sean 60 26198 
3 he (ELUSHOKD) 69 5 comsicwant HOVE eter eters 35634 
= "GGE Gar ee oe ee UB. ac Spore 35761 
4 ps SVB) omareieus ae IUGR o oe Ol Oc 08613 
p= CEH elo 6 oleic Goro ror uemey ua 0:8608 


Interpolating for the difference of F in each pair,* I obtain from these— 


1. +t=— 0000385 
2. .. .—0-000300 
3. .. .—0:000220 
4, ...—0:000385 


Mean, . — 0:000322 


The three first might induce a suspicion that + diminishes as F increases ; 
but the fourth disproves this ; and as the third set was less consistent than the 
rest, I regard the difference as mere error. I use the value 0:00033. 

Subsequent to these experiments Dr. Lloyd has discovered that the induc- 
tive power of terrestrial magnetism is increased by a small elevation of tempera- 
ture. Before this came to ny knowledge I had applied the wire of these 
helices to other purposes, or I would have examined the coefficient 7 at inter- 
mediate temperatures; I have, however, made a similar observation with 
respect to steel electro-magnets, and suspect it depends on the coercive force 
bearing a high ratio to the inducing force. In the present instances I do not 


* The interpolation was deduced from a special series; these values of Z not being comparable 
to those of the Table, as the helices have only half the number of spires, are of less diameter, and 
their tin bobbins add something to the mass of the magnet. 


306 The Rev. T. R. Roprson’s Experimental Researches on the 


think any change of sign occurs: were it otherwise I must have noticed its 
effect ; as in many of these experiments the magnet has been heated by the 
current above 100°, and an increase of Z must have been produced contrary to 
all my experience. I may, however, have occasion to re-examine the question, 
and will not neglect it. 

The fifth column gives Z, the number of pounds required to lift the keeper, 
obtained by reducing the observed number to 60° by the coefficient 7. It may 
seem an easy matter to obtain this, but no one who has not tried it will be pre- 
pared for the many precautions that are necessary. 

1. The utmost stability in the apparatus, absence of tremors, and delicacy 
of touch, are required. With a heavy lift, when approaching the limit of adhe- 
sion, the agitation caused by a step, the shutting of a distant door, or the action 
of a gust of wind on the building, will determine a break of contact, with a 
deficiency of 10 or even 20 lbs. 

2. These magnets (and it is the case also with permanent magnets) will 
bear a much greater load if the strain be gradually increased, than if it be ap- 
plied abruptly, the difference being sometimes 40 lbs. Therefore the weight of 
the steelyard must be slided along very gradually (and I need scarcely say with 
cautious handling), and allowed to rest at each step a few seconds, as it were, 
to let the acting forces adjust themselves. I do not see why this should be, 
unless, perhaps, the state of tension which is produced favours the development 
of magnetism, but the fact is very striking ; when the keeper is detached and 
immediately replaced, it will not nearly resist the load, even if that be upheld, 
and then lowered to its bearing. 

3. Time is an important element: I do not think any current which the 
wire of this magnet can conduct is capable of developing its full power in a few 
seconds. With the highest power which I have applied it must act for five 
minutes at least, and from /=0°3 downwards for full fifteen. This has been 
noticed, though in a far less degree, by Faraday, who observed the circular po- 
larization caused by the action of electro-magnets on dense glass to increase 
for a minute and a half after making the contact. That, however, is not avery 
delicate test ; and as the poles of his magnet were not connected by a keeper, 
the molecular excitement must have been far less intense than in this case. 
As a specimen of this sluggishness of inductivity (which, by the way, is a 


Lifting Power of the Electro-Magnet. 307 


serious impediment to electro-magnetic engines), I give the set which first de- 
cidedly convinced me of its influence. 


Mme —10"), 2 2— 20926... = O27ol 
Geog o des IIMS Sa 6s 02779 
Ne) SReres emer PALUS OP IRE oepwemel ie 0°2655 
Sagues cuauote UBS og oe oeeue 0:2603 
1 arsed cresting PAIGE Cxorouona 4 0°2568 


The increase of time more than compensates for a considerable diminution 
of current. Ihave regulated the duration of each set according to what I con- 
ceived to be a sufficient allowance of time. 

4. These causes are uniform in their action, and can be avoided or corrected, 
but there exists another, which is the chief source of error in these experi- 
ments, namely, the molecular change which iron suffers when exposed to power- 
ful magnetization. In consequence of this, however pure and soft it may be, 
it becomes capable of retaining permanent magnetism, and in the same proportion 
less susceptible of excitation by its helices. This magnetism (which I call A) is 
variable ; it may, perhaps, be intense while the magnet is excited, but on lifting 
the keeper it declines rapidly till it attains a certain amount, which is, however, 
not invariable ; and it always increases during a set, though after a few hours 
it returns to its ordinary quantity. It, however, occasionally happens that 
when the magnet has been powerfully excited for many days, its iron becomes 
disturbed in this respect, and then the values of Z fall far short of their legiti- 
mate magnitude. In such cases it is best to leave it at rest for a few weeks ; 
but I have found that if the current be reversed the Z becomes higher, and 
have therefore in many instances performed this for the alternate measures. 
The results thus obtained are tolerably uniform, but are always less than those 
given by a magnet that has never been excited, or has been long in repose. 
With excitation less than what is given to this magnet by a current = 1, this 
cannot be done, because then it will be seen from the Table that there isa real 
difference between the L’s produced by the direct and reverse currents. One 
consequence of this change deserves notice, which may be observed in almost 
every series,—the gradual decrease of the successive measures of a set. Thus 
in one taken with peculiar care, 

VOL. XX. 2s 


308 The Rev. T. R. Rosixson’s Lxperimental Researches on the 


Time =7™... £2=66165 ... F kept at 35938 


(Ora oad 6. ° 658°34 
7 . - 648°10 
wy Bao aoe 647-44 


S) oa ooo A (eas) 


From all this it follows that the values given in this Table can be offered only 
as a first approximation, but I hope aclose one. The negative values imply that 
the polarity is reversed. 

The sixth column contains the factor which gives the change of Z due to a 
small variation of F. It is the coefficient of the first power of the variable in 
the formula for interpolation when the distances of the values from which it is 
derived are unequal ; and besides its use in correction of results when there are 
small differences of power, it is given here, because it must be, nearly, what I 
call it at the head of the column, the first differential coefficient of Z in respect 
of /',and as such may be useful in testing the hypotheses which we form respect- 
ing the functional relation of these quantities. Into this inquiry, I have stated 
that I do not intend to enter, and I will at present merely direct attention to the 
entire want of proportionality between Z and F. 

Ascending from No. 26 we find that a current = 0:04 produces a power of 
10 lbs.; the addition of a second 0-04 adds 40; of a third, the same ; after which 
the rate of increase goes on decreasing. No. 13 shows that a unit current will 
excite an Z of 500 lbs.,and No. 1 that one nearly sevenfold will add to this only 
its half. The result is even more striking if we consider column 6. Were LZ 
as F, the numbers there should be constant ; whereas they decrease from 1028 
to 20; and were the series continued upwards, must vanish at a certain value 
of Z not very much greater than 800. This leads us to the remarkable con- 
clusion that Z cannot exceed a certain magnitude A, however intense the 
exciting power may be,* and as a necessary inference, that the separation of 
magnetic polarities has a limit. For if we revert to the conditions of an excited 
electro-magnet, which I have noticed at the commencement of this memoir, it 
is clear that at the surface of contact of the keeper we must have 

0=aH+bD-—cM - eC. 


* This has been announced by Mr. Joule (Phil. Mag.); it was, however, recognised by me long 
before I knew of his paper. 


Lifting Power of the Electro-Magnet. 309 


Now there is good reason to believe that C has a limit, or, in other words, that 
the molecules of iron can oppose only a limited resistance to induction ; D and 
M are as L, and therefore if H be infinite, so must the latter also be, unless J7 
too have a physical limit. What that limit is,—whether the expansion of the 
hypothetic fluid, or the impossibility of exciting vibratory movement beyond a 
certain extent,—I do not pretend to determine. For this magnet I believe the 
A to be under 1000 lbs. Secondly, I would call attention to some other facts 
that seem important. At No. 26 is found 4:44 for Z when there is no exciting 
force, it is the permanent magnetism A. If we apply a direct current 0:04, it 
adds to this 9:74 ; ifa reverse, it only subtracts 2:25 ; Z therefore is a function 
of X. as wellas of F. At Nos, 24 and 28 the differences are + 50°17, — 7:25; at 
23 and 29 still wider asunder, after which they begin to approach, but are not 
the same exactly till F passes + 0°7. At # = 1-24, the direct and reverse re- 
sults are identical. It follows from this that the coercive force consists of at 
least two terms, one changing sign with J’, the other depending on the habi- 
tual direction of the excitation ; the latter is not overpowered completely until 
£=4A, and does not vanish even when L = 0, as is manifest from Nos. 27 
and 28. As a practical deduction, we may infer that in all machines involving 
the reversion of an electro-magnet’s polarity, its excitation should not fall short 
of this. On the other hand, it should not much exceed it; for the increase of 
power gained by a given increase of current is constantly lessening, and the 
consumption of materials augments even faster than the current. 

The seventh column gives the value of A the residual magnetism, which, for 
reasons already stated, should be known, in order to compare Z with any for- 
mula. These numbers are given by from six to ten observations ; and it will 
be observed that they do not vary much. When the reverse happens (as in 


Nos. 4-7) it is evident from the irregularity of the quantity = that the values 


of Z are discordant from the rest of the series. It will also be noticed, in con- 
firmation of what was stated as to the coercive force, that in No. 28 A remains 
positive, although diminished, although LZ is negative. The highest value of it 
which I ever got is 8°88, which (the keeper being removed in the mean time) 
gradually decreased till, after 36 hours, it was permanent at 3°17. 
The last column gives A, the residual excitation, or the force which the 
282 


310 The Rev. T. R. Rozrnson’s Experimental Researches on the 


magnet retains when, after being excited, the current is withdrawn, and it is left 
with the keeper down, and which I consider to be the phenomenon that promises 
the most direct information as to the law of the coercive force. This state 
seems to continue for an indefinite time ; at least I have never found any dimi- 
nution of its intensity after many weeks. Accordingly, in observing it, I have 
either left it 10" or during the night. It corresponds to the state M— D=C. 
During the previous excitation these forces were of much greater amount, and the 
force C' had aided Jf—D against H: when the latter is withdrawn, M re-unites a 
portion of the opposite polarities, and decreases in consequence, so of course does 
D. As to C, there is some reason for believing that it may in the first instance 
aid this re-union ; and thata certain decrease of J is required to develop the 
molecular action on which it depends in the opposite direction. If so, it will 
depend not on the MW which co-exists with it, but a previous one. However, 
we know that it must also soon begin to oppose the force M—D. Now it is 
obvious that if C’ were constant, the final value of JZ — D, and therefore of A, 
must also be so ; ifit were proportional to M, A would vanish ; and if it were 
in any inverse ratio of it, the differences of Z and A would lessen as they in- 
creased. On inspecting the Table it does appear that all above No. 15 may be 
considered of the same value, in its mean 130°68: which amounts to this, that 
the force C cannot arrest the decrease of the magnetism as long as it exceeds half 
the maximum A. Is it constant above this, where, as has been shown, it yields 
equally to excitation in either direction, or does it merely suffer there some 
abrupt change of magnitude ? For lower values of Z it decreases, bearing 
always an increasing ratio to it; thus in No. 21 it is nearly half, in No. 23 two- 
thirds ; and in the negative values this continues to hold, although, as in the 
case of L, they are long less than the positive. If, while the magnet be in this 
condition, we pass through its helices a current that would in the ordinary mode 
give it a force equal to its A, its entire effect is not superadded to the other. 
Thus I found that, having passed / = 09864, which on this occasion gave 
A = 12518, if I passed then # = 0:1395, which would have produced 
L = 124:46, I had L’+ A= 169-81; so that it only added 44°63. This was to 
be expected from the principles already explained ; but I cannot so well ex- 
plain an experiment which shows that a current which can give L =34A pro- 
duces the same results even if the magnet have residual excitation. Ifa negative 


Lifting Power of the Electro-Magnet. 311 


current be passed, it destroys this condition, unless very feeble, but even then 
it lessens it; thus 0°0127 reduces A from 129°41 to 117°51. I may add, that 
even the fifteenth of this will excite this magnet, and change its residual 
magnetism. 

While the magnet is thus circumstanced, it shows faint traces of free mag- 
netism ; each cylinder having its accustomed polarity at its acting surface, the 
opposite at its other extremity, and a neutral point in the middle. The ends 
of the keeper and base have the same polarities as those of the cylinders with 
which they are in contact. If one cylinder only be excited, the value of A is 
the same as for the two, but the distribution of the magnetism is modified, as 
might be expected. 


vs 


313 


XIV.—Report on the Chemical Examination of Antiquities from the Museum 
of the Royal Irish Academy. By J. W. Matter, A. B., Ph. D. 


Presented April 11, 1853. 


THE examination of the antiquities to which the present paper refers was 
undertaken in the hope that more extensive and accurate chemical informa- 
tion, as to the nature of some of the materials employed by the craftsmen who 
so many centuries ago formed the numerous implements used for purposes 
of war and peace, which now are to be found in the Museum of the Aca- 
demy, might be found of value in elucidating the history of the ancient arts 
by which these implements were produced. 

This Museum has afforded peculiar facilities for a research of the present 
nature, as from the great extent and variety of the objects which it contains, 
and its general completeness as regards Irish antiquities, it was easy to procure 
a sufficient number of really typical examples in each of the departments exa- 
mined, without injuring the collection of specimens, as such. 

The greater number of the articles submitted to investigation were metallic; 
the universal applicability of the metals for the purposes of peace and war, of use 
and ornament, rendering everything calculated to throw light on the materials 
and processes employed in ancient metallurgy, most important and interesting. 

The specimens of this class were most carefully selected, and may, I think, 
be fairly taken as types of this department of the Museum. 

Commencing, then, with the ancient metals and alloys, the first to be de- 
scribed are the 

GOLD ORNAMENTS, 


of which class of Celtic antiquities I have seen no record of any previous 
analyses. 


314 Mr. J. W. Matret’s Report on the Chemical Examination of Antiquities 


Of this metal I analyzed eight specimens, viz.: 

No. 1. Fragments of one of the twisted “ torques,” supposed, I believe, to 
have been worn round the neck (Museum mark,513p). It consisted of a strip 
of thin plate gold, twisted so as to form a spiral, this being then bent into a 
circle, and the ends turned into two small hooks, by which the torque was 
clasped. The ornament had been broken up by the finder into pieces of about 
two inches long, but when entire its circle must have been ten inches in dia- 
meter. The part examined consisted of the two end hooks. The colour of 
the gold was a pale, rather sickly, yellow, and its specific gravity was 15°377. 

No. 2. Fragment of a torque similar to No. 1, and most probably found 
along with it, in the county of Sligo; but the locality of neither is certain. Mu- 
seum mark, 516 p. This specimen, which was of a rather deeper yellow colour 
than the last, was from the middle of the torque. Its specific gravity, 15-444. 

No. 3. Part of a twist of wires of about a tenth of an inch in diameter each, 
the whole length of the twist, which is straight, being about six inches. 
Locality unknown. This may have formed part of a bracelet, but there is no 
second specimen in the Academy Museum, and from its workmanship it does 
not seem likely to be by any means of so ancient a date as the majority of these 
gold ornaments. The colour was a very deep rich gold yellow, and the 
specific gravity, 18°593. 

No. 4. Two fragments of a lunette-shaped ornament, made of very thin gold 
plate, and having a little pattern round each edge. The whole must have 
measured ten or twelve inches across, and the greatest breadth of the flat plate 
itself was about two inches. It was probably a neck gorget, or ornament for 
the head, similar to many others preserved in the Museum of the Academy. 
The locality of the specimen is unknown. It is of about the same colour as 
standard gold, and of specific gravity, 17°528. 

No. 5 was a small plate or spatula of gold, about an inch and a half long, 
and a quarter of an inch wide. It was probably unmanufactured gold, not 
intended for any special use in its present form. It is not known where it 
was found. The colour was a little lighter than that of No. 4, and specific 
gravity, 17-332. 

No. 6. Fragment of very thin plate gold, which formed part of a boss or 
convex ornament, about four inches in diameter, very like those which cover 


From the Museum of the Royal Irish Academy. 315 


the ends of the ornaments supposed to be diadems, in the Academy Museum. 
Locality unknown. It was of nearly the same colour with No. 4, and its 
specific gravity, 15°306. 

No. 7. Specimen of supposed Celtic ring-money. It consisted of a bit of 
gold wire, of about three-fourths of an inch long, and nearly an eighth of an 
inch in diameter, bent into a circle, the ends being quite close, but not fastened 
to each other. It has been stated by Sir Wmu1am Beruam® that the weights 
of these rings used for money were graduated with reference to the unit of 
twelve grains, or half a pennyweight, Troy. This specimen weighed 62:13 
grains, or 2dwt. 12grs., five of Sir W. Bernam’s units, and 2°13grs. over. Co- 
lour about the same as No. 5. Specific gravity, 17-258. 

No. 8. Another specimen of ring-money. It was rather larger than No. 7, 
but composed of thinner wire. The colour was very much the same with the 
last, and specific gravity, 16°896. Its weight was 30°04 grains, which is ex- 
ceedingly close to 1dwt. 6grs., or two and a half of Sir W. Beruam’s units. 
Hence it was about half the weight of No. 7. The localities where these spe- 
cimens were found are not known. 

The results of the analysest of the gold ornaments were as follow:— 


Gold5aa on. 
Silver, ..| 23°67 18-01 2-49 11-05 10-02 12-18 12°14 12:79 
Copper, . . 4:62 2-48 | Trace. 12 1-11 594 1:16 147 
Lead, ...]| Trace. 6. oan & analc faa & See +28 Trace. Carica 
To) 65 15. Ge Ot llecy sce Becae wat kes Bold moe 


We observe here considerable diversity of composition, and on the whole 


* Transactions of the Royal Irish Academy, vol. xvii. Antiquities, p. 7. 

} The process of analysis calls for no particular remark, except that the gold was precipitated 
from the solution made nearly neutral by evaporation, by adding (hot) a slight excess of sulphate 
of ammonia, which re-agent throws down the metal in the form of a compact sponge, and does 
not produce the effervescence occasioned by oxalic acid. 


VOL. XXII. DoT 


316 Mr.J. W. Matzet’s Report on the Chemical Examination of Antiquities 


the existence of a greater amount of alloy than one would expect from reading 
the accounts of gold ornaments to be found in various books on antiquities, 
in which they are often described as of “pure gold,” “fine gold,” &c., the 
colour being apparently very often the only guide to sucha belief. Although the 
analyses here given differ much from each other, yet we find some traces of 
connexion between the composition of the alloys and the forms into which they 
were manufactured. 

Thus, Nos. 1 and 2 are greatly below the standard of the others, and these 
are both specimens of the same kind of ornament, the torque, and the only 
specimens examined. They do not differ much from the composition of the 
electrum of the ancients, as given by Pliny and others.* 

No. 6 is about on a par with these as to the quantity of gold, but contains 
a larger proportion of copper, and less silver. 

Nos. 7 and 8 accord very closely with each other, a circumstance particu- 
larly interesting from the probability of their having been used as money. For 
if, as is urged in the memoir on this subject before referred to, these rings 
really represent a metallic currency of graduated weight, based upon a fixed 
standard, it surely would be a strong confirmation of this opinion, as well as 
a fact highly illustrative of the advanced state both of commerce and of metal- 
lurgical skill on the part of the fabricators of these rings, if they were shown 
to be also of constant composition, and that therefore their relative values 
were actually represented by their proportionate weights. To decide this ques- 
tion, however, more numerous analytical results would be indispensable. 

Nos. 4 and 5 in the Table also agree very closely, from which we might 
surmise that the latter, which probably was not intended for use in the condi- 
tion in which it was found, was perhaps in process of manufacture into one of 
the thin lunette-shaped ornaments, like No. 4, which have often been found in 
Ireland. Its small size, however, renders this more doubtful. 

No. 3 is of a much higher standard than any of the others, and approaches 
fine gold. From its being wire-drawn in the ordinary way through a draw- 
plate, it is probably not nearly so ancient as the other specimens examined. 


* “Ubicunque quinta argenti portio est, electrum vocatur.”—Plinti Hist. Nat. lib. xxxiii. c. 4, 
“« Alia (species electri) ex partibus auri tribus et una argenti conflatur.”—WMargerit. Philos. 1523. 


from the Museum of the Royal Irish Academy. 317 


In the earliest ages wire appears to have been made by cutting thin plates of me- 
tal into strips* and rounding these upon the anvil; and Beckmann, in his His- 
tory of Inventions, seems to think that the modern method dates no earlier 
than about the middle of the fourteenth century. 

If these ornaments presented no appearance of determined composition, and 
on the whole contained less silver, it might be supposed that they were made 
of native gold, merely fused, and worked into the required shapes; but from 
the results actually obtained, although they are by no means conclusive on this 
point, I think it appears more likely, on the contrary, that these articles were 
made from alloys artificially produced, and perhaps from determinate quanti- 
ties of the constituent metals. If this supposition be correct, no information 
can be derived from these analyses as to the geographical source of the surpris- 
ing quantity of gold found in the manufactured state in Ireland. In Corn- 
wall along with the stream tin, in Scotland, and in much larger quantity in 
Ireland itself, in the county of Wicklow, native gold has been obtained, and this 
metal (as well as silver, iron, tin, and lead) is mentioned by Strabof{ among 
the products of Britain. It is therefore conceivable that much of the precious 
metal used in this country may have been found at home, though its quantity 
would seem to indicate foreign commerce as the more likely channel by which 
it was procured, unless native gold was anciently much more abundant in Ire- 
land than it has been in more modern times. 


SILVER ORNAMENTS. 


These are much rarer in Ireland, and throughout the north of Europe, than 
those of gold, as indeed might be expected in collecting the relics of so distant 
a period, when we consider that the latter metal occurs, it may be said, invari- 
ably in the native state, while the former is found so but rarely, and, in Europe 
at least, not in any very great quantity; and that the silver ores from which 
it is most abundantly obtained require the application of much metallurgical 
skill for the extraction of the metal. Apart, too, from the initial difficul- 
ties attendant upon the smelting of its ores, silver, when obtained, is by no 
means so malleable or easily worked as gold, a circumstance which in some 


* Exodus, xxxix, 3. Homer, Odyss. lib. viii. 273-278. t Vol. i. Art. Wiredrawing. 
} Lib. iv. 30. 
272 


318 Mr. J. W. Matiet’s Report on the Chemical Examination of Antiquities 


degree accounts for the rude workmanship of very many of the Celtic antiques 
of this material. 

Of the specimens in the Royal Irish Academy collection I selected and 
analyzed the following eight:— 

No. 1. A small ingot of silver, cast in an open mould. Museum mark, 
* fs|. It was of a long oval shape, about two inches in length, and half an 
inch wide. It had two small nicks in one side, close together, as if to mark its 
weight or value. Its weight was 377-23ers. = 15dwts. 12grs. (+ 5-23grs.). 
Hence if used for money it would have been equivalent to 31 or perhaps to 
32 of the half-pennyweight units. It was a little tarnished by superficial 
sulphuret of silver. Its specific gravity = 10°225. 

No. 2. A piece of hexagonal wire, very neatly made, probably by hammer- 
ing, about an inch and a half long, and an eighth of an inch in diameter. Mu- 
seum mark, 809 c. It was bent into the shape of a horse-shoe, and the ends 
were cut sharply off, so as to induce the belief that it too may have been used 
formoney. It weighed 103-86 grs. = 4dwts. 6grs. (+ 1:86grs.) or about eight 
and a half units. Its specific gravity = 10°253. 

No. 3. End of a taper bangle or penannular bracelet of very rude workman- 
ship. Also, perhaps, occasionally used as money. It was very hard, and 
rather brittle, breaking with a fine earthy fracture of a yellowish white colour. 
Specific gravity = 8-770. 

No. 4 was a specimen which appeared at first sight to be part of a flat 
silver bracelet or armlet, stamped with the triangular indentations so common 
on the silver ornaments of Celtica and Scandinavia, and not broken, but cut 
across at the ends. Museum mark, %. On attempting to cut it again, how- 
ever, it turned out to be a counterfeit, consisting in fact of a core of iron 
covered with an exceedingly thin plate of silver, which was so skilfully joined 
as to deceive the eye even on careful observation. ‘This imitation of articles 
in the precious metals has been observed before in gold rings, which are some- 
times found on a thin shell of the valuable material covering a large core of 
copper or occasionally of lead; but I can find no recorded instance of silver 
counterfeits of this kind being found among presumed early Celtic antiquities. 
The iron core of this specimen was much corroded, and the silver was tarnished 
by sulphuret. Specific gravity of the silver = 10°379. 


from the Museum of the Royal Irish Academy. 319 


No. 5. Fragment of a flat armlet, broken across at the ends, and stamped 
with small square indentations. Museum mark,‘“’. There were traces of 
chloride of silver upon the surface, which was much worn. Specific gravity 
= 10°335. 

No. 6. Two fragments of round wire, forming part of a torque large enough 
for the neck. They are stamped with a small pattern of alternate squares and 
little pellets in relief. Specific gravity = 10°519. 

No. 7. Two fragments of square wire, part of a number of wires twisted 
into a spiral bundle so as to form an almost solid cylinder. The twist formerly 
united two silver boxes covered with filigree work. Specific gravity = 10-468. 

No. 8. Part of the hinge of a chased hollow bangle, said to resemble com- 
mon modern Egyptian workmanship; found, it is believed, along with No. 7, 
and numerous other articles, in a railway cutting near Navan. Museum mark, 
<. The silver seems superior in malleability to that of any of the other orna- 
ments examined. Specific gravity = 10-198. 

The analysis of these specimens gave the following results: — 


Silver, .. 

Copper, . - 5°44 17°73 | 60°26 311 4:34 5°85 3°59 
Goldy a: 42 1:34 lll 1:80 1:31 "89 ‘17 
Heads is clint! |p clrace: 10 ae 06 Bm ate weecte 
Maine erm nets os Syocats 61 SerenOL0 veo 

Ua O40 || oOo son6 5 O10 “04 fre Saye 

Sulphuryy sn) pee = 5 Gide eee etal) GLTaACe. 


99°79 98°91 99°13 99°64 99°72 99°56 99°63 


The composition of these silver articles does not seem so varied, nor is 
there the same agreement between the constitution of the particular specimens 
destined for the same use, as in the case of the goldornaments. With the ex- 
ception of Nos. 2 and 3, the whole set contain from 92 to 96 per cent. of silver 
with 7 to 3 per cent. of copper, and a little gold. The copper might certainly 
have been derived from the silver ore smelted, and exist in purely accidental 
quantity; but this seems improbable from the very small quantity of lead detected, 


320 Mr.J. W. Matier’s Report on the Chemical Examination of Antiquities 


as this metal is a much more frequent mineralogical concomitant of silver than 
copper is, and from the fact that at least some of the ancients treated their silver 
ores, just as at the present day, with lead, either in the metallic state, or as sulphu- 
ret* (Galena), and subjected the alloy thus obtained to cupellation, which latter 
process would of course remove the copper. The silver was therefore, in all 
probability, intentionally alloyed. If ald these ornaments were, though used as 
such, occasionally employed also for money, as WorsAArjf and others seem to 
think, one would be led to suspect that with the silver, as with the gold ring- 
money, something like a recognised standard metal existed when these articles 
were in use. This may perhaps be too hasty a conclusion. 

Nos. 2 and 3 of these specimens are the only ones which differ remarkably 
in composition from the others, especially No. 3, which actually contains one- 
half more copper than silver, though preserving the colour and general appear- 
ance of the latter metal. Some, at least, of this large quantity of copper was 
probably added in the state of bronze, as shown by the presence of a little tin 
in the silver alloy. On dissolving the silver in nitric acid, the tin remained 
behind, with the gold forming a “purple of Cassius,’ of a very good purple 
colour verging on red.{_ The uniform presence of a little gold in all the silver 
articles examined is not surprising, since the ancients were, it is almost certain, 
unacquainted with the process of parting. 

I may mention here, in connexion with the silver antiquities, a bluish semi- 
metallic substance, something like dull or tarnished steel, but very much softer, 
and brittle, used in the inlaying of small shrines, relic-cases, croziers, &c., of 
the middle ages. It has not much lustre, but from its colour contrasts very 
well with either silver or brass, into works in which latter metal it was fre- 
quently introduced, but always sparingly. I had very little material to operate 
on, only about a grain and a half, and consequently was unable to do more 


* “Excoqui non potest nisi cum plumbo nigro, aut cum vena plumbi. Galanam vocant, 
quae juxta argenti venas plerumque reperitur.”—Plinii Hist. Nat. lib. xxxiii. ¢. 6. 

+ Primeval Antiquities, pp. 59, 60. 

{ “Purple of Cassius” was obtained in a similar way by M. H. Feneulle (Ann. de Chim. et de 
Phys., Xxxii. 320), on dissolving a number of ancient Roman silver coins in nitric acid. The 
results of his rather numerous analyses certainly seem to prove that the Romans fixed no stan- 
dard for their silver coinage. 


From the Museum of the Royal Irish Academy. 321 


than analyze it qualitatively. It was of a dark bluish-gray colour, approaching 
black, very brittle, and exhibited a small lamellar fracture when broken. 

It consisted, as had been previously known, or at least generally sup- 
posed, for the most part of silver; but contained besides, antimony, sulphur, 
and traces of lead and copper. It may very probably have been made by the 
partial reduction of some of the antimonial ores of silver, its sole essential 
constituents being, I believe, silver, antimony, and sulphur. 

Having discussed the results of the examination of the antiquities of gold 
and silver, which principally belong to the class of ornaments, the metallic re- 
mains next to be considered are those composed of the important alloy bronze, 
in primitive ages the universal material for all instruments or utensils in 
which tenacity and hardness were required, and that are formed of iron in more 
modern times. 


WEAPONS AND IMPLEMENTS OF BRONZE. 


These, the forms of many of which are very peculiar, and sometimes very 
beautiful, and their workmanship frequently such as would not disgrace the 
artificers of the present day, have early directed the attention of archeologists 
to the processes used in their formation by the smiths and metallurgists of the 
epoch to which they belonged. Hence we find several inquiries, more or less 
extended, on record, aiming at an elucidation of some of these processes by the 
assistance of chemical analysis. Thus, of specimens found in the British Isles, 
Mr. Atcuorny,* His Majesty’s Assay-master in 1774, examined two bronze 
swords found in a bog at Cullen, Co. Tipperary, and announced as the result, 
that the metal was “chiefly copper, interspersed with particles of iron, and 
perhaps some zinc, but without containing either gold or silver ;” adding, 
“But I confess myself unable to determine anything with certainty.” 

In 1796, Dr. Pearson} communicated to the Royal Society an account of 
his analysis of seven specimens of bronze, found in the bed of the river 
Witham in Lincolnshire, in which he found, copper, 85:7 to 91 per cent; tin, 
14 to 9; and in one instance, 0°3 of silver. In 1816, Professor CLarKE,{ of 


* Archeologia, vol. iii, p. 355. } Philos, Trans, 1796. f Archeologia, vol. xviii. p. 343- 


322 Mr. J. W. Matiet’s Report on the Chemical Examination of Antiquities 


Cambridge, analyzed portions of bronze vessels found near Sawstone, Cam- 
bridgeshire, and found them to consist of 88 per cent. of copper, and 12 per 
cent. of tin. This same composition has recently been found for Irish speci- 
mens by Dr. Ropryson of Armagh.* Professor E. Davy,} Mr. O’Sutrivay,* 
Mr. Donovan,* and Mr. J. A. Puiuirs,t have published more complete 
analyses of antiquities from the latter country, in which foreign metals (as 
lead, silver, and iron) have been carefully sought for, and their quantity de- 
termined; and a similar accurate examination of Scottish relics of bronze has 
been made by Mr. Wutson, Hon. Sec. of the Society of Antiquaries of Scot- 
land.§ Of these investigations that of Mr. Purtiips is the most important as 
regards Ireland. 

The specimens from the Museum of the Academy which I have examined 
were all found in Ireland ; and are, as a group, completely illustrative of the 
principal classes of antiquities belonging to that country. They are sixteen 
in number. 

No. 1. A flat celt or kind of hatchet, the most common weapon of bronze 
found in Ireland, Museum mark, ®. This specimen was discovered, it is be- 
lieved, in the county of Cavan ; it isa fine hard bronze, of a deep brass-yellow 
colour, the “Celtic brass” of antiquaries. It was in excellent preservation, 
being scarcely even tarnished on the surface. Specific gravity, 8-631. 

No. 2. Another flat celt, with rounded edges; locality unknown. Museum 
mark ** [ss]. It was slightly and uniformly corroded on the exterior, and 
on being filed proved to be a much softer bronze than No. 1; of a copper- 
red colour, a little lighter than that of pure copper. Specific gravity, 8°303. 

No. 3. A long hollow celt, resembling in shape specimens which have been 
found in Denmark, discovered in the county of Wicklow. Marked, M‘Enty. 
It was a hard and rather brittle bronze, of about the same colour as No. 1; 
slightly and uniformly corroded. Specific gravity, 7°960. 

No. 4. A short hollowcelt,ofvery good workmanship, andexhibiting scarcely 
a trace of corrosion ; supposed to be from the county of Cavan. Museum mark, 


* Proceedings of the Royal Irish Academy, vol. iv. pp. 430-469. 
+ Wilson’s Archeology of Scotland, p. 247. 

t Quarterly Journal of the Chemical Society, October, 1851. 

§ Wilson’s Archeology of Scotland, p. 245. 


from the Museum of the Royal Irish Academy. 323 


Farnham, 38. The metal was very soft, and resembled No. 2 in colour, but 
was not quite sored. Specific gravity, 8°428. 

No. 5. A long spear-head, ribbed upon each side ; of excellent workman- 
ship, and not at all corroded. Mark, 3. The bronze was hard and uniform, 
and had received and retained a very good edge; colour about the same as 
No.1. Specific gravity, 8-581. 

No. 6. Portion of a spear-head, marked ¥; a flat, thin blade, with a beauti- 
ful edge ; the surface perfectly smooth and polished, but tarnished of a deep 
brown colour, resembling, I believe, the appearance of the bronzes called “ Cin- 
que cento.” This skin of brown upon the outside was eaten through in some 
places by superficial corrosion. When filed, the metal was found to be ex- 
ceedingly hard, and of a yellow colour, something deeper than No. 5. Spe- 
cific gravity, 7°728. 

No. 7. A flat scythe, found in the county of Roscommon. Museum mark, “. 
Several similar articles were found with this ; they were slightly curved blades, 
of about twelve or fourteen inches long, and tapered in breadth from about 
three inches at one end to a rounded point at the other. They had been at- 
tached to a handle at the broad end by three rivets. The specimen examined 
was a copper-coloured bronze of no great hardness, and but slightly corroded 
on the surface. Specific gravity, 8-404. 

No. 8. Portion of a sword-handle ; locality unknown. Museum mark: 
= ||. It was part of the characteristic Celtic weapon, in which the heft of the 
handle and blade were cast in a single piece, the former part being generally 
remarkable for its shortness as compared with those of modern times. This 
specimen was made of a beautiful compact metal, very hard, and of a yellow 
colour like that of No. 1, but a little deeper. No corrosion upon the surface. 
Specific gravity, 8-819. 

No. 9. Part of the blade of a sword of the same character as the last, but 
made from a metal by no means so hard or good. Mark, * {1 |. It was simi- 
lar in colour internally to No. 8, but was much more corroded on the outside. 
Specific gravity, 8-487. 

No. 10. Portion of a dagger or Irish knife (found near Newry?) Marked 5. 
A good hard bronze, very like No. 8 in colour and external appearance, and 
rather more malleable. It was scarcely tarnished. Specific gravity, 8-675. 

VOL, XXII. 2U 


324 Mr. J. W. Matuer’s Report on the Chemical Examination of Antiquities 


No. 11. Fragment of a chisel, marked 57, made of very inferior bronze, 
copper-coloured, soft, and not uniform in texture. It contained cavities pro- 
duced by air-bubbles in the casting, and was very much corroded; oxide of tin, 
carbonate of copper, and the red dinowide of copper were observable on the 
surface. Specific gravity, 7°896. 

No. 12. Specimen of the bronze ring-money which is found in such great 
quantity in Ireland. It was a small ring (about an inch in diameter), in form 
a simple circle, cast in a single piece, and having no opening like those in the 
specimens of gold and silver, by which the rings might be strung together into 
a chain. Its weight was 100-53 grs. = 4 dwts. 4°53 ers., or about eight of the 
units spoken of before. The bronze was moderately hard, of a deep brass-yel- 
low colour, very little corroded, but having a slight film of green “ erugo” on 
the surface. Specific gravity, 8-072. 

No. 18. Specimen of ring-money of a larger size than the last, being about 
two inches in diameter: locality unknown. It differed from it also in being 
hollow, cast upon a core of fine siliceous sand, which had not been extracted, but 
remained firmly imbedded in the bronze. There were two small projections on 
opposite edges of the ring outside, and the metal and core were pierced at these 
bosses by a hole apparently intended to allow a string to pass, by which the rings 
might be strung together. If used as money, this method of attaching the sepa- 
rate pieces would be certainly less convenient than merely stringing the rings 
themselves through the centre. Might not these articles have been made as 
parts of necklaces, or other ornaments for the person, though perhaps also used 
occasionally as a circulating medium? The weight of the specimen, including the 
sand core, =388'43 grs. = 16 dwts. 4:43 grs. = about 32 of the half-pennyweight 
units. The bronze was very like that of No. 12, but much more brittle. Its 
surface had been smooth and polished, but was slightly pitted in some places 
by corrosion. Specific gravity, 8-231. 

No. 14. Fragment of a large cauldron or tall vessel of thin sheet bronze. 
From its size (about 2 ft. 6in. high), and the thinness of the plates of which it 
was made, it displays a degree of skill and neatness in the treatment of bronze 
most remarkable as existing at so early a period as this vessel probably belongs 
to. The metal is not very hard, but extremely tough, and is of a beautiful 
rich bronze-yellow colour (“gold bronze”), scarcely altered by time. Specific 
gravity, 8°145. 


Srom the Museum of the Royal Irish Academy. 325 


No. 15. Portion of a small oval-shaped bell, made of a deep yellow bronze 
or bell-metal, hard and brittle. The surface was rough, but not much corroded. 
Specific gravity, 8-094. 

No. 16. Fragment of a small square bell; the metal about as hard as No. 15, 
nearly of the same colour also, but not so brittle. It was more corroded, and 
did not seem so good a material for the purpose. Specific gravity, 7-708. 

These specimens, being carefully analyzed, gave the results contained in the 
following Tables. 

(In each case a minute qualitative analysis was first made, and the absence 
of other metals than those afterwards estimated in quantity ascertained). 


FS 


ite) 


2K 
+ WOK 


= 
e Ue. 
. Ww 


Arsenic, 
Antimony, 
Sulphur, . . 


Arsenic,. . 
Antimony, 
Sulphur, . 


202 


326 Mr. J. W. Matter’s Report on the Chemical Examination of Antiquities 


The composition of these specimens agrees in general with that of the articles 
which have been examined by the authors referred to before, and also accords 
pretty closely with the quantities synthetically employed by the ancient metal- 
lurgists of whose labours we have any account. Thus, Pliny tells us* of the 
method adopted in his day for making bronze, which, however, he obviously 
treats of principally as a material for statues and public monuments. “ Massa 
proflatur in primis, mox in proflatum additur tertia portio zris collectanei, hoc 
est, ex usu coempti. Peculiare in eo condimentum atritu domiti, et consuetu- 
dine nitoris veluti mansuefacti. Miscentur et plumbi argentarii pondo duodena 
ac selibree, centenis proflati. Appellatur etiamnum et formalis temperatura 
eris tenerrimi, quoniam nigri plumbi decima portio additur et argentarii vige- 
sima: maximéque ita colorem bibit, quem Grecanicum vocant. Novissima est 
quae vocatur ollaria, vase nomen hoc dante, ternis aut quaternis libris plumbi 
argentarii in centenas eris additis. Cyprio siaddatur plumbum, color purpure 
fit in statuarum pretextis.” The analyses also of antiquities, not of Celtic ori- 
gin, as those by Krarroru,} Dize,t Moneez,§ Goser, and pupilsof ERDMANN,** 
all approach each other within rather narrow limits, and differ little from those 
at present under consideration. 


The cause of this general accordance is obvious, namely, that the physical 
properties required in these alloys of copper and tin are only to be found 
within a small range of variation in chemical composition. Dr. Rosrnsoyt{ 
has given it as his opinion, that, when used for weapons, the atomic constitu- 
tion of Celtic bronze was constantly 14 Cu+ Sn; but though this formula 
may and probably does represent the best alloy for the manufacture of imple- 
ments for warlike purposes, or others in which similar requirements exist, yet it 
cannot be said that it invariably accords with the actual composition of the 
antiquities in question, as No. 6 of the analyses in the Table is near 11 Cu + Sn, 
while’ No. 4 approaches 39 Cu + Sn, and Nos. 2 and 7 contain still more copper, 
though perhaps the former of these should hardly be considered as bronze. 

As on the one hand we must not conclude that a simple and invariable 


* Hist. Nat. lib. xxxiv. c. 9. 

+ Gehlen’s Journal, No. 15, and Journal des Mines, Mars, 1808, p. 161. 

t Journ de Phys, 1790. § Mém. de l’Instit. || Schweig. Journ. 60, 407. 
** Journ. fiir pr. Chem, xl. 374. +t Proc. Royal Irish Acad., vol. iv. 


from the Museum of the Royal Irish Academy. 327 


proportion existed in the quantities of the component metals of these bronzes, 
so, on the other, it seems erroneous to infer, as Mr. Witson, in his Archwology 
of Scotland* has done, that the absence of such invariable composition neces- 
sarily proves that these antiquities were the work of native artists, who were 
unable to combine the metals they used with the accuracy and certainty of 
foreign metallurgists of the same epoch. For, passing over all the difficulties 
which the primitive modes of reduction of the respective ores, and the impurities 
consequently retained by the metals, must have presented to the early manufactu- 
rers of any nation, and supposing the copper and tin used to be each perfectly 
pure, the task of producing from these materials an alloy of definite and uniform 
composition is, even at the present day, one requiring great skill, both in the 
actual process of melting, and in the previous construction of furnaces, &c., so 
that for the purpose and at the period of the manufacture of the articles in 
question it must almost be deemed impossible of accomplishment. 

Hence the observed variations of composition between the several bronze 
antiquities found in Ireland by no means negative the possibility, to say the 
least, of their having been produced by a single people, and that one, far ad- 
vanced in the art of metallurgy for the age to which these articles are referred. 

Yet, although these differences of composition are probably to a very great 
extent owing to the want of sufficient skill and appliances to produce from the 
same materials uniform results,—difficulties enhanced to the last degree where 
many small articles are to be cast, at separate operations, and from alloys formed 
in small quantities,—and are therefore to be looked upon as unintentional,—yet 
some marks of design may perhaps be traced in the differences between the al- 
loys of articles intended for different purposes. Thus we find two of the celts 
(Nos. 2 and 4) and the war scythe (No. 7) consist almost entirely of copper, 
the quantity of tin amounting in No. 2 to only 1:09 per cent., a proportion so 
small that it might be supposed to be derived merely from the addition of frag- 
ments of old bronze to the copper, or from imperfect reduction of the ore. 


* Page 249. 

{ The principal difficulty arises from the “burning out” of the tin, which takes place with 
great rapidity on access of air to the melted bronze. The column in the Place Vendome, Paris, 
was a remarkable instance of mismanagement in this respect, almost the whole of the tin having 
disappeared from the metal employed to cast some of the blocks of bronze. 


328 Mr. J. W. Matzzr’s Report on the Chemical Examination of Antiquities 


The only analysis of Celtic bronze containing so much copper, that I have 
seen, is that of a broken spear-head found in Ireland, examined by Mr. Put- 
uirs,* from which he obtained 99°71 per cent. of copper, and -28 of sulphur. 
The composition of the metal used in casting the celebrated Quadriga of Chios 
(better known in this country as the Horses of St. Mark’s, Venice), as deter- 
mined by Kiarrotu,} was also very near that of the present specimens, being 
99°13 per cent. copper, and ‘87 tin. Some ancient nails analyzed by the same 
chemist, and Greek and Roman coins examined by Mr. Pumurs,§ and pupils 
of ErDMANN,|| also appear to have been made from nearly pure copper.** 

The other celts (Nos. 1 and 3), one of the spear-heads (No. 5), and one of 
the swords (No. 9), agree pretty closely in composition ; containing about 87 
or 88 per cent. copper, and 13 or 12 of tin, if we disregard all traces of foreign 
metals. This is the composition assigned by Dr. Ropryson as the best for the 
purpose, and his opinion seems in fact borne out by the results before us, as 
the specimens numbered J, 3, and 5, were certainly very far superior to most 
of the others in hardness, toughness, and uniformity ; and the alloy having this 
constitution may be considered as the normal one, at least where other metals 
than copper and tin are present only in insignificant quantity ; for 2 or 3 per cent. 
of a foreign metal, as lead, seems to exercise a very great influence in changing 
the character of the whole. Thus the sword (No. 8) in which the tinamounted 
to only 8°52 per cent., but which contained besides 3°37 per cent. of lead, fully 
equalled the weapons just mentioned in hardness, and perhaps even exceeded 
them in malleability and facility in working. 

The second of the two spear-heads (No. 6) was exceedingly hard, and had 
receiveda good edge, but it had not the same toughness as the others, and had 
broken across without bending; hence so large a proportion of tin as it contains, 
14:01 per cent., does not seem to yield a metal so well adapted for weapons. 

The two daggers or knives (Nos. 10 and 11) agree very closely in composi- 
tion, yet the difference in physical properties is most marked. 


* Quart. Journ. Chem. Soc., loc. cit. + Beitriage, vi. 89. Gehlen’s Journal, No. 15; 

{ Gehlen’s Journal, loc. cit. § Loc. cit. || Journ. pr. Chem, xl. 374. 

** The presence of sulphur is highly interesting as giving the strongest presumption that the 
copper of these ancient alloys was obtained from the imperfect reduction of sulphuretted ores of 
that metal. 


from the Museum of the Royal Irish Academy. 329 


No. 10 was a bronze of excellent quality, a little softer than No. 8, but 
still sufficiently hard, tough, and uniform, and not at all corroded; while No. 
11 was soft, full of cavities, not uniform in texture, and was covered with the 
results of corrosion. (Of course in this, as in every other instance in which 
the corrosion of metals is examined, regard ought to be had to the situation in 
which they have been discovered; but unfortunately, in the present case, 
information on this head is entirely wanting.) Additional analyses of very 
inferior bronzes and those which have suffered most from corrosion, taking 
care to examine fragments taken from different parts of the same article, might 
yield results of interest, and possibly of practical importance. 

The cauldron or vase of thin sheet bronze (No. 14) contained about the same 
per-centage of copper as the bright yellow-coloured alloy for weapons (rather more 
than 88 per cent.), but not quite so much tin, its place being partly supplied 
by about 2 per cent of lead, which tends to make the alloy more malleable.* 

The two specimens of ring-money (Nos. 12 and 13) contain quantities of 
copper differing by nearly 1:5 per cent., while the proportion of tin varies still 
more, being 9-58 per cent. in the former, and 13°83 in the latter. In the one 
we find 2°79 per cent. of lead, but in the other a mere trace of that metal is 
perceptible. Hence, it is obvious that, as far as these specimens are to be 
considered as representing the ancient Celtic currency of bronze, no very accu- 
rate standard of alloy was observed in its production. This is not surprising; 
the formation of such a definite and constant alloy being, as above mentioned, 
attended with so much difficulty, and the inferior value of the material rendering 
it by no means as important as in the case of gold or silver. The rings being 
merely cast, and not struck like ordinary coins, the physical properties of the 
metal did not need so much attention as in the case of arms or implements, 
where they were of the first importance. 

The samples of bell-metal examined, numbered 15 and 16, differ but little 
from each other. The quantity of copper is considerably greater than that gene- 
rally employed at the present day. This may have been owing to the desire 
of the early artists to avoid brittleness in the metal, but more probably to the 


* Modern workmen are well aware that the addition of about 2 per cent. of lead greatly 
improves the working qualities of brass and bronze, causing both to cut smooth and sharp in the 
lathe, or, as French brass-workers express it, to cut ‘‘ seché.” 


330 Mr. J. W. Matter’s Report on the Chemical Examination of Antiquities 


“burning out” of the tin by some rude and slow process of melting. The compo- 
sition of these specimens is very simple, copper and tin being, as in all the other 
ancient bronzes, almost the sole constituents. Modern bell-metal is occasionally 
much more complex, containing, according to THomrson,* 80 per cent. of 
copper, 5°6 of zinc, 10.1 of tin, and 4°3 of leadt Those Irish bells are, it is 
needless to say, of much more recent date than the bronze weapons, and belong, 
it is believed, to about the eighth or ninth century. 

With respect to the foreign metals found in minute quantities in these 
alloys, although, with the exception perhaps of lead, they may all be fairly 
considered as accidental, and merely introduced as impurities of the constituent 
metals, yet they are not to be neglected, as in the consideration of antiquities 
they may occasionally yield some valuable collateral information. The lead 
which is found in many of the specimens, and has been previously detected 
in much larger quantity in some bronzes, might have existed as an impu- 
rity of the copper, but was more probably added either intentionally in the 
separate state, or existing in older bronze remelted, which often contained this 

metal, particularly when used for statues. Zine was only observable in minute 
~ traces in three of the bronzes, but its presence in these was distinctly ascertained. 
In all probability it was introduced along with the copper, and was derived 
from blende occurring along with the ore of that metal, and imperfectly sepa- 
rated from it. Though found in large quantity in some early Roman coins, 
and by Goésetf in wire from a Livonian tomb, I believe it has not before been 
detected in Celtic bronze. Iron might have come in with either of the consti- 
tuent metals, and has been observed in previous analyses. Indeed, from its 
universal diffusion in nature, its absence in these alloys would be more sur- 
prising than its presence. Our finding the rarer metal, cobalt, though only in 
two instances, is more remarkable; these, however, are not the only antique 
bronzes in which it has been observed, as Mr. Putuirs, in his valuable paper 


* Ann. Phil. 2. 209. 

+ M. Girarpin found the composition of the “cloche d’argent,” an ancient bell at Rouen 
(previously thought to have contained a large proportion of silver, from oblations made at the time 
of its founding), to be, copper, 71; tin, 26; zinc, 1°80; and iron, 1:20=100, (Ann. de Chim. et 
de Phys. 50. 205.) The proportion of copper here is very small. 

} Schweig. Journal, 60. 407. 


from the Museum of the Royal Irish Academy. 331 


alluded to above, notices it and nickel as occurring in several early coins, and 
in one Irish specimen, a celt, to the amount of 0.34 per cent. (with a trace 
of nickel). The minute quantities of the Precious Metals were perhaps derived 
from fragments adhering to old ornaments of bronze, which were afterwards 
re-melted. It has been supposed that traces of silver found in one or two 
previous analyses were owing to the lead not having been freed from this metal, 
and this was probably often the case, but in two instances here (Nos. 1 and 2) 
it could not have been so, as no lead was present. Arsenic and antimony have 
not, I believe, except in one instance, been hitherto noticed in similar alloys,* 
and existing in such very small quantity, are not easily detected ; but by em- 
ploying a separate portion of bronze for the purpose, I determined rigidly the 
question of their presence or absence. The source of these traces found 
in the alloy is not difficult of explanation. Indications of sulphur (and of carbon, 
by Mr. Donovan) have been observed in several specimens previously ana- 
lyzed ; these, and the traces of arsenic and antimony, are interesting, as ren- 
dering it at least probable that some of the copper used by the ancients was 
smelted from sulphuret of copper or copper pyrites (probably the chalcitis 
or misy of Pliny), or other ores of the same class, and that native copper, red 
oxide of copper, and malachite, did not, as some authors seem to suppose, con- 
stitute their only sources of the metal. 

The question, from what countries were the copper and tin, employed to 
such an immense extent by the nations of antiquity, derived, is one of great 
interest, and has been already treated of, especially with reference to the source 
of the tin, by several authors of celebrity. They seem generally agreed that the 
former of these metals was discovered, and extracted at a very early period in 
several places in the south and east of Europe, and adjoining portion of Asia. 
At the period of the Trojan War, and at the time of the building of Solomon's 
Temple, the supply of copper must have been most abundant, and the name 
frequently occurs in the Pentateuch. The art of casting statues of bronze is 
ascribed by Pausanias to Rheecus and Theodorus of Samos (about 700 or 800 
B. C.), at which time it must of course have become common, though we have 


* Jahn (Ann. Pharm. 27-338) found 8-22 per cent. of antimony in an ancient weapon from 
the ruined castle of Henneberg. 


VOL. XXIL DEX 


332 Mr. J. W. Matter’s Report on the Chemical Examination of Antiquities 


but little knowledge of the localities from which it was derived. When 
Pliny wrote, its principal sources were Cyprus, Campania, Gaul, and Spain, 
especially the last-named country. Although England now supplies a very 
large proportion of all the copper made use of in the world, there are no 
traces in history of any having been smelted here so early as the Celtic 
period, and the contrary seems to be proved by a passage of Cxsar, De 
Bell. Gall.,* where he says of Britain: “Nascitur ibi plumbum album in 
Mediterraneis regionibus, in maritimis ferrum, sed ejus exigua est copia, wre 
utuntur importato.” Strabof also enumerates gold, silver, iron, tin, and lead, 
among the products of Britain, but does not mention copper, the sixth of the 
then well-known metals, which it is improbable he would have omitted if its 
being found there were familiarly known. 

It seems on the whole most probable that by far the largest portion of the 
tin used in the manufacture of the bronze of antiquity was brought from Corn- 
wall by Pheenician or other merchants, and by them distributed over the south 
of Europe, Syria, and Asia Minor. Strabof and Pliny§$ indeed state that it 
came from Spain, and tinstone is known to exist in that country in the pro- 
vince of Gallicia, but the quantity there found is not likely to have supplied 
the whole demand for this metal; “and their account is easily explained by 
the consideration that the great commercial depot of the eastern merchants was 
probably situated somewhere near Gades (now Cadiz) in the south of Spain, 
and that to this place the tin was brought from the west, and from it was again _ 
distributed to the consumers in the Mediterranean. Aristotle distinctly men- 
tions, “tév kasovtepov tov KeAtucv’ in his treatise, De Mirab. Auscult. 

Though Pliny|| tells us of tin, “ Nulli rei sine mixtura utile,” yet it was obvi- 
ously well known in the separate state, as in Homer we read of the breastplate 
of Agamemnon: : 

“Tov & fror b€xa ofpor Eoav péAavos KVAVOLO, 
Adiexa 8 xpuaoio, Kai e’xkoot KacarTépowo.” 
—It. xi. 24. 


And the same poet mentions metallic tin in several other places. Hesiod does 


* Lib. iv. c 34, f Lib. iv. 305. } Lib. iii. p. 219. ed, Almel. 
§ Lib. xxxiv.c. 16. || Loe. cit. 


from the Museum of the Royal Irish Academy. 333 


so too, and Aristotle and Pliny speak of it as a known and common substance. 
Yet antiquities of this metal unalloyed are very rare ; indeed there have been, 
I believe, but three instances recorded in which such have been found in Great 
Britain,—and these allin England.* Hence a single additional specimen found 
in the collection of the Academy acquires considerable interest. It filled the 
interior of a hollow bronze ring of about four inches and a half in external 
diameter, the thickness of the ring being about half an inch. It was easily 
recognised as tin by its colour and the resistance it offered to the knife, and on 
chemical examination it proved to be nearly pure, containing mere traces of 
iron and lead. Where partially exposed to the atmosphere it had acquired a 
coating of peroxide. From the way in which it is attached to the bronze, and 
the character of the latter, it would seem with little doubt to belong to the 
same period as the other early bronze antiquities in the Museum. 

In the collection there is an earthen vessel, apparently intended to be placed 
in the fire, in which were found several small fragments of bronze very much 
corroded, a brown earthy powder in which particles of the “ werugo” of bronze 
were observable, and a bit of a white metal of considerable lustre, and exhibit- 
ing a somewhat lamellar structure. This latter was hard and very brittle, so 
as to be easily reduced to powder in a mortar. There were no traces of corro- 
sion on the surface. Specific gravity, 8-107. On analysis it gave in 100 parts, 


UOppers su a 5 wt wt te DOD 
RR ce ct cen tt ot SOMO 
RUvieTs selcy ei ey ct at oe 13 
AMUNEIONY,:. 3 ep eet et OT 
Sulpuue yo ee ‘Il 

98-89 


Thus, though an alloy of copper and tin, it differs totally from bronze in the 
proportion of its ingredients. The only analysis I have seen which comes near 
this is that ofan antique Roman mirror by Kiarrotu,f in which he found, cop- 
per, 62; tin, 32; and lead,6;= 100. Whether the Irish alloy was intentionally 


* Phil. Trans. vol. xxiii. p. 1129, and vol. li. p. 13. Archwologia, vol. xvi. p. 137. 
+ Scherer’s Allgem. Journ. d. Chemie, No, 33. 
2x2 


334 Mr. J. W. Mattet’s Report on the Chemical Examination of Antiquities 


made to be used for a similar purpose,—a supposition in some degree counte- 
nanced by the presence of a little antimony,—or that the proportion of tin was 
accidentally large, and the specimen was about to be remelted, and perhaps cop- 
per added, is not easy to decide. The pulverulent substance found in the same 
vessel was neither an ore of any kind, nor a furnace product, but appeared on 
examination to have been merely dust of an earthy character mixed with the 
results of bronze corrosion (probably the sweepings of a workshop or some such 
place). The vessel and its contents constitute an interesting relic of early 
metallurgy. 

Although Zine in the metallic state was unknown, at least until the twelfth 
century, it seems certain that some of its ores were worked and used for making 
Aurichalcum or brass at an extremely early period, the valuable properties of 
that alloy being well known and appreciated in Aristotle’s time, although he 
speaks of it under the title yaN«ds Moosbvouos as a“rare variety of bronze. 
This Pliny also considered it, and it seems never to have come into common 
use amongst either the Greeks or Romans. Hence it is not surprising that no 
example of a brazen article of decidedly Celtic manufacture has yet been 
discovered. I analyzed a fragment of a shallow basin from the district of Castle- 
bernard, County of Cork, recently presented to the Academy Museum, and 
found it to contain :— 


Copper) <4, 2 tispcce ea rocnoS 
ADC wees ce Ke cope ae ae Zao, 
MOM Se fs. so oe ey oot sa egal 
Wedd. sc ce 2, . eS 
aM s,s, ss one omeraces 

99-05 


The specimen was soft, of a bright brass-yellow colour, and specific gravity, 
7:717. From its form, however, and composition, which is quite that of ordi- 
nary modern brass, it is probably of very little antiquity, and does not at all 
belong to the same class with the really Celtic articles in the Museum; an 
alloy therefore of copper and zine of equal age with the latter is still to be 
sought for. Amongst German antiquities Gésex (Schweig. 60. 407.) found 


From the Museum of the Royal Irish Academy. 335 


some of this composition, but I do not know to what date or people his speci- 
mens have been assigned by archeologists. 

Lead is another of the metals which was extracted from its ores and applied 
to many of the purposes for which it is used at the present day, at probably a 
a period nearly as ancient as that of the introduction of copper. With the 
exception of native metals, no ore would be more likely to have come under 
the notice and attracted the attention of primitive metallurgists than galena, 
the commonest form in which lead occurs, and from which its extraction would 
present scarcely any difficulty even with the rudest means for smelting. 
Mention is accordingly made of this metal among the Egyptians, Hebrews, 
Greeks, Romans, and other nations of antiquity, who not only used it in its 
separate state for water-pipes and other mechanical purposes, but were also ac- 
quainted with the method of employing it in the refinement of gold* and silver.} 
In Britain, particularly in Derbyshire, numerous remains of lead-workings have 
been discovered, probably belonging to the time of the Roman occupation, but- 
I have seen no account of any relics of this metal of similar antiquity having 
been found in Ireland; and in the Museum of the Academy, the only traces of 
lead that I could find were the cores or filling of one or two reliquaries of thin 
gold plate or foil, which are, I believe, considered as specimens of medieval art. 
The interior surface of one of these cores, which was itself hollow, was conside- 
rably corroded, being covered with a grayish crust of carbonate, the production 
of which was probably accelerated by the contact of the gold. Some ancient lead 
from an abbot’s coffin in the Cathedral of Christ Church, Dublin, which was 
deeply pitted by corrosion, yielded traces of sulphate along with the carbonate 
upon its surface, and on cupellation of the metal itself left a minute bead of silver. 

Of the numerous 


WEAPONS AND IMPLEMENTS OF IRON 


I examined four, namely :— 

No. 1. A sword found at Kilmainham, near Dublin. It is long and straight, 
adapted for both cutting and thrusting, and is one of those examined by M. 
WorsAaE on visiting the Museum a few years ago, and declared by him to 


* Theognis—T'vwyas, 1, 1101. { Jeremiah, vi. 28, Pliny, lib. xxxiii. c. 6. 


336 Mr. J. W. Mattet’s Report on the Chemical Examination of Antiquities 


agree in appearance with Norse swords preserved at Copenhagen and Stock- 
holm. The blade was covered with a thick coat of rust, on removing which a 
portion of metal beneath was reforged as the simplest way of determining its 
character. It turned out not to be steel, but moderately good soft iron, in- 
capable of being hardened by quenching when hot in water. On solution in 
dilute sulphuric acid it left a very slight black sediment, consisting of carbon 
with traces of phosphorus. 

No. 2. A knife, also found at Kilmainham, marked * ; still more corroded 
than the last, there being in fact very little metal left. The fracture was very 
close-grained, and of a bluish-white colour; and on reforging it proved to be 
steel of an inferior quality, leaving, on solution in a dilute acid, carbon, contain- 
ing phosphorus and silica, the quantity of which was, however, not determinable. 
The specimen is probably a very modern one, and ought not to be classed 
with the others here described. 

No. 3. A nail from Dunshaughlin in the county of Meath. It was not nearly 
so much corroded as the last two specimens, and the rust was hard and closely 
adherent, whereas that on the sword and knife was loose and easily detached. 
On the crust of oxide some traces of the blue phosphate of iron were observable, 
and more was to be found on breaking it off from the metal. The latter, on 
reforging, proved, as might have been expected, to be soft iron, containing, as was 
found on chemical examination, a large proportion of phosphorus as compared 
with the other specimens. 

No. 4 was another knife, of a small size, narrow-bladed, and thick on the 
back, discovered at Strokestown in the county of Roscommon. It was covered 
by very little rust as I gotit, but had apparently had some corrosion previously 
removed. It consisted, not of steel, which it somewhat resembled in appearance, 
but merely of malleable iron, of excellent quality, which dissolved almost per- 
fectly in dilute sulphuric acid, leaving a barely visible trace of carbon, and 
affording no indications of phosphorus. 

From these experiments we see, so far as their limited number renders it 
allowable to judge, that the really ancient weapons of this class found in Ireland 
do not consist of steel, but of soft iron. This would be in itself an interesting 
fact if confirmed by further investigation, as showing that the early Scandina- 
vians and Celts, or those who supplied them, though able to make good mal- 


Srom the Museum of the Royal Irish Academy. 337 


leable iron in the first instance, but were ignorant of the methods of giving it 
the properties of steel by any after-process, though it is plain from passages of 
Greek and Roman authors* that the latter substance was known to them. The 
subject, however, demands further investigation. 

Having concluded the account of the metallic antiquities, I proceed now to 
the examination of some other objects, principally used for ornament. And 
first of— 


PRECIOUS STONES. 


Of these I found seven varieties, at least according to the classification of 
the jeweller, though not all distinct mineralogical species, viz. sapphire, beryl, 
turquoise, garnet, amethyst, clear rock-crystal, and chalcedony. The deter- 
mination of the periods when these were used as ornaments is of course 
altogether an antiquarian question, and I do not know to what dates these 
individual specimens are referred; but with the exception, perhaps, of some of 
the articles of crystal, none of them seem to belong to the period of the Celtic 
makers and users of the gold and bronze objects above examined. Some of 
the amethysts found in crosses and other ecclesiastical relics are merely the 
uncut terminations of quartz crystals of the common form, no part of the prism, 
but only the hexagonal pyramid, being visible. Some of the sapphires, which 
are small and uncut, have been most probably found in the county of Wicklow, 
with rolled pebbles of the mineral occurring in which county they agree per- 
fectly in external characters. 

Four beads of amber which I examined, of different degrees of transparency 
and colour, were quite unchanged in chemical properties, and, except one, 
presented nothing remarkable in appearance ; this, on being split, was found to 
be white and nearly opaque (wax amber) in the interior, while the exterior, 
including the surface of the hole, piercing the bead, was orange-yellow and trans- 
parent, like the more ordinary variety of this substance, to a depth of about the 
twentieth ofaninch. This change of molecular condition must, Iimagine, have 


* See Aristotle, De Mirab. Pliny, lib. xxxiv.c. 14. Dr. Pearson (Phil. Trans, 1796) found 
all the supposed iron weapons, from Lincolnshire, which he examined, to consist of steel. 

+ See the author’s Examination of Gold Sand of Wicklow. Proceedings of Geological Society 
of Dublin for 1851-52. 


338 Mr. J. W. Mattet's Report on the Chemical Examination of Antiquities 


been the result ofage ; unless indeed the bead had at some time been immersed 
in oil or any similar fluid, which had penetrated it to the extent described. 

Two or three fragments of jet examined proved, as might be expected, unal- 
tered specimens of this variety of coal. 


COLOURED GLASS BEADS. 


These occur of several distinct colours ; the most common are, two shades of 
blue, a black (in reality intensely deep green), a very pale sea green, and white ; 
of each of which I received a specimen for qualitative analysis. 

No. 1 was a very fine dark-blue bead, from Kilmainham, quite resembling 
good modern cobalt glass in colour, but full of minute air bubbles. By fluxing 
with an alkali, solution in muriatic acid, and the application of the usual 
re-agents, the colouring matter was found to be oxide of cobalt, but the glass 
also contained a trace of copper. Whether the latter was accidental, or, being 
known to tinge glass blue or green, was added with the intention of improving 
the colour, it would be impossible to say. It was contended by Gmetin* that 
the blue glass of the ancients was not stained by cobalt but iron (that it was 
analogous to ultramarine) ; and an ancient specimen of a sapphire blue colour, 
analyzed by Knaproru,f gave no indications of the former metal ; but Sir H. 
Davyt found cobalt in all the glass vessels of this colour from the tombs of 
Magna Grecia, and the same colouring material has been detected in the beads 
found upon Egyptian mummies. The present is therefore but an additional 
instance of the use of a compound of this metal for a special purpose being 
known long before the metal itself or any of its preparations had been obtained 
in a state approaching purity. 

No. 2. A bead of so dark a bottle-green colour as to appear by reflected 
light quite black and opaque. In very thin splinters it was translucent, and 
of the above tinge. The colouring material was oxide of iron, in very large 
quantity, and traces of manganese were also distinctly perceptible. The spe- 
cimen was from Templepatrick in the county of Antrim, nearly spherical, well 
shaped, and had a finely polished surface. 

No. 3 was a blebby, light blue bead, verging on green, from Kilmainham. 


* Gotting. gel. anz. 1776. + Beitrige. s. 144. ¢ Phil. Trans. 1815, p. 108. 


from the Museum of the Royal Irish Academy. 339 


But for the contained air bubbles it would have been nearly transparent. The 
colour was due to oxide of copper ; and both in the staining of the glass, and in 
forming the bead, the specimen was a very rude result of early art. 

No. 4 was a flattened bead, also from Kilmainham. It was more nearly 
transparent than any of the others, and had only a very faint tinge of sea-green, 
so pale that it probably was not intentional ; on the contrary, this would seem 
more likely to have been an attempt at colourless glass, which we know was 
more highly valued by the ancients, at least in the south of Europe, than any 
other. Icould detect no colouring metallic oxide in the present specimen, 
except the merest trace of oxide of iron. 

No. 5. An opaque, white bead, of a flattened form, from the same locality 
with the last. On examination it proved not to be glass at all, but pure crys- 
talline white marble (carbonate of lime), which had been very neatly cut to the 
required shape, and the surface well polished. This material has not, I believe, 
been hitherto noticed among those employed for these primitive ornaments. 

The results of the examination of these glasses agree very well with those 
of some of the specimens of Kuarrot and Sir H. Davy; but further inves- 
tigation of the Celtic articles (and indeed of those from the south of Europe) 
would be important in order to elucidate the history of this ancient manu- 
facture, as it is only from the analysis of numerous examples, varying in date 
and locality, that we can hope to derive any valuable general information on 
the subject. 

Another highly interesting branch of an inquiry as to the means of decora- 
tion possessed by the ancients is that concerning their 


PIGMENTS, 


and hence I have been most anxious to examine such remains of this kind as 
might be in existence in Ireland; but have only succeeded in obtaining speci- 
mens (used in fresco painting) from a single locality, namely, Slane Abbey, in the. 
county of Meath ; and these probably do not belong to an earlier date than 
1512, as the Abbey, originally established in the seventh century, was re- 
founded in that year. These specimens were not contained in the Aca- 
demy Museum, but were detached by Mr. F. W. Burton, a member of the 
Academy, and presented for the purposes of this examination. There were 
VOL. XXII. 2¥ 


340 Mr. J. W. Matter’s Report on the Chemical Examination of Antiquities 


six varieties of colour examined, all of which had been laid on upon a uni- 
form white ground of about the twentieth of an inch in thickness, or perhaps a 
little thicker, as part of the ground had no doubt been lost in removing the 
stucco from the walls. The coats of colour were a little thinner, but were not 
uniform, being thicker in some places than in others ; they were all mixed with 
an oily substance used in very small quantity, which was soluble in alchol and 
ether, reprecipitable from the former on the addition of water; want of suffi- 
cient material made it impossible to determine its nature more accurately. The 
ground or basis upon which the colours were laid consisted of carbonate of 
lime mixed with a little silica, or rather white siliceous clay, which, as well as 
the colours themselves, had been carefully and finely ground. The examina- 
tion of the individual pigments gave the following results:— 

No. 1 wasa dull red, almost a brick colour, but somewhat brighter. Heated 
before the blowpipe on charcoal, it fused into a black shining bead, and in the 
reducing flame gave globules of a soft, white metal, which on examination proved 
to be lead. Digested in diluted nitric acid it partially dissolved with effer- 
vescence. The solution gave with hydro-sulphuric acid a black precipitate of 
sulphuret of lead, and with ammonia, after filtration and heating, a slight reddish- 
brown one of peroxide of iron, containing a trace of alumina. On fluxing the 
residue, insoluble in nitric acid with carbonate of soda, it was found to consist 
of highly ferruginous silica. Hence this colour appears to be an impure oxide 
of iron, probably iron ochre, mixed with carbonate of lead ; or possibly may 
have been red lead, mixed with ground hematite, the former having altered in 
chemical composition in the lapse of time, by the action of air and moisture, &e. 

No. 2. A pale yellow, verging on Naples yellow or yellowish white. Before 
the blowpipe it behaved nearly in the same manner as the red, but became much 
darker by the first application of the heat, before fusion. Treated in the same 
way as the last, it proved to be a light yellow ochre, mixed with a large pro- 
portion of ceruse, and containing a good deal of the oily matter with which the 
colours appear to have been mixed. Originally it may have been of an orange 
colour, and the lead, as in the last case, in the state of red lead. 

No. 3. A light blue ; the only one of the colours which had any pretensions 
to brilliancy. It invariably occurred over a coat of the red, No. 1; which 
probably was picked out or cut through in some places, so as to produce a 


from the Museum of the Royal Irish Acadeny. 341 


pattern of blue in relief on the red ground. It dissolved to a great extent with 
effervescence when heated in nitric acid, and the solution, on adding excess 
of ammonia, gave a pale blue solution of oxide of copper and a copious preci- 
pitate of oxide of lead. The insoluble residue was fluxed, and consisted of 
silica with alumina and oxide of copper, and probably an alkali. This colour, 
therefore, appears to have been partly a copper frit of the same kind with that 
found by Sir H. Davy, in the blue pigments examined by him in Italy, but 
differing from these latter in that some of the copper existed in a state soluble 
in acids, I believe as carbonate. Before the blowpipe, this, like the other 
colours, yielded metallic lead when heated on charcoal, and empyreumatic 
products in a closed glass tube. 

No. 4. White. This turned out to be slightly impure carbonate of lime, 
the same, in fact, as the basis of all the colours, though laid on in a separate 
layer. The fact of this being the white employed, and not white lead, which 
yet (or minium) was mixed with the other pigments, would seem to indicate 
either that the ceruse was prepared of so impure a character as not to be a good 
white, or that it was known to darken by long exposure, where traces of sul- 
phureted hydrogen were present in the atmosphere, and therefore was rejected 
as not a permanent colour. 

No. 5. A grayish black. It became white by the gentle application of the 
blowpipe flame, and dissolved in nitric acid with copious effervescence, leaving 
a slight carbonaceous residue of a black colour, perfectly dissipated, with the 
exception of a trace of silica, by heating to redness for an instant on platina 
foil. The nitric acid solution contained nothing but lime. This therefore 
was a mixture of carbon in some form, probably lamp-black, with carbonate of 
lime. 

No. 6 was a dull brown, which proved to be an ochre, containing silica, 
alumina, lime, and a large quantity of oxide of iron analogous to Nos. 1 and 2, 
but of a different shade. It was mixed, like them, with carbonate of lead. 

These results with respect to ancient Irish pigments agree, as far as they 
go, toa remarkable extent with those of Sir H. Davy’s interesting investiga- 
tion* of the ancient Roman pigments above referred to. The materials used 


* Philosophical Transactions, 1815. 
2x2 


342 Mr. J. W. Matret’s Report on the Chemical Examination of Antiquities, Sc. 


are in each instance the same, or nearly so. This is not wonderful, however, 
as we find that most of the materials are of the commonest and most easily 
obtained substances for the purpose, requiring but little preparation, and 
are of a durable and stable character ; hence naturally selected by the early 
artist, and, when once in use, not likely to cease to be so from the knowledge 
of them dying out, as that of difficult and rare preparations might easily have 
done. Two points of difference are, however, to be found between the Roman 
pigments and these Irish ones, namely, the use ofan oily medium for mixing 
the colours from Slane Abbey, whereas such was not apparently employed by 
the Romans in their fresco paintings ; and the occurrence in the former of large 
quantities of ceruse or white lead, which, although known and described by 
Pliny and Vitruvius as a common colour, was not found by Sir H. Davy in 
any of the specimens examined by him. Both circumstances tend to prove the 
more modern character of the Irish pigments. 


Such are the results of the examination of these antiquities so far obtained. 
It will be seen that some classes of objects in the Academy Museum have not 
been spoken of at all, and that this investigation is very far from exhausting the 
subject with respect even to the departments discussed. Conscious of my un- 
fitness for the task, I have left the bearings of these results upon archeology 
almost untouched ; yet the analyses and experiments above described are not, 
perhaps, absolutely barren in results of interest, and at least put on record a 
number of facts concerning the materials employed at early periods in Ire- 
land for various purposes of the arts, which may possibly in some degree 
assist the researches of archzxologists. In the hope that such may be the case I 
have ventured to lay them before the Royal Irish Academy, to the liberality 
of whose Council I am indebted for the specimens principally experimented 


upon. 


XV.—On the Properties of Inextensible Surfaces. By the Rev. Joun H. Jeter, 
A. M., Fellow of Trinity College, and Professor of Natural Philosophy 
in the University of Dublin. 


Read May 23, 1853. 


1. ALTHOUGH the celebrated theorems of Gauss have received from mathe- 
maticians much and deserved attention, inducing them to bestow considerable 
labour upon obtuining for these theorems simple and elegant demonstrations 
I do not find that any attempt has been made to extend his discoveries upon 
this subject. Yet the highly interesting character of the theorems alluded to 
might naturally induce the expectation of other important results connected with 
the theory of inextensible surfaces, sufficient to repay the labour of a more 
general consideration of the question than has been (so far as I am aware) as 
yet attempted. I propose, therefore, in the present Memoir to consider gene- 
rally what are the conditions to which the displacements of a continuous inex- 
tensible membrane are subject. These conditions are expressed (as will be 
seen) by a system of three partial differential equations of a very simple form, 
which contain the solution of all questions connected with this theory. From 
these equations I shall deduce general expressions for the variations which 
the differential coefficients, 


Ghee he Ghee hee hes 
undergo in consequence of the displacement of the membrane. These expres- 
sions give immediately the two theorems of Gauss. I shall then proceed to 
consider how far the flexibility of the membrane is destroyed by rendering 
rigid any curve traced upon its surfuce. I shall in the next place investigate 
the laws which govern the displacement of a surface which is partially exten- 


344 The Rev. J. H. Jetrert on the Properties of Inextensible Surfaces. 


sible (as hereafter explained), and how far the preceding theorems are appli- 
cable to such surfaces ; and, finally, I shall consider how far these conclusions 
are applicable to the laminz which we find in nature, which are neither wholly 
inextensible nor wholly devoid of thickness. The results arrived at will be 
found, I think, sufficiently remarkable to attract the attention of mathematicians 
to this subject. 

2. Definition of an Ineatensible Surface—Two definitions of inextensibility 
have been given by LAGRANGE and Gauss respectively. According to the 
former, who defines the force which resists extension to be the force which resists 
the increase of superficial area, a surface is inextensible if it be impossible to 
change the superficial area of any portion of it. But this definition seems to 
be hardly consistent with the meaning ordinarily attached to the word “ inex- 
tensible.” For if we conceive a membrane admitting of being indefinitely ex- 
tended in any direction, but of such a nature, that an extension in any one 
direction is always accompanied by a corresponding contraction in another, so 
as to preserve the area unchanged, such a membrane would be, according 
to Lacrance’s definition, inextensible. But it appears more consistent with 
ordinary ideas to consider an inextensible surface to be one which does not 
admit of any extension, rather than one whose capacities of extension and con- 
traction counterbalance one another in the manner above described. I shall, 
therefore, in the present Memoir adopt the definition of Gauss, as more ex- 
actly embodying the ordinary ideas on the subject, adding to it the definition 
of partially extensible surfaces, a class not noticed by Gauss, but presenting 
some remarkable properties. These definitions are as follows : 

I. A surface is said to be inextensible, when the length of a curve traced arbi- 
trarily upon it is unchangeable by any force which can be applied to it. 

Il. A surface is partially extensible, if there be at each of its points one or 
more inextensible directions ; in other words, if it be possible to trace at each point 
one or more inextensible curves. 

We shall now proceed to consider how these definitions may be mathe- 
matically expressed, commencing with the case of inextensible surfaces. 

3. Deduction of the Equations which connect the Displacements of an Inex- 
tensible Surface. Letds be the element ofa curve traced in any direction upon 
the surface, and let 6 be the symbol of displacement, i. e. a symbol denoting the 


The Rev. J. H. Jevterv on the Properties of Inextensible Surfaces. 345 


passage of a molecule, or physical point, from one geometrical point of space 
to another. Then, since the curve of which ds is an element, is by the assumed 
definition inextensible, we must have 


tds = 0; 
V/ (dx? + dy? + dz’); 
and performing the operations indicated by 6, 
dadix + dydéy + dzdéz = 0; (A) 


recollecting that 6 is a commutative symbol. But since the displacements 
dr, 8y, z, refer to a point on the surface, we must have 


or, putting for ds its value, 


. _ dia déaz 
diz = a dz dy dy, 
dey dey 
Ce Ce Se dy, 
hap Og diz 
diz = a d dy d 3 
x, y, being the independent variables. 
Let dz = pdx + qdy, 


be the equation of the surface. 
Substituting for déx, déy, déz, dz, in equation (A), we have 
dba déz diy dea déz doz diy fe 
(Gite) @ +2 tay +9 Gq tP 7) vdy +(e +952) dy ® 


But since the condition expressed in this equation is supposed to hold for 
every curve traced upon the surface, it must be true for all values of 


ay 
da™ 
We have, therefore, 
dia, ie _ 
de‘? dx” 
diy  dtx  _déz déz _ 
aemanttag ag (B) 
diy doz _ 0. 


dy dy ~ 


346 The Rev. J. H. Jevzert on the Properties of Inextensible Surfaces. 


These equations may be put under a somewhat simpler form, by assuming 


u = bx + prz, 
v = by + goz, 
w= oz. 


Making these substitutions, we find 


o — wr =0, 

1 1 

Free aaline (C) 
77 m= 0 


where 7, s, f, are used in their ordinary sense to denote the differential coeffi- 
cients 

Ge de dz 
derived from the equation of the surface. Any one of the quantities w, v,w, may 
be determined by means of a differential equation of the second order. Thus, 


for example, eliminating w between the equations (C), we find, 
Ldu_1 (du, do) _1 de 
mdz | 28 \dy de) s dy 

Hence, 


Differentiating the first of these equations with respect to y, and the second 
with respect to z, and subtracting, we find easily, 


eu @u du_1d(rt—s*) du 

: dy’ a dady tlie pda da’ oY 
and similarly for », 

av dv dv 1d(rt—s°*) dv 

"dy * Gedy * dat dy dy’ ce) 


The Rev. J. H. Jezerr on the Properties of Ineatensible Surfaces. 347 


The equation for w may readily be deduced from (C). Differentiating the 
first of these equations with respect to y, and the second with respect to x, and 


subtracting, we have 
dy, dw dw ds 


ara 8 = i "dy +w qe 
Differentiating this equation with respect to y, 
3 2 2 2 
wa 2s mre + ee re 
Again, differentiating the third of equations (C) twice with regard to z, 
Eu =t ai + de dw +w i 2 
da*dy dz’ dz dx dx? 
Subtracting these equations one from the other, we find, 


dw iw Cw (F) 


r ae 2s aay +t — 0! 


dx? 


Some interesting results followed at once from the fundamental equations. 
Thus, for example, if the displacements of the surface be all parallel to the 
same plane, we shall have, taking this plane for the plane of zy, 


w= 0. 
The equations (C) are thus reduced to 
du du dv dv 
aR dy * da ; Meee 


Integrating this system of equations, we find, without difficulty, 
“=A+ By w= C— Bz; 


or since iz = 0 


it =A+ By, y=C— Bz; 
A, B, C, being constants. These equations express the following theorem : 
If the displacements of an ineatensible surface be all parallel to the same plane, 
the surface moves as a rigid body. 
More generally, if we make 
w=tz=axr—by+e, 
VOL. XXII. 22 


348 The Rev.J.H. Jewett on the Properties of Inextensible Surfaces. 
in the equations (C) we shall find without difficulty the solution : 
ie =cy —az+e’, 


ty = bz — cx +e”. 
Hence we infer that— 
If the movement of an ineatensible surface, parallel to any one line, be that of 
a rigid body, the entire movement is that of a rigid body. 


4. Variations of the Differential Coefficients. —If we denote by & the variation, 
properly so called, i. e., the change which the function receives in consequence 
of a change of form, it is evident that 

oz = pou + gy + b2’, 
dp dp déz’ _ dp dp d (&z — pox — qéy) 
Ue gt eigen ae ze + yl nO ee 
a die __ dic diy (G) 
“de  ? de ~ 1 de” 
atic _ die aty 
1 dy ie dy tay" 
Eliminating 
diz = dey 
dz’ dy’ 


from these equations, by means of the first and third of equations (B), we have 
diz _ (dey diz 
2 
tp= (1+ p° Ba es m9 (Gea ge): 


déz dix doz 
6 = 2 2 See ad = 
g=(1+p ne (a +97,)- 
In the same way we find, 


dip dix dey 
dz" da ° de’ 
dép dee dix =e dey _ déq _ oe 2 oy 
dy dy dy dx omen 0 Tn’ 


The Rev. J. H. Jeizerr on the Properties of Inextensible Surfaces. 349 


Substituting for &p, 6g, and reducing the resulting expressions by means of 
equations (D), (E), (F), we find ultimately, 
9 dix dey 
(* ie ae) 


2 > I~ 
ins (It ptt) Se - r(Ge+ 52) — 
Sz dix dey dia dey 
dxdy ~ 28 (Fea SE) (re +t Te) (H) 


dx dy 
Fie dig? dee, dia | dey déa | , diy 
& = (1+p? + 1) Tp (eta) - 2(s aye ag 
From the two equations (G) it is easy to verify that the element of the su- 
perficial area remains constant ; for if we multiply the first of these equations 
by p, and the second by g, and add them, we find, recollecting the second of 
equations (B), 


és=(1+p’ +9’) 


di i 
pip + qq = (14+ P +1 (09 +49 a) 
or from the first and third of equations (B), 
dix dé 
pep + eq + (1+ p? +0) (7 +7!) = 0, (1) 
which is obviously equivalent to 


6/7(1+p?+ 9’) drdy = 0. 


Again, multiplying the first of equations (H) by ¢, the second by 2s, and the 
third by r, and subtracting the second product from the sum of the other two, 


we have 
tér + rét — Qsés = 6 (rt — s*) 


doz doz Piz dix dty 
=(14 p49) (09 FES aes oa) 4 (rt — °) (7 +9") 


dix +5%), 
=-—A(rt— (et 
(rt — s*) i 
Hence, and from equation (I), it is easy to see that 
BRE). g (Popaaae ot 
rt— 3" 1l+ps+¢7 


which is plainly equivalent to 


7) A Pe 


350 The Rev. J. H.Jeuierr on the Properties of Inextensible Surfaces. 


rt — 8° 1 
‘Cs ey He i 

This equation is the analytical statement of Gauss’s celebrated theorem, 
namely, that 

In all the possible movements of an inextensible surface, the product of the 
principal radii of curvature at every point of the surface is constant. 

Let S be a portion of the surface bounded by any closed curve. Conceive — 
this curve to be referred to the surface of a sphere, by radii drawn parallel to 
the normals, and let S’ be the included portion of the spherical surface. Then, 
if the radius of the sphere be supposed to be unity, 


afi. 
and therefore, 
6S’ = [le _ = (i) 


Hence, In all possible motions of an inectensible surface, the area of the sphe- 
rical curve corresponding to any closed curve described upon the surface (denomi- 
nated by Gauss the “curvatura integra”) remains constant. 

This is the second theorem of Gauss. 


5. We shall next proceed to consider the effect of jiving any curve upon 
the surface. The determination of the displacement of the surface in this case 
will obviously depend upon the following analytical problem :—‘ To find three 
functions u, v, w, which shall satisfy the partial differential equations, 


du 


Te 

du dv 

Tig ies os ae 
dv 

qo 


and shall, moreover, have the values 
“=0, v=0, w=0, 


for all points of a given curve or portion of a curve.” 


The Rev. J. H. Jeuerr on the Properties of Inextensible Surfaces. 3 


On 
pay 


mee dy = mda, 


be the equation of the projection of the given curve upon the plane of zy. 
Then since w, v, w, vanish for a continuous portion of this curve, we must have 


du, ,, dg 
de dy =" 
dv dv 
dw dw 
But if we make 
Bs 
in the first and third of equations (C), we shall have 
du dv 
Faz 0, agi 0. 
Hence and from equations (L) we have 
duo do 
dy dz 


Differentiating these equations upon the same principle, we have 


@u @u Pu Vu 


Fae. OE ian an) aye (wt 
dy on dv =o dv BY 2% 
de? Gedy“ dady t ™ayi =" 


Hence it is easily seen that the equations (D) and (E), p. 846, become for this 


curve 
Pu 
dady~ ”’ 


(r + 2sm + tm?) 
. (N) 
9 U — 
ieee te) gan 
Hitherto the reasoning employed has been perfectly general, embracing 
surfaces of every class. But in our subsequent investigations we must discuss 


352 The Rev. J. H. Jetrert on the Properties of Ineatensible Surfaces. 
severally the three great classes into which surfaces are divided with respect 
to their curvature, namely : 
1, Surfaces whose principal curvatures are similar, or those in which 
rt—s° > 0. 
2. Developable surfaces, in which 
rt— 3? = 0. 
3. Surfaces whose principal curvatures are dissimilar, or those in which 
rt—s' <0. 


I. Surfaces whose principal curvatures are similar.—In this case it is plain 
that the equation 


r+ 2sm + tm? = 0 
is impossible, whatever be the value of m. Therefore the equations (N) can 
only be satisfied by making 
au. dy 0 
dzdy dzdy 
Hence, and from equations (M), we find 


Pu du au _ 


=0 —_- = =) 
me ’ ? dy? ’ 
2, 2, 2, 
av _ @v 0 fey 


dz g dady’ dy 


which must hold throughout the fixed curve. Again, differentiating equations 
(D) and (E) (which are true generally) with regard to z, and rejecting diffe- 
rential coefficients of the first and second order, which vanish for the fixed 
curve, we have 
du du du 
Tap a dei ae (P) 
dv dv Pu 

aang et dig aes 


which must hold throughout the fixed curve. 


The Rev. J. H. Jettert on the Properties of Inextensible Surfaces. 353 


Differentiating equations (M) as before, and eliminating 


Du Tu 
dx*dy’ da’ 
from equations (P), we have 
Bu 
(r + 2sm + tm?) ——-, = 0, 
dxdy* 
Hl (Q) 


oe ORD 
Canaan) dedi 


Hence it is easy to infer, as before, that all the differential coefficients of the 
third order vanish for points of the surface situated on the fixed curve ; and a 
very slight examination will show that by proceeding in the same manner we 
shall find that all the differential coefficients of w, of all orders, vanish for the 
limiting curve. Now if wu be a function of the same form throughout the sur- 
face, it is plain that these conditions can only be satisfied by the supposition 
that w vanishes at every point. The same conclusion will hold if w change 
its form. For if w be supposed to have the same form for all points between 
the limiting curve and any other curve drawn arbitrarily, it is plain, from what 
has been said, that its value can be no other than zero. Hence for all points of 
the second curve 
= (0) 

Now it is evident that the same reasoning which was before applied to the 
limiting curve is equally applicable to this second curve, and so on for any 
number of curves bounding those parts of the surface for which the form of u 
is the same. It appears, therefore, from the foregoing reasoning, that we 
must have throughout the entire surface 

u=0. 
By precisely similar reasoning it may be shown that we have throughout the 
entire surface 

Has 
and on referring to equations (C), it will be seen that it follows at once from 


these equations that 
w= 0. 


354 The Rev. J. H. Jevterr on the Properties of Inextensible Surfaces. 


Replacing w, v, w, by their values in terms of éz, ty, &z, we have for every point 
of the surface 
Gm == (0) ay — 10; éz = 0. 


Hence we infer the following theorem : 
Tf any curve be traced upon an ineatensible surface, whose principal curvatures 


are finite and of the same sign, and if this curve be rendered immovable, the entire 
surface will become immovable also. 


More generally, let it be required to determine a system of values of u, v, w, 
which shall satisfy the equations (C), and which shall have at all points of a 
given curve, or part of a curve, the given values 


ui v=U, w= Wy. 
Then it is easy to show from the foregoing discussion, that there is but one such 
system. 
For, if possible, let there be two systems of values, 
a= UO, v= 1% w= W, 
Meat OF 2 V5, ys AG 
which satisfy the given conditions. Then since the equations (C), which these 


two systems of values are supposed to satisfy, are linear, it is plain that if we 
form a third system, 


0 — Ue v=V-V’', w=W_-W,, 
this system will also satisfy equations (C). But as the values of u,v, w are 


given for the limiting curve, the two assumed systems must be coincident 
throughout this curve, and therefore we must have for all its points, 


U-U=0, V—V' —0, wv =o. 
Now we have seen in the foregoing discussion that if u, v, w be a system of 
values satisfying these two conditions, we must have generally 
u—0, vt — 0; w= 0. 
Hence it is plain that at every point of the surface 


Tuo) hae. | WW" 9. 


The Rev. J. H. Jetrerr on the Properties of Inextensible Surfaces. 359 


The two systems of values are therefore identical. Hence we infer the 
theorem— 


Tf a curve be traced upon an inextensible surface, whose principal curvatures 
are finite, and of the same sign, and if any given determinate motion be assigned to 
this curve, the motion of the entire surface is determinate and unique. 


Thus, for example, it is easily shown that if the limiting curve be made 
rigid, the entire surface will become rigid also. 


II. We shall next consider the case of developable surfaces, or those in 
which 
rt—s =0. 
This case may be subdivided into two, which require to be considered sepa- 
rately. These cases are— 


1. When the fixed curve is either a rectilinear section of the surface or 
the aréte de rebroussement. 
2. When the fixed curve is not either of these. 


1. Let the fixed curve be a rectilinear section. Then it is plain that this 
curve must satisfy the equation 


r+ 2sm + tm? = 0, 


which expresses the fact that the radius of curvature of the normal section 

passing through this line, i. e. in the case of a developable surface, of the line 

itself, is infinite. 

Hence the equations (N) become identically true, without supposing that 

Mu dv 
ya aad 

It is plain, therefore, that the reasoning by which it was shown that the several 

differential coeflicients of w, v vanish for the fixed curve, is no longer appli- 

cable, and that the several conditions of the problem may be satisfied without 


supposing uw, v to vanish at every point of the surface. We infer, therefore, 
that, 


0. 


In a developable surface composed of an inextensible membrane, any one of its 
rectilinear sections may be fixed without destroying the flexibility of the membrane. 
VOL. XXII. 3A 


356 The Rev. J. H. Jetzerr on the Properties of Inextensible Surfaces. 


And it is easily seen that the same conclusion will hold if the fixed curve be the 
aréte de rebroussement of the developable surface. 

2. Let the fixed curve be neither a right line nor the aréte de rebroussement. 
Then since this curve does not satisfy the equation 

r+2sm + tm = 0, 
we must have, as in the first case, 
Pu av 

All the reasoning of that case is therefore strictly applicable, and it will appear, 
as before, that al/ the differential coefficients of w must vanish for the limiting 
curve. Hence, if w preserve the same form, it can have no value but zero. 
Now let it be supposed that w may change its form ; then it is easily seen that 
the zero value of wu can only change in passing across a curve whose equation is 


r + 2sm + tm? = 0. 


Every part of the surface, therefore, which can be reached from the fixed 
curve without crossing either the aréte de rebroussement or a rectilinear section, 
is necessarily fixed. The remainder of the surface is capable of motion, 
Hence we have the following construction : 

Let AB be a fixed curve drawn on the given membrane. 
Draw through the extreme points A, B, the rectilinear sections 
of the developable surface, and produce them to touch the 
aréte de rebroussement. Then itis evident, from the foregoing 
analysis, that all that part of the surface which lies between 
the two lines, and on the same side of the aréte de rebrousse- 
ment with the fixed curve, will itself be fixed. Beyond these 
lines the surface is flexible. 

To determine more accurately the nature of the motion of 
which the surface is capable, we shall now proceed to integrate A B 
the equation (D), which, for a developable surface, is in gene- 
ral possible. 

Since r¢ — s° = 0, equation (D) becomes in the present case 

du. du Pu (R) 


"yp - dady ue us 


The equations of the characteristic are therefore 


The Rev. J. H. Jetzert on the Properties of Ineatensible Surfaces. 357 


dy dy? ‘ 
Qo =f —— 
mF 28 aes My (S) 
au dy = du 
rd. — —~ .d.—=0. Ab 
fea ae dx (f) 
Let p=Q 
be the equation of the given surface ; then 
r= Q's, = (iy 
where Q' = dQ, 
dq 


Substituting these values in equation (S), we find easily 
dy _ 
dz 

Now since equation (S) represents a rectilinear section of the surface, it is evi- 

dent that in this equation Q’ must be constant. Hence it becomes 


yah 


y + Qa = const. 
Again, substituting for r, ¢, and on in equation (T), and integrating, we find 


Q’ = = = const. 
Then the integral of equation (R), which may readily be obtained in the ordi- 
nary way, will be 
u = af(q) + £(q)- (V) 
The following general property of the motion may be deduced from this 
equation : 
The rectilinear sections of the surface are rigid.* 
For, since in a developable surface q is constant for the same rectilinear sec- 
tion, the value of w for such a section will be 
u=Az + B, 
A, B being constants. 


* It is easily seen, however, that these sections may all bend at the aréte de rebroussement. 


3A 2 


358 The Rev. J. H. Jevrerr on the Properties of Inextensible Surfaces. 


Similarly we shall have 
0 = A’z + By’. 
w= AX“ r+ BY. 


Hence it is easy to see that if z’, y’, 2’ be the co-ordinates of the new position 
of the point 2, y, z, we shall have 
2’ =azr +b, 
y =a'e +0, 
Z = a'e+ Ke. 
where a, a’, a’, b, b’, b’, are constant for the same rectilinear section. From 


these equations it is plain that the locus of the points 2’, y’, 2’ is still a right 
line. 


III. Concavo-convex surfaces, or those in which 
mtt—s <0. 


It is a well-known property of surfaces of this class that at each point of the 
surface there are two real directions satisfying the condition 


7 cos’ a + 2s cosa cos B + tcos’ B= 0; (W) 


an equation which expresses the geometrical fact, that the normal section which 
passes through either of these directions will have at that point an infinite 
radius of curvature. We may therefore conceive the entire surface to be 
crossed by two series of curves, such that a tangent drawn to either of them at 
any point shall possess this geometrical property. These curves we shall de- 
nominate (for a reason which will appear subsequently) curves of flexure. We 
shall consider separately (as before for developable surfaces) the two different 
cases which arise, according as the fixed curve is or is not a curve of flexure. 

1. When the fixed curve is a curve of flexure it is evident, as in the case of 
developable surfaces, that the equation 


WP 
SA SE erty 


becomes identically true without supposing 


du 
dxdy — 


The Rev. J. H. Jetxerr on the Properties of Inextensible Surfaces. 359 


We conclude, therefore, as before, that any one of these curves may be fixed 
without destroying the flexibility of the surface. The reason for the name 
“curve of flexure” is thus explained. In fact we see that these curves, when 
fixed, allow the surface to bend round them, the flexure commencing at the 
curve itself. We shall presently show that this property is peculiar to the curves 
of flexure as above defined. 

2. When the fixed curve is not a curve of flexure, the reasoning before 
given in the case of developable surfaces will show that éz, éy, 2, and all their 
differential coefficients, vanish for the fixed curve. If, therefore, these func- 
tions retained throughout the same form it is plain that the value of each could 
be no other than zero. Before proceeding to consider how far this conclusion 
is modified by a change in the forms of the functions, we shall prove the fol- 
lowing theorems, which are essential to our purpose. 

(1.) If the functions which represent the displacements of an inextensible 
surface have different forms at different points of the surface, the parts of the 
surface for which these functions retain the same forms are bounded by curves 
of flexure. 

This theorem is proved by reasoning nearly identical with that of p. 354. 
For, if possible, let the forms of these functions change in passing across a 
curve which is not a curve of flexure. Let 

= (Ul os w= W, 
be the values which hold at one side of the curve, and 

1 — Di ee wu W?, 
those which hold at the other. Then it will appear precisely as in p. 354 that 
if we form a third system of values, 
u=U-U, i Va v w= WW, 
this system will satisfy the equations (C), and will, moreover, be such that for 
every point of the curve in question we shall have 
10; wi—()) w= 0. 

Since, then, the bounding curve is not a curve of flexure, and since U, V, W, 
U', V’, W’, are functions of determinate form, it is plain that we must have 


generally 
ie T= 0; V—V’=0, W— W'=0. 


360 The Rev. J.H. Jetzert on the Properties of Inextensible Surfaces. 


No one, therefore, of the functions w, v, w, can change its form, except in pass- 
ing across a curve of flexure. Hence the proposition is evident. 

(IL) Let AB, AC be two arcs of curves of 
flexure commencing at the same point A. Through 
B, C draw the curves of flexure BD, CD, meeting 
in D. Then if AB, AC be fixed, the entire qua- 
drilateral ABDC is fixed also. 

The truth of this theorem is nearly evident 
from the theory of partial differential equations, 
combined with the principle laid down in (I.), but it may be strictly proved as 
follows : 

Since w, v, w, can only change their forms in passing a curve of flexure, we 
may suppose them to retain the same form throughout the entire of the quadri- 
lateral Ad,d,c,, formed by drawing the curves of flexure b,d, ed. 

Let de Gc, 
be the equations of the two series of curves of flexure. Then, since the func- 
tions 0, 6’ satisfy the differential equations 

de? dodo _dé@& 
"ap 28 ay eae 
do” do’ do’ dé” 
dy = oF dy + aa =5 (0) 
if the independent variables , y, be changed into @, 6’, the equation 
e aw Qs lw f ,2" 
dy? dady  — da® 


will (as is well known) assume the form 


, 


=0 


a +P as + Q a = 0, (X) 
P, Q, being functions of 6, 6’. Now since w vanishes for the curve 
0=¢, 
it is plain that we must have throughout this curve, 
dw lw Bw 


aa Mapes Ser aor 5 oe 


The Rev. J. H. Jetxert on the Properties of Inextensible Surfaces. 361 
and for the curve 6 =0, 


dw _ 0 aw _ Pw 

COME dG dG 
For the point A, therefore, which is the intersection of these curves, both these 
systems of equations must be satisfied. Putting, then, in equation (X), 


== 05 &e: 


dw dw 
do 0, do’ — L 
we have aw 
dod!’ 


and it is easily seen that neither P nor Q will become infinite ; and by follow- 
ing the same reasoning with that of p. 352, we shall find that for the point A all 
the differential coefficients of # must vanish. Hence as the form of w remains 
the same throughout the quadrilateral Ad,dc,, we must have for the whole of 
that quadrilateral 
op = Ob 

Now it is evident that the reasoning which we have applied to the point A is in 
every respect applicable to 6,, and thus in succession to dy, b;,&c. The value 
of w will therefore be zero for all points of a second curve of flexure ¢,d,;. And 
by pursuing the same method we see evidently that w must vanish throughout 
the whole of the quadrilateral ABDC. Hence, the direction of the axis of z 
being indeterminate, we shall,have in general, 

oze— OF by = 0, Gin (0), 
throughout ABDC. The whole of this quadrilateral is therefore fixed. We 
shall now proceed to consider the general case. 

Let AB be any arc of a curve (not a curve of 
flexure) traced upon the surface. Through A, B, draw 
the curves of flexure, AC, AD, BC, BD. Then if AB 
be fixed, the quadrilateral ACBD is fixed also. 

For whatever law or laws we suppose the dis- 
placements to follow, it is plain that we may assume a 
number of points, b,, bs, b;, &c. so close that one of 
these displacements, w, for example, shall retain the 
same form throughout each one of the quadrilaterals 


362 The Rev. J. H. Junterr on the Properties of Inextensible Surfaces. 


Ab,, bbs, babs, &c., formed by drawing curves of flexure through },, b:, &c. 
Hence, and from p. 359, it is evident that w must vanish throughout the entire 
of each of these quadrilaterals. But if 

w=0 
for the quadrilaterals Ad, b,b., it follows from Theorem m1. p. 360, that w must 
vanish for the quadrilateral b,c, ; and by pursuing the same method we shall 
easily see that we must have 

w=0 
for each of the quadrilaterals into which ACBD is divided. Hence the truth 
of the proposition is evident. This proposition may be expressed by saying 
that 

If an are of a curve traced upon an ineaxtensible surface be rendered fixed or 

rigid, the entire of the quadrilateral, formed by drawing the two curves of flecure 
through each extremity of the curve, becomes fixed or rigid also. 


6. We shall now proceed to consider the case of surfaces which, without 
being wholly inextensible, have at each point one or more inextensible di- 
rections. 

Reverting to the discussion of p. 845, and making 


3 da dy 
Ae coe a, ae cos f, 


we find easily 
tds (du , du. dv dv ‘ 
Fae =(z - wr) cos’a + (a+ Tie 20s) cos a cosB + (= - ut) cos’p. (Y) 
From this equation it is plain that, unless the coefficients of 
cos’a, cosacosfB, cos’, 

vanish separately, there can be, for each law of displacement, but two values of 

cosa 

cos p’ 
which will satisfy the equation 

éds = 0. 


If these coefficients vanish separately, éds will vanish for every direction round 
the point. Hence it is easy to infer the following theorems :— 


The Rev. J. H. Jetrert on the Properties of Inextensible Surfaces. 363 


Tf a surface have at each point three or more inextensible directions, it is wholly 
mextensible. 

A surface may have at each point one or two ineatensible directions, without 
being wholly inextensible. 

Suppose that the given surface has at each point two inextensible curves 
included in the equation 

Rda? + 2Sdxdy + Tdy? = 0, 

or Reos’ a + 2S cosa cos B + T'cos’? B = 0. 


Then, as this equation must be identical with 


( _ wr) cos’ a + & ar = = 20s) cos a cos B + (5 - ut) cos’ B = 0, 


we shall have 


GL RN CS LC RO OR Z 

Plas te" Spe ag ae) pl a @) 
These two equations contain the entire theory of the surfaces under con- 
sideration. 


Suppose, for example, that the surface is one of dissimilar curvatures, and 
that its curves of flexure are inextensible. We have then 


R= it, S=s, If =H 
and the equations (Z) become 


lidu _ li fdu do\ «Vado j 
re =e tae) Te Co 
being identical with the equations which are found by eliminating w between 
the general equations (C), p. 346. The displacement w remains indeterminate. 


From these considerations it is easy to deduce the following theorem :— 


Tf the curves of flecure traced upon a surface with dissimilar curvatures be in- 
extensible, the most general displacement of which the surface is capable may be 
found by supposing it first to move as an inextensible surface, and then to receive at 
each point a normal displacement of arbitrary magnitude. 

VOL, XXII. 3B 


364 The Rev. J. H. Jetzert on the Properties of Inextensible Surfaces. 


Let W be an arbitrary function of z and y. Then the equations (A’) being 
put under the form 


Dida Te Cs doe 
ea dy dn es ly die 


the expression for the extension of any small arc ds (Y) will become 
tds = (W— w) ds (rcos? a + 2s cosa cos B + t cos”). 
Hence for the class of surfaces under consideration we infer that— 


The extension of any small are of a curve commencing at a given point, divided 
by the are itself, varies inversely as the radius of curvature of the normal section 
which passes through i. 


7. Having thus investigated the case of inextensible and partially inexten- 
sible surfaces, we should, in the next place, proceed to consider how far the 
results arrived at are applicable to the various membranes which we find in 
nature, and which are neither perfectly inextensible nor altogether devoid of 
thickness. But before entering upon this question we shall briefly examine 
the case of inextensible bodies. 

Conceive a curve to be traced in the interior of a body, passing through the 
successive physical points or molecules a, b, c,d, &c. Suppose now that the se- 
veral points of the body receive small displacements, and take the curve which 
is the locus of the points a, b, c, d, &c. in their new position. If the length of the 
second curve be equal to that of the first, and if this be true of all curves which 
can be so drawn, the body may be said to be inextensible. Adopting this defi- 
nition, we shall have the following theorems :— 


I. Every body which is perfectly inextensible is also perfectly rigid. 

Il. Any body may, without being wholly inextensible, have at each of its points 
an infinite number of inextensible directions, and these directions will be situated upon 
a cone of the second order. 


Let &, by, &z, be the displacements of any point in the body, and let ds be 
an element of a curve, making with the axes of co-ordinates the angles a, f, y. 
Then it is easily seen, that the variation of this element will be given by the 
equation 


The Rev. J. H. Jetterr on the Properties of Inextensible Surfaces. 365 


ids diz, dey 
Ss" a+ — 


—=— co Cai IT, 
ds dx dy dz x 


(B’) 
diz  dty dix dbz diy  déx 
+(Ge+ Ag TIL) cos feos 1+ (T= + Ta) cov eosat (Fe + 52) cosa cos 8 


Now if the body be inextensible, we must have for all values of a, 6, 7, 
éds = 0. 
Hence we have the six equations, 
dix 0 dey _ 0 diz 


4 ? dy ’ GE. 
doz dey _ dix doz yh dix 


dy egy tees aga ak Lanka tay 
Integrating this system of equations, which may be effected without diffi- 
culty, we find, 


(C’) 
=) 


ta = a+ Bz — Cy, 

ty = b+ Cx — Az, 

z=c+Ay—- Bz; 
the well-known expression for the displacements of a rigid body. These 
being the most general values which éz, éy, éz admit of, the truth of the first 
theorem is evident. 

With regard to the second theorem, if the body is so constituted that the 

displacements éz, 8y, 2 must satisfy the equations 


dix diy _ diz _ 

dorm Hye Ae (D) 
déz Aa , abe diz 2.1, diy , dix f 
ae ae ees F Saker es cae Ee eciaee 


A, B, C, a, b, c, being functions of «, y, z, the body will have at each point an 
infinite number of inextensible directions situated on the cone (real or ima- 
ginary), 

Acos’a+Bcos’B +C'cos*y + 2A’ cos B cos y+ 25’ cosy cos a+ 2C’ cosa cosB=0. 


If the constitution of the body be given, A, B, C, &c., will be given func- 
tions. In this case the equations (D’) furnish the means of determining 
3B2 


366 The Rev. J. H. Jewett on the Properties of Inextensible Surfaces. 


éa, 6y, 8z. Thus, for example, ifthe body be homogeneous, A, B, C, &c., will be 
constants, and it is not difficult to prove that éz, éy, éz will be of the form 
te =ar +by + cz +d, 
sy=ar +hy+cz+d, (E’) 
oe =a"etb"yt+elz4+d". 


Let 2’, y’, 2’, be the co-ordinates of the molecule in its new position. Then 


since 
iz = z' — 2, 
as / 
y=y -% 
iz = 2 — 2; 
we have 


aw@=(a +1)a+by+ez +d, 
y=ae+(l+1)yt+ez4+d, (F’) 
Z=a’etb’yt+(ce'+1) 24+". 

Hence it is easy to infer the following theorem : 

If a homogeneous body have at each point a cone of inextensible directions, and 
if in the interior of the body there be described an algebraic surface of any order, 
all the molecules situated upon that surface will after displacement be situated 
upon a surface of the same order. 

In general, whatever be the nature of the body, if ds be an element making 
with the axes the angles a, 8, y, which satisfy the equation 


ee ee 


dz dy 


(Ez a cos B co we nee Oo osy+ ee cosa cosB=0; 
wale a ack Can ag A ay ga 


it is plain that we shall have 


déz 
cos’ B + Fs: cos’ y 


ids = 0. 
Hence, 
Whatever be the law of the displacement, there will be at each point of the body 
an infinite number of directions (forming a cone of the second order), for which the 
length of the element will be unchanged. 


We shall now return to the case of surfaces. 


The Rev. J. H. Jettett on the Properties of Inextensible Surfaces. 367 


8. The preceding discussion of the properties of inextensible surfaces is 
of course a mathematical abstraction, not strictly applicable to any substance 
which we find in nature. Every membrane with which we are acquainted is 
possessed of some extensibility; and all substances have of course a certain 
thickness. Our definition, therefore, of an inextensible surface is not strictly 
true for any really existing substance. But as there are in nature many sub- 
stances for which this definition is very approximately true, it becomes a question 
of some interest to determine how far the results of the preceding investi- 
gation are applicable to such substances. We shall, therefore, proceed to con- 
sider the case of a membrane whose thickness is indefinitely small as compared 
with its other dimensions, and whose extensibility is such that in any dis- 
placement of the membrane, the variation in the length of any arc of a curve 
traced upon its surface is indefinitely small compared with the displacement 
of any of its parts. Thus, if z, y, z be the co-ordinates of any point on the sur- 
face, and s an arc of a curve traced upon it, the assumption which we shall 
make as to the inextensibility of the membrane may be mathematically ex- 
pressed by saying that 6s is indefinitely small compared with éz. If it be ne- 
cessary to take thickness into account, we must suppose s to be a curve traced 
arbitrarily in the substance of the membrane. Supposing, for the sake of greater 
generality, that this is the case, we may state the problem under discussion 
as follows : 

To determine the possible displacement of a membrane very slightly exten- 
sible, and whose thickness is very small compared with its other dimensions. 

Let 2’, y’, 2’ be the co-ordinates of a point in the substance of the mem- 
brane; 2, ¥, z, the co-ordinates of a point on the surface, indefinitely near to 
the first; and 7, a quantity of the same order of magnitude as the thickness of 
the membrane. 

Through the point z’y'z’ let a normal be drawn to the surface of the mem- 
brane, and let m represent the part of the normal between z’y’z’ and its inter- 
section with the surface, which we shall denote by a, y, z. Then if a, B, y be 
the cosines of the angles which the normal makes with the axes, we shall have 


c=xr+an, 


y’ =y + Brn, (G’) 


Z=2+ yn. 


368 The Rev. J. H. Jetterr on the Properties of Inextensible Surfaces. 


Differentiating these equations, and rejecting nda, ndp, ndy, on account of the 
small quantity , which is of the same order as the thickness of the membrane, 


we have 
da’ = dz + adn, 


dy! = dy + Bdn, (H’) 
dz’ = dz + ydn. 
If now we represent by ds’ an arc of a curve traced in the substance of the 
membrane, we shall have, as before, 
ds'éds! = da’ dba! + dy‘déy’ + dz'déz’. (I’) 


But if we regard éa’, &y’, 2’ as functions of the three variables z, y, n, we 


shall have 
dia! dea’! dia’ 


doz = aa dz+ ea Pies VERE dn, 
ea MLL diy! < diy’ / 
dey = dee Eyl! habia (K’) 
pendiz. dbz’ aoe 
doz’ = aa. dz+ Tag dy Bian: dn. 


Substituting in (I’) the values (H’) and (K’), and putting for dz its value 
pda + gqdy, we have 


ts! _ (dia’,  dic!\ de, (diy! | dod 

ds ~\de '? da ee +4 ay on 
dé’ déy/ " diz’ 4. déz’\ dz dy 

dy * da +? dy! de ) ds ds' 


doa pane cd y! déz'\ dx dn # 
+(Ge+ dn O egeiatt pS = a ie) ds’ eo 
eye. Malas a din’ déz’\ dy dn 
i ae dn + 1 an * 8 dy st dy ) ds’ ds’ 
{ déx' dey! id dn 
+(0g, +O a, hg He) ie 


Now since dés’ is by hypothesis indefinitely small, as compared with any one 


The Rev. J. H. Jetierr on the Properties of Ineatensible Surfaces. 369 
of the quantities déx’, déy', déz’, and since this is true for all directions of the 


arc ds’, it is plain that the coefficients of each of the quantities 


da* dy’ dxdy dxdn dydn dn’ 
dsaids* dads? dss” ‘asda? ds? 


must be indefinitely small as compared with &z, éy, &z. We shall, in the first 
place, consider the coefficients of the first three of these quantities. 

If we neglect, as before, quantities of the second order, we may evidently 
substitute in these coefficients 62, 6y, 6z, for &x’, by’, 62’. We shall have then 


dix i déz ai 
dx ED + lean 
dix dey diz déz : 
dy + ia SP DS dy 36 SS aa = 22), 
ae pope F 
> =, 
dy 71 ay 


be satisfied, where a, b, ¢ are functions of x and y of the same order of magni- 
tude as &z, y, 6z. 
Transforming these equations as in p. 346, we find 


u : 
— — ur = 14, 


dz 
du dv ; 
Ga Cs (MW) 
dv 
dy — wi = iC 


Now it is well known, that such a system of equations may always be satis- 


fied by the values 
U=U + ih, 


v=v' +m, 
w=w' + iw,; 


where u’, v’, w’, satisfy the equations 


370 = The Rev. J. H. Jetxerr on the Properties of Inextensible Surfaces. 


we wr = 0, 
du’ dv’ 
iy t de 728 =0 
ve wt=0. 


Hence it is plain, that the displacements of a surface which is but slightly 


extensible will differ from those of an inextensible surface, by quantities which 
are of the same order of magnitude as the extensibility of the surface. From this 
it is easy to infer, that all the theorems which are rigorously true for an inex- 
tensible surface are approaimately true for a surface possessed of an indefinitely 


small amount of extensibility. 
Let us now consider the coefficients of the quantities 


dzdn dydn_ dni 
ds' ds” ds'ds'’ ds'* 


These coeflicients give the equations 


dix’ _— dz’ pe dé sa déz! 


Gi sae alee tr ag a en 
déy! déz’ doa’ y! déz’ . 
an an eG at ay = Ds 
dix’ ia dd F 
“dn 748 din Lara iC, 


(N’) 


A, B, C being of the same order as 6a’, &y’, 82’. Since a, B, y are independent 
of n, the third of these equations may be integrated at once. Performing the 


integration, and supposing the integrals to begin when 


/ 


te ce Yee — 2, 
we have 
aba’ + Boy! + yo’ = ata + Boy + ye + if’ Cdn. 
Now it is evident that 
aie’ + pay’ + yo2’ = én, 
abu + poy + yoz = (EN)o, 


(0) 


The Rev. J. H. Jetzerr on the Properties of Ineatensible Surfaces. 371 


denoting by (&)) the normal displacement of the point on the surface. Equa- 
tion (O’) becomes, therefore, 


én = (on) + if’ Can. 


Now the definite integral 
f Cdn 


is evidently a small quantity of the second order ; if therefore we neglect 
quantities of the third order, we shall have 


én = (6n)p. 
Hence we infer that— 

In all possible displacements of a thin membrane or lamina which is very 
slightly extensible, the normal displacements of points situated on the same normal 
to the surface are equal. 

This would also follow from the next theorem. 


Substituting in the first two equations (N’) for a, B,y their values in terms 
of p and q, we have 


EL Ai iE nan ac Pe cu Jif ODE aah 5 OO ks BOO Nee 4 
dn? dn 'VAatp+@)\de ? de dpe (P”) 
din/ diz! 1 déz' dex’ diy’\ _. 
Ge eae * EF ED ap Py a) 


Now it is plain that without altering the form of these equations we may 
substitute, in the last three terms of each, éa, 8y, éz for éa’, éy’, 62’. For this 
substitution merely amounts to the addition of quantities of the same order as 
iA, iB, to the right-hand members of these equations. Again, referring to 
p. 848, we have 


i ea a igaa 
Ggrlvag = Diggin Es 


Making these substitutions in equations (P’), we have 
VOL. XXII. 3c 


372 The Rev. J. H. Jetert on the Properties of Inextensible Surfaces. 


déa’ 2 diz! op bay 
dn Pin *J/G+tp+g) 3 
dey’ doz oq 


dn ae (CPP Te 
Integrating these equations between the limits 0 and n, and neglecting as before 
quantities of the third order, we have 
nb 
6 (2-2) + po (2! -z) + Waa P EP = 0, 
(Q') 
F no 
8(y'/-y) + ge (2'-—2z)+ Waeres = (0): 
But since 
n 


panhcr a 
Cay a) ene 


these equations may evidently be written 
b{2’ -a#+p(2/—2)}=0, 
bly’ —y +9 (%—2)}=0. 


Hence recollecting that the points xyz, x'y'z’, were originally on the same nor- 
mal, we have still, after the displacement, 


zw —x+p(z—z)=0, 
y —ytq(-2)=0. 
We infer, therefore, that— 


In every possible displacement of a thin membrane or lamina whose eatensibility 
is very small, all points which were originally situated on the same normal to the 
surface will remain so after the displacement. 


This important theorem, which is assumed as an hypothesis by most writers 
on the equilibrium of elastic laminz, is thus established, independently of any 
theory of molecular force, as a mathematical consequence of the small amount 
of extensibility which is possessed by the lamina. 

It may be well, before concluding, to say a few words in explanation of the 
rule which we have followed in the rejection of small quantities. 

Small quantities of the first order, as 6x, &c., have been retained throughout. 


The Rev. J. H. Jetzert on the Properties of Inextensible Surfaces. 373 


Small quantities of the second order are rejected in the expressions for 
da’, dy’, dz, (H’), because the retention of these quantities would leave the 
form of the equations (M’) and (N’) altogether unchanged. 

Small quantities of the third order are rejected in equations (O’) and (Q’), 
because the differences 

&n — (Sn), Sa! — bx, &c. 
ought properly to be of the second order. If we retain these terms we may 
enunciate the foregoing theorem rigorously as follows : 

If a membrane which is but slightly extensible receive a finite displacement, the 
separation of any point from the normal drawn through the corresponding point on 
the surface, is indefinitely small, as compared with the distance of these points from 
each other. 

With respect to the comparative magnitude of the two small quantities 
i and n, depending respectively upon the extensibility and the thickness of the 
lamina, it may have been observed that throughout the preceding discussion 
they have been treated as quantities of the same order. Let us consider what 
would be the effect of a violation of this rule. 

As the thickness of the membrane is not supposed to be insensible, we can- 
not suppose 7 to be indefinitely small as compared with 7, without assigning to 
the membrane an amount of extensibility not indefinitely small. This would 
remove it from the class of substances which we have been considering. 

If we had supposed 7 to be indefinitely small as compared with n, we should 
not have been justified in rejecting nda, ndp, ndy in forming the expressions 
(H’), p. 368. Our investigation would not, therefore, have differed in any ma- 
terial respect from that of the displacements of a body of finite dimensions and 
of an indefinitely small amount of extensibility ; and in such a case it would 
readily appear from the discussion of p. 365 that the body would be, q. p., rigid. 
We see then that— 

No membrane can be flexible which does not possess an amount of extensibility 
Jinite, as compared with its thickness. 

It is, perhaps, superfluous to add, that it is not necessary to the truth of the 
preceding theorems that the membrane should be absolutely or approximately 
inextensible by any imaginable force. It is sufficient for our purpose if the 

2c2 


374 The Rev. J. H. Jextert on the Properties of Ineatensible Surfaces. 


forces which are supposed to be applied to the membrane are incapable of ex- 
tending it. And in such a case all the foregoing theorems will hold, if we sub- 
stitute for “all possible displacements,” “ all displacements which can be 
effected by any amount of force which is supposed to be present.” 

Some interesting practical conclusions follow from this discussion. Thus, 
if we desire to take advantage of the very slight extensibility of many species 
of lamin, to enable them to resist flexure, it appears, from p. 359, that we 
must be careful to form the lamina originally, while in a soft, semi-fluid, or 
otherwise extensible state, into a surface whose curvatures are similar, other- 
wise it will always be liable to bend along a curve of flexure. If sufficient 
force be used to make the lamina bend along any other curve or in any 
way violate the conditions which have been established, it will be found 
that there is always produced a crease, in other words a curve, along which 
the separation between one molecule and the next is not indefinitely small. 
In such a case there will in general be a permanent alteration in the sub- 
stance of the lamina. Thus, for example, it is easy to fold a sheet of paper 
into the form of a cone, without breaking or in any way injuring it. Let the 
base of this cone be rendered rigid by being attached to a ring, and it will be 
found that any further attempt to bend the paper will produce a crease, or 
curve of permanent alteration in its substance. 

Again, from the discussion of p. 361, we may deduce the practical conclu- 
sion, that the strength by which a surface of dissimilar curvatures resists flexure 
may be greatly increased, if it be traversed by a rigid rod attached to its sub- 
stance, along any curve not a curve of flexure. 


The Rev. J. H. Jetxerr on the Properties of Inextensible Surfaces. 375 


NOTE. 


Since the foregoing sheets were printed, I have arrived at the following theorem, which is 
of some interest, as connected with the class of surfaces which we have been examining: 


Tf a closed oval surface be perfectly inextensible, it is also perfectly rigid. 
To prove this, let us denote, as before, by oz, dy, dz, the resolved displacements of any 
point on the surface. Let dx,d'y,8z be its most general displacements considered as a rigid 


body; then it is known that 
oa =at+ Cy - Bz, 


oy =b+ Az - Ca, 
z=c+ Bu - Ay, 
a, b, c, A, B, C, being constants. Nowif we forma third system— 


Aa = 62 + 82, 
‘ Ay = oy + dy, 
Az = 62+ 8%, 
it is plain that Aw, Ay, Az will satisfy the conditions of the problem contained in equations 
(B) or (C). Moreover, if 2,72,, 2%/22, be two given points on the surface, the constants 
a, b, c, A, B, C, can always be so determined as to satisfy the equations 


Az =0, Az, =0; 
Ax, = 0, Az, =V, 


without in any way limiting the generality of the displacements dz, dy, dz. Suppose now 
that we assume, as in p. 346, 


u=Axv+pAz, w= dz, 


it is plain that w, w will satisfy the first of equations (C), and will vanish at the two points 
MYiriy LoY2%. Let these points be P, Q, and suppose, to fix our ideas, that the axis of z 
passes through them. The plane of xz will then intersect the surface in a closed curve, 
PRQS, passing through these points. Now since u vanishes at the points P, Q, if we 
trace its values in passing along the curve PRQS, we shall find a maximum value (dis- 
regarding its sign) somewhere between P and Q as at R, and again somewhere between 
Qand P asat S. We have, therefore, for each of the points R, S, 


du 


dz = ? 
since the equation of the curve PRQS is 
dy = 0. 


376 ~=The Rev. J. H. Jetxert on the Properties of Inextensible Surfaces. 


The first of equations (C) gives us then at each of these points 

w=. 
But since the position of the axis of x is indeterminate, it follows from what has been said, 
that, on every section of the surface made by a plane passing through the axis of z, there 
will be at least two points, for which 

w=0. 
Hence it is plain that there will be on the surface one or more closed curves for which this 
condition will hold. It will be sufficient to consider one of these curves, which, for the 
sake of distinctness, we may call an equator. 

We have seen, p. 347, that w must satisfy the equation 


Ae — 2s ca + ee 
dy? dady dx? 
or, as it may be otherwise written, 
are - 1s) + alta ~ 05) 0. 
dy\ dy dz} dx\ dx dy 
Multiply this equation by dxdy, and integrate it through the whole of either of the seg- 
ments into which the surface is divided by the equator. We have then 


leg ae da + («x AG dy = 0, 


the single integrations being extended through the whole of the bounding curve. But since, 
for every point in this curve we have 


= 0, 


w=0, 
if this equation be transformed according to the usual rule (Caleulus of Variations, p. 218) 
it will become 


| s dw? 9s dw dw x dw* 
dy? dy da dx? 
where ds is the element of the bounding curve, and 


dw?  dw*\- 
oa i= i 7 


) a= 0, 


Now since in the class of surfaces which we are considering, 
rt — 8 > 0, 
it is easily seen that all the elements of the foregoing definite integral must have the same 


sign. The total integral cannot therefore vanish unless each of its elements vanishes. Hence 
it is plain that we must have at each point of the equator 


dw dw 
a 0. 


The Rev. J. H. Jewtert on the Properties of Inextensible Surfaces. 377 


If we now follow the same reasoning as in p. 352 we shall readily see that all the diffe- 
rential coefficients of w will vanish at the equator, and therefore that we must have 
generally 

w=0. 
Hence, and from p. 347, it is evident that the displacements represented by Aw, Ay, Az, 
are those of a rigid body. Since then dz, dy, z are by hypothesis the displacements of a 
rigid body, it is evident that the differences between these quantities, Aw - dw, Ay — dy, 
Az - 82, or oa, dy, dz, are so likewise. We infer, therefore, that— 

The most general displacement which a closed, oval, inextensible surface admits of, is that of 
a rigid body. 

Such a surface is therefore inflexible. 


7 Lp) Sane 


Tré CaeAN eT. Ghdaodaat(s, \yrenet rages of: oo Tite ieh ep. vedio’ 


Sade Vin tard one YAlwin ede ew S2Sap pi dr gainpeneteine at) wollot won ow I] 
rtd Gere tw fl) eidiewd? Loe soteipa ods te deiser flier we Yo’ gnotmilions Lattagy 


- 
e ‘ ed Was ie Lio » & 7 gioraey 
ol o sr ip jowerT4 * wh Gy 
wt as ae brotatang “wn esyneoaiquil on? bait fashivs of at. TDS. a moe! bas sonal 
oe tfendrese lq) ont aieeliog pd yiita sib one coll sont tho bight ato seetlface 


Man th oo - od sence ead pomp apeenib alt spdt teetiive ai it. -phodulbiaes 


kK — lo orient oolmt a. onnatt es mn 428 005 2b 10 RL 
Wd “yc oty os ar pee 8 balaaiembla i Sere sbietelo » dotlen taneensddigell Letteunnty Want ff 
| “s19¥ @62 2 es u te “ afs08 igen 
. i hkigaltd overly a eatin x dan 
A ; i oo : 
pat Nite “y 
' _ ral Z s 
’ 


¢ ’ —d — ' Ais 
a , A 
14a 
=a ‘8 7 
* 
“he anf harem ria 
{ 
>. r 
a e f m ) —_ 
id « e oa - yy | Poeen: 
» 7 
I 
= 4 
f 
; 
+ = 
. , 


379 


XVI.—On the Attraction of Ellipsoids, with a new Demonstration of CLAirauT’s 
Theorem, being an Account of the late Professor Mac CutiaGn’s Lectures on 
those Subjects. Compiled by Guorcr Jounston AttMaN, LL. D., of Trinity 
College, Dublin. 


Read June 13, 1853. 


[Tue following Memoir contains the substance of a Series of Lectures deli- 
vered by the late Professor Mac Cutxacu to the Candidates for Fellowship in 
Trinity College, Dublin, in Hilary and Michaelmas Terms, 1846. 

It is now published by the Academy, with the view of securing to Professor 
Mac Cuttacu the merit of whatever is original in the investigation or its 
results. 

The present Paper may be regarded as a Sequel to the Account of Professor 
Mac Cuxtacu’s Lectures on Rotation, given by the Rev. Samurt Havcuton 
in a former part of the present volume of the Transactions of the Academy. ] 


VOL. XXII. 3D 


380 Mr. Grorce J. Atiman’s Account of 


Proposition I. 


Tf P be any point on the surface of an ellipsoid, and PC, be drawn perpen- 
dicular to an axis OC, and an ellipsoid be described through C, concentric, similar 
and similarly placed to the given ellipsoid ; then the component of the attraction of 
the given ellipsoid on P in a direction parallel to OC is equal to the attraction of 
the inner ellipsoid on the point C,. 


This theorem is an ex- 
tension of that given by 
Mac Lavrn® relating to 
the attraction of a sphe- 
roid ona point placed on 
its surface. It may, more- 
over, be established by 
means of the same geo- 
metrical proposition from 
which Mac Laurin de- 
duced his theorem. 

Through the point P BES 
let a chord PP’ of the given ellipsoid be drawn parallel to the axis OC; now 
suppose both ellipsoids to be divided into wedges by planes parallel to each 
other, and passing respectively through this chord and the parallel axis of 
the inner ; and suppose the wedges to be divided into pyramids, the common 
vertex of one set being at P, and of the other at C,. Observing that any two 
of these parallel planes cut the two surfaces in similar ellipses, such that the 
semi-axis of one is equal to the parallel ordinate of the other, it is easy to see 
that the reasoning employed by Mac Laurin may be used to establish the 
truth of the theorem stated above. 


* De Caus. Phys. Flux. et Refl. Maris, sect. 3. Or see Airy’s Tract on the Figure of the 
Earth, Prop. 8. 


Professor Mac Cutiacn’s Lectures on the Attraction of Ellipsoids. 381 


Proposition II. 


To calculate the attraction of an ellipsoid on a point placed at the extremity of 
an axis.* 


Let the semi-axes of the ellipsoid be a, b,c, where a > 6 > c, and let the 
point on which it is required to find the attraction be C, the extremity of the 
least axis. 

Suppose the ellipsoid to Rt ed Dee es 
be divided by a series of iM NX. 
cones of revolution which f Aa \ie 
have a common vertex C 
and a common axis COC’, C’ 
being the vertex of the ellip- 
soid opposite to C ; it will 
be sufficient to find an ex- 
pression for the attraction 
of the part of the ellipsoid 
contained between two con- 
secutive conical surfaces, 
whose semi-angles are 6 and 
6+ dé@ respectively. Sup- 
pose now the part of the 
ellipsoid between two con- 
secutive cones to be di- 
vided into elementary py- Fie. 2. 
ramids with a common vertex C. Let CP be one of these elementary pyra- 
mids, whose solid angle is w; let PQ be drawn perpendicular to CC’; from 
the centre O draw a radius vector OR parallel to CP, and from the extremity 
R let fall a perpendicular RS on the axis CC’. 

Now the attraction of the elementary pyramid CP on the material point p, 
placed at its vertex = yfpw.CP; and the component of this attraction in the 
direction of the axis is 


* Proceedings of the Royal Irish Academy, vol. iii. p. 367. 
3D 2 


382 Mr. GrorcE J. ALLMAN’s Account of 


2 2 
Lfpw . CQ iii ee 
Now suppose the radius vector OR to revolve around the axis OC’, then 
the attraction on the point C of the portion of the ellipsoid bounded by the 
two cones of revolution, whose semi-angles are @ and @ + dé respectively, 
since it is made up of the components in the direction CC’ of the attractions of 
all the elementary pyramids CP, is 


on cos?0 (OR? w) = — cos? 6d0= (OR? d¢), 


d@ being the angle between two consecutive sides of the cone generated by the 
revolution of OR. 

But = (OR? d@) is equal to twice the superficial area of the part of this cone 
which is enclosed within the ellipsoid ; moreover, the projection on the plane 
ab of this portion of the surface of the cone is an ellipse whose semi-axes are 
r, sin 0, r: sin 6, and whose area is 77,7; sin’ 6, 7; and 7; being the maximum 
and minimum values of OR: the superficial area of the portion of the cone within 
the ellipsoid is therefore 7, r, sin 0. 

Hence it follows that 

= (OR?dp) = 2xr,r: sin 0. 

The attraction on the point C of the part of the ellipsoid contained between 
the two cones of revolution, whose common vertex is at C, and whose semi- 
angles are @ and @ + dé respectively, is therefore 


cos?@ d@r, r, sin 0, 


1 cos’?@ — sin?@ 1 cos’@ sin? @ 
ee ae I eed op 
ry c a YT, Cc b 


On substituting these values, the expression given above becomes 
fee : abe a sin ode ibe ; 
Y (a? cos’?6 +c? sin?6) /(b* cos’?@ +c? sin?@) 
Hence the attraction of the solid ellipsoid on the point C at the extremity 
of tne least axis is 


4 mufp 
c 


where 


Professor Mac Cutiacu’s Lectures on the Attraction of Ellipsoids. 383 


4 Z abe cos*@ sin 0d0 
mfp | /(a’ cos’6 + ¢’ sin’? 0) /(b? cos*@ + c’ sin’@)’ 


0 


Let cos @=w, and this expression becomes 
1 abew du 
4 9 9 9 9 e 9 9 . 
ie|, etwe—e)| Viet we) @) 
In the same way it may be shown that the attraction of the ellipsoid on a 
point » placed at the extremity of the mean axis, is 


1 abe wv du 


Annfp| ViP+u(e—B) | ViP+u (a? —B*)}? 
and on a point at the extremity of the greater axis, 


4nufo | i Aa abe wu du 
oVie+w(b—a)\/\a+uw(e—a’)} 

It will be seen in a subsequent proposition, that these three expressions are 
not independent of each other, the values of the three attractions in question 
being connected by an equation. 


Proposition III. 


To give geometrical representations of the attraction of an ellipsoid on points 
placed at the extremities of its least and mean azes.* 

On the greater axis = 
OA, of the focal ellipse 
assume a point K, such 
that 

b 


OK, = 4 OA; 


from the point K, draw a 
tangent K,Q, to the focal Fie. 3. 

ellipse, and let 7'= tangent K,Q, — are A,Q,, then the attraction of the 
ellipsoid on the particle » placed at the extremity C of the least axis is 


4 mf pabe 2 
(fe) =e) ©) 


* Proceedings of the Royal Irish Academy, vol. iii. p. 367. 


384 Mr. Grorce J. Attman’s Account of 


For let a point K be assumed on the greater axis OA, of the focal ellipse, such 


that 
OA, 


c 


Oke 


Vie+w(P—c’)}; 
from K let a tangent KQ be drawn to the focal ellipse, and let OP be the per- 
pendicular let fall from O on KQ, then ¥ denoting the angle A,OP, 


a— Cc 
5 
a 


OR. cos! y= 5" fet 4 wf (8 08). cos" y. 


Moreover, __ BAM 
OK?. cos’ = OP? = (a? — ¢’) cos’ y+ (0° — ¢°) sin’ ¥. 
Equating these values, and solving for sin*y, we get 


(f@-—¢)w 


eC+w(a—e) 


sin? yy = 
Now 
d. (tan KQ—are A,Q) = sinyd . OK* 

AG =) (F— Cc) wdu 

= E Vie+e(@—e)} Vie + 2 (e — &)} 
By comparing this expression with (1) given in the last proposition, it appears 
that the attraction on the point C of the portion of the ellipsoid contained be- 
tween the two conical surfaces whose semi-angles are @ and @ + dé respec- 
tively, is 


esr gel 
(a —c’) (bP —e 


2) d. (tan KQ — arc A,Q). 


Now in order to obtain the attraction of the whole ellipsoid on the point C, 
we have to integrate the expression given above between the limits w= 0 and 
u=1, or OK = OA, and OK = OK, ; from which it appears that its value is 

Arpfpabe 
CEP) (a 
It is easy to see that the attraction of the part of the ellipsoid contained within 
the conical surface, whose semi-angle @ is equal to cos” u, is 


1h 


* Transactions of the Royal Irish Academy, vol. xvi. p.79. Proceedings of the Royal Irish 
Academy, vol. ii. p. 507. 


Professor Mac Cuttacu’s Lectures on the Attraction of Ellipsoids. 385 


abe? 
a 9 2 2 9 T- t 3 
mfp 2G = Dy ( ), (3) 
where ¢= tan KQ — are A, Q. 
To represent the attraction on a point » placed at the extremity of the 
mean aXis, assume on the transverse axis OA, of the focal hyperbola a point 


K, such that OK, = OA, ; and from K, draw a tangent K, Q, to the hyper- 


bola, and let 7 = tan K, Q, —are A, Q,, then the attraction of the ellipsoid on 
the point p is 
abe 


— Anufp Go ELA a (4) 


ivi ewe BY}; 


from K draw a tangent KQ to the hyperbola, and from O let fall a perpendi- 
cular OP on this tangent, then if y = angle A,OP, 


ae (a —b) w 
> pe (a? —b’) 


To prove this, assume a point K such that OK = 


Hence by following a method similar to that used in finding the representation 
of the attraction on a point at the extremity of the least axis, the expression 
given above may be easily obtained. 

The attractions C, B of the ellipsoid on points placed at the extremity 
of the least and mean axes are thus represented by means of arcs of the 
focal ellipse and hyperbola respectively. In consequence of the third focal 
conic of the ellipsoid being imaginary, no direct geometrical representation can 
be given for the attraction A on a point placed at the extremity of its greater 
axis. It will, however, be found, as was intimated above, that a simple rela- 
tion exists between the three attractions, which enables us to represent this 
last by means of ares of both focal conics. 

The relation alluded to is 


A BC : : 
Sty +5 = 4p. (5) 


* Proceedings of the Royal Ivish Academy, vol. ii. p. 525. 


386 Mr. GrorceE J. ALLMAN’S Account of 


This can be easily proved by the help of the following geometrical 
theorem : 

If from the extremities A, B, C of the three axes of an ellipsoid, three 
parallel chords Ap, Bg, Cr, be drawn, and if these chords be projected each 
on the axis from whose extremity it is drawn, then the sum of these three 
projections, Aa, Bp, Cy, divided respectively by the lengths of the axes AA’, 
BB’, CC’, on which they are measured, will be equal to unity. 

Now conceive three chords Ap, Ap’, Ap”, to be drawn from A, making 
each with the other two very small angles, and so forming a pyramid with a 
very small vertical solid angle w; and from B and C let two systems of chords 
Bq, Bq’, By”, and Cr, Cr’, Cr”, be drawn, each system forming a very small 
pyramid whose three edges are parallel to the three edges Ap, Ap’, Ap”, of the 
pyramid which has its vertex at A. 

The attractions of the three pyramids, reduced each to the direction of the 
axis passing through its vertex, will be equal to ufpw.Aa, ppfw.BB, pfpw.Cy 
respectively, and, therefore, the sum of those attractions divided respectively 
by the lengths of the axes will be 

EG ie 

Let pyramids thus related be indefinitely multiplied, and the ellipsoid will 
be simultaneously exhausted from the three points A, B, C. 

Hence the sum of the whole attractions at A, B,C, divided respectively by 
the lengths of the corresponding axes, will be 27/p, or, 


Alt Ba s€ 


Proposition IV. 


To find an expression for the potential V of a system of particles at a point M 
whose distance from the centre of gravity of the system is very great compared with 
the mutual distances of the particles. 

It is proved by Potsson,* that if the origin of co-ordinates be at the centre 
of gravity, 

* Mecanique, tomei. p. 178. 


Professor Mac Cuxzacn’s Lectures on the Attraction of Ellipsoids. 387 


M, 3 
V=— +55 = (a0 + yy’ + 22’)? 7 empee = (2+ y? + 2°) dm 
#2 2r’s d 
zy’ z being the co-ordinates of the distant point, and r’ its distance from the 
origin. Let now the principal axes at that centre be taken as axes of co-ordi- 
nates ; then, since 


Laydm = 0, =zzdm = 0, Lyzdm=0; 


v= = + = = (va? + yy? + 227?)dm — = = (2? + y? + 2) dm. 
Hence, if A, B, C be the three principal moments of inertia, and J the mo- 


ment of inertia round OM, 


nik A 
V=— +5 (A+B 4C—31). (6) 


Proposition V. 

A system of material \ 
particles attract a point : ace 
M, whose distance from 
the centre of gravity O of 
the attracting mass is very 
great compared with the 
mutual distances of the . 
particles ; then if a tan- eda 
gent plane be drawn to 
the “ ellipsoid of gyration,’* perpendicular to OM, the whole attraction lies in the 
plane OST, where S is the point in which this tangent plane intersects OM, and T 
the point of contact. 


* The centre of this ellipsoid is at the centre of gravity; its axes are in the directions of the 

principal axes, and their lengths are determined by the equations 
Me=A, MP=B, Me=C. 

This ellipsoid is used by Professor Mac CutuacH in his Theory of Rotation; see Rev. S. 
Havucuron’s Account of Professor Mac Cutitacu’s Lectures on that subject, Transactions R.I. A. 
vol. xxii. p. 139. 

VOL. XXII. 3 E 


388 Mr. GrorcEe J. ALLMAN’s Account of 


Let a, 8, y be the direction angles of OT; a’, p’, 7’, of OM; a, fi, mn, of 
TS; and a, fy, yo, of the normal to the plane OST; and let OS, OT, and the 
angle SOT, be denoted by p,r, and @ respectively. It will be sufficient to prove, 
that the component Q of the attraction in the direction of the normal to the 


plane OST is cypher. 


We shall first find the components X, Y, Z, of the attraction in the directions 


of the axes, and thence deduce the value of Q. 


Now, 
x=-o - Foose’ + 3°; (4+B+C— 31) cosa’ + ==. 
Y=-— y= Ti cos + = al a + Ba CR 31) cos p’ + a 
Za = 7 003 7/ + gon (A + B+ 0-81) cosy + 525 
but, 


IT 2(A—I)cosa’ di _2(B—T) cosp’ a _2(C-T) cosy’ 


/ 


da! — r dy! . Giz r 


Hence we have 


X = Ah cosa! +5 57(A+ B+ C~ 51) cosa + 32 98 * 
V =A cos 8+ 5 (A+ Ba 1) cosg + SB 08 
Z = 7 cosy + SAE OE) leoary ge 


Now, 
Q= X cosa + Y cos B) + Z cos y ; 


but, 
sin @ cos a, = cos B cosy’ — cosy cos f, 


sin @ cos By) = cos y cos a’ — cos a cos 9, 


sin @ COS Y% = cos a cos f’ — cos B cos a’; 


the following relations moreover exist, 


a cosa’=rpcosa, & cosp'=rpcosp, c* cosy’ = rp cosy; 


(7) 


(8) 


Professor Mac Cuitaau’s Lectures on the Attraction of Ellipsoids. 389 


hence, by substitution, we have 


b? — ¢? C= a 
COS a7 = ———— cosf' cosy’, cos By) = ———— cosy cosa’ 
pr sin pr sing 
a = pe ; ; 
COs Yo = cosa cosp. 


pr sin p 
Substituting these values for cos a), cos By), cosy, in the expression for Q, 
and observing that 
cos a’ Cos a) + cos f’ cos By + cosy’ cos Yo = 0, 
we get 
8M a (be —e) + (ee — a’) +e (a? — 3B’) 


== = cosa’ cosp’ cosy’= 0. (9 
Q=-a anne B cosy =0. (9) 


Proposition VI. 


The same things being supposed, to find the components of the attraction, namely, 
R in the direction of the centre of gravity MO, and P in the transverse direction TS. 


To findR; 
R= X cosa’ + Y cos p’ + Z cosy’, 


MES al 
R= +5n(At+B+C-51)+7, 
R= a +55(4+B+C-8)) (10) 


To find P; 
P=X cosa,+ Y cosf, + Z cosy; 
but, 
sin @ cos a, = cos a’ cos @ — cosa, 


sin @ cos B; = cos B’ cos @ — cos f, 
sin d cos 7; = cos 7 cos @ — Cos ¥. 


Substituting for cos a, cos B, cosy, their values from (8), we get 


2 2 2 2 
a je 
COs a; = — Be EE eas a, cospj=— SP hos B, 
pr sin pr sind 
2 2 
(b _— 
cosy, =— P Y. 


pr sin ad 
3E2 


390 Mr. Grorce J. Atiman’s Account of 
Substituting these values of cos a, cos B,, cosy, and observing that 


cos a’ cos a, + cos f’ cos B, + cosy’ cosy = 0, 


we have 
38M P(r—-P7r 38M : 
-- 57 Ee — sar (pr sin @) ; 
or, 
38M (11) 


P= ~~ (OS x ST). 


The negative sign indicates* that the force P acts in the direction TS, i.e. 
from the radius vector towards the perpendicular of the ellipsoid of gyration. 
If the force P be resolved into three others in the directions of the axes, it is 
evident from the values given in PropositionV. for X, Y, Z, that these com- 


ponents are 


3(A-J) cos a’ 7. 
yt 3 r r 


CE Rae Jae (12) 


Proposition VII. 


An ellipsoid is composed of ellipsoidal strata of different densities and of variable 
but small ellipticities ; find the components, central and transverse, of its attrac- 
tion on an external point. 


The values found in the last Proposition for the components of the attrac- 
tion of any mass on a very distant point, will be found to hold in the present 


* The direction of the force P, which Professor Mac CuttacH determines by the interpre- 
tation of the negative sign, may be very clearly seen from the following considerations. This 
force exists in every case where the three principal moments of inertia are not all equal, 
that is, when the ellipsoid of gyration is not a sphere. The greatest axis of that ellipsoid is 
manifestly towards that part of the body in which there is a deficiency of attracting matter. If 
we consider now the position of a perpendicular on a tangent plane of an ellipsoid with relation to 
the corresponding radius vector, we shall find that it always lies away from the greatest axis. 
But the transverse force has been shown to be in the plane of radius vector and perpendicular. 
Therefore, the direction of the transverse force, being towards the preponderating matter, must 


be parallel to TS. 
+ The results given by Professor Mac CuLLaGH in Propositions V. and VI. may be otherwise 


Professor Mac CuttaGu’s Lectures on the Attraction of Ellipsoids. 391 


case, whatever be the position of the attracted point. In order to show this, 
we shall first prove it for a homogeneous ellipsoid of small ellipticities. Such 
an ellipsoid being given, another, confocal with it, can be constructed so 
small, that the distance to the attracted point may be regarded as very great, 
compared with the axes of this ellipsoid: the components of the attraction of 
this small ellipsoid on the distant point are given by the expressions (10) and 


obtained, and, perhaps, with greater facility, by introducing the consideration of the statical mo- 
ment of the attracting force.* 
If the three principal moments of inertia were equal to each other, then the whole attraction 
would be in the direction of the centre of gravity, and its magnitude would be 
M 
aoe 
In general, however, the attracting mass will be of an irregular shape; there will exist then, 
in addition to the principal part of the attraction which will be central, a transverse force which 
will cause a motion of rotation about the centre of gravity. 
The components of the moment of this transverse force in the three principal planes are 


2Y-yX, yZ-27Y, wX-2Z, 


but from (7), 
= M 
vY-7yX=- a cosa’ cos B/= - ae (a? — b*) cosa’ cos fp’, 
- M 
yWZ-27Y=- 3B os fr 003 = = = (5° — c*) cos B’ cos 7’, 
¢x - 20 =O eos y cos at = - 3 (es — a*) cos y/ cosa’. 


Now it is well known, that } (a*—b*) cos a’ cos A’, 4 (6? — c*) cos B’ cos y', 3 (c? — a*) cos y/ cos a’, 
are the areas of the projections of the triangle OST on the principal planes. Hence it follows, 
that the resultant moment lies in the plane of the radius vector OT, and the perpendicular OS to 
a tangent plane of the ellipsoid of gyration; the tangent plane being perpendicular toOM. It 
appears also, that the magnitude of the resultant moment is 

iM 
- = (OS x ST), 
and therefore that the transverse component of the attraction 
3M 
ae aa (8 x ST). 


Or the values of the central force and the moment of the transverse force may be obtained 
directly from the expression (6) for the potential V. This function is of such a nature, that its 
differential coefficient with relation to any line (the sign being changed) is equal to the re- 


® See Rev. R. Townsend, in the University Examination Papers, 1849, p. 51. 


392 Mr. Grorcr J. Attman’s Account of 


(11); now the attractions of two confocal ellipsoids on an external point are 
in the same direction, and proportional to their masses; the components of the 
attraction of the proposed ellipsoid will, therefore, be 
M 3M 
BET CEC g (A, + B, + C, -3],), 


3M 
P= Es (OS, x 8,T)), 


the letters with suffixes referring to the small ellipsoid. 
The attracting ellipsoids being confocal, their ellipsoids of gyration are con- 
focal also; hence it follows, that 


an car 
1 
and OS, x Ss: wy = OS x Si 


It appears from this, that the central and transverse components of the at- 
traction of a soid ellipsoid of uniform density, and whose ellipticities are small, 


solved part of the attraction in that direction; and the differential coefficient with relation to any 
angle (the sign being changed as before) gives the component in the plane of that angle of the 
moment of the attractive force. 


Hence, 
dv M 3 
Be oa ea (44 BA C-31), 
since 
ar 
dr! 


Again, if V be the component of the moment of the attractive force round OZ, 


d ,a 
W=-(e 5-9 ae 
but 


d d - : . 
(w ae y! =) F (x? + y) = 0, where F is any function. 


BEES RE eC! i rd esa ee 
poh eg-v a) - Seg -«f) a 


N=- ee) cos a’ cos f’. 


The two other components of the moment may be similarly obtained. The remainder of the 
proof is the same as in the former part of this note, 


Professor Mac Cuttaau’s Lectures on the Attraction of Ellipsoids. 393 


on any external point whatever, are given by the same formule as the corre- 
sponding components of the action of any mass on a distant point. 

Now it is a property of moments of inertia, that they are subtractive, 
that is, the difference of the moments of inertia of two masses with relation 
to any axis is equal to the moment of inertia of the difference of those 
masses with relation to the same axis. And the values at which we have 
arrived for the central force, and for the three components of the transverse 
force, contain in each term either the mass or a moment of inertia in the first 
power, and, therefore, these values also are subtractive. Hence the two com- 
ponents of the attraction of a homogeneous mass contained between two con- 
centric and coaxal ellipsoids of small ellipticities, are given by formule (10) and 
(11). Now suppose an ellipsoidal mass to be composed of strata bounded by 
ellipsoids of different but small ellipticities, each stratum being homogeneous 
throughout its extent, while the density varies from one stratum to another 
according to any law; then, since those formule hold for the action of each 
stratum separately, and since the terms of which they are made up are in their 
nature additive, they hold for the entire mass.* 


Proposition VIII. 


An oblate spheroid is composed of spheroidal strata of different densities and 
of variable but small ellipticities ; find the components of its attraction on any 
external point. 


The expressions given in the last Proposition for R and P become simpli- 
fied in this case. Let OZ be the axis of revolution, and let A denote the angle 
which OM makes with the plane XY; then since A and B are equal, we have 

IT=A cos’A + C sin?A, 


and therefore, 
A+B+C-3/7=(C—A) (1-8sin’A), 


M (OS x ST) = (A —C) sind cosa. 


also, 


Substituting these values in the expressions for & and P, we have 


* See Professor Mac Cutaau, in the University Examination Papers, 1833, p. 268. 


394 } Mr. Grorce J. AuLMan’s Account of 


d M 3C-A . 
B= geega (he SDA), SS 
P=3 z, cosA sinA. (14) 


The direction of the force P is towards the plane of the equator ; this appears 
from the shape of the “ellipsoid of gyration,” which in this case is a prolate 
surface of revolution. 


Prop. LX. Cxrarraut’s THEOREM. 


Whatever be the law of variation of the earth's density at different distances 
from the centre, if the ellipticity of the surface be added to the ratio which the 
excess of the polar above the equatorial gravity bears to the equatorial gravity, their 


aie : ; : 
sum will be ke where q is the ratio of the centrifugal force at equator to the equa- 
torial gravity. 
For suppose the attracted point M to be on the surface of the earth, which 


is known to be an oblate spheroid of small ellipticity. Then, from the prin- 
ciples of Hydrostatics, since the tangential force is cypher, we have 


R cos @ — P sin 6 — w’r cosA cos (9 — A) = 0, (15) 


where w denotes the angular velocity, and @ the angle which the tangent to 
the meridian through the attracted point makes with the radius vector; de- 
veloping cos (6 — A) and arranging, we obtain 


(R — w*r cos?) cos 6 = (P + w’r cosA sind) sin 6. (16) 
But from the property of the elliptic section made by the plane of the meridian, 


we have 
e sinA cosA 


Cold Saari a 2esinA cosA, 4q.p., 


where ¢ is the excentricity and e the ellipticity of this ellipse. 
Substituting in (16) this value of cot 6, and the values of & and P from (13) 
and (14), the equation of equilibrium becomes 


Professor Mac Cuttacn’s Lectures on the Attraction of Ellipsoids. 395 


=a 
+ wr) sin cosa, 


ee OSs wr cos” » | 2esindcosr= eo 
or, approximately, 


= a ce een Ny eae a COS r boe= go +04. 
If we neglect quantities of the second order, this equation becomes 
2eM_,C- ips (17) 


a 
We have thus arrived at a relation which enables us to express the un 
known quantity C'— A, in terms of quantities which are all known, and, there- 


fore, to eliminate the former from any other equation in which it may occur 
Now let R, and #, denote the equatorial and polar attractions respectively ; 


we have from the general value of R (13), 


but 
1 
C 


e—=a(l—e), 2 = = a (1+26)and 5 = 5 (1 +40), 


P 2 a at 


M 2Me_,C-A. 
a 


But, 
G, = K, and G,= R, — wa; 


Eliminating Gs 


or, 
G, — G. (18) 


VOL. XXII. 


TRANS. R. I. A. Vor, XXII. SCIENCE, p. 398. 


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XVII.—WNotice of the British Earthquake of November 9, 1852. By Ropert 
Mattet, C.#., MRA. 


Read February 13, 1854. 


ALTHOUGH earthquakes are recorded as occurring in very considerable 
numbers in Great Britain, yet their effects have usually been so slight and 
transient, that a new one is always an object of popular interest, though, fortu- 
tunately, from these circumstances, of no more abiding importance generally. 
For objects beyond merely learned curiosity, as aiding in the compilation of 
that base of induction that is yet destined to make the earthquake part of exact 
science, it seemed desirable to collect and arrange, in as authentic and clear a 
form as the author found possible, the facts of the earthquake of 1852,—one 
of the most widely diffused and simultaneously felt shocks of any recorded as 
affecting our islands. 

For this purpose, shortly after the occurrence, the author published in several 
newspapers an invitation to all observers of the earthquake to forward to our 
fellow-labourer, Mr. Edward Clibborn, on his behalf, communications as to such 
facts as they might be in possession of respecting the event, and accompanied 
his invitation by the statement of the four most important points of fact to 
which attention was principally desirable. 

He also applied officially to the heads of the Dublin Metropolitan Police, 
requesting a systematic examination of the men on duty on the night of No- 
vember 9, 1852, and that their answers to certain questions given, should be 
transmitted back to him. 

The author, with regret, deems it due to science to mention, that the leading 
London journal to which he transmitted his request for English communica- 
tions, with an apathy or ignorance scarcely credible, declined publishing it. 

3F2 


398 Mr. Matuet’s Notice of the British Earthquake of November 9, 1852. 


The police authorities promptly answered the author’s desire, and the testi- 
mony of the police on duty having been taken by one of the inspectors, they 
forwarded to him documents of which the following embraces the sum. 

1. A great number of the police observed a shock. 

2. Several of the men state that the motion was sideways, others that it 
was up and down. They are also divided in opinion as to whether it was from 
east to west, or from north to south. 

3. All agree in stating that the time was two or three minutes before or 
after 4 o’clock, A.M. 

4. All heard a rumbling noise, somewhat like distant thunder ; they also 
heard a rattling of windows as if shaken by a concussion. 

The result proves how little reliance as to accuracy or amount of informa- 
tion is to be expected from persons untrained in habits of exact and faithful 
observation. 

Through the zealous co-operation of Mr. Clibborn, a very large number 
of private letters and other communications were received, and many others, 
as well as newspaper notices, were transmitted directly to the author. The 
great mass of these, however, were liable to the remarks just before made. 
A very few, selected for their graphic character, were sufficient to read to 
the Academy, though not to publish in eztenso. All that appeared worthy of 
credit for accuracy, &c., were arranged and discussed in the form following, 
very much upon the model of the Great Earthquake Catalogue of the Trans- 
actions of the British Association ; and from the combination of information 
from all sources the Seismic map accompanying this paper was prepared. Upon 
it all places at which a record exists of the shock having been felt are marked 
in red letters. Wherever the time of the occurrence of the shock was noted 
it is marked after the name of the place of observation. The time in Ireland 
is assumed as that for the meridian of Dublin; that in Great Britain is, with one 
exception (Congleton), Greenwich mean time. Wherever the horizontal direc- 
tion was noted, it is marked by a red arrow passing through the place in that 
direction. The broad shaded line generally circumscribes the space within 
which the shock is recorded to have been actually felt, or may be inferred that 
it might have been felt. But it will be understood that such a boundary is 
wholly imaginary, and serves merely to convey a general notion of the form of 
the territory shaken, as the motion due to the earth-wave (like all other 
elastic waves in media of indefinite dimensions) passes away from the point of 


Mr. Matxet’s Notice of the British Earthquake of November 9, 1852. 399 


greatest disturbance or summit of the wave, and is gradually lost in all di- 
rections to observation, whether unaided or instrumental. Were our earth 
perfectly elastic, in fact every earthquake, however slight, would shake the 
whole globe. 

The author’s own experience at Glasnevin, near Dublin, was that of being 
suddenly aroused from sound sleep, with some slight sense of alarm by, as 
it seemed to him, a tremulous shock, with a dead, heavy, thump-like sound, 
such as a very heavy bag of wet sand might make if dropped from some 
feet above, upon a large planked floor ; his immediate thought was, that some 
heavy man had jumped upon the floor of the room beneath his bedroom ; and 
conceiving the possibility of house-breakers, he looked out of the window and 
listened attentively for a few seconds. Not a sound disturbed the singular still- 
ness of the dull, dark-gray leaden haze that hung over the winter morning ; 
he fancied his wife must have started in sleep, and returned directly to bed 
again. The notion of an earthquake never occurred to him, and it was not 
until its occurence was remarked to him by others at noon, that he connected 
his disturbance with such an event. Several families residing in the author’s 
neighbourhood, however, were so much alarmed by the disturbance (more par- 
ticularly in a few instances where some of the members had been familiar with 
earthquakes abroad, and at once recognised this as one), that they remained up 
all the rest of the night, or rather early morning. 

On arriving in town he found a large framed drawing of 4 feet 9 inches 
long, by 2 feet 7 inches deep, and weighing about 7 lbs., which had hung by 
two brass rings attached by leather straps to the frame against a wall of his 
office, ranging S. by W. and E. by N. fallen down and wedged diagonally in 
its own plane between two walls which started at right angles from the wall 
against which it hung, and at an interval not much wider than the breadth of 
the framed drawing. The leather straps of the rings were torn asunder, and 
on examination proved to have been a little decayed by age and drought ; but 
the leather, on trial, was still found to possess such toughness that a weight 
much beyond that of the drawing and frame would have been incapable of 
rending either of them. 

The author made these observations before the occurrence of an earthquake 
had been noticed to him; he afterwards returned to the matter and carefully 
observed the conditions in which the drawing hung, and under which it was 
found fallen. Of this, more hereafter. 


400 


LOCALITY. 


Mr. Mattet’s Notice of the British Earthquake of November 9, 1852. 


APPARENT DIREC- 
TION. 


BRITISH EARTHQUAKE OF NOVEMBER 9, 1852. 


SCOTLAND, ENGLAND, AND WALES. 


SHOCKS, NUMBER. 


DURATION AND 
TIME. 


OBSERVED PHENOMENA. 


AUTHORITY, 


Glasgow, 


Ramsay, 


Harrogate, 


Southport, 
Lytham, 

Fleetwood, 
Liverpool, 


Manchester, 


Holyhead, 


Beaumaris, 


Bangor, 


Caernaryon, 


Llanberis, 


Gifach, in 


Wales, 


Congleton, 


Birmingham, | 


Cheadle and | 


| 


various 
places in 
Stafford- 
shire, 


North and South, 
or N. E.& S. W. 


S. to N., or 10” 
to 15° W. of N. 


W. to E. (?); 
oscillatory. 


One or more. 


One. 


One. 


One. 
One. 
One or more. 
One. 


One. 


A continued vibra- 
tion. 


Continued vibra- 
tion about 60 se- 
conds. 


One. 


A few seconds ; 
415 AM. 


4AM. 
Some seconds ; 
4 30 aM. 


4 30 a.m. 


From 3 or 4 to 30 
seconds. 
4 350 A.M. 


4 30 AM. 


While counting ra- 
pidly 100; 20 to 
30 seconds. 


4 30 AM. 


20 or 30 seconds; 
time not given. 


4 AM. 


4 30 A.M. 


A lady awaked by shaking of her bed. 


Awakened by noise as of house-breakers; shook every 
house in the place; weather for some days before wet 
and boisterous. 

Numbers roused from sleep ; windows, doors, and movables 
violently shaken ; dogs barked. 


Beds shaken, doors rattled, &c, 

A lady awakened at 43 a.m. Then recollected having felt 
something of the sort before earlier in the same night. 
Furniture shaken ; a strong oscillation of the ground and 
buildings; a deep rumbling noise distinctly heard by 
many persons; children screamed when awakened. One 
observer felt five or six vibrations ; day dark and misty, 

with drizzling rain. 

A tremulous vibratory motion, like that of the rolling of 
many waggons ; furniture seen to move ; several per- 
sons experienced nausea; dogs trembled and were much 
frightened ; no noise was heard but that produced by 
movables shaken. The shock considered by those who 
felt it both more violent than that of March, 1843 ; tem- 
perature at the time about 50° Fahr. The morning 
very dark, but calm and fair. 

A shock felt, accompanied by a very loud noise; wind 
8. E.; cloudy. 


Large things, that required an effort to shake by hand, 
shook audibly in bed-room; a noise before, during, and 
after, heard by several. 


A shock accompanied by a very loud noise; wind S. E.; fog. 


A fearful rolling noise, like-a whole brigade of fire-engines 
running over a paved street, suddenly broke an oppres- 
sively calm morning, it died gradually away; every- 
thing shook. 


A tremendous blow; slates clattered on the roof, and 
everything shook; a rumbling sound, which seemed to 
travel away into distance, 


A hollow noise like distant thunder, coming and going 
from N. W. to S. E.; a trembling increasing to a rapid 
rocking. 


A smart shock. 


In Birmingham felt but slightly ; noise and shock both 
perceived. 

At Cheadle, seemed to most persons like the shock and 
noise of a heavy person falling out of bed. At Barnage 
the sound was like that of a rushing wind; some evi- 
dence of a previous shock on the night of the 8th of 
November, at 10} P. m. 


Correspondent of 
North British 
Mail, November 
16, 1852. 

Correspondent of 
the Times, No- 
vember 13, 1852. 

Correspondent of 
Times, Novem- 
ber 13, 1852. 

Saunders’ News- 
letter, Novem- 
ber 13, 1852. 

Liverpool papers 
quoted by Times, 
November 10, 
1852. 


Correspondent of 
Saunders’ News- 
letter, November 
11, 1852. 


Correspondent of 
Times, Novem- 
ber 10, 1852. 

Andrew Ramsay, 
Esq., Geological 
Survey, Beauma- 
ris; private let- 
ter, November 9, 
1852. 

Electric Telegraph 
to Times, No- 
vember 10, 1852. 

Evening Post, No- 
vember 13, 1852, 
copied probably 
from a Manches- 
ter paper. 

Rey. R. Eyre; let- 
ter in Western 
Star, November 
12, 1852. 

A mining captain’s 
letter in Saun- 
ders, November 
13, 1852. 

Electric Telegraph 
to the Times, No- 
vember 10, 1852. 


LOCALITY. 


Mr. Mattet’s Notice of the British Earthquake of November 9, 1852. 


APPARENT DIREC- 


SCOTLAND, ENGLAND, AND WALES—continued. 


SHOOKS, NUMBER. 


OBSERVED PHENOMENA. 


Shropshire, 

Shrewsbury, 
Iron Bridge, 
Bromley, &c. 


Wolverhamp- 
ton, 


Haverford- 
west, 


Gloucester 
and Bristol, 


Co. Antrim, 


Newtownards, 


Tanderagee, 


Glaslough, 


Carlingford, 


Newry, 


Balbriggan, 
the Naul, 
Swords, 
Ardgillan 
Castle, 


APPARENT DIREC- 


according to Rev. 
D, Nihil. 


One. 


SHOCKS, NUMBER. 


At Fitz the shock 
lasted 30 seconds, 


| 


DURATION AND | 
TION. TIME. 
Ene 
W. S. W. and Three or four. 4 30 aM. | A severe shock felt all over the county, getting fainter to 
N.N. E. | the westward ; pheasants crowed at Acton Reynal pre- | 


serves ; sleepers awakened ; doors rattled ; houses shook | 


bodily. 


The weather had been wild and stormy, with lightning and 


hail, some days before, but was quite calm at the time; | 


no sound was observed ; bells rung at Ellesmere church ; 
at Newton a wood bridge over the Severn thrown down; 
30 yards of strong wall thrown down at Shrewsbury. 

A severe shock; blowing and hailing before; many people 
up and awake. 


Stated to have been felt plainly in both. 


IRELAND. 


DURATION AND 


OBSERVED PHENOMENA. 


| Mr. 


One, lasting 15 se- 
conds. 


One. 


One. 


48 am. 


TION. TIME. 
. c . One. 4 30 a.m. The shock distinctly felt in several parts of the country. 
Noticed by two persons. 
Probably from One. ~ Shortly after 4 o’c. | Undoubtedly felt, accompanied by a dull, heavy sound; 
South to North. houses shaken; the motion vibratory ; thirty printers 
at work in the Belfast newspaper offices were not con- 
cious of the shock. 
One. A person awakened by oscillation of his bed, and noise of 
the window bars of his bed-room. 
Ono Two within a few 4 AM. The whole room shook twice; furniture creaked and was dis- 
seconds. placed ; the observer was awake and reading. 
Two. 4 10, or 4 12 a.m. | The bed of the observer was twice heaved up as if by a 


large dog turning nimbly underneath, the second heave 
shorter than the first; all in the house felt it and got 
up from bed and assembled at once. 

Every movable article set in motion from top to bottom of 
the house; many of the family did not awaken; great 
terror produced. 


Experienced with great alarm by many individuals while 
in bed. 


Houses shook at Swords; felt very intensely at the Naul; 
the family awakened at Ardgillan Castle, and the 
steward fired a gun out of the window, fancying he 
heard housebreakers. 


401 


AUTHORITY. 


Clibborn, 
M.R.I.A. private 
communication 


| Belfast Mercury, 
November 12, 
1852. 


AUTHORITY. 


Coleraine Chro- 
nicle, November 
14, in Saunders’ 
Newsletter, No- 
vember 15, 1852. 

Private comunica- 
tion from Dr. 
Robinson, No- 
vember 10, 1852. 

Belfast Mercury, 
November 11, 
1852. 


Belfast Mercury. 


Saunders’ News- 
letter, November 
10, 1852. 

Correspondent of 
Saunders’ News- 
letter, November 
12, 1852. 

P. Darcy, corres- 
pondent of the 


Evening Post, 
November 13, 
1852. 


Newry Telegraph 
and Saunders of 


November 12, 
1852. 
Saunders’ News- 


letter, November 
11, 1852. 


402 


LOCALITY. 


Dublin City, 


Suburbs of 
Dublin, 

Kingstown, 

Rathmines, 

Mountplea- 
sant. 


Bray, 
Delgany, 
Ballyboden, 
Rathfarnham, 
Wicklow, 
Arklow, 
Newtown- 
mountken- 
nedy, 


Kilkenny, 


Wexford, 


Mr. Matuet’s Notice of the British Earthquake of November 9, 1852. 


APPARENT DIREC- 
TION. 


ing on end fell 
towards the north 
in Nassau-st,— 
G. Feates. 
Apicture was shak- 
en down from 
its fastenings on 
a wall runing S. 
by W., and N. 
by E., and so 
circumstanced as 
to prove that the 
direction of emer- 
gence of shock 
was upwards at 
a _ considerable 
angle from S. to 
N.—R. Mallet. 


SHOCKS, NUMBER. 


IRELAND —continued. 


DURATION AND 
TIME. 


One, and probably 
one at a previous 
part of the night. 


It seems very pro- 
bable that there 
was a previous 
shock on the 
night of the 9th 
of Nov. at about 
12 o'clock, and 
some likelihood 
of another or se- 
veral minor ones 
having been felt 
on the night of 
the 11th Novem- 
ber, 1852. (Let- 
ters from Mr. 
Clibborn and Mr. 
Malone.) 

Some observers 
were conscious of 
three distinct 
heaves during the 
continuance of 
the tremor. (Let- 
ter, I. Farrell, 
Gt. Brunswick- 
street.) 


Two heavy thumps 
witha continuous 
vibratory jar. 


Shaking for several 
seconds. 


4to 415 am. 
Most probally at 
4 5 Dublin time. 
Whole time of tre- 
mor about 8 or 
10 seconds. 


Delgany, 4 15. 
Bray, 4. 


Arklow, a few mi- 
nutes after 4. 
Arklow, 4 5. 

Castle Howard, 


OBSERVED PHENOMENA. 


AUTHORITY. 


The shock perceived by multitudes both awake and sud- 
denly aroused by it from sleep; those who were awake 
and standing, or in motion, felt little ; those who leaned 
against walls or other objects were fully alive to the 
reality and extent of the motion. 

Observers who were awake differ as to accompanying noise, 
but evidence for its occurrence preponderates. The 
sound is variously described as of “a rushing wind,” a 
“rumbling sound like a fire-engine on pavement,” &c. 
Almost all sleepers suddenly aroused by the shock were 
conscious of a heavy, hollow sound, like the fall of a 
heavy soft body on a large hollow floor. 

The motion is generally described as vibratory, ending in 
one or two sudden heaves. It is uncertain whether 
the sound accompanied or closely succeeded the shock ; 
most probably the latter. 

Houses were heavily shaken; a shattered chimney thrown 
down at Phibsborough ; water thrown out of full vessels. 

A few minutes after the shock, the street gas-lights were ob- 
served to be agitated as ina storm, arising obviously from 
the agitation of the water in the gasometer tanks at the 
works. (Letter from Mr. Wilson, Christ-Church-place.) 

The balance-weights of window-sashes swung against the 
sash-casings, north side of Dublin. 

Sparrows were thrown from their roosting-places, Great 
Southern and Western Railway goods shed, and Mount- 
joy-square, and many picked up dead on the ground in 
the morning. 

Watchmen at the Dublin and Drogheda Railway termi- 
nus saw the drag-chains hanging from trucks set to 
oscillate. 

Caged birds in some instances began to sing ; dogs barked ; 
the printers at work in Saunders’ News Office were uncon- 
scious of anything unusual. 

Chairs standing on an oilcloth floor in Lincoln-place slid 
along the floor out from the wall. 

The night of the 9th was oppressive and sultry for the time 
of year; a leaden sky, more than usually light for the 
time and season, obscuring all stars, and a death-like 
calm. A few drops of rain fell in some places. 

Passengers in the Liverpool and Holyhead steam-boats felt 
no shock. 

Phenomena similar to those felt in the city and parts imme- 
diately adjacent. 


At Delgany a bunch of keys was shaken and rattled in 
a chamber candlestick, where they had been left. 

Sound generally described as continuing after the principal 
shocks. 

Phenomena generally as at Dublin. 

Sleepers awakened ; houses shook; a chimney-piece clock 
stopped at a place near Wicklow town, at 700 feet eleva- 
tion over sea. The shock very severe at Castle Howard, 
described to have shaken to its foundation ; it lies on a 
hill-side. 

Houses vibrated in an alarming manner; the oscillations 
were not thought to be accompanied by any noise. 


A slight shock which shook the observer’s house and bed, 
and those of his neighbours. 


Public papers of 
Dublin, and sun- 
dry private com- 
munications. 


Evening Post cor- | 


respondent. 
Sundry 
communications. 
Private communi- 


cationsand Saun- | 


ders’ Newsletter 
November 
1852. 


Saunders’ News- 


letter, November | 


Correspondent of 
Saunders’ News- 
letter, November | 
12, 1852. ; 


private | 


11,) 


Mr. Matet’s Notice of the British Earthquake of November 9, 1852. 403 


In the preceding columns the directions, where given, are those of true me- 
ridian. The times of shock (as in map) are Greenwich mean time in Great 
Britain (except as to Congleton); and in Ireland, assumed Dublin time. Most 
of the newspaper correspondence adopted was authenticated. The names of 
private correspondents are not in all cases given ; and their information must 
be taken on the author’s authority. 

The more important points to arrive at in every earthquake, of course, are: — 

1. The direction of emergence of the earth-wave of shock. 

2. The moment of its emergence in time. 

3. Its velocity of emergence. 

4. The dimensions of the wave, or rather its altitude at each point of ob- 
served emergence. 

In the present instance the observations collected afford but a very meagre 
basis even for approximate answers to any one of these inquiries, and such 
must-ever be the case until self-registering seismometers are to be found in all 
our observatories, &c. 

The following conclusions, however, are justifiable :— 

1. The general direction of emergence of the earth-wave was from south 
to north, making a considerable vertical angle with the horizon, i. e. emerging 
upwards from the ground. 

The following is some of the evidence that it had both a horizontal and a 
vertical component of motion. As regards horizontal direction (that which is 
commonly best observable, and popularly assumed to be the only element of 
direction ), there is abundant testimony that it was from south to north, varying 
more or less to the eastward or westward. There is also the decisive evidence 
of the fall of a pocket telescope to the northward, which stood on end in a glass- 
case in Mr. Yeates’ optician shop, in Grafton-street. Its fall towards the north 
does not invalidate the other evidence that the primary motion was from south 
to north; as there exist numerous observed cases of objects disturbed by the 
primary or forward movement of the earth-wave, and thrown down by its return 
movement. (See First Report on Earthquakes, Trans. Brit. Ass.) 

As respects the vertical component, in addition to the testimony of many 
who felt an up and down movement, the conditions of fall of the picture in the 
author’s premises, already noticed, afford conclusive evidence. The wall against 
which it hung ranged nearly east and west ; a shock coming horizontally, or 

VOL. XXI. 3G 


404 Mr. Mattet’s Notice of the British Earthquake of November 9, 1852. 


nearly so, from the north towards the south could produce no effect but that of 
pressing it closer to the wall ; or, if from south to north, of causing it to swing 
outwards from the wall, like a pendulum, suspended from the rings. No motion 
(within the limits here in question) from east to west, horizontally, that is, in 
the plane of the wall, could affect it at all. The vertical element of motion is 
indispensable to account for its having fallen. 

If this vertical motion had been one emerging upwards from north to south, 
unless the angle were almost perfectly vertical, its effect would be merely to 
increase a little the strain upon the points of support for the moment, and to 
cause the lower part of the picture to swing out from the wall. But if the 
direction of motion were diagonally upwards from south to north, the whole 
force due to the vertical component, less the friction of the picture against the 
wall, would be expended in straining the points of support, and that due to 
the horizontal component in throwing the picture bodily off from the face of 
the wall. The picture was actually found thrown forward about eighteen 
inches from the wall at the point where it was arrested in its descent, after a 
fall of about four feet. I conclude, therefore, that the actual direction of 
emergence of the wave in the city of Dublin was from south to north (with 
probably a few degrees westerly bearing), and upwards at an angle of from 25 
to 80 degrees with the horizon. The following diagram may make this more 
intelligible. 


Fic. 1. 


Fic. 1. Plan of passage, 

Fic. 2. Vertical section through BC, looking southwards. 

Fic. 3. Vertical section through DE, looking westwards, 

The dotted lines show the original position of the picture; the hard lines its position when 
founddislodged and wedged between the side-walls. 


Mr. Matter’s Notice of the British Earthquake of November 9, 1852. 405 


The general form of the area of sea and land shaken assumes on the map 
the form of a large irregular ellipse of small eccentricity. Were observations 
to the south-west of this region available, it is likely that it might enlarge the 
curve in that direction.* Within this space the point of maximum disturbance 
seems to have been at and about Shrewsbury, where more serious results of the 
shock were experienced than in any other quarter. A strong wall of thirty 
yards in length was there overthrown ; and at Newton, not far distant, a 
wooden bridge over the Severn is said to have fallen ; while the bells rang in 
Ellesmere church. 

The circumstances both of direction and of centre of maximum surface dis- 
turbance, therefore, seem to point to the great volcanic focus of which the Azores, 
Portugal, and the Canary Islands, form the well-known centres of convulsion— 
as the region of the origin of the shock in the present case—the point from which 
the blow was delivered, which transmitted the elastic wave, would, on following 
the general direction to the south, pass through the group of the Canaries. 
And assuming that we have arrived with any tolerable approximation at the 
angle of emergence, the vertical depth of the origin, if taken below these islands, 
would be very great indeed. It is quite likely, however, that an intermediate 
point of convulsive energy exists in or about the latitude of Lisbon, and thus 
at a less profound depth. 

It is worthy of remark that the circumstances of this shock, viz., the 
previous increasing tremor, accompanied by the “ Bramidos,” the horrible 
subterranean thunder, and ending with the violent single or double shock, are 
precisely those of the terrible Lisbon earthquake of 1755, and of all others in 
that region. 

The Portuguese focus was in energetic action about the precise time of our 
earthquake, as the following notice proves :— 

“ A shock of an earthquake had been felt at Malaga, which spread general 
consternation among the inhabitants of that city. At half-past 1 o’clock a.m. 


* T have obtained no observations made at sea. Professor Haughton stated when the author’s 
paper was read, that the shock had been felt at Clogheen, county of Tipperary; and the Rey. 
S. Smith, that it had been felt at Enniskillen. As these gentlemen, however, did not communi- 
cate their information at the proper time, the author has been unable to adopt it, or to know to 
what extent the evidence may be received. 


ONGee 


406 Mr. Matrer’s Notice of the British Earthquake of November 9, 1852. 


strong oscillations shook all the edifices. The people immediately sallied out 
of their houses, and sought refuge at La Alameda and in the public squares. 
Fortunately, the shock was not renewed. The temperature was suffocating ; 
the cloudy aspect of the sky induced a belief that another earthquake would 
take place the following night. Many families accordingly retired on board 
the vessels in the harbour. The shock was preceded by a loud noise.” — Times” 
Newspaper, 10th November, 1852. 

The date actually referred to will be the 7th or 8th of the month. 

It may be remarked, that the basin of the Greek Archipelago appears to 
have been in activity a little before the same period, an earthquake having 
overthrown the magnificent columnar remains of the Temple of Jupiter Olym- 
pias at Athens. (‘“Times,” 24th November, 1852.) 

As respects the time of the shock, it appears to have been felt almost, if 
not altogether, simultaneously over the whole area shaken in Great Britain and 
in Ireland,—a circumstance in itself corroborating the evidence for the consi- 
derable angle at which it emerged, for shocks nearly horizontal are always 
observed to have a progressive translation over the shaken country. 

There is no evidence of a sufficiently precise character to warrant any con- 
clusions, either as to the velocity of emergence of the wave, or as to its altitude, 
i. e. the actual range of shaking produced at any point by the shock. Com- 
paring the evidences of disturbance in Dublin and other places, with the effects 
of many other earthquakes, the author is disposed to attribute the safety from 
serious calamity fortunately experienced by us, in great measure, to the vertical 
element in the direction of the shock, which, with only the same velocity and 
range, had it been been much more nearly horizontal, might probably have pro- 
duced great disaster. 

On examining the lines of horizontal direction for different localities as 
recorded on the map, they will be found to differ considerably. In this there 
is nothing unusual or irreconcilable with faithful observation or with science. 
Local changes in the true direction, and still more in the apparent or horizontal 
direction, of translation of the earth-wave are due to many causes, principally to 
changes in the geological formations at different points, or to the structure of 
the earth’s crust, and to abrupt changes in the physical features of the surface 
of the country. Instances are not wanting of the same shock being felt in di- 


Mr. Maturt’s Notice of the British Earthquake of November 9,1852. 407 


rections almost opposite, at the same moment, in places not far apart, and this 
circumstance constitutes one of the difficulties of disentangling the true elements 
of almost every shock, and of the construction of seismometrical instruments. 

Some very local points of greater disturbance were observed. Thus, at 
Castle Howard, in the Vale of Avoca, county of Wicklow, Ireland, the shock 
was experienced with great severity, due to the circumstances of its position. 
It stands upon a spur of mountain jutting out towards the westward from a 
north and south range. It rests on slate rocks, having a generally north and 
south strike, and its elevation on the hill is considerable. A shock from south 
to north would therefore affect it with exaggerated power. The shock was 
not felt at all by any one on board any of the steam-vessels passing either way 
between Liverpool or Holyhead and Dublin, on the night of the 9th November, 
nor was it felt by the printers up and at work in the several newspaper offices in 
Dublin, Liverpool, or Manchester. In all these cases the local vibrations going 
on by the machinery at work obviously prevented the earthquake jar being ob- 
served, or confounded it with those taking place from the local causes. 

A few of the more remarkable secondary effects observed may be noticed. 
The flickering of the gas-lights in the streets of Dublin, observed by the writer 
from Christ-Church-place (see ante), occurring some minutes after the shock, 
was doubtless due to the depression of the gasometers at the gas-works into 
the tanks by the vertical direction of the shock, and by the surging of the water 
in the tanks themselves, the time that elapsed being that necessary to transmit 
such disturbance from the gasometers through the elastic fluids in the street 
mains, tubes, &c., to the lights. 

Very many small birds, chiefly sparrows, were found dead upon the ground 
onthe morning after the shock, as at the goods sheds of the King’s-bridge Ter- 
minus, Great Southern and Western Railway, and in Mountjoy-square. This, 
which has been often observed in earthquake countries, is due to the creatures 
being shaken while asleep off their roosting-places, the involuntary muscles of 
the claws, which hold them on, not being prepared to resist so sudden and 
unexpected a shock. 

Clocks were stopped in some places, unfortunately without the time of stop- 
ping being noted. _ 

As the relations of earthquakes with meteorology are as yet uncertain, it 
appeared desirable to obtain returns on this subject from several stations within 


408 Mr. Matter’s Notice of the British Earthquake of November 9, 1852. 


the region of shock for the day of the earthquake, and for the one preceding 
and following. ‘The results are given in the subjomed Table. 


MerKoroLocicaL TABLy, referring to the British Earthquake of November 9, 1852, 
for five principal Stations. 


OBSERVING STATIONS. 


INSTRUMENT. . 
mag! igo. = 
Armagh, Sligo, York, 


reduced to 50° Markree Castle, 
Fahr. 9 a.m. 10 o'clock A.m. 


Greenwich 
9 o'clock A.M. means for the day. 


29°820 29°504 29°712 29°848 29:976 
Barometer, . 30116 29°994 30°105 30°208 30°025 
30°044 29°933 30:002 30104 29°915 


58°5 57°-0 52°9 55°°0 52°8 
59 °0 48 :2 48 ‘7 48 0 515 
52:0 43 -2 a4"9 40 ‘0 40 °3 


Thermometer, 


Inches.} Inches. Inches. Tnches. Inches. 
5 F 0-136 0313 0:05 
Rain-gauge, { 9, 0:280 0:036 0:063 0:05 
10, 0-030 1-043 0:001 0:00 


Miles, last 12 hours 
travelled. 


2 We 251 S. b W.S.W. 
Wind; ins) - { ; 46 8. S. W. . E. BE W.-S.W.-W.S.W. 
25 E.N. E. .N.E. .W. calm, N.E.-E.N.E. 


On the 11th Aurora, 
and magnets greatly 
disturbed. 


Notr.—The whole winter of 1852 was one of unusual wetness, followed in early spring 
by hard and protracted frosts, and was probably the most severe winter, on the whole, re- 
corded for twenty or thirty years in the British Islands. 


Thesé results confirm the view (so far provisionally) deducible from all 
earthquakes, namely, that meteorological phenomena have probably no true 
causative connexion with these disturbances, although they are often acted on 
and modified by the secondary effects due and subsequent to earthquakes. 


Mr. Matxet’s Notice of the British Earthquake of November 9,1852. 409 


There are good grounds for supposing that during the night of the 9th No- 
vember, 1852, several minor shocks of earthquake took place, and were felt 
more or less in and around Dublin by different individuals, who, before the severe 
shock of 4 o’clock a.m., did not attribute them to any natural cause: and a let- 
ter to our fellow-member, Mr. Clibborn, from a trustworthy observer, renders 
it probable that on the succeeding night there was a continuance of subterranean 
commotion of a diminished character, and such, very probably, might have con- 
tinued during the intervening day also, but without attracting the attention, 
which the silence and increase of sound at night induced. 

The last shock of earthquake of any note occurring in Great Britain was 
experienced with various degrees of intensity throughout the greater part of 
Lancashire, and the adjacent districts of Westmoreland, Cumberland, Cheshire, 
Flintshire, and the Isle of Man, and took place a few minutes before 1 o'clock 
on the morning of Friday, March 17, 1843. On that occasion, as on the pre- 
sent, somewhat varying statements were made as to the duration and severity 
of the visitation, but there was a material difference in the state of the weather 
and of the atmosphere. After the last shock in 1843, accounts were received 
from the West Indies announcing that a severe earthquake had taken place 
there about the same time, and that a great number of lives had been sacri- 
ficed. 

Of preceding British earthquakes, out of 116 recorded by Milne, 31 
(according to him) had their centres in Wales, 31 along the south coast of 
England, 14 on the borders of Yorkshire and Derbyshire, and 5 or 6 in Cum- 
berland. 

In the south of England he is of opinion that most shocks have an E. and 
W. direction, while those of Anglesea, North Wales, and Cheshire are N. W. 
and §. E., in both cases coinciding with the general lines of great faults. 

He considers, from the discussion of 130 Scottish and of 116 English earth- 
quakes, that there is a maximum of occurrence for the former in November, 
and for the latter in September ; taken all together, there occurred 74 in the 
three winter months, 44 in spring, 58 in summer, and 79 in autumn ; or 50 in 
the summer half year against 89 in the winter half. 

M. Perrey, in his Memoir on British earthquakes, from a discussion of 234 


410 Mr. Mauret’s Notice of the British Earthquake of November 9, 1852. 


recorded, extending over a period of ten centuries, viz., from the ninth to the 
nineteenth, distributes them thus :— 


Winter,’ re eo eee 06 
Springs, Pe. Vey eere edd 
Summer Hee at ih) fete A aeire 95D 
HOUT, 6 bo bo a) 


On the whole, whether it may ultimately appear that earthquakes have some 
distinct relations to season all over the globe, in Great Britain the base of in- 
duction is too small, and the numbers approach too near to equality, to warrant 
such conclusions at present. 

M. Perrey has also classified the directions of shocks (horizontal or apparent 
directions only) of the preceding British earthquakes, as follows :— 


S: toN ae ay ot ee et O48 
INGIDS WONSS Wey a 6 6 a ORS 
Heto Ws, ga oc 1 ees S70 
hl Dy ONG Wha Gog 5 Obie 
Seo ae aces POTTS 
So Wato Neb ee TAG 
Wito Esra: eee, 2 Sede 
N. W210. SE, oe 097 


If we unite those having the same direction, but merely opposite primary 
motions, we have, 


INorthyand||South.=y (5) -see ees eee lial 
Bast andwWiestsa ee tes 2 ct alaw be Ce ae tie eS le 
Intermediate points to the Eastward of North, . . 1:94 
Intermediate points to the Westward of North, . . 1:70 


If this result be relied upon as on,a sufficient basis, it would indicate that 
British earthquakes most frequently come from other and more distant centres 
of disturbance than that assignable to the shock here treated of. 


41] 


XVIII.—WNotes on the Meteorology of Ireland, deduced from the Observations 
made in the Year 1851, under the Direction of the Royal Irish Academy. By 
the Rev. Humenrey Luoyp, D.D., FR.S.; Hon. F.R.S.E.; V.P.R.IA.; 
Corresponding Member of the Royal Society of Sciences at Gottingen ; Honorary 
Member of the American Philosophical Society, of the Batavian Society of 
Sciences, and of the Societe de Physique et d Histoire Naturelle of Geneva, 


Ge. Fe. 


Read June 27 and December 12, 1853. 


THE science of meteorology is, perhaps more than any other, dependent upon 
co-operation and upon method. Individual observers may investigate success- 
fully certain detached meteorological problems, such as the laws of the diurnal 
and annual changes of temperature, pressure, and humidity, at a given place ; 
but little progress can be made in Climatology, or in the knowledge of the greater 
movements of the atmosphere, and their relation to the non-periodic variations of 
temperature and pressure, without the co-operation of many observers distri- 
buted over a large area, and acting upon a common plan. 

For this task the voluntary association of individuals is insufficient. However 
zealous such persons may be, it is not possible to bind them to that uniformity 
of system without which little can be effectively done. Observations taken at 
different hours, or by different methods, can never be compared satisfactorily ; 
and any comparison will involve an amount of labour in the processes of re- 
duction which may render them impracticable. In addition to this, certain 
rules of observation are imposed by the conditions of some of the great problems 
of meteorology; and no co-operation in which these rules are deviated from can 
contribute to their solution. 

VOL. XXII. 3H 


412 The Rev. H. Luoyn on the Meteorology of Ireland. 


For these and other reasons it is desirable that, in every country, such ob- 
servations should be provided for by the Government, and placed under the 
direction of one of its official departments. And there can be no doubt of the 
services which meteorology, properly studied, may be made to contribute to 
those interests which it is the duty of every Government to promote. The 
health of man, the operations of agriculture by which he procures his food, 
and many other of his material interests, are dependent upon climatological 
relations, which must be known and studied before they can be applied. Every 
one acknowledges the fact, that the salubrity of a district, and its adaptation (or 
the reverse) to particular human constitutions, is intimately connected with its 
meteorological conditions. And the same thing is true of all organized beings, 
and especially of those which are subservient to the uses of man. Thus, 
the question of the naturalization of exotic plants is, mainly, a meteorological 
problem, dependent upon the climatological relations of the region to which 
the plant is indigenous, and of that to which it is to be transferred; and the 
importance of obtaining accurate data for its solution will be recognised, when 
it is borne in mind that, in Europe, most of the plants useful to man belong 
to this class, and that those hitherto acclimatized probably bear a very small 
proportion to the whole. Lastly, the processes of cultivation, to which these 
vegetables are to be subjected, are also connected in an intimate manner with 
meteorological knowledge. We may instance this connexion in the operations 
of irrigation, and of drainage, both of which are dependent upon the knowledge 
of the amount of rain-fall in the district to be operated on. 

It is true that meteorological science has been hitherto comparatively bar- 
ren in such applications; and the fact itself, with many persons, would be 
accepted as evidence that abstract and practical knowledge are wholly separate 
and unconnected. But, when properly understood, it leads to a different con- 
clusion. Superficial knowledge in this science can indeed yield but few prac- 
tical results; and those by whom such results have been hitherto sought have ex- 
pected to find them at the surface. There are indeed cases—such, for example, 
as the one last referred to—in which the connexion between meteorological 
science and its applications is obvious and simple, and in which, accordingly, 
that connexion has been traced and made use of. But in general it is other- 
wise. Ina subject so complex as the laws which govern the aerial envelope 


The Rev. H. Luoyp on the Meteorology of Ireland. 413 


of the earth, and where so many causes are in operation, practical applications 
can be obtained only from mature theoretical knowledge. Thus, it may be 
shown that the knowledge of the phenomena of temperature, requisite for the 
determination of the possible geographical limits of a single species of plants, is 
by no means inconsiderable ;* and when to this we add the consideration of the 
other agencies which are at work in the atmosphere, all influencing vegetable 
life, it is plain that we are not in a condition to deduce any useful result con- 
nected with the distribution of species, until we have mastered a much larger 
amount of theoretical knowledge than is usually brought to bear in such de- 
ductions. 

It would seem, therefore, to be the duty of the Government of every civi- 
lized state to provide the statistical data which have so many important 
bearings upon the material welfare of the people, and in the form best fitted for 
their discussion and examination. And to the lover of truth itself, for its own 
sake, the fulfilment of this duty would, fortunately, supply the wants of science 
in the most complete and satisfactory manner. 

In many countries, accordingly, provision has been made by their respec- 
tive Governments for the collection and discussion of meteorological data upon 
a uniform and well-digested plan. The Government of Prussia appears to have 
taken the lead in this important labour. Its example has been followed by 
those of Russia, Austria, Bavaria, and Belgium; and the names of Dove, 
Kurrrer, Krew, Lamont, and QuETELET, to whom the superintendence of these 
observations has been intrusted, afford the surest warrant of their successful 
prosecution.t But perhaps the most important undertaking of this nature is 


* For each plant there is a lower limit of temperature, below which it will cease to vege- 
tate; while, in order that it may blossom and bear fruit, it must receive, between the two 
seasons of this minimum temperature, a certain amount of heat beyond this limit which is con- 
stant for each species. It is upon this integral of effective heat, as has been shown by DE CanpDoLte, 
that the existence of the species depends. For information on this and other subjects connected 
with the applications of meteorology, see the interesting introduction, by M. Martins, to the 
Annuaire Meteorologique de la France. 

+ The results of many of these series have been already published. Professor Dove has pub- 
lished the results of the observations made in Prussia in the years 1848 and 1849. The observa- 
tions made at the Russian observatories have been published from time to time by M. Kuprrer, 
in the Recueil des Observations faites dans ’ Empire de Russie. The results of the Bavarian obser- 


3H 2 


414 The Rey. H. Luoyp on the Meteorology of Ireland. 


the recent organization of a system of meteorological observations at sea by the 
Government of the United States. There are, at the present time, nearly 1000 
masters of ships, belonging to the navy and merchant services of the United States: 
engaged in such observations; and the discussion of the results, by Lieutenant 
Maury, has led to many consequences of great value to the sciences of meteor- 
ology and hydrography, and rich in practical applications to navigation. The 
Government of the United States has earnestly sought the co-operation of the 
Governments of the several maritime nations of Europe in this enterprise, 
and the demand has led to a Conference at Brussels, for devising a uniform 
system of meteorological observations at sea. This Conference, held in August 
and September last, was attended by individuals representing the respective 
Governments of Belgium, Denmark, France, Great Britain, Netherlands, Nor- 
way, Portugal, Russia, Sweden, and the United States. 

Impressed with the conviction that it was the duty of each country to take 
its part in these labours, and especially in the investigation of its own clima- 
tology, the Council of the Royal Irish Academy directed their attention, early 
in the year 1850, to the object of organizing a uniform system of meteorological 
observations in Ireland. And the peculiarity of the climate of this island 
perhaps more than balances the smallness of its extent, in giving an interest to 
the investigation. Situated as it is at the north-western extremity of Europe, 
and exposed to the full influence of the northern branch of the gulf stream 
which sweeps its western shores, its winter temperature is as high as that of the 
southern shores of the Euxine; while, on the other hand, the great precipi- 
tation of vapour, due to the same cause, gives it a summer heat as low as parts 
of Finland. 

The questions, whose solution was aimed at by this measure, are thus stated 
by the Council in their second Report :— 

1. The distribution of temperature, humidity, and rain, as affected by geo- 
graphical position and by local circumstances; and the other phenomena of 
climate. 

2. The effect of season (combined with the influences already referred to) 


yations have been given by Dr. Lamont, in the Annalen der Meteorologie; and those of the 
Belgian system, in the admirable series of papers drawn up by M. Querexet, Sur le Climat de 
Belgique. 


The Rev. H. Luoyp on the Meteorology of Ireland. 415 


upon the distribution of temperature, and the varying position of the isothermal 
lines from month to month. 

3. The non-periodic variations of pressure, temperature, and humidity, and 
their connexion with the course and direction of the aerial currents. 

4. The phenomena and laws of storms, whether revolving or otherwise. 

5. The periodical winds prevailing during certain seasons, and their modifi- 
cations from geographical position or local causes. 

6. The course and rate of progress of atmospheric waves. 

Concurrently with the meteorological observations, it was determined to 
institute an extended series of observations on the phenomena and laws of the 
tides around the coasts of Ireland, the results of which will shortly be laid before 
the Academy by Mr. Havcuron. The observations of the former class having 
been intrusted by the Council to my care, for reduction and discussion, I now 
proceed to lay before the Academy their principal results. It will be neces- 
sary, however, in the first instance to describe the plan of observation itself. 


Stations.—The meteorological stations are :— 

1. The Coast-guard stations at Portrush, Buncrana, Donaghadee, Courtown, 
Dunmore East, Castletownsend, Cahirciveen, and Kilrush ; and, for observa- 
tions of sea temperature only, those of Cushendall and Bunown. At all of 
these the observations were taken, with the permission of the Lords of the 
Treasury and of the Comptroller-General, by the boatmen belonging to the 
Coast-guard Service, the individuals having been specially selected for the duty 
by the inspecting officers, and having been instructed in the mode of observing 
by members of the Council of the Academy. 

2. The Lighthouses at Killough, Inishgort, and Killybegs, where, with per- 
mission of the Ballast Board, the observations were made by the lightkeepers, 
instructed as before. 

3. The Astronomical Observatories of Armagh and Markree, where the obser- 
vations were taken by the Observatory assistants, with the permission of Dr. 
Rosrnson and Mr. Cooper; the Magnetical Observatory of Dublin, where they 
were made with the permission of the Board of Trinity College; and the sta- 
tions at Portarlington and Athy, where they were undertaken by Dr. Hanton 
and Atrrep HavueurTon, Esq. 


416 The Rev. H. Luoyp on the Meteorology of Ireland. 


In addition to these the Academy has received observations, made upon the 
prescribed plan, from the Royal Observatory of Dublin, and from the Queen’s 
Colleges at Belfast and Galway, which could not conveniently be included in 
the following discussions, not having extended over the whole of the period 
discussed. The observations at the Royal Observatory, and at the Queen’s 
College, Belfast, commenced in April, 1851, and have been continued to the 
present time; the necessity for their omission is the more to be regretted, as 
they appear to have been made with every possible care. 

The positions of the several stations, together with the heights (in feet) of 
the cisterns of the barometers above the mean sea level,* are given in the an- 
nexed Table. They are shown in Plate vu. 


Taste I. Names anp Positions oF THE METEOROLOGICAL STATIONS, 
: - | Height 
No. Station. County. Fey Les above Locality. 
I) Portrush; .... | Antrim, 2 2) 55013") (os4l7 29 | Coast-guard station. 
IL. | Bunerana, Donegall. -yuloomecu| Mate 48 Do. 
III. | Donaghadee, .. | Down,..... 64 38 | 5 33 16 Do. 
IV. | Killybegs, Donegal,.. .. | 54 34 | 8 27 | 20 | Lighthouse. 
V. | Armagh, . . | Armagh, 54 21 (ay BXo) | Sala Observatory. 
WAT eallouphir: sens DOW nee ccs 54 13 | 5 40 23 Lighthouse. 
VIE; | Markree;)j,.:-...| Sligo, (5152.5: 54 14 | 8 28] 132 Observatory. 
IU. | Westport,. ...|Mayo,..... 53.50 | 9 37 17 | Lighthouse. 
IX. | Dublin, 7... . | Duablinses 2 .2)/'53ee2l 6 15 19 Magnetical Observatory. 
X.| Portarlington, . | King’s County, | 53 9 | 7 12 | 230 | Dr. Hanlon’s residence. 
2A Pil Gi Slels ols Kildare, ...~.1/53 0 | 6 581} 200 Mr. Haughton’s residence. 
XI. | Courtown, Wexford, -.. | 5239 | 6 13 34 Coast-guard station. 
IIT. | Kilrush, Clary ieee: 52 38 | 9 30 19 Do. 
XIV. | Dunmore, Waterford, ../52 8| 6 59 66 Do. 
XV. | Cahirciveen, Kerrys sie e)) l|oleoGal al Ome 52 Do. 
XVI. | Castletownsend, | Cork, ..... Sleisaul 9s 9 18 Do. 


The instruments were furnished by the Academy to the coast-guard and 
lighthouse stations; and were constructed under the direction of the Council, 
and upon a common plan. They consist of a barometer, a pair of ordinary 
thermometers (dry and wet bulb), a pair of self-registering thermometers, a 


* At Portarlington and Athy these heights have been taken from the Contour Maps of the Ord- 
nance Survey, and must, therefore, be considered as only approximate: at all the other places they 
have been obtained by actual levelling from the nearest Ordnance bench-marks. 


The Rey. H. Luoyp on the Meteorology of Ireland. ALT 


wind-vane, Lind’s anemometer, a rain-gauge, and (at the coast-guard stations) 
a thermometer adapted to the observation of sea temperature. The thermo- 
meters were previously compared in Dublin with the standards belonging to 
the Magnetical Observatory, and their errors exactly determined. The barome- 
ters were compared with the Dublin standard after they were placed at the se- 
veral stations, by means of good portable barometers; and the heights of the 
cisterns above the sea were ascertained by levelling. All this was done by 
Members of the Council, under whose superintendence the instruments were 
erected. 

The following were the positions of the instruments :— 

Portrusu.—The barometer was put up in the guard-house, which is situ- 
ated on an eminence facing the harbour; and the thermometers and the rain- 
gauge in a small attached garden. The four thermometers at this, and at 
every other station, were inclosed in a shallow box with a sloping roof, and 
wire-gauze front. A vertical gnomon was fixed at most of the stations in the 
window-sill of the guard-house, for the purpose of determining the time of noon; 
and the observers were furnished with a Table of the equation of time computed 
for the year 1851, and for the mean longitude of Ireland. 

DonacGHapDEE.—The meteorological instruments were favourably placed: 
the barometer in the guard-house, and the thermometers and rain-gauge in an 
inclosed yard connected with it. The meridian line was traced on the sill of a 
window in the guard-house, the shadow being given by a vertical iron bar. 

Kittoucu.—Lighthouse, St. John’s Point.—The barometer was put up in 
the hall of the light-keeper’s dwelling; the other meteorological instruments 
were well placed in a garden attached to it. The meridian line was traced on the 
flagging, at the south side of the house, the shadow being given by a vertical 
iron rail. ; 

Courtown Harzour.—The barometer was erected in the guard-house of the 
station; the thermometers in an inclosed yard at the rear, attached to a wall 
facing northward; and the rain-gauge on an eminence behind it. 

Dunmore East.—The barometer was put up in the guard-house of the sta- 
tion; the thermometers were attached to the northern external wall, and were not 
completely guarded from radiation. The rain-gauge was fixed to a wall in front. 


418 The Rev. H. Luoyp on the Meteorology of Ireland. 


Buncrana.—The meteorological instruments were put up at the guard- 
house,—the barometer within, and the thermometers on one of the external 
walls facing to the north; the site was not favourable. 

Kuttysecs.—This lighthouse is admirably circumstanced for meteorolo- 
gical observations. The Academy’s barometer was not put up, the baro- 
meter belonging to the lighthouse being found sufficiently good; it was favour- 
ably placed in the sitting-room of the light-keeper’s dwelling. The thermometers 
were fixed in an angle of the yard at the rear of the house; the rain-gauge 
was attached to an iron railing in the front yard. There is a sun-dial in the 
front yard, the position of which was examined, and found correct. 

Wesrrort—Inishgort Lighthouse.—The meteorological instruments were 
erected at the lighthouse of Inishgort, in charge of the light-keeper. The 
barometer belonging to the lighthouse was found sufficiently good for the ob- 
servations ; it is placed in the sitting-room of the light-keeper. The thermo- 
meters were fixed to one of the external walls facing northward, and the rain- 
gauge in the small garden attached to the lighthouse. 

Kirrusu.—The meteorological instruments were erected at the guard-house, 
close to the quay; the barometer within the guard-house, and the thermo- 
meters attached to an external wall. The rain-gauge was fixed at the foot of 
the flag-staff. 

CanircIvEEN.—The barometer was erected in the house occupied by the 
boatman in charge, in the town of Cahirciveen, and the thermometers and 
rain-gauge in the yard and garden attached toit. Their site was not favourable. 

CASTLETOWNSEND.—The barometer was placed in the guard-house, and the 
thermometers on one of the external walls facing northward. The rain-gauge 
was fixed at the foot of the flag-staff. The time of noon was found by means 
of a dipleidoscope belonging to the officer in command of the station. 


Plan of Observation.—It is probable that over a tract of country so limited 
as this island, the distribution of temperature, humidity, and rain, does not vary 
materially from one year to another; and that, consequently, a tolerable approxi- 
mation to the laws of this distribution may be obtained from the results of a 
single year, if every precaution be adopted to insure the perfect comparability 


The Rev. H. Luoyn on the Meteorology of Ireland. 419 


of the results. It was arranged, accordingly, that the observations should be 
continued at the coast-guard stations until the end of the year 1851, so as to 
embrace a period of at least one year reckoned from the time when the obser- 
vers had acquired the power of observing with accuracy. The monthly means 
for this year may be reduced to their absolute mean values, by the help of the 
more extended series of observations made in Dublin, by which the deviations 
of any monthly result from its absolute mean value is sufficiently known. 

The Committee, upon whom the duty of superintending these arrangements 
devolved, were desirous that the plan of observation should be the least one- 
rous that could lead satisfactorily to the results aimed at. One of the princi- 
pal of these—the determination of the movements of masses of air, whether 
in storms, or in the displacement of atmospheric waves,—demands, as has 
been said, that the observations should be taken at equal intervals of time; 
and the only condition imposed by the other meteorological problems is, that 
these times should be so chosen as to furnish the daily means of the elements 
sought. Now any three observations, taken at equal intervals throughout the 
day, are suflicient to eliminate the diurnal variation, and therefore to give the 
daily means of all the meteorological elements; and undoubtedly, where such 
a system is practicable, the observations should be taken at 6 A.M., 2 P. M., and 
10 e.m., which has been shown to be preferable to any other eight-hourly group 
for meteorological purposes.* 

At the coast-guard stations, however, sucha plan of observation would have 
been incompatible with the regular duties of the men; and it was advisable to 
adopt a less complete system, which might be followed at all the stations, and 
in which interruptions were not likely to occur. Fortunately, two observations 
in the day, taken at equal intervals, are sufficient to give the daily means of all 
the meteorological elements, excepting the atmospheric pressure; and, as the 
diurnal variation of the pressure is very small,—much smaller than its irregular 
fluctuations in these latitudes,—it may be disregarded, and the objects for which 
the present system was instituted may be attained by taking two observations 
in the day, at homonymous hours. 


* Transactions of the Royal Irish Academy, vol. xxii. p. 65. 
VOL. XXII. 31 


420 The Rev. H. Lioyp on the Meteorology of Ireland. 


The best pair of homonymous hours, for the determination of the mean 
temperature, and nearly also for that of the mean humidity, are 9" 46" A. M., and 
9°46" p.m.* Limiting themselves to the exact hours, the Committee might 
accordingly have chosen either 9a.m. and 9Pp.M., or 10 a.m. and 10 Pp. M.; 
the former pair was adopted, its superior convenience seeming to outweigh the 
advantage of the latter in accuracy. 

For the fuller elucidation of some of the questions proposed, it was further 
arranged that hourly observations should be taken at all the stations for twenty- 
four hours, at the equinoxes and solstices, according to the plan laid down by 
Sir Jonn Herscuet. It was likewise provided, that hourly observations should 
be taken occasionally, under special circumstances, such as storms, unusual dis- 
turbances of barometric equilibrium, &c. 

For further details of the plan of observation, the reader is referred to the 
“ Instructions” prepared by the Council of the Academy. I now proceed to 
the results of the observations. 


TEMPERATURE OF THE AIR. 


Corrections. —It has been already stated, that the thermometers employed in 
measuring the temperature and humidity of the air were carefully compared with 
a standard thermometer, and their errors noted. When the errors differed by 
more than 0°-2 in different parts of the scale, the instrument was rejected ; when 
they did not, the mean of the observed errors was adopted as a constant error 
for the whole scale of the instrument. Table n. gives the numbers thus obtained 
for the several instruments; these numbers are applied, with the contrary signs, 
as corrections to the observed results. 

It has been stated that the mean of the temperatures observed at 9 A. m 
and 9 p. M. is, very nearly, the mean of the entire day. The small corrections 
required, in order to reduce the former to the latter, are obtained from the 
bi-hourly observations made at Dublin in the years 1840-1843. Table 11. con- 
tains the results of that series, giving the mean differences between the tem- 
perature at each hour of observation, and that of the entire day. 


* See the paper already referred to. The hours 9’ 30" 4.™., and 9” 30” P.M., are better for 
humidity. 


The Rev. H. Luoyp on the Meteorology of Ireland. 421 


Taste II. Errors oF THE THERMOMETERS. 


Dry Therm. Wet Therm. 


Station. 
No. of Inst.| Error, || No. of Inst.) Error. 


Porinushsendiete ; +03 
Buncrana, .... 4 +04 
Donaghadee, . . Y +06 
Killybegs, ...-: ? . + 0-4 
Armagh, ..... Y 0-0 
Killough, 


Markree” =... 
Westport,*... 
Dublins . 4.6.5 6 
Portarlington,* . 
Athy, 

Courtown, .... 
Kilrush, 
Dunmore, 
Cahireiveen, .. . 
Castletownsend, . 


Tasre IJ. Mean DirrERENCES BETWEEN THE TEMPERATURE AT EACH Hour oF OxsER- 
VATION, AND THAT OF THE ENTIRE Day, at Dustin. 


iste SOc lay Gel Crea Wa oaihicce cl eePat ewe | Atcha PKOn 11 aT 
January, . . |- 1°3 & 143) = ea fe 1°91 0°-8}+ 2°-2!+ 3°°6]+ 30-014 1°-0|— 02-2|— 0°5|- 0°°8 
February, . |- 1 -2|-1 *6|-2-2|-2-1|-0-4|+ 2-444-043-3141 -0|-0-41-0-7-0°9 
March, . « - | 3°5|-3°7|-3°7|- 31+ 0-714 4 °1/+6 04 5 51+ 2 -9|- 0 -4/-1-7- 24 
April,.... |-4°9/-5 -4/-5 6)- 1342 5+ 5 4/46 61+ 6-44. 4-1,-0-11- 2-7-3 9 
May, ~/5°7/-6 5|—5 -2|4+ 05+ 2 81+ 4-914 5-816-144-1140 61-2 -9)- 4-4 
June, .... |- 6 -2/-7-0/- 4-914 20+ 3-114 4-714 5-414 5-2-4 -21 1-01-2846 
July, .... | 4°9|-5 -7/- 49/4 0-8+2-51+ 4-61 5-144 5-11 3-710 -6|- 2-7, 4-2 
August,. . . | 5-0/5 -4/-5 *7|/- 09+ 261+ 5-1): 5-9]: 5 -6/+ 3-9} 0 -2|- 26-37 
September, . |- 3-7} 4 -2)-4 -2/-2 41+. 1-7|+ 481+ 6 -0/+ 5 -0}+ 2-9-0 6|- 2:1,-3 2 
October, 2-6 3 -2|— 3 -9|— 3 5+ 0-24 4-3/4 5 51+ 4-64 1 “9-0 «1-1 -3|-1°9 
November, . | 1-2-1 -5|- 1 -7|-1-‘8|- 0 6|+ 2 -2|+. 3-514 2-5/4 0-6-0-1/-0-8-1-0 
December, . cn ak —1-3/-1-2-0-8+ 1 -6/+ 2 614+ 1 -5|+ 0-4-0 -2|-0 4-05 
Meat arias = 374} 39-9) 3°°8)— 12+ 1-1 i+ 3791+ 5°04 4951+ 261+ 00/— 1°-8/— 2°-6 
Summer, . . |- 5 ‘1-5 -7|- 5 *1/- 02+. 25+ 4 9+ 5 8+ 5 61+ 3 -8|+ 0 3|- 2 -6|- 4-0 
Winer, 18-2125 23-03428449+3441 3109-09019 


* At Westport and Portarlington the errors of the thermometers were not determined. 


pled 


422 The Rey. H. Luoyp on the Meteorology of Ireland. 


From the preceding Table we obtain the following corrections, which are to 
be applied to the means of the observed temperatures at 9 A.M. and 9 P. M., in 
order to reduce them to the mean of the day :— 


April, . . . corr. = + 0°1 October,. . corr. = + 0°5 
Misi cow seones + 0:1 November, ,, TORT 
June, .-- » — Ort December, __,, +06 
July, ---  » +0jt SAHUATY, fe 4s +07 
August, .- 5 +00 February,. _,, +0°6 
September, _ ,, +0°2 Marchi: a, boss +0°5 


It hence appears that the correction is nearly constant throughout the sum- 
mer, and throughout the winter months, respectively. The mean summer cor- 
rection is + 0°1; the mean winter correction + 06. 


Mean Monthly Temperatures.—The mean temperatures have been obtained, 
at all but three of the stations, from the observations at 9 a.m. and 9 P.M., by 
the application of the preceding corrections. At Markree the observations 
were taken at 10a.M. and 10 p.m.; and the reducing numbers are therefore 
somewhat different, and smaller in amount. At Portarlington and Athy the 
observations were taken but once in the day, namely, at 9 A.M.; and at these 
stations, accordingly, the mean temperatures are inferred from the maximum 
and minimum temperatures as given by the self-registering thermometers. The 
formula employed is that of Karz, viz. :— 


mean temp. = min. + a (maz. — min.) 


The mean value of the coefficient,* as deduced from the observations at the 
observatories of Armagh, Markree, and Dublin, is a= 0-41. 

The following Table contains the resulting values of the mean temperature 
for the several months of the year 1851 :— 


* The coefficient in Kxmrz’s formula appears to vary considerably at different places, both in 
its mean amount, and in the law of its variation from month to month. At Armagh and Markree 
its greatest value is in December, and its least in July; at Dublin, it is the reverse. I have taken 
above the mean of the yearly values for the three stations. 


The Rev. H. Luoyp on the Meteorology of Ireland. 


Taste 1V. Mean TEMPERATURES FOR EACH MontTH OF THE YEAR 1851, AT THE 


Station. 


Portrush, 
Buncrana, ice 
Donaghadee, .. . 


Killough, 
Markree, 


Westport,..... 


Dublin, 


Portarlington, .. | 


Athy, 


| | 


'42°-0 42°+3'42° 9} 


641 
843 
843 
‘441 
644 
‘441 
§ +345 
643 
640 
‘740 


SEVERAL STATIONS. 


843 - 
1/43 - 
‘945° 
‘7.42 - 
043 - 
*2\42 -3} 
246° 
644 0) 
640 « 
941° 


. | Apr. 


45°-7 
450 
650 
151 
4.50 
T51 
3.50 
352 
852 
“149 
450 


856 
8/57 
6158 
2157 


959 
058 


160 


158 


159 
5 658 
360 
"2162 
‘357 


260 


May. | June, | July. | Aug. 


355 
856 


851 
"3/51 


758 ° 


655 - 


157 
‘755 
958 
055 
‘753 
8153 


50°-2155°3'56°'5'58°°8'55°-5\51°-3.44°-4 
5155 * 
"B55 ° 
456° 
356 2 
055 S) 
1155 Ov Al 
1/56“ 
558-86 
1/54 -8| 
6/56 * 


2.42 
843 
745 
441 
2/43 
‘841 
‘T47 
‘941 
139 
039 


6 44 
945 
6 46 
043 
046 


“8.42 


‘2/47 
2/43 
440 
‘741 


‘4/49 
350 
248 
650 
248 
851 
350 
‘3/47 
3/48 


| 
44°-7/49°] 
“3/49 ° 


23 


‘560 °756 
“1/60 *858 
6.62 +359 
‘262 058 ‘547 052 
7/61 859 6/54 145 +746 “9.52 
od 

Before we proceed to discuss the mean temperatures in the several months 
of the year 1851, it is important that we should know the absolute mean tem- 
peratures at some one station, and thereby the deviations from the means in the 
several months of the year in question. Over a tract of country so limited as 
Treland, these deviations will not differ much in different localities; and there- 
fore, knowing them for one station, we are enabled to reduce the results of the 
single year, with probably sufficient exactness, to their absolute mean values 
at all the rest. 

The absolute mean temperatures of the several months are known, at Dub- 
lin, by means of the series of observations made during twelve years at the Mag- 
netical Observatory. The monthly mean temperatures, deduced from that series, 
are given in the following Table. From the year 1840 to 1843, inclusive, the 
daily means are those of twelve equidistant hours; from 1844 to 1850, inclusive, 
they are inferred from the temperatures observed at 10 a.m. and 10 p.m.; and 
in 1851, from those of 9 A.m.and 9 p.m. In the last line of the Table are 
given the deviations of the monthly means in 1851, from the mean monthly 
means, as deduced from the twelve years. 


645 
745 
6.46 


150 
1/50 
‘251 


‘557 “3k 
‘7|56 °3 
.3/58 °2) 
657 * 


3.43 
"2/45 
444 
646 
4.46 


“844 - 
5/45 +2) 
844 - 
2.46 - 
0/46 - 


"652 
051 
453 
553 
7 °953 


Courtown, 
Kilrush, 
Dunmore, 
Cahirciveen, ... | 
Castletownsend, . 


AAs SAGAS SH od 
KH wWADHEL WY ATNNWADAS 


424 The Rev. H. Luoyp on the Meteorology of Ireland. 


Taste V. Mean Montuty Temperatures at Dustin. 


| Jan. b . | May. | June. | July. | Aug. . | Nov. | Dec. | Year. 
| 


| 
1840 41°-9 544 | 59°-4| 59° 2] 621 39°83 497-0 
1841 | 36 « 55 °2|56 5/57 °3| 59 +1 | 48 -3/ 42 3141-8149 - 
1842) 38° 53 0 60 °5|58°9|61 45 -4| 48 -8| 
1943 42° 51-356 -4| 60-3 60 44 - 
1844 41° 52-9 58-759 8/57 47° 
1845/41 - 51-3 |58 9/58 0/57 46° 
1846 | 46 - 54-4 |63 3/61 -7 60 48° 
1947 42° 53 6 |57 -7|64 059 48 8 | 
1848 | 37 « 56 9 |56 5/60 -4 56 43 2 
1849 | 42- 53 657 -4/60 °3 60 47° 
1850 51 -8|60 47 5 | 


61-2158 
1851 | 43° 52 5/58 8/60 -2 62 412 


AHASWwW-THHA-7 
AhABHANVUWASOAT 
SRARHDASHOE 
DOBRAAWHSTAAR 
SOSHROARSADS 
HATARKRSOASAS 


DORDNYNANAHEAS 
AROADABR WO w 
WAR AWAAVH TNH 


} 


ES 
ca | 

2 
i=) 


58°°7| 60°.1 59°7 | 56°:3| 494 | 45°5 | 43°0 | 50°0 
FOTO T+23-0-4425-43403103 


I 
° 
i) 


It will be seen from this Table, that the temperature in the months of 
January, February, and October, 1851, was higher than the average temper- 
ature, while, in November, it was considerably lower. The mean temperature 
of the entire year was only 0°3 above the average. 

The depression of temperature in the month of November is a remarkable 
case of those non-periodic fluctuations to which the attention of meteorologists 
has been drawn by Professor Dove. This fluctuation appears to have pro- 
ceeded from north-east to south-west, and to have been nearly obliterated when 
it reached the western coast of the island. At the northern and eastern sta- 
tions the unusual cold began on the 24th day of the month; at the southern 
and western it commenced on the 26th and 27th. It reached its maximum 
about the 30th, and ceased about the 3rd of December. When we compare the 
mean temperatures of November and December at Killough, Dublin, Courtown, 
and Dunmore, on the eastern coast, with those at Killybegs, Westport, Kilrush, 
and Cahirciveen, on the western, we observe that the temperature of No- 
vember is less than that of December by 3°3 at the former stations, while the 
defect is only 0°6 at the latter. 

Upon a comparison of the mean yearly temperatures of the several stations, 
we observe that those of the inland stations are in defect, as compared with the 


The Rev. H. Lion on the Meteorology of Ireland. 425 


corresponding coast stations. Thus the mean temperature of Armagh (48°6) 
is less than that of Donaghadee by 1°, and less than that of Killough by 1°'6. 
The mean temperature of Markree (48°-2) is less than that of Killybegs by 
2°-6, and than that of Westport by 3°5. The mean temperatures of Portar- 
lington and Athy (47°38 and 48°-4) are in like manner in defect, when compared 
with those of Dublin and Courtown, and by an intermediate amount. I shall 
return to this subject hereafter, and merely notice it at present for the purpose 
of observing that no satisfactory conclusion can be drawn as to the dependence 
of temperature upon geographical position, unless the inland and coast stations 
be compared separately. 

Confining ourselves for the present to the coast stations, which are the 
most numerous and the most widely distributed, we observe that there is an in- 
crease of mean annual temperature in proceeding from north to south of the 
island, the mean temperature of Portrush and Buncrana being 49°:0, and that 
of Dunmore, which is nearly on the intermediate meridian, 51°°6. Similarly 
there is an increase of temperature in proceeding from east to west, the mean 
temperature of Killough and Dublin being 50°-2, and that of Westport, which 
is nearly on the intermediate parallel, 51°-7. 

But for an accurate determination of the rate of increase of temperature 
in the two directions, it is necessary to combine the results by the method of 
least squares. For this purpose let ¢ denote the observed mean temperature 
of any month, at any given station; 7 the probable temperature of the same 
month at an assumed central station; and let the distances (in geographical 
miles) of the former from the latter, measured on the meridian and perpen- 
dicular to the meridian to the north and west, respectively, be denoted by y 
and «; then, if V and U be the increase of temperature corresponding to a 
single mile in each direction, 

t= T+ U2+ Vy. 


There will be a similar equation for each station; and combining them by the 
method of least squares, we shall obtain the most probable values of the un- 
known quantities 7, U, and V. 

The simplest mode of employing this method in the present instance is to 
take, as the arbitrary central station, that whose latitude and longitude are the 


426 The Rev. H. Luroyp on the Meteorology of Ireland. 


arithmetical means of the latitudes and longitudes of the stations of observa- 
tion. The resulting equations are thus reduced to the following :— 


pil => (a) 
US (2) + V= (ay) = = (2#), 
Uz (zy)+ VE (y*?) == (yt). 


For the reason already stated, I shall employ in this calculation only the 
results obtained at the coast stations. These are, in the order of latitude, 
Portrush, Buncrana, Donaghadee, Killybegs, Killough, Westport, Dublin, 
Courtown, Kilrush, Dunmore, Cahirciveen, Castletownsend. The mean latitude 
and longitude of these stations are 53°29’, and 7°39’ respectively. And we find 


E(2?) = 39094, LB (ay)=— 22569, 5 (y*) = 65811. 


Substituting and eliminating between the second and third equations, we 
obtain— 

U = 0000819 = (at) + 0000109 & (yt) ; 

V = 0000109 = (at) + -0000189 & (yf). 


By these formule the values of 7, U, and V, for each month are calculated. 
They are given in the following Table :— 


Taste VI. Exements or Monruty IsorHermat Lines. 


T 
U V Ww u 
1851. Mean. 
es es 
January, ..... 44°] 41°7 + 0080 — 0102 0130 52° 
February, ....| 44:2 42 °3 + 0093 — 0119 “0151 52 
iMerchssreu aren: 44°6 44:1 +0131 — 0064 70146 26 
‘Mitt ooo a 6 46 9 47:1 + 0043 — ‘0070 0082 59 
WES Blo oo a aie 52-0 529 + 0012 — 0139 0140 85 
June,....... 56°38 | 56°7 — 0031 — ‘0109 0114 106 
dilly ooh cncc 58 °9 58 °8 — 0049 — 0202 70208 104 
PATE US ta tenel saan 60 6 58 °3 + °0029 — ‘0121 “0124 77 
September,....| 57°4 | 57°8 +0101 — 0090 0135 42 
QOctoberiiesi. ne EVACH 50 °2 + 0059 — :0070 +0092 50 
November, ....{| 44:1 48 -4 + 0304 + ‘0077 0313 -14 
December, ....]| 45°7 45 4 +0103 - 0017 0104 9 
DENS G-6 Orord all Oz 50 °3 + ‘0073 — ‘0085 +0112 49° 


The Rev. H. Luoyp on the Meteorology of Ireland. 427 


The values of 7 and V being known, the positions of the isothermal lines are 
determined. The inclination of the isothermal lines to the meridian, measured 
from north to west, u, and the rate of increase of temperature in the direction 
perpendicular to them, W, are known by the formule 
Tv’ 


Their values for the several months are given in the foregoing Table. 


° tan u = 


W=y(U?4+V). 


We see then that, on the mean of the whole year, the isothermal lines are 
inclined to the meridian by the angle N. 49° W.; and that the temperature in- 
creases in a direction perpendicular to these lines, by -0112 ofa degree for each 
geographical mile, or at the rate of 1 degree for 89 miles. The increase of 
temperature, in proceeding from north to south, is V = 0085, or 1° in 118 
geographical miles ; the corresponding increase, in proceeding from east to west, 
is Y= -0073, or 1° in 137 geographical miles. 

We learn further, that the mean annual isothermal lines furnish a very in- 
adequate representation of the progression of temperature; and that when we 
follow the course of these lines from month to month, we find them to vary within 
very wide limits. The extreme positions of these lines, as given in the preceding 
Table, are those for the months of June and November. But the result obtained 
for the latter month must, I think, be regarded as anomalous, on account of the 
irregularity in the distribution of temperature already noticed; and, rejecting 
it, the extreme positions correspond to the two solstitial months. They are 


the following :— 
june a — No LOG Wayne We 0114, 


December, u=N. 9° W., W=-0104; 

so that the direction of the isothermal lines varies through an angle of 97° in the 
course of the year, being nearly parallel to the meridian in December, and nearly 
perpendicular to itin June. (See Plate vu.) 

We may now employ the formula 

t= T+ Uz + Vy, 

to deduce the probable temperature at any place, and compare it with that ac- 
tually observed; we shall thus find the effect due to local causes. Making this 
calculation for the four inland stations, we obtain the results given in the fol- 
lowing Table :— 

VOL. XXII. 3K 


428 The Rev. H. Luoyn on the Meteorology of Ireland. 


Tasre VII. Catcuratep TEMPERATURES AT INLAND STATIONS. 


] 
Station. Jan. a ee April.| May. | June.| July.} Aug. | Sept.) Oct. | Nov. | Dee. | Year. 
a (—_|—_—_|—_ |__| | 1 
Armagh, ... .| |43°-2 43° age *8}46°4)51° 2}56°-3|58°0)}59" 956 °6152°1 43° Ales 3)50° 
Markree, . . 143 8.43 944 -7\46 751 4/56 2/57 "8160 ‘157 *3)52 °5 45 ° 3/45 « 950 °5 
Portarlington, . . [44 244 “344 “6/47 052 ‘257 -0/59 °3'60 857: 4152 743 5/45 -6)50 °7 
Athy,....+- 44 an ee “5/47 fhe we "2/59 wat ia id *843 1/45 ‘5/50 ‘7 
| | 


Defect of observed Temperatures. 


Station. |= Feb. | Mar. April. | May. Pane! Aug. | Sept. | Oct. | Nov. | Dec. | Year. 

| 
Armagh, . . ‘ 1°8 eae 1°0 | 0°9 O° 1 | O%9 | 193 | 1%3 | 197 | 2:04 | V1 | 1%4 
Markee... 4-4/2 °7/2 4/1 -4]1-3/0-5]1 -2)1 °4/2 °2/2°7)3 5/3 -7)2°3 
Portarlington, . | 3 6|3°71/4-1/3°9/3 1/2 °2)2:0/3:1/3°7)2°6/4°1/5 3/3 4 
IN WAcI OG OO 3513 -4/2-°7/ 1-6/1 -8/0°3)1 -4)0°1)/3 °8)1 81/3 -4)4 -2)2°3 


We learn that the defect of temperature due to inland position is, as might 
have been expected, least in summer and greatest in winter. A small part of 
this defect is due to elevation: but itis easily eliminated. The mean height of 
the instruments at the coast stations above the level of the sea is 30 feet. We 
have, therefore, only to subduct this from the known heights at the inland sta- 
tions, and to correct for the difference of level at the rate of 1° Fahr. for 276 
feet, which is the mean of the determinations made by Mr. Wetsu in his bal- 
loon ascents, for the lower portion of the atmosphere lying beneath the great 
vapour plane. The mean yearly results at the four inland stations, thus corrected , 
are as follow :— 


OMe aberSen «Comet, re 
Anmaghy: 5). = 1°-4 211 —0°7 0°-7 
Markrees.) 2 3) 4 2B 182 — 0-4 1-9 
Portarlington, . . 34 230 —0O7 2-7 
Athy, . Hilo 6 2°3 200 - —0°6 ren 


Mean = 1°8 


ive) 


The Rev. H. Luoyp on the Meteorology of Ireland. 42 


Drurnat RANGES oF TEMPERATURE. 


Climatology depends upon the ranges of temperature (whether diurnal, 
monthly, or annual), no less than upon mean values ; and their investigation is 
accordingly a necessary part of the present inquiry. In the present series of 
observations, the diurnal ranges of temperature are given by means of the results 
obtained with self-registering thermometers. These results are the least satis- 
factory portion of the whole series. It is well known that the ordinary self-regis- 
tering thermometers are extremely apt to get out of order, the maximum by the 
index becoming entangled in the mercury, and the minimum by the distillation 
of the spirit into the upper part of the tube; and although the observers were 
carefully instructed in the mode of remedying these derangements, no one (I 
believe) who has handled such instruments will wonder that men previously 
unaceustomed to them should have sometimes failed in what is in all cases a 
somewhat delicate operation. The blanks in the Table of maximum temper- 
ature at Buncrana and Killybegs, and those in the Table of minimum tem- 
perature at Killybegs and Dunmore, are due to this cause. 

But there is another source of error affecting the maximum thermometer, 
which it is still more difficult to avoid. If the instrument be exposed to the 
influence of radiation for any portion of the day, however short, it will, from its 
construction, retain the impression made upon it; and consequently, if the ab- 
normal temperature to which it has been thus subjected exceed the greatest 
temperature of the air in the day, an erroneous result will be recorded. The 
difficulty of guarding thermometers completely from such influences is well 
known; and although some trouble was taken to insure this protection, the 
observations themselves show that it was not effective at all the stations. I 
have, accordingly, been compelled to reject a portion of the results obtained 
with the maximum thermometer at Killough, Courtown, Kilrush, and Dunmore, 
as defective from this cause. 

The results are given in the following Tables. Table vu. contains the 
monthly means of the maximum temperature in each day; Table rx. those of 
the minimum temperature; and Table x. the differences of the two preceding, 
or the monthly means of the diurnal ranges. 

3K 2 


430 __ The Rev. H. Lroyp on the Meteorology of Ireland. 


Tasre VIII. Maxrmum Temperatures (Montuty Means). 


| | 
Station. | Jan. | Feb. | Mar. | April. | May. | June. | July. | Aug. | Sept. | Oct. | Nov. | Dec. 
a | | 
Portrush, - . . |47°5 |47°.7 |47°7 | 52°-2 | 56%5 | 61°-9 | 63°-9 | 65°-7 | 63°3 | 56°6 | 49°-0 | 48°-2 
Buncrana, . . |45 9/47 -1|48 -8|52 -6|57 -1|63°9| — | — |.— | — | — | — 
Donaghadee, . |47 ‘8 |48 -0|48 -5|52 -3/57 6/63 5 | 64 -2|66 -3/63 -2|57 0/47 °8|48 8 
Killybegs,. . . |47 °8|48 -4/50 1/55 -1|59-2/62-4)| — | — | — | — | — | — 
Armagh, .. . |47 °5|47 -6|48 -4|52 -8|57 -4| 64 °5| 64 8/67 0/62 -9|56 -4)45 -7|47 0 
Killough, .. . }48 8,47 6/48 8] — ; — | — ; — | — | — /[59°1/48°5/48 6 
Markree, . . . |46 6/48 0/49 5/53 -3|58 -4|67 -4| 65 “9/67 -2| 64 ‘1| 56 -3!48 0/46 9 
Dublin, . . . . |50°1/49 5|49 -8|53 3/58 -3|65 5 65 °7|68 -4|62 -9| 58 -4/ 46 -7| 48 6 
Portarlington, | 48 -0/| 48 -3| 48 -8|52 -8 58 8/66 -0 66 -0| 67 -6|64 -9| 57 ‘9 46 6/46 6 
Athy suoweieoua 47 -5|47 7/49 -2|54 -2/ 59 -0|66 -6| 66 -7| 69 6 62 6/57 .7 45 -8) 46 -4 
Gourtown, . 4, = >= | = | = 67 2\69 -2|64-6| 58-7 47 -4)489 
Kilrush,. . . . |49 0/49 -3/50-4| — | — | — isc ie! la 57 3/49 -0|48°1 
Dunmore,. . . |48 6/48 -4/50°5} — | — | — | — | — — |54°9)45 0/48 +1 
Cahirciveen, . |50 2/49 -6/49-7} — | — | — | — |63 -5|57+1|50°2| 49 °7 
ee "1 | 50 -5 | 52 0/54 +1 61 -3| 64 -3 | 66 -7| 68 -3|65 °3| 57 9 AT 6 | 47 0 
\ | | 


| | | 
Station. Jan. | Feb. | Mar. April. | May. | June. | July. | Aug. | Sept. | Oct. | Nov. Dec. 
Portrush, . . . | 36°2 | 36°8 | 37°-2 40°-0 | 45°°4 49°°8 | §2°-5 |53°°0| 49°:6 | 46°-1 | 39°°6 | 38°'8 
Buncrana, . - |37 *1| 36 *8| 38 *1/ 39 -4| 45 4/49 -9/52 4/53 5) 49 +1 45 °8| 37 °8| 38 °9 
Donaghadee, . | 39 °3| 40 -0| 39 6| 43 -4/ 46 -9/50 -9/53 0/54 3/53 -0 47 6/39 9/41 -9 
Killybegs, . . |39 -9|39 7/41 -1|41 -5|/46-5|49-1) — | — SES | S| 
Armagh, .. . | 35 °7| 36 -9| 36 °7| 39 -3| 44 °3|50 -2/52 °3|53 3/50 °3|45 9 36 6 | 38 ‘6 
Killough, . . . |40 -2| 39 -0)39 2/41 6) 44 6 49 -8/ 52 °3)53 -6)51 -6| 47 0 | 36 5 |40 -0 
Markree, .. . 134-4! 36 0/36 *1! 38 -9| 44 ‘8/50 -0|52 9/54 -4| 49 ‘7/46 8) 38 1/38 ‘0 
Dublin, ... . |41 -0|41 -2|40 -6| 43 -0| 47 -0| 52 0/54 8/57 -2|51 -0| 48 -4/ 38 -7| 40 °6 
Portarlington, | 35 °5| 35 +1|34 -8| 36 -4|42 -4|47 -1|51 -2|50 -7| 45 -9| 44 “7 | 34 4) 35 9 
IMA 6 ooo | 36 -0| 36 *1 | 36 -7| 39 -2| 44 -8|50 -1|52 -4|54 -7| 47 -3) 46 -3| 35 -4) 37 “7 
Courtown, .. | 36 ‘2/38 -0/38 ‘0/41 -2)46 -0/ 50 -9|54 1/55 -6|50 6) 46 3, 361/40 4 
Kilrush, .. - |39 -5| 40 +2|40 -3) 42-1 |47 -4) 49 -0|52 -2|54 -0|50 0| 45 -2) 38 -3|41 -4 
Dunmore, . . - | 39 ‘2/39 9/40 -0| 42 -7| 47 5/53 0/56 -6|58 -8)55 5) — | — | — 
Cahirciveen, . | 41 *2| 42 -3/42 -2| 43 -9| 49 -1|53 -2'56 -0|58 *6|54 4/50 -2) 43 0) 43:1 
Castletownsend,| 40 -7| 41 -6|40 4 | 42 9/47 7/51 °3|55 -1|57 -4|55 -0| 49 *6|40 ‘7/42 -7 
| | | 


The Rev. H. Luoyp on the Meteorology of Ireland. 431 


Tasre X. Drurnar Rances or TEMPERATURE (Monruty Means). 


l 

Station. Mar. | April. | May. | June. | July. | Aug. | Sept. | Oct. Nov. | 

| 
Portrush, . . . |11°%3|10%9|10%5 | 12°2| 11° | 12°1|11%4|12%7 |13°°7| 10°-5) 9%4| 9°4 
Buncrana, . | 8°8)10 °3)10°7|13 .2 11-7 | 14:0) =i) e— _ — —|— 
Donaghadee, . | 8°5) 8-0) 8°9| 89/10 -7 |12°6|11 -2)12-0/10-2/ 9-4) 7:9) 6-9 
Killybegs, T9187 uorOl 13-0 F2'7 13-3 |e | ee een ee ie a 
Armagh, .. . {11 °8/10 -7|11 -7/13 5/13 -1 |14 -3/12 -5|13 -7|12-6|10-5| 9-1| 8-4 
Kallonenye seal Sole Oi-6 en) ay g| an | | een eed 12-0) 86 
Markree, . . . [12 2/12 -0/13 4114 -4|13 6 |17 -4|13 0/12 -8|14-4! 9-5) 9-9) 8-9 
Dublin, ....| 9-1] 8-3] 92/10 -3/11 -3 |13 :5|10 9/11 -2/11 9/100) 8-0] 8-0 
Portarlington, | 12 °5|13 -2/14 -0/ 16 4/16 -4 |18-9| 14 -8)16 -9|19 0) 13 -2| 12 -2,10 7 
Athy, ....~ [11 °5/11 6/12 5/15 -0| 14 -2 |16 5/14 3/14 -9|15 3/11 -4) 10-4) 8-7 
Courtown, — | — | — | — | —-| — 113°1)13 6/14 0/12 -4) 11-3) 85 
Kilrush, GO) 3i) GoM a) he S| a Ns TN <eAll ai <7/ 
Dunmore,... | 9-4] 8°5|/10°5; — | — —)/—-}]—/]—);—-);-)j)=— 
Gahirciveens) 919-0) 7-37 ole | oe, ee | — =) 2 get) 69) 7-21) Gira 
Castletownsend,| 9°4} 8 9/11 -6/11°2)13-6 13-0} 11 6/10 °9|10 -3| 8:3} 6°9) 4°3 


In the following Table are given the results of the last of the preceding, 
combined in yearly and half-yearly periods, retaining only those stations at which 
one or other of the two half-years is complete :— 


Tasre XI. Drurnat Ranczs (Hatr-yearty anp YEarty Means). 


T 
Station. Summer. | Winter. | Year. 


° 
° 


— 


Portrush, , 
Donaghadee, . . . 
Armagh, 
Killough, 
Markree,..... 
Dublin, 
Portarlington, . . 


- 
— 
Too 


PISADSHSHWY 


i 
TID HN DH OODS 
ya 
we OW | 

SOER DAW 


Cahirciveen, ... 
Castletownsend, . 


we 


Coast Stations, . 
Inland do, ... 
Differences, . . 


432 The Rev. H. Luoyp on the Meteorology of Ireland. 


From the mean results of the preceding Table, we learn that the diurnal 
range is greater at the inland than at the coast stations, the mean excess being 
2-8 degrees. The excess is greater in summer than in winter, being 3°3 in the 
former, and 2°-4 in the latter season. 


We are now in a position to refer to one, at least, of the practical inferences 
which may be deduced from the preceding results. 

The climatological conditions connected with temperature, which favour 
the prevention or cure of diseases of the lungs, are, firstly, a high winter tem- 
perature ; and secondly, a small amount of diurnal range. It has been already 
stated that Ireland is well circumstanced as to these conditions; let us now in- 
quire which is its most favourable region as respects them. 

The months of lowest temperature in Ireland, and which are on that 
account the most trying to the patients above alluded to, are those of 
December, January, February, and March. During these months the mean 
temperature varies very little, the mean range at Dublin being from 41°-7, in 
January, to 45°-4, in March, or only 3-7 degrees. Now the mean direction of 
the isothermal lines for these four months is N. 37° W.; so that the highest 
mean temperature for these months is to be found on the south-western coast, 
not far from Valentia. 

The second condition above mentioned, although not frequently taken into 
account, is, perhaps, still more important. In proof of this it may be men- 
tioned that in Norway, which is remarkable for the small amount of the diurnal 
range of temperature, consumption is uncommon, even in the highest latitudes ; 
while in parts of Sweden, where this condition does not hold, it is very 
prevalent. Now, we learn from Table x1, that among the stations at which 
observations were made in 1851, the winter diurnal range of temperature is 
least at Cahirciveen. Both conditions, therefore, point to the south-western 
coast of Kerry as the region in Ireland most favourable to patients affected with 
these formidable maladies. 

I am not in possession of any statistical data bearing upon this question, 
and am therefore unable to say how far the conclusion thus drawn is borne out 
by facts. 


Oo 


The Rev. H. Lioyp on the Meteorology of Ireland. 43 


TEMPERATURE OF THE SEA. 


Provision was made that the temperature of the sea should be observed at 
all the places at which tidal observations were made. For this purpose each 
station was furnished with a thermometer, having its bulb inclosed within a 
small reservoir of copper, for the double purpose of guarding it from accident, 
and of protecting it (by means of the contained water) from rapid changes of 
temperature when it was lifted into the air for observation. The observer was 
instructed to note its indications twice in the day, at intervals of about twelve 
hours, the thermometer being attached to a pole, and plunged to the depth of 
about one foot in deep water. The diurnal change of the temperature of the 
sea being very small, it is completely eliminated by two such observations. At 
many of the stations the instrument was lost, or broken, in the attempt to use 
it during boisterous weather. We are, therefore, only in possession of results 
from six stations, which are contained in the following Table :— 


Taste XII. Trmprrature or THE SEA (Montuty Means). 


| | | 

Station. Jan. | Feb. | Mar.| Apr. | May. Spel Hae Aug. | Sept. | Oct. Nov. | Dec. Year, 

fil | GF Oba eT Bees 

} | | 
Portrush, . .- + | 46°9 |45°-6)45°7/47 *9.50°-6 54°. 3\57° 5 58° 7158°7 54°-9149°-6 47°-8 5 1°-5 
Cushendall, . .- . | 46 6 |45 “7/45 *6)47 -2.49 -1/52 155 -457 058 355 “651 649-451 *1 
Donaghadee, .. | 46 °5 |45 *6/45 ‘6/48 -1/50 -3/52 5/55 857 457° 554 ‘7150 149 -3'51 +1 
Bunown, . - - - | 48 °7*|49 -4'50 -9/51 4:54 -4.57 ‘860 -262 -961 -555 149 3/48 °1/54 +1 
Courtown,.... | 46 :0*/45 1/45 8/48 -3/53 -2'58 461 -8) |63 .5.60 -9.56 *1/47 -9.46 8528 
Castletownsend, | 47-1 |46 -646 -8/49 ‘7.53 ‘5.56 360 3161 -360 °354 ‘8 149 248 -652 9 

idl atoll Bebe he | | | | 

Means,).15:t-,«'. « 47 0 |46°3 46°-7/48°8 51°-9'55° o.9\58°- 560° 1 po 5 55°2)4 Peal sales 

Differences, . . . |—5 ‘3 |-5 9-5 ‘6|-3 ‘5-0 443 sik ane ‘OT 243 ‘0|-2 6-3 9 


In the last two lines of the Table are given the mean results of the six sta- 
tions, and the differences between them and the mean of the entire year. These 


* At Bunown and Courtown no observations of sea temperature were made in January. 
The results in the Table for that month are the means of the temperatures of December and 
February. 


434 The Rev. H. Luoyp on the Meteorology of Ireland. 


numbers accordingly exhibit the law of the annual variation of sea temper- 
ature, around the coasts of Ireland; and the remarkable regularity in their 
progression shows that, even from the results of a single year, we obtain a 
close approximation to the actual law. 

We learn from these numbers that the annual change of the sea temper- 
ature, at the surface, differs considerably from that of the air above it, the 
difference consisting chiefly in a retardation of the epochs of maximum and 
minimum. Thus the minimum temperature occurs in the middle of February, 
and the maximum in the middle of August,—or about a month after the cor- 
responding epochs of the temperature of the air. The annual range is also, as 
might have been expected, considerably less than that of the air. These re- 
sults accord sufficiently well with the conclusions drawn by Kurz, from a 
comparison of the results of many voyagers. 

But the most interesting result is that concerning the relation between the 
temperature of the sea at the surface, and that of the superincumbent air. Upon 
this subject the greatest discordance exists in the statements of different ob- 
servers. According to Humpotpt, the mean temperature of the Atlantic 
Ocean, at the surface, is in all cases higher than that of the atmosphere above it- 
This conclusion is confirmed by the observations of Prron and Firzroy, and is 
contradicted by those of Irvine, Forster, and Korzesur. From an elaborate 
discussion of the observations of many voyagers, K xmrz infers that the temper- 
ature of the sea is Jess than that of the air over the land in the lower latitudes, 
while in the higher latitudes it is greater ; the difference seldom, however, ex- 
ceeding 1° Fahr. The original conclusion of Humsoxpr, however, seems to be 
placed beyond all doubt by the recent observations of Captain Duprrrey, which 
appear to be more numerous, and taken with more precautions to insure accu- 
racy, than any preceding. It seems now to be generally admitted that, in the 
temperate and polar regions, the temperature of the sea is hégher than that of the 
air; and the only question that remained was as to the tropics. Now the ob- 
servations of Duperrey were made all round the globe, between 10° N. and 
10°S. latitude ; and they were taken at intervals of four hours, so as completely 
to eliminate the effects of the diurnal change. From these observations it ap- 
pears that the temperature of the sea is higher than that of the air within the 


The Rev. H. Luoyp on the Meteorology of Ireland. 435 


zone already mentioned, the mean excess in the Atlantic being 0°83 Fahr., and 
in the Great Ocean about half that amount. 

The present observations possess much interest in connexion with these 
questions. In order to perceive their bearing, I have, in the Table which fol_ 
lows, given the half-yearly and yearly means of the sea-temperature at the 
several stations, together with the differences between them and the corres- 
ponding means of the temperature of the air. At Cushendall and Bunown no 
observations of the temperature of the air were actually made; and for these sta- 
tions, consequently, the latter means are calculated from the isothermal lines, 


Taste XIII. Temperature oF THE SEA (YEARLY AND Hatr-yearty Mays). 


Summer. Winter. 


Station. 
Temp. Excess. emp. Excess. Temp. 


Portrush. = 3 | 64°06) +120 g° + 3°8 5125 
Cushendall, ... 53 °2 -1:-0 < +44 51:1 
Donaghadee,...| 53°6 | -0°6 Gus 0) || pole 
Bunown, 58-0 | +2°4 2) |) 23)-2) | 541 
Courtown, ....| 57°7 | +2°2 : +30 52 °8 
Castletownsend, .| 56°9 | +0°1 : +15 52 °9 


| 


Means, wow | $0°7 es Leo ere 
| 


It appears from the last line of this Table, that the temperature of the sea is, 
upon the mean of the entire year, 20 higher than that of the air above the coast. 
The excess is 3°3 in winter, and 0°7 insummer. There appears also to be 
considerable diversity in the amount of the excess at the different stations ; 
it is greatest, on the mean of the entire year, at Bunown, and least at Castle- 
townsend. 

This excess of the temperature of the sea above that of the air furnishes the 
explanation of the fact already noticed,—namely, the diminution of the temper- 
ature of the air in proceeding from the coasts inland; for it is obvious that the 
air in the vicinity of the sea must have its temperature raised by contact with 
the water. 

VOL. XXII. 3L 


436 The Rev. H. Luoyp on the Meteorology of Ireland. 


It follows also, that the absolute excess of sea temperature considerably ex- 
ceeds that above stated. Thus, we have seen, the temperature of the sea, on 
the average of the entire year, exceeds that of the air over the coasts by 2°0; 
while the latter temperature exceeds that of the air inland (for the same la- 
titude and longitude) by 1°°8. The total excess of the sea temperature above 
that of the air amounts, therefore, to 3°8 Fahrenheit. 

This excess, which appears to be much greater than has been observed 
elsewhere, is to be ascribed, mainly, to the influence of the gulf-stream upon 
the temperature of that part of the ocean which bathes our shores. But there 
is likewise another cause which undoubtedly contributes also to the effect. It 
has been shown by Mayer and Jouts, that heat is generated by the friction of 
fluids in motion, and the latter experimentalist has established the important 
physical law, that there isa definite relation between the heat so produced, and 
the mechanical power expended by the moving mass. Mr. Ranxive has already 
applied this principle to explain the fact, observed by M. Renou, namely, that 
the temperature of the river Loire at Vendéme is higher than that of the air 
above it; and it is obvious that a similar explanation is applicable to the phe- 
nomenon under consideration. There is no doubt as to the reality of the 
cause; the only question can be as to the magnitude of the effect to be ascribed 
to it. That such effect is, at all events, sensible, Linfer from two circumstances. 
The first of these is, that the phenomenon of the excess of sea temperature appears 
to be general, and must, therefore, be the effect of some general cause; the se- 
cond is, that on the coasts of Ireland there is no sensible difference between the 
amount of the excess on the eastern and on the western shores.* 

Should the effect of this cause be found to be sensible, and its amount be 
determined, our views of the cycle of meteorological phenomena would be much 
enlarged. The elevation of temperature rarefies the air; the denser air flows 
in to supply the partial vacuum, and wind is produced; and finally, this wind, 


* There is another corroborating circumstance which perhaps deserves also to be mentioned, 
Most bathers have, I believe, noticed the fact that the sea appears warmer, ceteris paribus, when 
agitated than when at rest. Iam not aware that any direct thermometrical measures have ever been 
made to establish the fact thus evidenced by the senses; and I need not say that, if established, it 
would bear the whole weight of the hypothesis above proposed. 


The Rev. H. Luoyp on the Meteorology of Ireland. 437 


both by its own motion, and by that of the ocean which is so subject to its power, 
restores again the heat which had been converted. Thus the normal condition 
of temperature is preserved, not only throughout the changes which render it 
latent and sensible, in the generation and condensation of vapour, but also in 
its conversion into mechanical power and its reproduction, in the phenomena of 
the tempest and of the billowy sea. 


BaroMETRIC PRESSURE. 


The following Table contains the ee means of the observed pressures, 
diminished by 28 inches, and reduced to 32° Fahr. : 


Taste XIV. Monruty Means or Barometric Pressure.* 


Station. Jan. | Feb. | Mar. | April. | May. | June. | July. | Aug. | Sept. | Oct. | Noy. | Dee. 
| | | 

| = ae 

Portrush, . . . |1°444/)1:901 |1:628) |1°840 2-030 1-888 |1°790 | 1-939 24 50,1:703 1976/2 123 
Buncrana,. . . |1°377|1 827 1580 1-777 1-968 | 1-849 |1-760 |1-886 |2-1 18 1-681 | 1°972 | 2°102 
Donaghadee, . |1°496|1-930| 1-652 | eee: 036 1: 915 |1-798 | 1-948 |2:152 | 1-728 | 1°950| 27148 
Killybegs,. . . |1-415 )1-868 |1-622 | 1-822 |2:032 1-918 1-828 1-938 2-126) 1-718 2°008 | 2° 112 
Armagh, .. . |1:284|1°722) 1-448} 1-640 | 1:836 | 1-716 |1-603 \1-757 |1-958 |1-540/1- 7961 942 
Killough, . . . |1°614 )1-932 | 1-666 | 1-852 )2-030 | 1-922 /1:806 | 1-963 |2°138 | 1-751 | 1-943 | 2:083 
Markree, . . . |1°356 |1°833|1°537 | 1-741 |1-954 | 1-828 | 1-730) |1-859 2-051 1-648 1-933 ! 2040 
Westport, .. . |1°323 |1:877 1-655 | 831 |2 2-042 |1-900 |1-802 pono 092 | 1°705 | 2:013 | 2074 
Dublin, ,. . . . ;1:569 |1:989| 1-718 |1:887 ‘2-088 | 1-986 |1-860 |2:046 2°206 1-815 | 2-040 | 2-221 
Portarlington, | 1286 |1-687) 1419/1595 | |1-834 ‘1-646 1 592 1-696 |1- *897 | 1-520 | 1-764 | 1:922 
Athy, ... . . 1259/1658) 1-416 1-566 | 1-763 |1-665 |1-556 IG68 1-389) 1533 | 1-753 | 1-914 
Courtown, .. |1:570/1:974|1°710/1:861 2 (066 | 1-983 | 1-852 |2:008 |2-192 | 1-836 | 2-020 | 2-205 
Kilrush, . . . . |1-428 |1-852)1-646 |1-783 |1-998 | 1-896 |1°798 )1-925 }2-117 |1-781 |2:047 |2'120 
Dunmore,. . . |1°511 |1-910|1-666 |1:804 | 2010 |1:930 | 1-804 | 1-942 2-130 1-786. 1-980 | 27144 
Cahirciveen, . |1°484 |1-:884 1-678 |1 ‘787 | |2-026 11-926 1- 826 | 1-949 |2-121 | 1-797 | 2-078 | 2158 
Castletownsend,| 1°528 | 1-948 | 1°741 |1- =) 2: O72 |1-986 y 854 | kai 152 | 1-831 (2084 2:192 


The next Table contains the constant corrections to be applied to the pre- 
ceding results. The first column gives the diameters of the tubes ; the second, 
the instrumental corrections obtained by comparison of the several instruments 
with the Dublin standard by means of portable barometers; the third, the re- 
ductions to the sea-level, calculated at the rate of (0011 of an inch for each 


* The pressure for January, at Westport, is the mean of 17 days only, viz., Jan. 15-31; and 
that for August, at Dublin, is the mean of 15 days, viz., Aug. 1-14. 


3) ih 2 


438 The Rev. H. Luoyp on the Meteorology of Ireland. 


foot of altitude; and the fourth, the sums of the two preceding, or the total 
corrections. 

These results are incomplete, no comparisons having been made of the ba- 
rometers at the four inland stations. For this reason, and also because of the 
uncertainty attending the comparison of barometers by means of portable in- 
struments, I have thought it necessary to seek the corrections also by compa- 
rison of the observed results themselves. In comparisons of the latter kind, 
where the stations are widely separated, it seems necessary to employ the means 
of somewhat extended series of observed results, during which the fluctuations 
of barometric pressure are small. I have accordingly selected for the pur- 
pose the monthly means of May, July, and September, in which months there 
was but little variation of barometric equilibrium. The defects of the means 
at each station compared with those at Dublin, for these months, are given in 
the fifth, sixth, and seventh columns of the Table; and the last column contains 
the inferred corrections, which are equal to the mean differences + ‘021 (the 
reduction of the Dublin results to the sea-level). 


TasLte XV. Barometric Corrections. 


Nae Diameter eat ear. Total Difference from Dublin. | ae 

AE of Tube. Correction.| Sea-level. | Corre ton| Moe Tale Sept. | parison. 
Portrush,... 28 + 032 | +032 | + 064 ‘058 ‘070 “056 + ‘082 
Buncrana,.. . “34 +017 | +:°053 | +-070 120 100 ‘O88 + °124 
Donaghadee, . 30 +049 | +:'018 | + -067 “052 “062 “054 + ‘077 
Killybegs,. . . = — 052 | +022 | — -030 “056 “032 “080 + ‘077 
Armagh, ... ‘67 — + °232 = °252 257 248 | + 273 
Killough, ... ‘28 — 030 ; +°025 | —-:005 058 “054 “068 +081 
Markree, ... — — +7145 = 134 130 155 | +161 
Westport,... — — 007 | +019 | 4-012 “046 058 114 + +094 
Dublin... 55 +003 | +°021 | +:021 “000 “000 ‘000 + :021 
Portarlington, as = e253 — 254 268 309 + 298 
iin Soo do = — + +220 = 325 304 ‘317 + °336 
Courtown, .. 28 +028 | +:°037 | + :040 "022 ‘008 “014 + 036 
Kilrushy.... +32 +:095 | +°021 | +:116 “090 062 “089 +101 
Dunmore,... 32 +:019 | +:°073 |} +-092 ‘O78 "056 ‘076 +091 
Cahirciveen, . 38 +034 | +:°057 | +:091 “062 034 “085 +081 
Castletownsend,, -26 +:012 | +020 | + -072 “016 “006 054 + 046 


It will be seen by comparing the resulting corrections, in the fourth and last 
columns of the preceding Table, that the agreement is satisfactory, except at 


Le 


5 


The Rey. H. Luoyp on the Meteorology of Ireland. 459 


the four stations, Buncrana, Killybegs, Killough, and Westport; the correc- 
tions inferred from a comparison of the results being, at these stations, con- 
siderably greater than those deduced by a comparison of the instruments. This 
may possibly be due, in part, to the entrance of air into the barometer tubes; 
but there seems reason to apprehend that the discrepancy may be also partly 
due to errors of observation, and that of a systematic kind,—the observers at 
the foregoing stations, having shown less aptitude than others for this kind of 
duty. Under the circumstances, the corrections deduced by the latter method 
seem the more reliable. They have accordingly been applied to all the selected 
observations hereafter discussed. 

Applying the foregoing corrections to the results of Table x1v., we obtain 
the numbers of the following Table :— 


Taste XVI. Monruty Means or Barometric PREssuRE, CORRECTED AND REDUCED TO 
Mean SEa-LEVEL. 
| | | 
Station. Jan. | Feb. | Mar. aa May. June. | July. | Aug. | Sept. | Oct. | Nov. | Dee. | | Year. 
| | | | 

Portrush, .. . |1°526}1-983)1- 7101-922 2:112 1-970/1:872/2°021 ‘9. 232 1° 7852-0582 205 1-950 
Bunerana,. . . {1°501/1-951 1°704/1:901 2092 1-973)1 *884/2'010/2-242 1-805 2° 096 2 2°226 1-949 
Donaghadee, . /1'573 2-007 1° 729) 1-929 2-113)1-992)1-875)|2 2 oe 29 1-805 2° 0272 *225/1-961 
Killybegs,. . . |1°492)1:945 1-700 1:900 2-110 1:995)1- 905 2° 015/2°203)1- 795 2 2:085/2°190'1-944 
Armagh, .. . |1°557/1-995 1*721)1- 913 2°110)1°989}1- 876)2 -030|2-231 /1-813/2-069)2-215 1 “960 
Killough, . . . |1°595/2-013!1-747)1-933)2-111)2-003)1-887) 2 044/2°219 1-832 2 2°024)|2°164)1-964 
Markree, . . . |1°517/1-994/1°6981°902 2-115 1-989|1-891 2: 020)2- *212)1-809 2-094)2-201 1-954 
Westport, . . . |1°417|1-97 11 149) 1-925 2-136 1-994 1-896 2:003 27186 1-800 2-107 2: 168 1-946 
Dublin, ... . |1°590/2:010)1: 739| 1-908 2°109/2:007 1-881 2-067 2: 227) 1-836 2-061 2°242 1-973 
Portarlington, {1.584/1-985)1-717)1°893/2°132)1 944) 116 89011: 994 2° 195) 1-818 2-062 2-220 1-953 
Athy, ..... |1*595/1-994)1-752)1-902/2-100 2-001/1-892/2:004 2-225 1-870|2°090)2:250 1-973 
Courtown, 1:606 2-010/1- 746) 1 8972 2°102)2:019 1-888 2+ 044)2" 228)1:872 2: 056 2-241 1-976 
Kilrush,. . . . |1°529/1-953/1:747)1-884|2- 100)1-997)1- 900)2: 026)2° 218)1:882)2- 148 2 221 1-967 
Dunmore,. . . |1'602/2:001/1°757/1°895/2- 1012 2: 021) 1895/2 033 2° 221/1- 877| 2-071/2-235 1-976 
Cahirciveen, 1-565 1-965 1°759|1-868)2-107 2: 007 1-907|2- 0302 2°202)1° Bias 159/2°239 1-974 
Castletownsend, Bi hoe4 787\1 pale 1182 24 032) 1 Ble 0262 27198 1-87 a2 “130 2 238 1-980 


In order to perceive more clearly the simultaneous variations in the distri- 
bution of pressure, I have, in the following Table, combined the stations, and 
their results as given above, into four groups, as hereafter described in treating 
of the observations of wind-force. These are the following :— 


440) The Rev. H. Luoyn on the Meteorology of Ireland. 


Taste XVII. Monruty Means or BARometric PressuRE FoR THE Four Groups oF 
STATIONS. 


April. Dec. | Year. 


May. Sune July. 


Jan. | Feb. | Mar. 


Aug. fear Oct. 


Noy. 


5752-005 1°732 alt: 925|2: 111/1:995 1 *879|2° 035/226 1: 8172-0402 *201)1-962 
475 1 ‘970)1° 715 1 908 2° 120)1-992,1-897 20122: 200 1:801/2-095|2:186]1'948 
‘600 2:007|1°748)1° 900 2+ 104/2:016 1 *888)2-048)2: 226) 1 -862)2°063|2:240|1:975 
556 ova eae 8792 1082" 0121 "902)2" foe 206)1 ‘879.2 mp2 *233|1-974 


North-east, 
North- irae 
South-east, . 
South-west, a 


Cairdurbed 


The phenomena of the distribution of pressure are very clearly shown in 
the foregoing Table. It will be seen from it that, on the average of the entire 
year, there is an excess of pressure in the south of the island, and a defect in the 
north, the minimwm being at the north-western extremity. This excess of 
pressure in the south is likewise shown in the means for the seasons of summer, 
autumn, and winter, respectively; and the cause of it will, I think, hereafter 
appear upon the discussion of the phenomena of storms. In the separate months, 
the points of greatest and least pressure vary somewhat irregularly; but they 
are, in almost every month, at opposite extremities of the island. Thus, in 
January, the maximum pressure is in the south-east, and the minimum in the 
north-west; and so for the others. This circumstance is what should have been 
expected d priori; and it affords satisfactory evidence of the general accuracy 
of the results themselves. 


DimEcTION AND FoRCE OF THE WIND. 


Direction of Wind.—The direction of the wind was observed, at most of 
the stations, by means of the ordinary wind-vane. Much care was, however, 
taken, not only in placing these instruments truly in azimuth, but also in se- 
lecting positions for them which seemed least exposed to eddies or other local 
irregularities. At Armagh and Dublin the direction of the wind was recorded 
continuously, by means of self-registerg anemometers. . 

The following Tables give the number of times, out of 100, in which the 
wind blew from each of the eight points at the several stations ; Tables xvim. and 
XIX. containing the results for the summer and winter half-years, respectively, 


The Rev. H. Luoyp on the Meteorology of Ireland. 441 


and Table xx. those for the entire year. The winds from the intermediate points, 
when observed, were divided equally between the two adjacent principal 
points :—- 


Taste XVIII. Frequency or Tue severat Winps (Summer). 


Station. N. N.E. E. 8. E. Ss. S. W. W. N. W. 
Portrush; =. . 20 5 6 6 24 15 ll 13 
Bunerana, ... 13 8 6 12, 11 19 12 19 
Donaghadee,. .| 23 6 5 13 11 14 16 11 
Killybegs,...| 15 Onl ata TMM: | 13s, | On ae 
Armagh,.... 12 9 1 6 16 19 18 15 
Killough, ... 11 if 14 12 16 18 8 14 
Markree,.... 14 5 4 17 14 15 10 21 
Westport, ...]| 10 10 14 10 3 3 32 19 
Dnblintaeeee sere 2 10 12 13 8 23 11 19 
Portarlington, . 5 28 2 11 7 14 13 21 
AGH YA Gis o 13 1 2 12 16) oh2 25 19 
Courtown,... 13 17 5 Uf 8 23 15 13 
Kalrush:ees 12 10 14 8 8 13 19 17 
Dunmore, ... 15 8 14 5 7 18 8 16 
Cahirciveen. . . 11 9 12 9 12 18 16 14 
Castletownsend, 8 9 11 12 2 37 15 6 


Taste XIX. Frequency or THE SEVERAL WINDS (Wiyter). 


Station. 


Portrush, 
Buncrana, . . 
Donaghadee, . . 
Killybegs, . . . 
Armagh,.... 
Killough, 3 
Markree,. . . 
Westport, ... 
Dablins.. «As. 
Portarlington, . 
IMAM 65 on 
Courtown,... 
Koirrisheeeene 
Dunmore, ... 
Cahirciveen, . . 
Castletownsend, 


= 

AD ROAN KE AHR RADHA 
= 

BWKWOReE ENN ARN DORO DP 


— oe 


442 The Rev. H. Luoyp on the Meteorology of Ireland. 


Taste XX. Frequency oF THE SEVERAL Winps (YEAR). 


Station. N. | NE | E. S.E. 8. S.We |) Ve N.W. 
Portrush, ... 17 4 5 6 30 19 10 8 
Bunerana, ... 12 7 6 11 13 23 14 16 
Donaghadee,..| 16 it 4 10 13 19 21 10 
Killybegs, ...|] 13 8 11 8 10 16 20 15 
Armagh,.... 9 1 4 5 21 27 15 12 
Killough, ...{ 10 5 9 8 17 21 10 19 
Markree,.... 13 4 4 18 17 19 10 16 
Westport, ...| Il 7 13 10 4 5 29 20 
DD ablins were te) © 2 6 7 14 ill 31 1153 16 
Portarlington, . 5 19 1 7 9 16 16 25 
Athy, »...- 10 2 1 13 22 12 24 16 
Courtown,... 10 11 4 6 13 23 19 14 
Kilrush, .... 11 9 12 7 12 18 16 16 
Dunmore, ... 15 6 9 5 11 19 20 16 
Cahirciveen, .. 9 8 13 10 12 19 17 12 
Castletownsend, | 10 7 q 9 3 36 18 9 


The following are the mean results for the whole island:— 


N. N. E. E. S. E. S. Ss. W. W. N. W. 
Summer,. .. 12:3, 9:4, 89, 10:0, 107, 171, 163, 157. 
Winter, ... 9:6, 52, 50, 86, 16-4, 234, 17-6, 14-4. 
Year... - 108) 73, BO. 98, - 13672209, 17-0, 150. 


We learn from them that, in the year 1851, the wind blew, on the average 
of the entire year, most frequently from between S.W. and W., and least fre- 
quently from between N.E. and E. The same thing holds also for the sum- 
mer half-year, the point of maximum frequency being, very nearly, W.S.W., 
and that of minimum frequency E.N.E. In the winter half-year the point of 
maximum frequency is more nearly S. W., that of the minimum being as before. 
The ratio of the numbers representing the greatest and least frequency is greater 
in winter than in summer. 

It is not necessary to enter more minutely into the discussion of the num- 
bers of the preceding Tables, as it is probable that the results of a single year, as 
to the frequency of the several winds, will deviate considerably from the means 
of several. I may observe, however, that they afford some indications of a law 


The Rev. H. Lioyp on the Meteorology of Lreland. 443 


of distribution, depending upon the aspect of the coast. Thus, on com- 
paring the numbers denoting the frequency of any particular wind at the se- 
veral stations, with their mean for the whole island, it would seem that easterly 
winds are slightly in excess on the western coast, and westerly winds on 
the eastern. In other words, there appears to be a preponderating tendency 
of the wind to blow from the land, at each place, as compared with the mean 
of all. It will remain for future inquiry to ascertain whether this holds good 
in other years, and is, therefore, to be referred to a general law. If so, it 
is probably the effect of the land and sea breezes, the former preponderating 
in the average of the winds at 9 a.m. and 9 Pp. M. 


Pressure of the Wind.—For the measurement of the pressure of the wind, 
a Lind’s anemometer was furnished to each station. The difficulty of ob- 
taining accurate results with this little instrument arise, partly, from the small- 
ness of its indications, and, partly, from the oscillations of the fluid in the 
tube; the latter are so considerable as to render the instrument of little value, 
except in the hands of a patient and somewhat practised oberver. After 
some trial, accordingly, it was deemed advisable that the force of the wind 
should be in all cases estimated, and that the use of Lind’s anemometer should 
be limited to that of furnishing a check upon this estimation in the case of the 
stronger winds. 

The first thing to be determined, then, was the choice of a scale of force. 
The scales in use are various: in one of them there are four degrees of wind- 
force ; in another, siz; and ina third (the Admiralty scale) there are twelve. The 
last of these appears to be too minute for the ordinary powers of unaided esti- 
mation, and the first not sufficiently so. The intermediate scale (from 0 to 6), 
was accordingly adopted; and it appears to be further recommended by the 
circumstances,—1, that it is the subdivision most generally used on the Conti- 
nent; and 2, that, as its numbers represent the same degrees of wind-force with 
the alternate numbers of the Admiralty scale, the latter are convertible into the 
former by simply dividing by two. The six degrees of wind-force were desig- 
nated as follow :—1. Light breeze ; 2. Moderate breeze ; 3. Strong breeze ; 4. Mo- 
derate gale; 5. Strong gale; 6. Storm. 

VOL. XXII. 3M 


444 The Rev. H. Luoyp on the Meteorology of Ireland. 


In order to know the amount of confidence which may be placed in such 
observations, it is necessary to determine how far, in respect of accuracy, six 
degrees of wind-force can be estimated, the observations being supposed to 
be made by practised observers. And to be able to apply the observations, we 
must further know, what are the pressures and velocities of the wind corres- 
ponding to the several terms of the scale. For these purposes I made a somewhat 
extended series of observations, estimating the force of the wind according to 
the prescribed scale, and, at the same time, measuring its velocity by means of 
Robinson’s anemometer. The following Table gives the mean results of these 
observations. The numbers in the first column are the terms of the scale; those 
in the second are the corresponding times of 100 revolutions of the instrument, 
expressed in seconds ;* the third column contains the corresponding velocities 
of the wind, in feet per second; and the fourth the calculated velocities, de- 
duced as hereafter described. 


TasLte XXI. Vetociries oF THE WIND CORRESPONDING TO THE TERMS OF THE 


Scare (0 - 6). 
n vi V (observed). iv (calculated). 
if 71 Oona 
II. 35 ee | een23 
0G 25 35 35 
IV. 20 43 46 
iV; 16:8 51 58 
VI. 116 ii |) ee 


* Dr. Rosinson has shown (Transactions, vol. xxii. p. 167), that the velocity of the wind is to that 
of the centres of the hemispherical cups, as 3to1. But 7 being the length of the horizontal arms of 
the instrument, measured to these centres, the circumference of the circle described by them is 27r; 
and if 7 be expressed in feet, and m be the number of revolutions performed in a second, their 
velocity is 2xr xn. The corresponding velocity of the wind therefore is V=6zrxn. In the 


c $ ; eK. : 11 ain 
instrument in my possession, the radius is 5°5 inches. Hence 27 = 12’ and substituting for 7 


its numerical value, V = 8°64 x n. 
Instead of noting the number of revolutions, and parts of a revolution, performed in a given 
time, I have found it convenient to observe the time of performing 100 revolutions. I have had 


The Rev. H. Luoyn on the Meteorology of Ireland. 445 


We see that the terms of the estimated scale correspond, nearly, to an 
arithmetical progression of velocities, and not of pressures. This fact has been 
already noticed by Dr. Roxrnson. 

The common difference in this series, which is equal to its first term, is 
obtained from the numbers of the third column by means of the formula 
V=nV,. The following are the deduced values :-— 


Vig 9 == PY, Vee —sl0re 
Il. 12°5 V. 10:2 
IIL. bile WAL 12°5 


The mean of these values is V,=11°6. The calculated values of V, con- 
tained in the last column of the foregoing Table, are, accordingly, obtained from 
the formula 

VEMW6xn- 
their agreement with the observed values is sufficient to establish the assumed 
law. 

As a verification of the preceding result, I took also a tolerably extended 
series of measurements of the pressures of the wind, corresponding to the highest 
term of the scale, with Lind’s anemometer. Their mean gave 2:06 inches for 
the reading of the instrument corresponding to that term; and the corre- 
sponding pressure on one square foot of surface, computed in the proportion of 
5:20 pounds to the inch, is 10°7 pounds. Hence, the pressure belonging to 
the unit of the scale is P; = 0°30. The corresponding velocity is inferred from 
the formula V?= 437 P. Its value is V; = 11°5; a result which agrees very 
closely with that already deduced from Rosryson’s anemometer. 

The results hitherto given rest only on my own estimations; it remains 


the instrument accordingly provided with a little hammer, which is pressed against the regis- 
tering wheel by a spring, and which, being raised by a projecting pin at one point of its circum- 
ference, falls again with a sharp noise when this has passed. The interval between two such 
strokes of the hammer, therefore, is the time of one whole revolution of the registering wheel, or of 
100 revolutions of the arms. Accordingly, a chronometer being held close to the ear, the whole 
observation is effected by the help of that organ, The velocity of the wind in this case is given 
by the formula V = Boe T being the observed time of 100 revolutions. 


Tt 
3M 2 


446 The Rev. H. Luoyp on the Meteorology of Ireland. 


to see how far they accord with those of other observers. I have selected for 
this purpose the results of the observations with Lind’s anemometer, made 
at Portrush and Donaghadee by two of the best of the coast-guard. observers, 
and have placed my own beside them, for comparison. The results, converted 
into pressures (expressed in pounds on the square foot), are contained in the 
following Table. The numbers in the last column are the calculated pressures, 
deduced from the formula 
[Ps IEF 


n being the number of the term of the scale, and P, (= 0°30) the pressure cor- 
responding to the first term. 


Taste XXII. OsservaTIONs OF THE PRESSURES OF THE WIND CORRESPONDING TO THE 
TERMS OF THE ScaLE (0 — 6). 


Calculated. 


. in, Donaghadee. 
L 05 0-4 05 
IL. 1:3 fe 1-1 


13 
III. 3:0 2-9 29 
TVs 4:2 | 53 53 
V. 70 | 3 79 


It will be seen, that the differences of the corresponding numbers at the 
three stations are small, and that their means agree very well with the calculated 
pressures. It seems therefore to be fully proved, that the velocity of the 
wind may be estimated to six degrees, by practised observers, with sufficient 
accuracy. 

The following Table contains the monthly means of the observed wind- 
force, in the terms of the prescribed scale. At Buncrana and Westport the 
force appears to have been over-estimated; at the other stations it seems to 
have been correctly observed :— 


The Rev. H. Lioyp on the Meteorology of Ireland. 447 


Taste XXIII. Monruty Means or THE Force or THE WIND. 


Station. 


by} 
is 
ia 
—] 
= 
= 
By 
eo 
S 
ot 
oy 
=] 
=z 
io 
i] 
oR 
vA 
° 
a 
\~] 
8 


Portrush, 
Bunecrana, . 
Donaghadee, . . 
Killybegs, ... 
Armagh,.... 
Killough,.... 
Markree,.... 
Westport, . 


Portarlington, . 
Athy, 
Courtown,... 
Kilrush, .. 
Dunmore, 
Cahirciveen, .. 
Castletownsend, 


Nee RRP wR NHE NEN 
WAWAKRSCONAN®WSO 


SS 
ro) 


WSSHOAHKHHAALSNASA 
tS 
wo 


Oe Oe ne 
OURO et RO = te) ROO) Ee ae eS 
BH BOAANWARKAWHDHNS 
WAEOAARMWWEAARAKRK WAG 
a el ell lal 
ADBDABAN ANANWARN=T 
ROT Ileal Neel <add order Ly 
=H KH SORNOCAINAOHS AAA 

ADSSNHARAKOA-URSA 
TAOARANOSDANACSAWOW 
et ee 
ADARDOKHKNADEASHRH 
NNWNK RK RK KON RK NR Re NH 
ANKE ADBSOSHUAWHHOAKE TD 


to 
n 


| 
| 
| 
| 


Means,. . 


— 
a 
_ 
— 
1 
co 


The lowest line of the preceding Table contains the mean results of all the 
stations, or the average forces of the wind in the several months for the whole 
island. The mean force for the entire year is 1:76, corresponding to a velo- 
city of 20-4 feet per second. The force is, of course, greater in winter than 
in summer, the mean force for the winter half-year being 1°87, and that for the 
summer half-year 165. The law of the annual progression is, however, greatly 
masked by irregularities; thus, the minimum force for the year 1851 occurs 
in the month of September, while the force in June is above the average of 
the entire year. 

In the following Table are given the results of the preceding for the entire 
year, and for its two principal divisions. The excess of the force in winter 
appears at all the stations, excepting Dublin, Portarlington, and Athy.* At 
these three stations, also, the force of the wind is much below the average. 


* Buncrana is likewise an exceptional case; but the exception is there probably due to 
inaccuracy of observation. 


448 The Rey. H. Luoyp on the Meteorology of Ireiand. 


Tante XXIV. Mean Force of THE WIND FOR THE SUMMER AND WINTER Hate-YEars, 
AND FOR THE WHOLE YEAR. 


Station. Summer. Winter. Year. 
Portrush,. ...- | 1°68 1°85 1:77 
Buncrana, ....- 2:15 2:15 2715 
Donaghadee,...| 1:50 1:82 1-66 
Killybegs, ..-- 1:40 1°75 | 158 
Armagh, ..... 1:23 1-78 151 
Killough,..... 1:60 1:92 1:76 
Markree,.....- 168 1:82 1-75 
Westport, ....- 2°20 2°78 2:49 
Dwbling aon ecrets 1:33 1:32 1:33 
Portarlington, . . 1-42 1:27 1:34 
Rigo ok ae 1-42 1-20 131 
Courtown, .... 1:40 1:70 1:55 
Kilrush, .....- 1:72 2:02 1:87 
Dunmore serene 1:88 2:03 1-96 
Cahirciveen, ... 1:80 2:17 1:98 
Castletownsend, . 1:93 2°38 2:16 


If, to eliminate local irregularities, we combine the preceding results in 
groups, according to the arrangement hereafter described, we find the following 
values for the mean forces of the entire year: 

North-east, . . - 1°64 North-west, . . . 1°94 
South-east, . . . 161 South-west, . . . 2°00 


From this it appears that the mean force of the wind is considerably greater in 
the west of the island than in the east, the ratio being somewhat greater than 
that of 1:2 tol. There is but little difference between the forces in the northern 
and southern portions of the island. 


Cyctonic MovEMENrts. 


In analyzing the phenomena of rotation, the first step was to note those 
cases in which the mean directions of the wind, in any two districts, differed by 
90°, or upwards. It was soon perceived, that no conclusion could be drawn as 
to a general movement of the atmosphere, when the wind was very moderate, 
the direction being then greatly influenced by local causes. Accordingly, ex- 
cluding those cases in which the wind did not exceed a light breeze at most 
of the stations, the remainder were examined in detail, by laying down the 


The Rev. H. Luoyp on the Meteorology of Ireland. 449 


simultaneous directions of the wind upon a series of skeleton charts prepared 
for the purpose ; and there was no difficulty in ascertaining, by the inspection of 
these charts, the existence or non-existence of rotatory movement. The same 
means sufficed to determine, very nearly, the position of the centre of the vor- 
tex at each epoch; and the places of the centre being thus found, for epochs 
distant by intervals of twelve hours, the direction and velocity of its progres- 
sive movement are ascertained. 

The position of the centre of the vortex at any instant may be determined, 
more accurately, by calculation. Thus, if y and « denote the distances (in 
geographical miles) of the place of observation from any assumed central 
point, measured on the meridian, and on the perpendicular to the meridian, 
respectively ; y and a the corresponding co-ordinates of the centre of the vor- 
tex; and @ the angle which the direction of the wind at the point (y, v7) makes 
with the meridian, measuring from north to east; 

¥ — Yo + (a — %) tan 0 = 0, 

the direction of the wind being perpendicular to the line connecting the points 
(y, 2) and (y, 2). Now, all the quantities in this equation are given, ex- 
cepting y, and 2; so that, if the direction of the wind be accurately known 
at two stations, the co-ordinates of the centre of the vortex may be completely 
determined. The irregularities due to local causes, and the errors of obser- 
vation themselves, forbid this; and, in order to lessen their influence, it is ne- 
cessary to know the direction of the wind at several stations. There will then 
be as many equations of the preceding form, as there are places of observation ; 
and the unknown quantities, y and x), are to be determined by combining 
these equations by the method of least squares. 

It is found, that the centre of the vortex is also the point of least barometric 
pressure, and that the pressure increases regularly with the distance from it. 
Hence the position of the centre may be inferred from the barometric observa- 
tions alone. The positions thus determined have been found to coincide in all 
cases, very nearly, with those deduced from the observed directions of the wind. 

The following are the well-marked instances of aerial rotation which have 
occurred in Ireland in the course of these observations. No case has been in- 
cluded in the enumeration, in which the simultaneous directions of the wind 
did not differ, at two points, by at least 90°; and thus, probably, many cases 


450 The Rev. H. Luoyp on the Meteorology of Ireland. 


of cyclonic movement are passed over, in which the centre of the vortex was 
remote. The observations themselves are given in detail in Table xxxu1., at 
the end of this Paper.* The following are their principal results ;— 


1850. Oct. 6, 7.—Cyclone and storm, moving from 8. W. to N.E., with a 
velocity of about 290 geographical miles per diem. (Plate vim. Figs. 1, 2, 3.) 

Oct. 6, 9 A. m.—Centre of the vortex on the south-western coast of Ireland, 
west of Kilrush. Least pressure at Cahirciveen. Mean velocity of the wind 
= 25 feet per second; greatest do. (on the west coast) = 45 feet. The atmo- 
sphere at the northern stations unaffected by the vortex at this epoch. 

Oct. 6, 9 Pp. Ma—Centre of the vortex over the north of Ireland, a few miles 
north of Killybegs. Absolute barometric minimum (= 28°836) at Killybegs ; 
increase of pressure in 100 miles =0°30 inch. Mean velocity of wind = 35 feet 
per second; greatest do. (Markree)=70. Southern stations unaffected by the 
vortex. 

Oct. 7, 9 A. m.—Centre on south-western coast of Scotland. Least pressure 
at Donaghadee. Mean velocity of wind = 45 feet per second; greatest do. 
(north coast) = 60 feet. Hail fell at Markree; wind amounting to a gale in 
the north, in the evening of the same day. 

The diameter of the vortex may be estimated with tolerable precision in 
this case, by measuring from the centre to the limits of the region affected by 
the movement; it was about 280 geographical miles. 


Oct. 22, 23.—An interesting and instructive case of conflicting currents 
generating a rotatory movement. The velocity of the wind was uniform 
throughout the island, and was from 30 to 35 feet per second. (Plate vim. 
Figs. 4, 5, 6.) 

Oct. 22, 9 p. am—Wind from N. W. in the north of Ireland, and from 8. W. 
in the south-east. The central point of junction of these currents was over 
the channel, to the north-east of Dublin. Least pressure at Donaghadee. 


* It seems certain that a careful study of the simultaneous atmospheric phenomena, even in a 
limited district, will throw more light upon the “ law of storms,” than any other mode of inquiry ; 
and for this reason, as well as for the authentication of my own inferences, I have thought it right 
to give these observations in ertenso. Itis probable that an attentive examination of them may elicit 
many conclusions which have escaped my notice. 


The Rev. H. Luoyn on the Meteorology of Ireland. 451 


Oct. 28, 9 a.m.—A distinct rotatory movement, whose centre was a little 
to the north-east of the point of junction above referred to, not far from Donagh- 
adee. Least pressure at Donaghadee, as before. 

Oct. 23, 9 p. m.—Rotatory movement continued. Centre of vortex had 
moved from S. W. to N. E., at the rate of about 100 miles per diem. Absolute 
minimum of pressure (= 29°360) at Donaghadee; increase of pressure in 100 
miles = 0:10 inch. 


Nov. 18, 19.—A cyclone, with violent storm, crossing the island from 
W.S.W. to E.N.E. (Plate 1x. Figs. 1,2,3.) The movement of the centre of 
the vortex appears to have been curvilinear, and to have varied considerably 
in velocity. Between 9 p.m. of the 18th, and 9 a.m. of the following day, its 
path was from 8. W. to N.E., and its velocity about 320 miles per diem; in 
the succeeding twelve hours its course was nearly from W. to E., with a greatly 
diminished velocity. The mean velocity of the wind, throughout the storm, was 
from 45 to 50 feet per second. 

Nov. 18, 9 vp. a—Centre of the vortex on the south-western coast, about 30 
miles to the north of Cahirciveen. Least pressure at Kilrush. Maximum ve- 
locity of wind (in south of island) = 60 feet per second. 

Noy. 19, 9 A. m.—At this epoch the wind was blowing from N. at Killybegs, 
and from §S. at Donaghadee; it was blowing from S. E. at Portrush, and from 
N.W. at Castletownsend; from §.S.E. at Armagh, and from N. N. W. at Mark- 
ree. The centre of the vortex was therefore over Ireland at that time,-and 
between the stations above mentioned, its exact position being about 15 miles to 
the west of Armagh. Absolute minimum of pressure (= 28-248) at Armagh; 
increase of pressure = 031 inch. Maximum velocity of wind (in south) = 65 
feet per second. 

Noy. 19, 9 p. m.—Centre over the Channel, to the south-east of Donaghadee. 
Absolute minimum of pressure (= 28-410) at Donaghadee; increase of pres- 
sure = 0°28 inch. Maximum velocity of wind (in south) = 55 feet per second. 

We have seen that the centre of the vortex was between Armagh and 
Markree at 9 a.m. of the 19th; and, as the direction of its progressive move- 
ment was not far from the line connecting these places, it must have passed 
nearly centrally over both. Hence we should expect there the peculiar phe- 

VOL. XXxIl. 3.N 


452 The Rev. H. Luoyp on the Meteorology of Ireland. 


nomena—the /ull of the wind, and the sudden reversal of its direction—which 
are observed to occur at places in the path of the centre of a cyclone. I shall 
therefore briefly describe the series of changes at these two stations. The 
observations at Armagh are taken from the records of the self-registering ane- 
mometer, which were, of course, continuous; those at Markree were made at 
short intervals. 

At Armagh the wind began to blow at 7 p.m. of the 18th, with a velocity 
of 32 feet per second. The maximum velocity, with the exception of a short 
squall* at 5 a.M., occurred at 7 a.m. of the 19th, and amounted to 43 feet per 
second, From this time the wind abated rapidly almost to a calm, its velocity 
at noon amounting only to 6 feet per second; but at 3 P.M. it rose again, with 
a velocity of 22 feet. The initial direction of the gale was from the E. S. E. 
From 9 p.m. on the 18th, to 1 a.m. on the 19th, it veered to S., at which point 
it continued for several hours, including the period of greatest force of the 
gale. At 11 a.m. its direction had returned to S.E., and it then suddenly 
shifted to W.N.W., altering through 160° in 24 minutes. The minimum of 
pressure took place at 11" 30":, at the close of this movement; its amount 
was 27°930 inches. 


* During the squall, which lasted only three minutes, the velocity reached 90 feet per second. 

{ The following are the anemometric observations above referred to. The direction is mea- 
sured from $. through W. to N.; the velocity is expressed in miles per hour. On the 19th, from 
4.M. to 8 A.M., the direction-registering pencil was thrown outof gear, but there appears to have 
been no change of any magnitude in the interval: 


Noyv.18 a.m. | Noy.18 p.m. |} Nov. 19 a.m. | Nov. 19 p.m. 

Hour. | Vel Dir. | Vel. | Dir. | Vel. Dir. | Vel. Dir. 
0 12°2 | 28°°8| 4°8 |212°°3) 23°4 |835°°2) 4:1 |124°-0 
1 8°3 | 28 °2| 5°38 |243 +6) 24°4 |354 -3| 10°5 |104 °4 
2 5°9 | 47 °8] 8°7 |276 °2| 22°2 |353 °4| 12-0 | 93 °9 
3 7°2 | 49 °8| 7°8 |274 °5! 238°6 |345 -6, 15°4 | 90-2 
4 8°1 | 48 1) 14°7 |278 +8, 23-2 —_— 16°9 |108 -8 
5 8°8 | 41 *3| 16°1 |281 -7| 25°3 _ 13°8 |136 °7 
6 2°9 | 75-0] 16°6 !281 °9, 27°4 — 151 138)°s 
7 3°7 |162 +3] 22-0 |283 -5| 29°4 — 16°2 |151 *1 
8 1°5 |162 0} 19°2 |285 +5; 29-0 —s 16°6 |153 °6 
9 2°38 212 -4) 19°3 |282 +1; 17°6 |339 -8) 15°8 |151 -2 
10 4°9 |205 -4| 17°6 |321 °8 14°6 |320 °6| 9:2 |147°5 
11 | 5°9 |209 -2) 20°1 |830°6 7:6 |824 °5| 11°8 |159 °5 


The Rev. H. Luoyp on the Meteorology of Ireland. 453 


At Markree the gale commenced at 4": 30": p.m. of the 18th, with a rapidly 
falling barometer. At 7 p.m. the wind abated to a breeze, the barometer still 
falling. It recommenced at 10 p.m. from the 8. E.; and at 3 a.m. on the 19th 
it appears to have attamed its maximum. At 6 a.m. the wind again abated; 
and at 7.A.M. there was a calm. The minimum pressure took place at this time, 
and amounted to 28:170 inches. At 9 a.m. the wind rose again from the 
N.N.W., but not with such force as before; and in the afternoon there was 
a strong gale again.* 

From these facts it is evident, that the centre of the vortex passed nearly over 
Markree at 7 a.m., and over Armagh at 11" 30": a.m. At Donaghadee, which 
is nearly in the prolongation of the line connecting the two former places, the 
wind ceased at 1 p.m., and recommenced at 5 p.m.; so that the vortex passed 
nearly centrally over this station at about 3 p.m. From these data we learn 
that the cyclone moved from W.S.W. to E.N.E.; and that the velocity of the 
progressive movement was then about 12 miles. per hour. 


* The following are the extra observations at Markree above referred to. Reduction of baro- 
meter to sea-level = + 0°161 inch:— 


Date. Hour. Bar. Therm. Remarks. 
Nov. 18, 4h 30m- | 1-124 46°°8 Blowing a gale; storm and rain began about noon. 
6 1°002 48 ‘8 Ditto; rain. 
7 0-926 49 °5 Strong breeze; heavy rain. 
8 0°835 50 °5 Ditto; ditto. 
10 0°652 53 °7 Gale. 
11 0°577 54 °0 Wind rising to gale; mizzling rain. 
12 0°538 52 °5 Strong breeze ; ditto. 
Noy. 19, 3 A.M. 0°315 50 *5 Wind higher than at any previous time. 6 
5 0-120 46 °5 Gale; mizzling rain. 
6 0-027 45 °5 Strong breeze. 
7 0-009 47 °3 Calm. 
8 0°023 48 +2 Light breeze; mizzling rain. 
9 0°067 45 °8 Gale. 
10 0°124 46 °0 Strong breeze; wind N. N. W. 
3 P.M. 0°303 48 +8 Strong breeze. 
7 07483 49 +5 Strong gale. 
10 0-533 48 *0 Gale from N. W. ; light showers. 
11 30 0-578 49 -0 Strong gale. 
Nov. 20, | 10 a.m. 1 084 48 +4 Ditto ; showers. 
il 1°128 48 °3 Ditto. 
1 30 1°227 47 °5 Ditto. 
3 1°282 46 °5 Ditto ; heavy rain. 
5 1°376 44 *8 | Moderate (GUE of OR Beer ee ee 


=< 1, eee fe elena amare mcioama as 


454 The Rev. H. Luoyp on the Meteorology of Ireland. 


The dimensions of the vortex may likewise be collected from the same data. 
The interval between the commencement of the storm, and the passage of the 
centre, at Armagh, was 16} hours; and, the velocity being 12 miles an hour, 
the radius of the vortex was about 200 miles. The magnitude of the nearly qui- 
escent portion of air in the centre of the vortex is better defined. At Armagh 
the lull lasted from three to four hours; at Markree three hours; and at Do- 
naghadee four hours. The diameter of the quiescent central portion was, there- 
fore, about 40 miles. 

We may now refer to some particulars connected with this gale, which ap- 
pear to merit attention—although probably, in the present state of knowledge 
on this subject, we should not be justified in offering any suggestions in ex- 
planation. 

Among the first of these are the abnormal variations in the rotatory 
movement, especially along the track of the centre. The most curious of these 
irregularities is that of the direction. At Armagh this began to change rapidly 
at 9 p.m. of the 18th. At9p.m. it was E.S.E.; at 10p.m., S.E.; at midnight, 
S.S.E.; andat1la.m.onthe 19th, S. At this latter point it remained for several 
hours; and the direction then retrograded through an are of about 45°. At 9 a.m. 
on the 19th, it was S.S. E.; and at 11 a.m. it came back to S. E., after which 
the sudden shift to W. N. W., already noticed, took place. 

The next point which seems to merit notice is the fact, that the force of 
the gale was considerably greater to the south of the line of passage of its centre, 
than on that line itself, or to the north of it. Thus, at Killiney, where I made 
frequent observations during the gale, I found the maximum velocity to be 80 
feet per second; at Armagh it was little more than half that amount. 

It has been already mentioned that the greatest force of the storm occurred 
at Armagh and Markree, before the epoch of minimum pressure, the interval at 
both places being about four hours and a half. A similar interval took place 
at Killiney, but in the opposite direction, the epoch of greatest intensity fol- 
lowing that of least pressure by four hours and a half. 

The last point which appears to demand notice is the fact, that there was 
a considerable interval between the epochs of the greatest intensity of the 
storm at Dublin and at Killiney, places only ten miles apart. The greatest 


The Rev. H. Luoyp on the Meteorology of Ireland. 455 


force of the gale, at Dublin, took place between 1 P m. and 2 p.m.; at Killiney 
it occurred between 5 p.m. and 6 p.m. There isa similar interval between the 
times of minimum pressure at the two places, the least height of the barometer 
occurring later at Killiney than at Dublin by two or three hours. These differ- 
ences are probably connected with the difference of altitude of the places of 
observation. 


1851. Jan. 15, 16.—A remarkable case of a double cyclone with storm, and 
a double minimum of pressure. (Plate rx. Figs. 4,5, 6.) The first of the two vor- 
tices crossed the island from §. to N. on the 15th, and the second traversed the 
north-western portion of it, from S$. W. to N.E., on the following day. The 
velocity of the former is not well determined; that of the latter is about 270 
miles per diem. The mean velocity of the wind was from 30 to 35 feet per se- 
cond on the former day, and from 55 to 60 on the latter.* 

Jan. 15, A. m.—Centre of vortex about 20 or 30 miles south of Dunmore. 


* The following extra observations were taken at Markree, January 15, 16. Reduction of 
barometer to sea-level = 0-161 inch:— 


Date. Hour. Bar. Therm. Wind. Cloud. Remarks, 
Jan. 15, 1 30") 0°786 42°°1 N. W. 4) 10 N Mizzling rain. 
2 30 0°832 41 N.W. 4/10 N Mizzling rain. 
4 0°921 40 °°8 W.N.W. 4/1 10 N Rain. 
5 0°986 41 °5 W.N.W. 4] 10 N Rain. 
6 1°040 42 °5 W.N.W. 4/10 N,CK | Clouds breaking all round. 
10 1°204 37 °°9 Ss. W. 2 0 0 Began to clear at 6’ 30” 
12 5 1-242 34 °4 8. W. Pe Cc Clouds rapidly rising from south-west. 
12 17 1°240 34 +1 Ss. W. 1 
Jan. 16, 1A.M. 1°225 34 °°3 S. W. 1 9 Cc A large halo round moon, 
8 30 0°776 42 +0 8. E. 5 | 10 N Mizzling rain. 
9 0°751 43 +7 8. E. 5 ; 10 N 
9 30 0°726 45 +5 S.S.E. 5 | 10 N 
10 0-718 AT °2 S.S. E. 5 | 10 N Lind’s anemometer = 0°85 inch. 
11 0°668 49 +7 S. 5 | 10 N Wind not quite as strong as at 10 A. M. 
12 0°614 50 *0 8. 4/10 N Rain ; rough, with heavy rain a little 
1P.M. 0°566 51 °5 S. 4/10 N [before this time. 
2 0°534 50 °5 s. 4| 9 N,KS]} Clouds began to break at 1 P.M. 
) 0°620 46 °8 S. W. 5 fo) N 
9 30 0°661 46 °7 Ss. W. 5 | 7 N,K | Gusts very high occasionally. 
10 0°715 46-1 Ss: W. 5 9 N,CK | Lind’s anemometer = 0°80 inch. 
11 0°794 45 *2 Ss. W. 4 8 N,KS 
11 30 0°824 44 °8 Ss. W. 5 | 10 N Rain. 
12 0°835 43-0 8. W. 4 2°*KS,CK 
Jan. 17, 1A.M 0°890 43 °5 S. W. 4 1 K 
0-920 42 ‘7 S. W. |} 2 KS,C 


456 The Rev. H. Luoyp on the Meteorology of Ireland. 


Absolute minimum of pressure (= 28°718) at Dunmore; increase of pressure 
= (015 inch. Maximum velocity of wind (west coast) = 60 feet per second. 

Jan. 15, 9 p. m—Centre of vortex appears to have been at this time a few 
miles north of Buncrana; the cyclonic movement was, however, not distinctly 
marked, probably owing to the influence of the second cyclone. Least pressure 
at Buncrana. Velocity of wind uniform throughout the island. 

Jan. 16, 9 A. m—Centre of second vortex to the south-west of Westport. 
Least pressure at Westport. 

Jan. 16, 9 p. m@—Centre about 20 miles west of Buncrana. Absolute mini- 
mum of pressure (= 28°671) at Buncrana; increase of pressure = 0:20 inch. 


Jan. 30, 31—A very interesting cyclone traversing the western portion of 
the island, in direction from N. to S. nearly, at the rate of about 150 miles per 
diem. The wind light, the mean velocity being about 20 feet per second. 

Jan. 30, 9 p.m.—Centre of vortex over north-western portion of island, 
a little to the north of Killybegs. Least pressure at Killybegs. Maximum 
velocity of wind (in south-west) = 40 feet per second. 

Jan. 31, 9 a.m.—Centre a little to the eastward of Westport. Absolute 
minimum of pressure (= 29:032) at Westport; increase of pressure = 0°10 inch. 
Maximum velocity of wind (in south-west) = 25 feet per second. Lightning 
observed in north in evening of this day and day preceding. 


March 18.—A cyclone, with storm, traversing the island from S. to N., at 
the rate of about 200 miles per diem.* 


* The following extra observations were taken at Markree, March 18, 1851 :— 


Date. Hour, Bar. Therm, Wind. Cloud. Remarks. 


March 18,| 7 A.M. ‘ a9 5) OF 100 rey. in 29*-; pouring rain. 
8 100 rev. in 42°; light rain. 


9 SWE 
10 : Se i 5 | 100 rev. in 60°-; a shower. 
11 2 2 5. W. 100 rev. in 36*-; intermittent sunshine. 


12 . : . We Rain. 
100 rey. in 22°-; rain; blows a strong 
j gale when raining, but a moderate 
gale between showers. 


The Rev. H. Luoyp on the Meteorology of Lreland. 457 


March 18, 9 a. ma—Centre of vortex near Markree. Absolute minimum of 
pressure (= 29°328) at Armagh; increase of pressure = 0°10. Mean velocity 
of the wind = 45 feet per second; greatest do. (west coast) = 50 feet. 

March 18, 9 p.m—Centre of vortex north of the island. Absolute mini- 
mum of pressure (= 29°371) at Portrush; increase of pressure = 0°13 inch. 
Mean velocity of the wind = 35 feet per second; greatest do. (north-west) 
= 50 feet. 

March 19, 9 a. .—Rotatory movement broken up, and wind lessened. 
Barometer fell, and wind rose again to a gale in the evening; greatest velocity 
(north-west) = 65 feet per second. 


March 25.—A distinct rotatory movement at 9 a. m. of this day, the centre 
of which was a little to the north of Westport. Absolute minimum of pressure 
(= 29-408) at Westport; increase of pressure=0713inch. The velocity of wind 
uniform, and about 30 feet per second. The wind was very light at the pre- 
ceding and subsequent observations, so.that the progressive movement of the 
vortex cannot be traced. 


June 11, 12.—Cyclone crossing the island from 8. W. to N. E., with a velo- 
city of about 260 miles per diem. 

June 11, 9 rp.m—Centre of the vortex a little to the west of Cahirciveen. 
Least pressure at Cahirciveen. Mean velocity of wind = 40 feet per second. 

June 12, 9 4. m.—Centre over the island, between Kilrush and Westport. 
Absolute minimum of pressure (= 29°347) at Kilrush; increase of pressure 
= 0°04 inch. Mean velocity of wind = 25 feet per second. 

June 12, 9 p.m.—Centre over the channel, to the east of Killough. Least 
pressure at Dublin. Mean velocity of wind = 20 feet per second. 


July 27, 28.—Cyclone traversing the western coast, in direction from 
8.8.W. to N.N.E. Velocity of wind = 30 feet per second. 

July 27, 9 a. m.—Centre of vortex west of Cahirciveen. Least pressure at 
Cahirciveen. Greatest velocity of wind in south-west. The wind at the north- 
eastern stations uninfluenced by the vortex. 


458 The Rey. H. Luoyp on the Meteorology of Lreland. 


July 27, 9 p. m—Centre south of Westport. Absolute minimum of pressure 
(= 29:559) at Markree; increase of pressure = 0:10 inch. Velocity of wind 
uniform. 

July 28, 9 a.m.—General current from $.W.; mean velocity = 30 feet 
per second. 


August 23, 24.—Well-defined cyclone advancing in a curvilinear path, the 
movement of the centre being at first from N. W. to S. E., and afterwards from 
S. W. to N. E.* 

Aug. 23, 9 p.m.—Centre of the vortex north-west of the island. Least 
pressure at Buncrana. Mean velocity of wind=25 feet per second. Lightning 
along the whole of the eastern coast during the day. 

Aug. 24, 9 a.m.—Centre near Armagh. Absolute minimum of pres- 
sure = 29:439) at Armagh; increase of pressure = 0:13 inch. Mean velo- 
city of wind = 35 per second; greatest do. (south) = 55 feet. The centre 
of the vortex appears to have passed over Donaghadee about noon. At 
9 a.m. the direction of the wind there was E.S8.E.; at 12 (noon) W. S.W.; 
and at 1*: 30": p.m. W.N.W., the shift being accompanied by strong gales and 
heavy rain. 

Aug. 24, 9 p. m—Centre north-east of the island. Least pressure at Do- 
naghadee. Mean velocity of wind = 25 feet per second. 


September 29, 30.—Interesting cyclone and storm, crossing the island 
from S. S.W. to N.N.E., with a velocity of about 270 miles per diem. 


* The following extra observations were taken at Donaghadee on this day (August 24). Re- 
duction of barometer to sea-level = + 0:077. The force of the wind is expressed in inches of 
Lind:— 


Barometer. Direction. Remarks. 


Light showers. 
Squall, with heavy rain. 


The Rev. H. Luoyp on the Meteorology of Ireland. 459 


(Plate x. Figs. 1, 2, 3.) Mean velocity of wind on the 29th = 45 feet per 
second.* 

Sept. 29, 9 a. ua.—Centre of vortex off the south-western coast, to the west 
of Cahirciveen. Force of wind greatest at the same station at 3 A.m.; but the 
barometer continued to fall until noon, when the pressure was 28:970. Increase 
of pressure = 0°22 inch. Greatest velocity of wind (north-west) = 60 feet per 
second. 

Sept. 29, 9 p. m—Centre over the island, about midway between Kilrush 
and Dublin. Absolute minimum of pressure (= 29-030) at Markree; increase of 
pressure = 0:12 inch. Least pressure in south-east at 6 p.m. Greatest velo- 
city of wind (north-east) = 55 feet per second. 

Sept. 30, 9 a. m—Centre near Malin Head, at northern extremity of the 
island. Absolute minimum of pressure (= 29020) at Portrush; increase of 
pressure = 0°15 inch. Mean velocity of wind = 35 feet per second; greatest 
do. (north-west) = 55 feet. 


Sept. 30, Oct. 1.— Cyclone moving apparently in curvilinear path, its course 
being at first from W. to E., until it reached the centre of the island, and 
afterwards from S. 8. W.to N.N.E. Mean velocity of wind between 25 and 39 
feet per second. 


* The following extra observations were taken at Markree, Sept. 29, 30, and Oct. 1:— 


Date. Hour. Bar. Therm. Wind. | Cloud. Remarks. 
Sept. 29, Was ere ||) LO, 50°°3 Sa de |) 10) Nt Rain; 100 rey. anem. in 29°: 
8 1°169 51 °1 S. E. 5 10 N Ditto. 
9 1°145 Gls S. E. 5 10 N Ditto. 
10 1°125 51 +4 8. E. 5 10 N Ditto; 100 rey. anem. in 29*- 
11 sbeiti ing 52) 7 S. E. 5 10 N Ditto. 
12 1-070 54 °2 S. E. 5 10 N Ditto. 
1pm, 1°059 55 °0 S. E. 5 10 N Ditto. 
3 0-998 56 *2 S. E. 4 10 N,S Ditto. 
5 0°955 55 °3 E. 4 10 N Ditto. 
eh 0°932 55 *0 E. 5 10 N Ditto. 
| 10 0°869 55 °0 BO TE! 10 N 100 rey. anem. in 164°; aurora. 
Sept. 30, | 7am 0°952 55-0 W. 4 10 N A little rain. 
8 0°979 54 °4 W.N.W. 4 10 N Mizzling rain. 
10 0 948 54°°0 Ww. 4 10 S,N 
11 1-062 54 °2 W.S.W. 4 10 S,N 
llp.m 0°833 50 <2 S. E. 5 | 4 8,KS 
12 0-801 | 50-2 Sie 5) || 10 Nes | 
Oct. 1, 1AM 0°752 51 °0 S. E. 5 10 N 
2 0°700 51 °0 S. E. 4 10 N 


VOL. XXII. 30 


460 The Rev. H. Luoyp on the Meteorology of Ireland. 


Sept. 30, 9 p. m.—General southerly current. Centre of vortex to the west 
of the island; least pressure on west coast. Greatest velocity of wind (on 
west coast) = 45 feet per second. 

Oct. 1, 9 A.m.—Centre of vortex over the island, between Kilrush and 
Courtown. Absolute minimum of pressure (= 28°838) equally distant from 
Dublin, Courtown, and Dunmore. Northern stations beginning to be affected 
by vortex. Greatest velocity of wind (north-east) = 50 feet per second. 

Oct. 1, 9 p.a.—Centre north of Portrush. Absolute minimum of pressure 
(= 28°853) at Portrush ; increase of pressure = 0-09 inch. At Donaghadee a 
sudden shift of the wind from §. 8. E. to W. took place at 4"°30™ p.m. 


Oct. 4, 5.—Distinct cyclone moving from W.S.W. to E.N. E., and passing 
over (or near) the northern extremity of the island. (Plate x. Figs. 4, 5, 6.) 
Mean velocity of wind = 35 feet per second. General electrical disturbance. 

Oct. 4, 9 A. m—General current from 8. W.; centre of vortex north-west of 
island. Greatest velocity of wind (on west coast) = 45 feet per second. 

Oct. 4, 9 p.m.—Centre close to northern extremity of the island. Abso- 
lute minimum of pressure (= 29-182) at Portrush; increase of pressure = 0:11 
inch. Greatest velocity of wind (north-west) = 55 feet per second. 

Oct. 5, 9 A.m.—Centre north of the island; least pressure at Portrush. 
Greatest velocity of wind (north) = 60 feet per second. 


From the facts above stated, we may draw the following general con- 
clusions :— 

1. The oceurrence of cyclonic movements in the atmosphere is not infre- 
quent in Ireland, and may be traced even in the case of moderate winds. 

9. The rotatory movement is invariably in the same direction, namely, that 
opposite to the diurnal movement of the sun in azimuth. 

3. This rotation is always accompanied by a considerable disturbance of 
barometric equilibrium, which is greater in proportion to the velocity of the 
rotatory movement, the pressure being a minimum at the centre of the vortex, 
and increasing regularly with the distance from that point. 

4. The place of greatest velocity appears to have no very definite relation 
to that of the centre of the vortex, sometimes nearly coinciding with it, and 


The Rev. H. Luoyp on the Meteorology of Ireland. 461 


at others being situated in front, or in the rear, on the right hand or on the 
the left, of the centre. In the remarkable cyclone of Nov. 18, 19, 1850, the 
wind raged with greatest violence on the right hand of the centre (looking in 
the direction of the progressive movement); and this appears to be the case of 
most frequent occurrence. 

5. The vortex itself has a progressive movement, at the rate of from 100 to 
300 miles per diem, the average velocity of those observed being 220 miles per 
diem. The direction of this movement is generally from §.W. to N. E. 

6. Ifa line be drawn through the centre of Ireland, in the direction from 
S.W. to N.E., the track of the centres of by far the greater number of the cy- 
clones, passing over or near Ireland, lies to the north of that line. 

7. There is reason to conclude, that these rotatory movements are caused 
by the conflict of two rectilinear currents moving in different directions. 


STORMs. 


For the purpose of eliminating local irregularities, and (to a certain extent 
also) inequalities of estimation, I have, in examining the distribution of the 
higher winds, combined the stations into four groups, omitting Portrush and 
Buncrana, which lie somewhat apart. These groups are as follow :— 

I. Norru-EAstern.—Donaghadee, Killough, Armagh. Mean latitude 
54°24’, mean longitude = 5°57’. 

Il. Norru-wrstern.— Killybegs, Markree, Westport. Mean latitude 
54°13’, mean longitude = 8°51’. 

III. Sourn-Eastern.—Dublin, Courtown, Dunmore. Mean latitude = 
52°43’, mean longitude = 6° 29’. 

IV. Sours-western.— Kilrush, Cahirciveen, Castletownsend. Mean lati- 
tude = 52° 2’, mean longitude = 9° 37’. 

The line joining groups I. and 1v. lies, almost exactly, N. E. and 8. W.; and 
that joining groups u. and ut., N. W. and S.E. 

The following are the numbers of times in which the average force of the 
wind, in each of these groups, amounted to a strong breeze; or the average ve- 
locity to 35 feet per second, and upwards. 


Il 


30 2 


462 The Rev. H. Luoyp on the Meteorology of Ireland. 


Taste XXV. Nomser or Times IN WHICH THE VELOCITY OF THE WIND 
was 35 Fert pER SECOND AND UPWARDS. 


Month. 


North-East. | North-West. | South-East. | South-West. 


January,...... 18 19 13 29 
February, vb 15 10 13 
March ie) cietebens 5 15 4 14 
Arrilip cage 3 ll 3 12 
WEN ola bBo ao 2 10 1 
Ohrots 5 Go orc o-c 2 15 5 
alba oro ai'e'a ad 3 9 4 
IMDS Gea qc 0 9 3 
September,.... 2 11 3 
Q@etober;, = «<<. 3 21 4 
November,. ... 0 14 1 
December, .... 3 9 9 


oes Gop Oso 10 36 8 
Summer, ..... 5 33 12 
Autumn,..... 5 46 8 
Wanter: 2 snus sere 28 43 32 


Wear tt, csdeyounue 48 158 60 


From the foregoing numbers it appears, that high winds are much more fre- 
quent on the western than on the eastern coast, the numbers denoting the re- 
lative frequency, on the average of the entire year, being nearly as 3 to 1. 
This preponderance of high winds on the western coast holds at all seasons of 
the year, the maximum occurring at the north-western extremity in autumn, 
and at the south-western in winter. The greatest frequency is in the north-west, 
on the average of the entire year. 


The following are the cases in which the mean force of the wind, over the 
whole island, amounted to a gale; or in which the mean velocity was 45 feet 
per second and upwards :— 

Nov. 23, 24, 1850.—Storm along the western coast, blowing at first from 
S.S.W., and veering through 8.W. to W. Least pressure in north-west 
throughout. ’ 

Nov. 23, 9 p.m.—Storm began at south-western extremity of the island; velo- 


city = 45 feet per second. 


The Rev. H. Luoyp on the Meteorology of Ireland. 463 


Nov. 24, 9 A.m.—Wind continued to blow in same district; velocity in- 
creased to 60 feet per second. Absolute barometric minimum (north-west) 
= 28644. 

Nov. 24, 9 p. mu—Storm extended over whole of western coast; velocity of 
wind = 55 feet per second. 


Dec. 14.—Storm affecting the whole island, but chiefly the western coast. 
Wind at first from §. S$. W., but veering to W.S.W. at 9 p.m. Least pressure 
in north-west throughout. Electrical disturbance over the whole island. 

Dec. 14, 9 A. m.—Velocity on western coast = 65 feet per second. Abso- 
lute barometric minimum (north-west) = 28-952. 

Dec. 14, 9 p. M.—Velocity on western coast = 50 feet per second. 


Dec. 31, Jan. 1, 1851.—Storm from 8. W. and S., beginning on western 
coast, and extending over whole island.* 

Dec. 31, 9 A.m.—Velocity on western coast = 50 feet per second. Direction 
8. S. W. and S. W. 

Dec. 31, 9 vp. m.—Gale affecting whole island, except north-eastern extremity. 
Greatest in south-west; velocity = 60 feet per second. Direction as before. 
Absolute barometric minimum (north) = 29-177. 

Jan. 1, 9 A. ms —Wind abated. 

Jan. 1, 9 p.m.—Gale from §. W. and S. over whole island, except north- 
western extremity. Velocity (south-east) =55 feet per second. Absolute ba- 
rometric minimum (north) = 28°975. 

In this case, therefore, there were two storms succeeding each other on con- 
secutive days, with a double fall of the barometer. The direction of the wind 
Jan. 1 p.m. was remarkable. The prevailing current was from S. W., and 


* The following extra observations were taken at Markree on December 31, 1850:— 


Date. Hour. Bar. Therm. | Wind. Cloud. Remarks. 
Dee. 31, 1lam.| 1°122 52°°0 8. 4 10) Ni Light rain. 
12 1°090 53 °7 8. 4 10 N Ditto. 
1P.M 1°070 53 °75 sS. 4 10 N Mizzling rain. 
3 1-040 Pei ee) | eo gt 10 N Rain. 
5 1-036 52-0 Sa 3 | 10 S,N Wind falling since 4 P.M. 


464 The Rev. H. Luoyp on the Meteorology of Ireland. 


extended over the central parts of the island; while there appears to have 
been an indraught towards it, from the north-western and south-eastern quarters. 


Jan. 12, 13.—Storm from §S. and §.W., beginning in the north-west, and 
advancing in the direction from N.W. to S.E. Velocity of wind = 60 feet 
per second. Least pressure in north-west throughout.* 

Jan. 12, 9 p. m.—Gale in north-west. 

Jan. 13, 9 A.M.—Storm advanced to line joining north-east and south-west 


centres. Absolute barometric minimum (north-west) = 29-174; pressure least 
at Markree at noon. 


Jan. 27.—Storm from §. and §.W. in the afternoon of this day, chiefly along 


the western coast. Velocity of wind = 55 feet per second. Absolute baro- 
metric minimum (north-west) = 29°309.7 


* The following extra observations were taken at Markree, January 12, 13, 1851:— 


iss] 

& 
4 
i=} 
a 
Q 
S 
=] 
a 


SI 


Rain. 
Moderate rain 
Light rain. 


wn ¢ 
DnB RnD A 
Aid A '2i 2 


44 3H 
rs 
A 


Bright sunshine. 
Faint sunshine; a little rain. 
A little rain. 


ric 
1° 
1: 
1: 
0: 
0: 
‘ic 
1: 


xy 
Qa 
A 


one Eanas 
Omak ooo 

pee ee 
wonessoscs 


A 


+ The following extra observations were taken at Courtown on this day:— 


| 
Date. Hour. Bar. Dir. Force. Remarks. 
Jan. 27, Noon. 1°755 8. 8. W. 1 Cumulus clouds, with cirrus above ; partially overcast. 
1851. 1P.Mm. 1°737 5.5. W. 1 Sky becoming overcast. 
2 1.697 S. 2 Wind veered from 8. S. W. to S. 
3 1°665 5. 3 Cloudy and sultry. Lind = 0°4 inch. 
4 1°637 8. 3 Wind increasing. Lind = 0°6 inch. 
5 1°597 Ss. 4 Ditto; dark in S. 8. W. 
6 1-563 5. 4 Rain; force of wind greatest, Lind = 0°8 inch. 
7 1°517 Ss. 4 Ditto; darkly overcast. Lind = 0°8 inch. 
8 1°507 Ss. 4 Ditto; ditto. Lind = 0°8 inch. 
9 1°500 s. 3 | Sky brightening in W. Lind = 0°6 inch. 
10 1°500 8. 3 Flashes of lightning in S.S.W. and W. Lind=0-4 inch. 
11 1°500 8. 2 Sky brightening. 
| 12 1°501 Ss. W. 2 At 11°45 wind veered from S. to S. W. 
| 


The Rev. H. Luoyp on the Meteorology of Ireland. 465 


June 15, 16.—Gale from S.W. and W., on the western coast. Velocity 
about 50 feet per second. 

June 15, 9 A.m—Wind from §.W. Velocity on western coast = 50 feet per 
second. Least pressure in north-west. 

June 15, 9 p. m.—Velocity = 45 feet per second. Absolute barometric mini- 
mum (north) = 29°575. 

June 16, 9 a.m.—Wind from W. Velocity = 50 feet per second. 


July 13, 14.—Storm chiefly in north-west, blowing at first from S. S. W., 
and veering through §.W. to W. ‘This appears to have been a cyclonic gale, 
the centre of the cyclone passing to the north of the island; it is not included 
in the former series on account of this circumstance. The velocity of the wind 
was greatest in the north-west throughout; the barometric pressure was least 
in the north-west on the 13th, and in the north-east on following day. 

July 13, 9 a. m.—Storm from §.S.W., in the north-west of the island. Ve- 
locity = 60 feet per second.’ 

July 13, 9 p.m.—Gale veered to S. W., and affected a large portion of the 
island. Velocity of wind = 60 feet per second, as before. Absolute barometric 
minimum = 29-052. 

July 14, 9 a. m—Wind veered to W. Velocity in north-west increased to 
65 feet per second.* 


Dec. 7.—Storm began in south-western extremity of the island, and ex- 
tended thence over the whole. Direction of wind between S. and S. W. 


* The following extra observations were taken at Markree, July 14, 1851. The wind column 
contains the time of 100 revolutions of Robinson’s anenometer :— 


e] 
-) 
4 
5 
5 


Remarks, 


Strong gale; mizzling rain. 
Strong gale; rain. 

Ditto. 

Ditto, 

Ditto; a little rain. 

Ditto. 

Ditto. 

Ditto. 

Moderate gale. 


1 12, 
1 "2 
1 “4 
1 “4 
1 3 
1 “4 
1 “8 
1 8 
1 9 


466 The Rev. H. Luoyp on the Meteorology of Ireland. 


Dec. 7, 9 A.m.—Gale from S. 8. W. in the south-west. 

Dec. 7, 9 Pp. m.—Storm over the whole island. Greatest velocity and least 
pressure in north-west. Velocity = 70 feet per second. Absolute baro- 
metric minimum = 29-267. At Cahirciveen the barometer fell until 7 p. m.; 
and the wind shifted from S. to W. at the same time.* 


Dec. 9.—Storm from §.W. along the western coast. Least pressure in 
north-west throughout. 

Dec. 9, 9 a. M—Velocity of wind in west = 50 feet per second. 

Dec. 9, 9 p. M—Velocity = 60 feet per second. Absolute barometric mini- 


mum = 29°632. 


Dec. 20.—Gale blowing from S. 8. W., beginning on western coast, and ad- 
vancing to eastern. Least pressure in north and north-west. 

Dec. 20 a. m.—Gale on west coast. Velocity = 55 feet per second. 

Dec. 20 p.m.—Gale transferred to east coast. Velocity = 50 feet per second. 
Absolute barometric minimum (north) = 29-457. At Markree there was a 
sudden shift of the wind from 8. S.W. to N. W.at 7" 35™ P.M. 


From the foregoing facts we may draw the following conclusions :— 

1. The greater gales are much more frequent on the western, than on the 
eastern coast, the numbers denoting the relative frequency being nearly as 5 to 1. 
The frequency of storms is nearly the same in the northern and southern portions 
of the island. 

2. The direction of the wind, in all the cases enumerated, was between S. 
and W. In about half of these cases the wind blew, throughout, from the 


* The following extra observations were taken at Cahirciveen on this day :— 


Heavy rain, and squally. 
Ditto, ditto. 


Ditto, ditto. 
Squally ; light rain. 
Ditto, ditto. 
Drizzling rain. 
Cloudy. 


The Rey. H. Luoyp on the Meteorology of Ireland. 467 


same point; in half it veered from 4 to 6 points of the compass, the veering 
being in the direction produced by a cyclone moving from 8. W. to N. E., and 
having the path of its centre to the north of the island. 

3. The axis of the gale is in some cases transferred parallel to itself, to the 
eastward. Remarkable instances of this movement occur in the gales of January 
12, 18, and December 20. 

4. The least barometric pressure occurs, in almost every instance, in the 
north-western quarter of the island.* 

5. The locality of the highest wind sometimes coincides with that of least 
pressure, and sometimes does not. In the latter case, the axis of least pressure 
is generally to the westward of the axis of the storm. 

6. On either side of the axis of a storm, the wind appears to blow towards 
that line. A remarkable instance of this phenomenon occurred in the storm of 
January 1. 

We are now in a position to consider the question, whether al// storms 
are cyclonic? And if not, what proportion do rotatory storms bear to the 
whole? Of the greater storms which have occurred since the commencement 
of these observations, the rotatory character of five (those of October 6, 1850, 
November 18, January 15, 1851, March 18, and September 29) has been 
completely established. We have seen in this section, that the same character 
may be predicated, with great probability, of five more; while there remain 
five in which the wind has blown, throughout, in the same direction. In fifteen 
months, accordingly, there have occurred fifteen storms, of which two-thirds 
were cyclonic. As respects the remaining one-third, the phenomena are cha- 
racterized, not only by the absence of any veering of the wind, but also by the 
fact, that the pressures appear to increase with the distance from a line or azis 
of minimum pressure, rather than from a point; or, in other words, that the 
isobaric lines are parallel right lines, instead of concentric circles. It is true 


* Tn one case only, the locality of least pressure shifted from the north-western to the north- 
eastern extremity of the island. Thisis consistent with the supposition, that the storm in question 
was a cyclone, whose centre had a progressive motion eastward, 

+ The conclusions numbered 3, 5, 6, have already been drawn by Mr. Espy, from an exa- 
mination of the storms in the United States in the early months of the year 1843.—First Report 
on Meteorology. 


VOL. XXII. 3) Ie 


468 The Rev. H. Luoyp on the Meteorology of Ireland. 


that these facts are by no means decisive in disproving rotatory movement; for 
they are consistent with a rotation of the wind in a plane perpendicular, or 
highly inclined, to the horizon. Still we are perhaps not justified in assuming 
the existence of a rotation of this kind, without further evidence; and it seems 
more reasonable, in the present state of our knowledge, to admit two different 
kinds of winds, than to endeavour to reduce all to one by the help of a gra- 
tuitous hypothesis. 


Hourly Observations.—It has been already stated, that hourly observations 
were appointed to be made during twenty-four consecutive hours, at the equi- 
noxes and solstices, in the hope that their results might throw light upon the 
simultaneous atmospheric changes occurring over the island, and especially 
upon the direction and rate of progress of atmospheric waves. The observa- 
tions on the first two of these term-days (March 21 and June 21) at six of the 
stations, are given in detail at the end of this Paper (Table xxxiv.). Those of 
the two latter (September 22 and December 22) have been omitted, no atmo- 
spheric change of a marked kind having occurred during them. 

March 21.—A gale occurred on this day, accompanied by a marked baro- 
metric depression. The minimum of pressure took place during the obser- 
vations, the time of its occurrence varying considerably at the different stations. 
At Cahirciveen, there was a sudden fall of the barometer between 9 A. m. and 
10 a.m. followed by a sudden rise between 12 and 1 p.m., the mercury being 
nearly stationary from 10 a.m. to 12. A similar change took place at Dun- 
more East, and at the same hours. For these two stations, accordingly, the 
epoch of minimum pressure may be taken to be 11 a.m. ; the subsequent changes 
were small and irregular. At Courtown, the barometer descended very slowly 
and gradually until 5p.m.; it then ascended until 10 p.m., after which it de- 
scended again. All the changes were, however, very small. 

At the northern stations the fall of the barometer was more considerable, 
and more regular. At Markree, where it was most rapid, it amounted to 0:210 
in 6 hours. The minimum at Markree occurred between 3 p.M. and 4 P.M.; 
at Armagh, the minimum took place at 6 p.m.; and at Portrush, at 8 p. M. 

From these results it would appear that the trough of the wave travelled 
from south to north, nearly, with a velocity of about 22 miles per hour. The 
barometric depression was greatest at Markree, where the barometer stood at 


The Rev. H. Luoyp on the Meteorology of Ireland. 469 


28-689, when lowest. The lowest pressure increased from that point in the 
south-easterly direction, being 28-972 at Dunmore. 

At Markree the wind shifted from S$. 8. E. to $8.8. W. at the time of 
greatest depression. The same phenomenon took place at Armagh and Portrush, 
although not with such precision; the change of direction at the former station 
being from §. 8. E. to §., and at the latter from $8. E. to S$. No similar change 
occurred at the southern stations. 

It should be observed, that the foregoing phenomena are not necessarily to 
be ascribed to the transit of a rectilinear wave. They are all consistent with 
the effects of a cyclone, coming from the S. or 8. W., the track of its centre 
lying to the west of the island. 

June 21, 22.—The changes of the direction and of the pressure of the wind, 
on this day, are manifestly the effects of a cyclonic movement, the centre of 
the vortex sweeping round the north coast of Ireland, in a somewhat curvi- 
linear path, from west to east. It has not been included in the former series, 
the force of the wind having been below the limit there adopted. At 9 a. m. 
of the 21st, the centre of the vortex was off the north-west coast, to the west of 
Killybegs. At 9 P.M. of the same day, it had arrived to the north of Port- 
rush; and at 9 A.M. of the 22nd, it was to the north-east of Donaghadee. 

The veering of the wind was, on the average, about 90°; its duration was 
very different at the different stations, being shortest for those near the path of 
the centre of the vortex, and longest for those remote. The wind, which was 
very light throughout, fell about the time of veering at most of the stations. 

The descent and subsequent rise of the barometer were regular, and 
the minimum well-defined. The time of least pressure coincided at all the sta- 
tions, very nearly, with the middle of the time of veering of the wind; it was 
earliest on the western coast, and latest on the eastern, the epoch of its occur- 
rence being between 12 and 1 p.m. at Markree and Cahirciveen, and between 
5 p.m. and 6 p.m. at Dublin and Courtown. The barometric depression was 
small, the mean pressure at the epoch of minimum being 29°74. 


Humiity or THE Arr. 


The following Tables give the results of the psychrometrical observations. 
Table xxvi. contains the monthly means of the temperatures of evaporation at 
3P2 


470 The Rey. H. Luoyp on the Meteorology of Ireland. 


the several stations ; and Table xxvu. those of the tension of vapour, calculated 
by Reenautt’s Table :— 


Taste XXVI. TeEmpERATURE or EvaporatIon. 


| | ] 
Station. Jan. | Feb. | Mar.| Apr. | May. ae July. Aug. | Sept.| Oct. | Noy. | Dec. | Year 
ses P| | 
| Fiera | | 
Portrush, ... Fake eee ae ees 42°-0/43°:2 47°-1 
Buncrana, . . . |39 4/39 640 ‘642 5/47 5/52 °353 -956 °2'53 *1/48 -4/40 -2/42 146 3 
Donaghadee,. . |41 a 941 043 5 AT 652 -7/54 -356 554 0/49 -4)41 *1/43 -4/47 71 
Killybegs, . . . |41 ‘6/41 ‘7,42 6/44 6149 3.53 655 5 58 °1/55 “7/50 +1|43 4/44 448 -4 
Armagh,... . |39 439 5 40 -2.42 ‘QAT 252 354 055 552 ‘7/18 0.38 “9/41 146-0 
Killough, .. . |42°341 841 6.44 848 953 ‘256 (157 2.55 ‘0/50 “7/40 6)44 .2.48 -0 
Markree, .. . |39 :2:40 ‘7|41 4.43 “7\48 0.52 954 -8)56 9.53 949 -3/41 3/41 -9/47.-0 
Westport, . . . |44 244 “0/44 ‘7/46 3/51 +1155 ‘7/57 ‘860 °3/58 °1/52 “7/46 -3/46 -8|50 7 
Dirblins ieee el 241 "2/41 5 43 ‘8/48 6.54 +255 “8/58 *8/53 1/49 °3/39 -1/41 ‘3147 2) 
Portarlington, {41 942 0/42 -8 44 -4 8/56 -2/59 1/55 ‘2151 -4)41 -3/42 -0/48 6 
DMN SS 4 oe 40 pe 641-4446 6.56 558 7/53 3.49 ‘8/38 ‘5/41 3/47 5 
Courtown,.. . |41 ‘Tal 8/42 0.44 -2 9/56 4/57 9/53 °9 49 -9/39 4/43 247 °8 
Kilrush,. .. . 42 ‘843 “7/43 4.45 °3 456 -7\59 “2 6 350 ‘8/43 1/43 449-1 
Dunnore, . . . |43 542 942 845 5 457 459 3555 850 7/40 0/43 948 9 
Cahirciveen,. . 43 ‘54 1/44 245 6 857 459 6155 951 ‘7/44 3.45 049 7 
Castletownsend, 43 8/43 9/43 5 45 -2 4158 1/59 9/57 ‘851 -7/43 4/45 -1 ie 8 
| | | 


Taste XXVII. Tension or Vapour. 


| { 
July.| Aug. Sept. | Oct. | Nov. | Dee. | Year. 


Station. Jan. | Feb. | Mar. | Apr. | May. | June. 
ee eee ae | uit 
| | | 
Portrush, ... « *243 |-242 |-239 256 -317 “382-414-442 “399 *337 252 +274/-316 
Buncrana, . . . |:227 |-230)}'229|:243 | 301 |-365 |'387 42) 379 |316 |-233 | -256 |-299 


Donaghadee, . |+250 +241 |-239|-250 -299 -370 "395 |-434 -397 338-236-268 310 


Killybegs, . . . |-248|-248 |-253]-269 |-334 -389|-415 |-461 423-342 /-268)-282 |-328 
Armagh, . . . . |-231 |-228 231 |-250 |-295 |-357 |-388 |-412  -376 |-320 |-224) 246 |-297 
Killough, . . . |-256 +249 +245 |-279 |-329 389-434-451 414-352 |-237|-271 |-326 
Markree,. . . . |:244|-252)-252|-267 315 |-378/-411 443-407 |-349 -263)-271|-321 
Westport, . . . |-277|*285 |-288 | -306 |-370 |-443 /-476 523 -486|-398 |-315|-321 |-374 
Dublin, . . . . |-248|-243 |-242 |-258 |-306 |-377 402-466 +382 -336 |-229|-252|-312 
Portarlington, |-250 -245 247 249 -332 390 -401 -457 “384-359 |-250|-259 |-319 
Athy, 28 = 254 249 252 -275 324 -417/-432 -475 -403 -356|-232 -261 | 328 
Courtown, . . . |°258):251/-250 -266 312 -386 424 -455 -395 -351 -227 -269 |-320 
Kilrush, . . . . |-269 275 -270 |-285 |-339 -412 436 -488 -437 -364 -271 275 |-343 
Dunmore, . . . |-271|-264 |-262 |-288 /-349 +380 427 -477 415 -349 -230 +273 | -332 
Cahirciveen, . . |:269 |-277 |-274 -277|-333 -400 -444/-488 -421 -371 -277 290 -343 


Castletownsend, elie ela hae 275 feslrevg hie? bap bets +370 267 |-291 |349 
| | | | | | | 


—_— 


The Rev. H. Luoyp on the Meteorology of Ireland. 471 


Very few results of a general nature can be drawn from these observations, 
the distribution of vapour being governed by the proximity of the station to the 
sea, or by other local circumstances. It will be seen, from the last column of 
Table xxvi., that the yearly mean tension of vapour increases, although not in 
any regular progression, in proceeding from the north to the south of the island. 
Its mean value for the entire island is 0°326 of an inch; its greatest value (at 
Westport) is 0°374. 

The following Table contains the values of the relative hwmidity, the state 
of complete saturation being represented by 100 :— 


Taste XXVIII. Humipity or tHe Arr. 


j ' | | | | 
Station. Jan. | Feb. | Mar. | Apr. | May.) June.| July.! Aug. | Sept.! Oct. | Nov. | Dee. | Year. 

“THe parol ac fel 
Portrush, .. . | 92 | 90 | 87 | 82 | 86 | 86 | 90 | 88 | 90 | 90 | 87 | 93 | 88 
Buncrana, . . .| 87 | 87 | 82 | 79 | 81 | 81 | 83 | 83 | 84 | 85 | 86 | 88 | 84 
Donaghadee,. . | 92 | 87 | 86 | 78 80 | 82 | 84 | 87 | 87 | 89 | 83 | 89 | 85 
Killybegs,. ..| 88 87 | 85 | 82 | 87 | 84 | 85 | 86 | 87 | 87 | 88 | 91 | 86 
Armagh,....| 89 87 | 8681 | 80 | 78 | 82 | 83 | 85 | 88 | 88 | 89 | 85 
Killough, ...| 88 | 87 | 86 | 86 | 87 | 88 | 89 | 89 | 88 | 88 | 86 | 86 | 87 
Markree,.. . .| 99 | 96 | 92 | 87 | 86 | 84 | 89 | 89 | 93 | 96 | 98 | 99 | 92 
Westport,. .. | 89 | 95 | 93 | 93 94 | 96 | 97 | 97 | 99 | 97 | 98 | 98 | 96 
Dublin, ... ./ 88 | 86 | 85 | 80 | 77 | 75 | 76 | 83 | 85 | 88 | 89 | 90 | 84 
Portarlington, | 87 | 84 | 80 | 72 | 72 | 72| 74 |77 | 74 | 86 | 90 | 91 | 80 
Athy, .....|98|95 | 91 | 85 | 81 | 84/| 85 | 88 | 95 | 95 | 95 | 98 | 91 
Courtown,.. |93 89 | 86 | 83 | 78 | 81 | 83 | 85 | 86 | 92 | 87] 90 | 86 
Kilrush, ... .| 94 91 | 90 | 87 | 87 | 90 | 86 | 91 | 90 | 93 | 92 | 92 | 90 
Dunmore, . . .| 90 | 90 | 89 | 87 | 85 | 78 | 77 | 84 | 82 | 85 | 85 | 88 | 85 
Cahirciveen,. .| 89 | 89 88 | 80 | 79 | 82 | 84 | 87 | 85 | 90 | 88| 91 | 86 
Castletownsend,| 92 | 89 | 86 | 81 | 82 | 85 | 86 | 90 | 90 | 89 | 88 | 92 | 88 


The distribution of humidity is still more under the influence of local cir- 
cumstances, and therefore still less regular. Thus, Portrush and Castletown- 
send—the one at the northern, the other at the southern extremity of the island— 
have nearly the same mean humidity; while Portarlington and Athy—places 
near each other, and both inland—are almost at the opposite extremities of the 
scale. The driest station is Portarlington; the most humid, Westport. At the 
latter place, in fact, the air is nearly saturated with moisture, the place of ob- 
servation being entirely surrounded by water, and but a few feet above the sea. 
The mean humidity for the entire island, for the year 1851, is 87. 


472 The Rey. H. Luoyp on the Meteorology of Ireland. 


Rain. 


Before proceeding to the observations of rain-fall throughout Ireland in the 
year 1851, it is important that we should know its normal amount at one or 
more stations, as deduced from the mean of several years. We have, for this 
purpose, two series of observations, one at Dublin, and the other at Armagh, 
extending uninterruptedly over eleven and twelve years respectively. The 
results of these two series are contained in the following Tables. 


Taste XXIX. Mownrnry Fatt or Rar ar Dusty, in Incuzs (1841-1851). 


| | | | 
| Jan. | Feb. | Mar. | Apr. | May. | June. | July. | Aug. | Sept. | Oct. | Nov. | Dec. | Year. 

| =} | | | 

| 
1841 | 241 | 1-00 | 2.12 | 1-12 | 1:94 | 1-84 | 282 | 222 | 1-88 | 4-89 | 3:58 | 298 |28-50 
1842) 1-41 | 3-11 | 2-47 | 0-81 | 3-18 | 2-00 | 2:57 | 1-24 | 460 | 1:54 | 4:37 | 0-78 |28-08 
1843/ 215 1-84 | 1-65 | 3-34 | 4°51 | 2°60 | 1-93 | 212 | 067 | 3-44 | 3-10 | 0:35 |27-70 
1844 | 154 237 | 234 | 0-95 | 0-21 | 169 | 183 | 3-77 | 2:55 | 3:32 | 5-24 | 2-60 |28-41 
1845 | 448 O81 | 1-72 | 0-88 | 154 | 4-00 | 3:33 | 2:52 | 0-95 | 3-92 | 3:56 | 3°77 |31-48 
1846 | 343 1-42 | 2°85 | 5:97 | 214 | 1:50 | 3-14 | 4°33 | 2-98 | 4-72 | 280 | 0°83 [36-11 
1847 | 357 2-63 | 1-22 | 3-42 | 2-21 | 1-91 | 0°64 | 1-43 | 1-35 | 213 | 2-09 | 3-20 |25-80 
1848 | 1-88 | 3.23 | 240 | 315 | 0:93 | 3:92 | 2°37 | 5-10 | 242 | 438 | 150 2°83 |3411 
1839 3:30 072 1-07 | 257 | 207 | 0-47 | 269 | 333/383 3-93 | 180 | 403 |2981 
1850 | 225 | 1-47 | 1:14 | 3:63 | 2-42 | 1-69 | 2-26 | 1:38 | 1-99 | 1-24 | 2-32 | 2:39 |24-18 
1851) 6-28) 049 | 238 | 177 |131 | 271 [348 | 201 | 181 | 327 | 101 | O88 |26-40 
| | | 

Means 288 | 1-74 |1:94 | 251 | 204 221 2-43 | 2-68 | 228 3:34 | 2-85 | 2-24 |29-14 


Taste XXX. Monruty Fatt or Rar at Armacn, tn IncuEs (1840-1851). 


id 


Jan. 


June. | July. 
| 


1840) 4:94 | 2°75 
1841] 2:00 | 2:27 
1842| 2:79 | 2-73 
1843] 2:25 | 1-27 | 
1844| 2°64 | 3-24 | 
1845 | 4-99 | 1-33 
1846) 4°58 | 1°86 
1847 | 3:03 | 1:97 
1-87 | 6°75 | 
6:30 | 2°51 | 
4:08 5-04 
5°53 | 2°83 


| 


2°50 | 315 
2°60 | 2°35 
2-42 | 3-01 
3°34 | 4:16 
4-47 | 2-36 | 
5°57 | 3:63 
2°10 | 3°85 | 
1-91 | 1:08 
2°73 | 3-92 
0-87 | 3:98 
2°37 | 3:14 
3-45 | 3-66 


Sp) IS eT CS) 
An par hAIAwDOoOw A 


OR DUNMONOWWAD 


3:75 2°88 | 2-42 2:23 | 215 | 2-86 | 3:19 


The Rev. H. Luoyp on the Meteorology of Ireland. 4 


9 
a 


~l 


The lowest line in each gives the mean monthly fall of rain. It will be 
seen, from an inspection of the numbers, that there is no regular progression 
in the amount of rain-fall throughout the year, such as is observed in the phe- 
nomena of temperature or humidity. In Dublin the greatest rain-fall, in the 
mean of the eleven years, occurs in October, and the least in February; their 
amounts are 3°34 and 1:74 inches respectively. At Armagh the maximum is 
in January, and the minimum in May; and they amount to 3°75 and 215 
inches. The mean yearly rain-fall at Dublin is 29-14 inches; that at Armagh 
is 34°68 inches. 

The following Table gives the monthly fall of rain in the year 1851, at 
all the meteorological stations :— 


Taste XXXJI. Monruty Fatror Rarn 1 tor YEAR 1851, at att THE METEOROLOGICAL 


SraTions. 

Station. Jan. | Feb. | Mar. | Apr. | May. June. | July. | Aug. | Sept. | Oct. | Nov. | Dec. 
Portrush,.... | 569} 2.71 | 3:45 1:20 | 191 | 3:12 | 2°86 | 3:52] 1°36! 5°10 4-34] 1:98 
Buncrana, ... | 4:91/ 2.89) 3:36] 178} 1:69 | 2°83 | 3-41 | 3°30) 2-48) 5:20) 5-04) 2°39 
Donaghadee, . . | 5-45] 151) 3:38} 1°30/ 1:40} 2°93} 2:16) 3:18] 096} 1°82) 2°38] 1:46 
Killybegs, ... | 4:26 | 2°84] 2-20] 158) 1-82 | 3:08 2°84 | 2°93 | 2°84) 3:46) 3-25] 2-10 
Armagh, .... | 5.81 | 2°83) 2°65] 154} 1°92 | 3:13| 3°81 | 2°56) 1-84) 3-48/ 1-47} 2-01 
Killough,. . - . | 4:00 | 1:18] 2:47] 1:03 1:29 | 2°63 | 2°73 | 2°06} 1:00; 2°69 1:19! 0-92 
Markree, -... | 5:01 | 2°89; 3°07) 2°23; 1°53 | 2°67 | 5:20) 5°15] 2:40) 4-42, 3-68] 2-06 
Westport,* ... | 5°06! 4°37 | 561! 4°85 | 1:24! 4:55 3°78 | 3-431 2:02! 5-55 2°60 | 2°80 
Daoblinkyong te 5:28] 0°49 | 2°38 | 1°77] 1:31 | 2°71 3-48} 2°01] 1-81 | 3°27} 1:01 | 0-88 
Portarlington, . | 4:11] 052) 2:07| 0:94} 0°82 | 251) 2°59) 161) 0°84| 259] 1:15] 1-48 
JN eo loca a 5:10) 0°93 | 2°37 | 1:29 | 1:35 | 2°68 | 2°73 | 2°91) 1:24] 3-24] 1-41} 149 
Courtown, ... | 7:°98| 0°95 | 3°44 | 2°14} 1:17} 3:08) 2°67) 165] 063 | 3:41) 055) 1:97 
Kilrush, .... | 6°42] 1°69] 3°99} 1°75 | 0°96 | 2°50) 2°83 2:85 | 0°79] 4-44 | 2:10] 2-26 
Dunmore, .. - | 8:33 | 0:97 | 3°87 | 169} 1:26] 3°82| 2°67] 2:80] 0°66 | 4-29 | 0-74] 2-41 
Cahirciveen, . . |11:22| 4:90| 6:41 | 2°17) 2°31) 4°71 | 5°51 | 5°31 | 263] 7-74| 2:13) 4:33 
Castletownsend, | 9°76 | 367 | 403 | 153| 1:87| 487 | 479 | 380 | 068] 459 | 0-82) 212 


It will be seen from the foregoing Table, that the greatest diversity exists 
in the amount of rain-fall in different localities. To render this more apparent, 
and to facilitate the examination of the causes which influence the distribution, 
I have, in the following Table, given the yearly rain-fall at the several stations 
arranged in the order of magnitude, beginning with the smallest :— 


* The amount for the month of January at Westport is incomplete, the observations having 
commenced in the middle of the month. 


474 The Rev. H. Luoyp on the Meteorology of Ireland. 


Taste XXXII. Torat Rain-Fatt in rue Year 1851, at THE SEVERAL 
METEOROLOGICAL STATIONS. 


90-295 inches oe wen. . 2 23tinehes: 
Kalloushy 92 eats) eek Oia, 
(Dublin Sse wee eee BO eZoOl, fos 
aca ae LG aie War aati y Wen” a7 ae 
Donaghadee,; 5. - . 2093 5; 
Courtowny 6 = = 4 3s 297644, 
Kalrushy seep Gl sp om S208 a5 
aga. ues StS | ger 3305) es 
Kullybeps). 200s) feieute S3120) iy 
[ Dunmore wee OOO AT Gs 
Portrushs; mepne Merete Toul tenes 
—40 ” 
2 Buncrsnaee. sae ei SOO AOn ess 
WHR Be as og Dal 
AQ==A5 00 2 4 
Castletownsend, . . . 4253 ,, 
45—50  ,, porn AEN I 5 6 0 oS 45°86 ,, 
D0 =—GU mms see Cahirciveeny7. 2% 3 =, O9'S%, 5; 


Thus, it will be seen, the greatest rain (at Cahirciveen) is nearly treble of 
the least (at Portarlington). The mean rain-fall throughout Ireland, in the 
year 1851, is 34°50 inches. 

If we assume the proportion of rain at the different stations to be constant, 
or nearly so, the numbers of the preceding Table may all be reduced to their 
mean values, by multiplying by the factor which expresses the relation of the 
rain of 1851 to the mean at any one station. We already possess two such 
mean values: viz., at Armagh and Dublin. They are 29:14 and 34°68 inches 
respectively; and the factors thence deduced are 1:10 and 1:05. 

When we examine the results of the preceding Table, taken in connexion 
with the geographical position and physical circumstances of the stations, we 
arrive at the following conclusions :— 

1. The places of least rain are either inland, or on the eastern coast ; while 
those of greatest rain are at, or near, the western coast. Thus the stations at 
which the yearly fall of rain exceeds 40 inches are all on the western and south- 
western coasts; while those at which it is below 30 inches are either inland or 
on the eastern. 


The Rev. H. Luoyp on the Meteorology of Ireland. 475 


2. The amount of rain is greatly dependent on the proximity of a mountain 
chain or group, being always considerable in such neighbourhood, unless the 
station be to the east or north-east ofthe same. Thus, of the places of least rain, 
Portarlington lies to the north-east of Slieve-bloom ; Killough, to the north-east 
of the Mourne range; Dublin, to the north-east of the Dublin and Wicklow 
range ; while, on the other hand, the places of greatest rain—Cahirciveen, West- 
port, and Castletownsend—are in the vicinity of high mountains, but on a dif- 
ferent side. 

These facts are easily explained. The prevailing wind blows from the S. W., 
and reaches this island loaded with the vapour of the gulf-stream. This vapour 
is condensed and precipitated in rain, when it first meets the colder air over 
the land, namely, on the western and south-western shores. But the principal 
condensing centres are the mountains, in the neighbourhood of which, conse- 
quently, the precipitation is more abundant, and especially on their western and 
south-western sides. And the same circumstance which causes the greater 
precipitation at these points must also protect the region over which the wind 
next passes (the north-east), the air being thus deprived of a large portion of 
its vapour before arriving there. 


TABLES. 


The following Tables contain the portions of the individual observations, 
the results of which are referred to in pages 450—469. 

Table xxxim. contains the selected observations on days of storm, or of 
marked cyclonic movement. It comprises the direction and force of the wind, the 
pressure, temperature, and amount of cloud, at the time of observation ; as also 
the greatest and least temperatures, and the quantity of rain fallen, in the pre- 
ceding twenty-four hours. The pressures are, for comparison, reduced to the 
mean sea-level; the numbers in the Table are the excesses above 28 inches. 
The force of the wind is expressed in terms of the scale (0 —6). 

Table xxxtv. contains the hourly observations on the term-days, March 21, 
22, and June 21, 22, at Portrush, Armagh, Markree, Courtown, Dunmore, and 
Cahirciveen. The velocity of the wind at Portrush, Armagh, Markree, and 
Courtown, was observed by means of Ropinson’s anemometer; it is expressed 
in feet per second. 

VOL. XXII. 3Q 


476 The Rev. H. Luoyp on the Meteorology of Ireland. 


Taste XXXIII. SeExecrep OBSERVATIONS. 


1850. Ocroper 6, 9 A.M. OcToBER 6, 9 P.M. 
Station. = | \ 

sie YOR I eae Therm.) Cloud. | Rain. loca Wiad Barom.| Therm.| Max. | Min. 

Direction. |Force ° Direction. Force 
Portrush,...|| 8. | 2 |1873|46"7| 8 | -04 | sg. | 2 |0-952/ 505 | 56°-0| 41°-0 
Buncrana, . . S. 1 |1527|49°6|} 10 | 36 || S. 0 |1:022 | 50 6| 55 -0| 43 -0 
Donaghadee, . S.W. | 0 1-590 | 49 ‘7; 10 | 01 | S.W. | 5 |0:998|51 +1) 54 -7|43 °5 
Killybegs,... Ss. — |1:387)| 48-71 —.) 47 Naw) | 5 0:836 | 53 -0! 55 -0| 48 .0 
Armagh, ...|| 5. 1:9 |1:558| 47-3} 10 | -03 Ss. 3:0 |0°906 | 49 2) 55 0/44 °5 
Markree, ees S. E. 4 |1:383/47°1] 10 | -27 | W.N.W.| 6 /|0:908 | 52 0) 55 5} 40 °2 
Dublingwe ens 8. E. 1 )1°562)49-1] 10 ; :09 8. 4 |1:063 | 52 -5| 60 5) 45 °3 
Courtown, . - S. 2 11:550/50°5| 10 | 710 S.W. 2 |1:180 | 52 -2| 59 -2|42 0 
Kilrush, S.W. | 3 |1:392/54°3} — | 04 ||S.S.W.]| 5 |1:242} 49 -3) 59 0) 49 °5 
pon foe Wy Ba ; ames 53 °8 ae ai eG 3 |1-242| 53 -3| 53 5/47 5 
ahirciveen, . .5.W. _— (a ee aw. . a= — ‘ee 23 
Castletownsend, W.S.W.| 3 |1°423/55 5} 10 — |S. S.W.| 5 |1:382/51 5 | 61 0/50 °5 

| 

| OcToBER 7, 9 A.M. OcrToBER 22, 9 P.M. 

Station. rand ’ 

— ae : Barom.| Therm.| Cloud. | Rain. || ——————_—_— wi Barom.) Therm.| Max. | Min. 

Direction. | Force | Direction. | Force} 
Portrush, ... || N.W. | 5 [1:245|48°5| 7 | 42 | NW. | 2 |1-645 | 50°7|54°0/41°°0 
Buncrana, .. || N.N.W.| 4 {1-458 | 49 6) 5 | 58 | N. W. | 3 |1-721)|48':6) — |36-0 
Donaghadee, . N.W. | 5 |1:190|52 -2| 10 | -25 || N.W. 3 |1-610|49 -4| — |41-0 
Killybegs,. . - N.W. | — |1:460 |52 8] — | °15 N.W. | — {1-708} 51 0/53 5 | 42 3 
Armagh, ... N.W. | 2°6 |1:340 jol ‘O| 8 | *28 N.W. |2°3 |1:640 | 47 -5|49 -9| 41 -0 
Markree, .. . ||W. N. W. 5 11:-493/51°:0| 7 | 23 || N.N.W.| 3 1|1°682) 48 :8|52 -6|31 :7 
Dublin, 5 2: s S.W. | 4 |1425|)50°9; 1 07 S.W. | 3 |1-649/ 48-9151 -2|35 5 
Courtown, - - W. 4 |1488|50°5| 3 | 12 S. W. | — |1°736 | 45 -2/ 48 -0| 34 :0 
Kilrush,.... || N. W. | 4 [1590 |49 G3) [}- | ss N.W. 4 |1°851 | 52 -3|54 -0/ 39 0 
ne bee Ne ; tose 52 °3 E: a4 eae ; 2-233?) 43 3 49 5/36 °0 

ahirciveen, - - WwW. 226?) — ; || W.N. W. 1:831 | 53 -6| 55 0} 39 0 

Castletownsend,|| W.S.W.| 1 |1:714|54 5) 3 — |W.S.W.) 3 |1:°837|51 |e 0 | 39 -0 


REMARKS. 


Oct. 6, 9 A. M—Rain throughout the island; heavy rain at Cahirciveen. 

Oct. 6, 9 Pp. @_—Storm in north-west from 10 30 Pp. mM. to 3 A.M. of following day. Showers 
in south; hail at Markree. 

Oct. 7, 9 A. &—Showers at Portrush, Donaghadee, and Cahirciveen; hail at Markree. 

Oct.22, 9 p.m.—Heavy clouds at Buncrana, rising from the horizon in north-east, at 

this and at succeeding observation. Rain in south. 


The Rev. H. Luoyp on the Meteorology of Ireland. 477 


Taste XXXIII. (continued). SELECTED OBSERVATIONS. 


| OcroberR 23, 9 A.M. OctoBER 23, 9 P. M. 
Station. 
Wind. a Wind. | ee 

|__| Barom.| Therm.| Cloud. | Rain. || —————___Barom.| Therm.| Max. | Min. 

Direction. | Force Direction, | Force! | 
Portrush,. .. || N.E. | 2 |1-489|47°0] 4 24 || N. 2 1-439) 47°°3 | 47°-0 | 43°-0 
Buncrana, .. | N.N.E.| 2 |1-543/40-6| 6 | 68 | N.N.E.| 4 [1512/44 6) — | 380 
Donaghadee, . |, N.E. | 3 |1:422]47°6] 5 | -13 ||N.N.W.| 2 |1:360|44 -4|50 0) 42 6 
Killybegs, .. N. — |1°540/43 -°3) — | -27 N. — |1464/46 -8|49 -2|42 0 
Armagh, ... || N.N.W./1°1 |1:478|}40 5) 2 23 |W. N.W.| 1-1 |1:414/41 -8| 47 8) 38 5 
Markree, ... N. 3 |1:552)44 9) 9 ou) EN: 3 |1:469| 44 °3) 48 -2) 41 0 
Dublin, .... N.W. | 2 |1°454/44 4) 1 05 a 3 |1-407|43 :1|50 5/39 3 
Courtown, .. || N. W. | — |1445/44-0! 2 08 N.W. | — |1:413)43 0/51 -0| 42 2 
Kilrush, N.N.W.) 5 |1°628}47 -3| — | :27 N. 4 |1593|45 -4|49 0) 44 -2 
Dunmore, N. W. | 3 |1:470/45 -8| — | -18 || N.W. | 3 |1:425/43 -3|48 0/41 5 
Cahirciveen, N. 3 |1619}49 8} 10 | 57 N. E. 3 |1621|46 -8|48 0/45 6 
Castletownsend, N 1 |1:610) 48 -5 9 | -00 N. 1 |1544)| 44 5 |52 0/46 0 

NoveEMBER 18, 9 P. M. NoveMBER 19, 9 A.M. 
Station. | 
Wind. ae} Wind. | - 

——_——Barom.|Therm.| Max. | Min. ||; __________| Barom.| Therm.) Clond. | Rain. 

Direction. | Force Direction. | Force | 
Portrush,... || S.E. | 2 |1:169)47°-8|55°-0|43°:0 |) S.E. | 2 |0-408/47°5) 9 | 67 
Buncrana,. . . |) S.S.E.| 5 |1:205)46 -8| — |42°0| Ss. 3 |0-411/45 -7| 10 ‘88 
Donaghadee, . || S.E. | 4 |1:195|48-5) — |41°5 Ss. 5 |0-438/48 -9| 10 | 59 
Killybegs, .. . S. E. 5 |0°991)49 5/54 0/438 N. — |0°307|44 -9| — 50 
Armagh, ... 8. E. | 2°3/1-055|50 0) 54 5/39 0) S.S. E. | 3:-4/0°248| 44 -5| 10 70 
Markree, ... || S.E. | 5 |0:813|53 3/54 4/35 -9||N.N.W.| 3 |0:285|45 6| 10 | 61 
Dublin, .... || S.S.E.| 2 |1:126/55 -4|58 -2| 44 -0 Ss. 5 |0:383|45 2] 10 | ‘51 
Courtown, §.S.W.| 3 |1-214/55 -2'57 -0!42 0||S.S.W.| 5 !0589/48 -0| 10 70 
Kilrush,. ... S. E. 5 |0:916|48 -6|55 -6|46 -0|| W.NW.| 6 |0-542|56 -2?) 10 | 2-40 
Dunmore,... || S.W. | 5 |1:146/49 8/53 5/460] W. 6 |0671/48 -8) — | -72 
Cahirciveen, . Bas 5 0923 | 55 8/58 5/45 -8|/W.N.W.| 5 |0°825|/48 -2| 10 | -97 
Castletownsend,|| S.W. | 5 |1:148|54 5/56 -0|42-0 | N.W. | 5 |0°864)47 0} 10 | 1:00 

| ) \| | 

REMARKS. 


Oct. 23, 9 a. m—Squally day. Showers on west coast; hail at Markree. 

Oct. 23, 9 ep. m—Showers throughout, except south-eastern quarter; hail at Buncrana and 
Markree. 

Nov. 18, 9 p. m.—Rapid fall of barometer. Continued rain throughout the island. 

Nov. 19, 9 a. M—Surface of mercury concave at Dublin. Rain throughout; heavy at Kilrush 
and Castletownsend. Spray from the sea supposed to have reached the gauge at Kilrush. 


478 The Rev. H. Luoyp on the Meteorology of Ireland. 


Taste XXXIII. (continued). Sztecrep OBSERVATIONS. 


NovemBer 19, 9 Pp. M. NovemBer 20, 9 a. m. 


Station. 


| 


| Barom.| Therm.| Max. | Min. 


Wind. 
——F Barom.| Therm.| Cloud. 
| Direction. | Force 


Direction. Force! 


44°-0 | 
44 
43 
44 
44 
40 
45 
49 
44 
46 
47 
AT 


0, 


1113 49°-6 
1172 44 
1001 49 
1:214 | 47 
1-096 48 
1-245 | 48 
1-003 | 48 
10-947 | 47 
1:354| 47 
\1:071)| 48 
1-435 | 46 
1-240 | 48 


| | 

0587 | 49°5 
0610 47 
(0-410 46 
(0-714 49 
0571) 46 
0694) 47 
0549 | 47 
0°585 | 47 
0-794) 45 
0-711) 46 
1-147) 48 
0949 45 


bo 


Portrush, . . 

Buncrana,... 
Donaghadee, . || 
Killybegs,. . . || 
Armagh, 

Markree, 

Dublin, . 
Courtown, | 
Kilrush,. . . . || 
Dunmore, .. . 
Cahirciveen,. . || 
Castletownsend, 


Ar Or rr 
bo 


WARANwWAS |] PRw 


SADSHS S 


SS6UNSANSSSS 
ANDwWSROAASH 


ADDWWASAOWAN 
Srey | SSS et) 


Cis 
Soon 


CAR He ND | OO 0D 


NovEMBER 23, 9 P. M. NovemBeEr 24, 9 a. M. 


Station. 


Wind. | Wind. 
|__| Barom.| Therm.| Max. in. || ————————————__ Barom.| Therm.} Cloud. 
Direction. | Force || Direction. | Force 


1-235 | 434 | 52°-0 S.W. | 2 [0-741|48°2 
1:197 | 42 - 2 0°770 | 47 
1-362 44 1 |0-775| 48 
1-243 46 - 3. 0684 | 50 
1-294 42 2°9 |0°723 | 50 
1-210 42 (0605 | 49 
1-389 43 (0-797 |51 
1-446?) 43 - 0:870 | 54 
1-247 48 0-718 | 52 
1-380 53 0°895 52 
1-215 52° 0834 | 51 
137649 + (01922 53 


Portrush, .. . 
Buncrana,. . . 
Donaghadee, . 
Killybegs,.. . 
Armagh, ¢ 
Markree, ... 
Dublin ys. 
Courtown, . . 
Kalrush;s: +) « 
Dunmore, . . . 
Cahirciveen, 

Castletownsend, | 


m 
4 


150 * 
(G49 
62)" 
151° 
157 = 
56 
56° 
153 * 
57 * 
55° 


nw 
| coww 


OP RW Ww Gree mw 
= 


A44455 


Aowwoedwmnce 
SRANSGAAKH WSN 
ARDBSARHSASH 


44s nmnmnm: 
ig) 
4 


44%: 
Sol 


REMARKS. 


Nov. 19, 9 p. m—Showers throughout, except south-eastern quarter. 

Noy. 23, 9 p. Mi—Rain on west coast. 

Nov. 24, 9 a. m.—Showers in various places; thunder and lightning at Cahirciveen. 
Noy. 24, 9 p. m—Showers throughout the island. 


The Rev. H. Lioyp on the Meteorology of Ireland. 479 


Taste XXXII. (continued). SrLecTED OBSERVATIONS. 


NoveEMBeER 24, 9 Pp. M. | DeEcempeER 14, 9 A.M. 
Station. | | 

Wind. | 34) Wind : 

|| _——————__ Barom.| Therm.) Max. | Min. — ——|Barom.|Therm.| Cloud.| Rain. 

|| Direction. sas | || Direction. | Force] 
Portrush, ... Ss. W. 4 |0°568 | 47°-9 52°-0| 41°0 S. 4 |1:164 40°-2 9 | 03 
Buncrana, .. || N.W. | 5 |0°498/46-6} — | 41-1) S.S.W.| 5 {1-079} 42 6} 10 | -06 
Donaghadee, . || W. | 3 |0:586|47 -4/51 -4/43-1|'S.S.W.] 4 |1:353/42-4| 10 | -16 
Killybegs,.. . ||W.N.W.| 5 |0°715] 48 -5|/52°3/45 0), S. 6 |0:948 | 47 5 ==, |.:06 
Armagh, .. . |W. 5S. W.| 2°6 |0°690/ 45 -2] 51 8 | 42 -0|| S.S. E. | 4:1]1-185) 42 -2| 10 .03 
Markree, ... | W. S.W.| 5 |0°777, 42 -6| 50 8/41 2|| S. S.W.| 6 0-955 44 ‘6, LOM G23 
Dublin, .... || S.W. | 5 |0-776) 45 -4| 56 -5| 44 -2||S.S.E.| 2 |1-347|47°4| 10 | -04 
Courtown, W.S. W.| 3 |0'850) 45-0 55 5|40-0) S.W. | 3 |1-429/39-0) 10 | 00 
Kilrush,. .. . ||W.N.W.| 5 |0-914! 44 -8| 53 5/48 -5|| S.W. | 5 |1:174|43°3] 10 | -55 
Dunmore,... || W. | 5 |0:947|52-37 500/49 -5|| S.w. | 4 |1-386/49 3) — | -23 
Cahirciveen, .| W. 5 | — |47 -8| 56 -0| 47 0| W. 5 |1-242/45 -2| 8 | -50 
Castletownsend,|) W. 5 |1:°013 48 -5| 55 -0| 46 “| S.W. | 5 |1:297)50 5| 10 | -26 


DerceMBER 14, 9 P.M. | DeEcEMBER 15, 9 A. M. 
Station. 
Wind. el Wind. 

|———_____—— Barom.| Therm.) Max. | Min. | Barom.| Therm.| Cloud. | Rain. 

| Direction. Force || Direction. | Force 
Portrush, +++ || S.W. | 3 |1:055|38°-6|47°0 | 37°0|] S.W. | 4 |1:055|40°-0 3 
Buncrana,. .. || W.S.W.| 3° |0-982/38 6] — |38-0|| W. 4 |1:026/39 -6| 4 
Donaghadee, . | W.S.W.) 3 |1:118) 39 4/48 -0 | 40 ‘|| Ww. 3 |1:137| 37 °4 8 
Killybegs,. . . W. | 5 /1:104| 42 -3/45 -0|38-0 W. 5 |1:146] 42-3) — 
Armagh, ... S.W. |3°4 |1:163 36 ‘7|46 8 |34-0]) S.W. |3:0 1163 | 387 -5 9 
Markree, ... || S.W. | 3 |1:156|36 2/45 -7 | 37-8|| S. W. 1 |1:061,/ 39-6; 9 
Dublin,.... || S.S.W.| 4 |1:276/38 -4|52-°8/41 -0||S.S.W.|] 2 |1-255|42 -4| 10 
Courtown, 8. W. | 3 |1:314/37 -5|41 5 /36-0] SW. 1 |1°316'40-0) 10 
Kilrush,. .. . ||W.S.W.) 5 |1:326 39 -8|45 -0|41 -0|W.S.W.| 2 |1-294) 46 iyi 16) 
Dunmore,... | N. W. | 5 /1:396/ 40 8/51 0/41 5) S.W. | 2 |1:310/46-3) — 
Cahirciveen, . |) W. 5 |1-404 | 42 -8) 43-0 |} 41-0) S. W. 2 |1:213/47 4] 10 
Castletownsend, W.8.W.| 5 [1-409 445/510 42-0, S.W. | 3 1-300) 46 5) 10 


REMARKS. 


Nov. 24, 9 p. M.—Gale from 6 P.M. to 9 p. Mm. at Markree, 

Dec. 14, 9 4. m—Thunder and lightning at Cahirciveen and Kilrush. 

Dec. 14, 9 p. m.—Thunder and lightning throughout theisland. Hail fell in several places 
during the day. 


480 The Rev. H. Lioyp on the Meteorology of Ireland. 


Taste XXXIII. (continued). SELECTED OBSERVATIONS. 


DECEMBER 31, 9 A.M. DEcEMBER 31, 9 P.M. 
Station. 
Wind. Wind. 

—____—_——_ Barom.| Therm.| Cloud. | Rain. || —_———————_| Barom. | Therm.| Max. | Min. 

Direction. | Force Direction. Force! 
Portrush, .. . S. 3 |1:430] 444 9 12 8. 3 |1:173/50°-0 | 56°0 | 40°0 
Buncrana,. . . || S.S.W.| 4 |1-400/47 6] 10 | -00 ||S.S.W.| 4 |1:180)48°6| — |42°0 
Donaghadee, . || S.S.W.| 3 /1525/44°9/ 10 | 04 | S. W. 2 |1:291|49 -4/52-0/ 41-5 
Killybegs, S.S.W.| 4 |1:317/50:2} — | -06 ||S.S.W.| 5 |1:171]49 4/52 -0) 44 0 
Armagh, ... | Ss. 3°8 | 1-463 47 0} 10 | :05 Ss. 30 |1-264)51- 1/53 +8 | 46-0 
Markree, ... Ss. 4 {1:311|/50°2) 10 | -11 S.S.W. | 3 |1:204/50 ‘2/54 -2 | 38 -6 
Dublin, .... Ss. 2 |1:°543/51 °9} 10 | -03 S. 3 |1:306| 54 -9 57-8 |48 +5 
Courtown, 8. 3 11:631/50°5| 10 | 00 || S.S.W.| 5 |1:399 53 °2/55 ‘0 48 0 
Kilrush,.... || S.W. 3 |1:455/52 3) 10 | -15 || S.S.W.] 5 |1:270)51 3) — |42°5 
Dunmore,... || S. W. 3 |1:606/51°8| — | -02 || S.S.W.| 5 [1405/52 °8|52 -5 | 47-0 
Cahirciveen, Ww. 5 |1:405|/55 °2} 10 | -00 S.W. 5 |1:314/51°6/)56 -0 51-0 
Castletownsend,| S.S,W.| 5 [1:580/52-0| 10 | -10 S.W. | 6 |1:379| 53 °5 |54 :0 |48 °5 

| 

1851. January 1, 9 A.M. JANUARY 1, 9 P.M. 
Station. 
Wind. Wind. 
——— #44 _|Barom.| Therm.] Cloud. | Rain. || ____—__—___| Barom.| Therm.] Max. | Min. 
Direction. | Force Direction. | Force} 

Portrush,. .. || S.W. | 3 |1:282/46%4] 4 | -12 Ss. 1 |0°949) 47°0 | 51°:0 | 43° 0 
Buncrana,. . . || S.S.W.| 2 |1:298/44°6] 8 | 08 |IN.N.W.| 2 |1:000/43 -6| — |43-0 
Donaghadee, . || W.S.W.| 2 |1-370/47-4] 9 | 08 | S. WL | 4 |1:055)/49 9/53 -0 45 -2 
Killybegs,. . - S. W. 2 |1-285'47°5| — |-15 |IW.N.W.| 1 |1:066)/43 5/47 -2!45 -0 
Armagh, : S.W. | 38/1383 48-0] 10 | -29 Ss 3°8 0:998) 53 +1 /54 +5) 41-5 
Killough, ... S. W. 3 1-444 48 *3 7 |-00 Ss. 6 |1:108| 47 -5|52 0/48 -0 
Markree, ... S. 2 |1:319 44-6} 10 | °38 N.W. | 3 |1:078) 42 -7 | 48 :3| 44-0 
Dublin, ....||S.S.W.| 3 |1:-4211/51°5} 10 | -20 Ss. 4 |1:109) 56 5/58 :0| 52 -2 
Courtown, .. || S.S.W.| 3 |1:-455)51°5| 10 | 15 S. 5 |1:230) 53 °5/55 -5/50 -0 
Kalrush;. -< - S.W. | 2 |1:503/50°3) 10 | -08 || S.S.W.| 5 | 1029/53 -3) — |49-0 
Dunmore,... ever Se | MeaToke 8 lie) S. 5 |1:210)53 °8/54 0/49 5 
Cahirciveen, S.W. | 3 |1-427|/50 8] 10 | ‘60 Ww. 2 | — |46-8/56 .0/49 -4 
Castletownsend,|| S.W. | 5 |1:463)51°5| 10 | 55 || S.S.W.| 6 |1:144)52 5/55 0/48 -0 


REMARKS. 


Dec 31, 9 4.m.—Rain on west coast. 

Dec. 31, 9 rp. m.—Rain in south; light rain on the east coast. Lightning observed at Killy- 
begs. At Markree gale abated at 4 p.m. 

Jan. 1, 9 A. m—Lightning observed at Markree. Rain in south-west. 

Jan. 1, 9 p. Ma—Rain throughout; continued rain in north. 


The Rev. H. Lioyp on the Meteorology of Ireland. 481 


Taste XXXII. (continued). SELEcTED OBSERVATIONS. 


JANUARY 12, 9 P.M. JANUARY 13, 9 A.M. 


Station. 
Wind. 


| Direction. | Force 


| Wind. 
Barom.| Therm.| Max. in. || ————————|Barom.| Therm.| Cloud. 
| Direction. | Force 


1-697) 42°5 49°-0 | 
1-669 | 43 
1-800) 44 - 
1535 | 45 - 
1-720) 43 - 
1-776 46 
1:560| 43 
1-797 | 44 
1°830 | 45 
1651) 47 
1-801 | 46 
1-628) 48 
1-719) 47 - 


Portrushes. als 
Buncrana,.. . 
Donaghadee, . 
Killybegs, . . 
Armagh, 2 
Killough, ... 
Markree, .. . 
Dublinsys 1. 
Courtown, 
(Kolrughyee. s- 
Dunmore, . 
Cahirciveen, 
Castletownsend, 


1-283 | 48°-4| 10 
1-254 | 49 10 
\1-407 | 47 10 
1157 | 49 
1-327 | 49 
\1-377 | 49 
1-190 | 49 
1-455 | 51 
1507 | 50 
1543?) 49 
1-463 | 50 
1-244 | 52 
1-347 | 50 


a 
a) 
fe) 

So 


ASAKRSOAGBSBNASS 


49 
51 
50 
53 
40 
53 
51 
51 
50 
52 


> Ow eo 


10 
8 
10 
gi 
10 
10 


Din D nn m mm tn 
Bie 
ite) 


ae 


10 
10 


AhOWSANDNWASB 
AnAnNnwwanho kaw 
SHUDANAWSAGA 


or 
= 
SSASUSHSSONWA 


Cre Go OD to BOO 


January 1 ime | JANUARY 15, 9 P.M. 


Station. e 
Wind. , Wind. 
——_—_—_—_ | -| Therm.) Cloud. | Rain. || —__——___| Therm.| 
Direction. | Force | Direction. Force, | 


Portrush, . . « . B. 2 | 43°2 | 76 
Buncrana,.. . . K. 2 44 55 
Donaghadee, . 44 “82 
Killybegs,. . . 43 68 
Armagh, 44 “76 
Killough, ... 45 ‘61 
Markree, ... 42 78 
Westport,.. . 42 56 
Dubliners 47 81 
Courtown,. . . 48 ‘90 1-424 
Kilrush,.... 39 1:06 

Dunmore,... 47 98 


1-428 
1485 
Castletownsend, 40 115 || 


44°°7 
42 6 
43 9) 
1321/44 0 
1-312) 41 -2 
1349 | 42-5 
1-365 | 37 5 


Fe = 
wewnw|] wwgworw 


1-361 


COR AWN ANH 6 OF 
Ad dwKSHSOHSH= 


1-499 


REMARKS. 


Jan. 12, 9 p.m.—Showers on west coast. Lunar halo observed at Buncrana, Donaghadee, 
and Courtown. 

Jan. 13, 9 a. m—Rain in several places, but not universal. 

Jan. 15, 9 a. M.—Rain throughout the island. 

Jan. 15, 9 Pp. m.—At Markree, gale lasted from 1 p.m. to6 P.M. Lunar halo observed at 
Markree and Donaghadee. 


4§2 The Rev. H. Lioyp on the Meteorology of Ireland. 


Tasre XXXIII. (continued). SELectED OBsERVATIONS. 


| January 16, 9 A.M. January 16, 9 P.M. 
Station. | | 
| Wing. =| ? Wind. =| | 
|_——————— Barom.| Therm.| Cloud. | Rain. || ———_——___. Barom, Therm.| Max. | Min. 
Direction. F°rce | Direction. | Force) | 
Portrush,... || S. 3 |1:138/40°3| 10 | -28 S. 3 |0:723 49°0 | 52°-0 35°0 
Buncrana, .. . Ss. 5 |1:087|41 6] 10 | 35 ||S.S.W.| 5 |0-671/48-1| — |37°0 
Donaghadee, . Ss. 6 |1:254|/43 4] 10 | -49 S.W. | 4 |0:872 48 -4/50-1/ 39-0 
Killybegs, .. S. E. 5 (0925/45 3) — | -28 ||W.N.W.| 6 (0-:772) 48 -0|54 -2 |38 5 
Armagh, ... || S.S.E. | 5:0 1:072|44-1| 10 | ‘61 S.W. | 4-5 |0°858 | 47 -8 52 2/38 -0 
Killough,... |} 5S. 6 |1:153)45 -4; 10 | -42 S. W. 6 |0:948 | 48-3 51-0) 40-0 
Markree, ... || S.E. 5 0°879\46°8) 10 | °31 S.W. | 5 |0°876|45 -7 |52 -0|33 -7 
Westport,... || 5. 6 (0:812/54-0| — | 69 SEER ye (Reha ree ee 
Dublin, .... {| S.E. | 4 [|1-182/47--1| 10 | -73 s. 4 |0-966 49-3 56-0 39-7 
Courtown, Ss. 5 |1:209 47°5| 10 | 54 |S. S.W.| 3 |1:059/48 -0|53 5 |33 °0 
Kilrush, S.W. | 5 |0°922|50°8/ 10 | -50 S.W. | 5 |0:980| 48 -8? 52 -0/39 5 
Dunmore,.. . | S. 5 1144/48 -8} — | -96 || W.S.W.) 5 |1-112)47 -3/51 5/38 -0 
Cahirciveen, . || S.S.W.| 5 (0863 54 ‘0; 10 | -00 W. 5 {1041/46 0/550) — 
Castletownsend,|| S.W. | 5 |0°857/51°5| 10 | -73 || W.S.W.| 6 |1:093) 48 ‘5 54 0/40 0 
| i 
JANUARY 27, 9 P.M. JANUARY 28, 9 A.M. 
Station. : Nl l I ; | l 
Wind. | ge || Wind. Lies | 
——_—__—_  Barom.| Therm. Max. | Min. | —_________Barom. Therm. | Cloud. | Rain. 
|| Direction. | Force, | | | Direction. Force | 
Portrush, ... || S.E. 3 |1-456| 45°7|47°-0/33°-0|| —S. 1 |1:547|38°8} 2 S) 
Buncrana,. . . Ss. 5 |1:378| 45 6 46 0/35 0) S.S.W.| 3 |1506 39-6] 4 03 
Donaghadee, . || S.S.E.| 5 |1°575|}45 6/47 0 36°5)) S.W. | 1 |1634/39-9) 2 | -22 
Killybegs,. . . Ss. 5 |1-285| 45 -7|47 5/38 -0|| W.S. W.| 3 |1-487|42 -7| — | -03 
Armagh, ...|| S. 3'8/ 1439/45 -9| 46 0,35 0) Ss. 30/1588 39 4} 0 08 
Killough, ... | S. | 3 |1542)44 5/45 -0|36-0|| S.W. | 3 |1665/41 6 | 2 | -18 
Markree, | 8. 4 /1:°333| 41 -4,45 8/298) S.E. 2 |1:507;38 6) 10 ; -23 
Westport,... |} — =|) | | SS = |) ite 8 1-461 | 46 *0)|, —smr48 
Dubliny =). 2) |(eess 2 |1516| 45 5} 49 0/35 -0|| ~~ S. 1 |1645)/40°9) 6 15 
Courtown, ..||_ S. 3 [1542] 43 8] 49 -0/31-2|| S.W. 1 |1690|37:°0) 3 | :34 
Kilrush,.... || S.W. | 5 |1:329| 41 -8| 48 -0| 37 -5 Ss. 3 /1514 | 42 -3)|| 10) shiee23 
Dunmore,.. . || S.S.W.| 5 |1516) 46 -3| 47 0) 35 0) S.W. | 2 1-658 | 47 “3 isis 
Cahirciveen,. . || S.W. | 5 |1:349/ 43 -8|49 -6|36°6) S.W. | 4 |1:470| 44 -4| 10 67 
Castletownsend,|\W.S. W.| 5 |1:452)| 44 ‘5| 50 0} 37 bal SW. | 5 |1620/44-5; 10 Se 
| | 
REMARKS. 


Jan, 16, 9 a.m.—Lightning at Westport. Rain throughout the island. 

Jan. 16, 9 p. M.—Lunar halo at Dublin and Courtown. Showers at various places. 

Jan. 27, 9 p. M.—Rain at both extremities of the island; hail in south. Gale lasted from noon 
to 3 P.M. at Castletownsend, from 4 P.M. to 7 P.M. at Markree. 


The Rev. H. Luorp on the Meteorology of Ireland. 483 


Taste XXXIII. (continued). SELEcTED OBsERVATIONS. 


JaNuARY 30, 9 P.M | January 31, 9 A.M. 


Station. | Wind. ] ] 


|| Direction. | Force 
Portrush,... || S. W. 
Buncrana,... |S. 


Donaghadee, . Ssh AVE 
B Vie 


l Wind. | 
|Barom.| Therm.| Max. Barom. Therm.| Cloud. 
| 


| 


Direction. | Force 


1:162 |35°1 | 39°-0 , 1:168| 33°4 
1-217? 33 -6 | 39 -0 Sim 1-090) 36 - 
1189 |32 -6 | 40 -0| | $.S.E. 1:175| 35 . 
1:128 |37 “5 | 41-5]: cE 1-082| 38 - 
1-185 |31 -9 | 38-8 1°137|35 ° 
1-191 |41 -82| 47 -0 1-168! 42 
1:149 |32 -3 | 38-7 1-058) 34° 
1-032 44° 
1-127 | 35 
1:124 | 35° 
1:100/ 42 
1-157 | 38 
1-070 | 43 
1-184) 41 


_ 
S| Nolo sor) 


Killybegs,.. . 
Armagh,.. . 
Killough, ... | 
Markree, ... 
Westport,... 
Dublin, .. 
Courtown,. . . 
Kilrush,.... |] 
Dunmore,... 
Cahirciveen,. . 
Castletownsend, 


So 
a” 


_ 
oa 


1-220 |35 -0 | 42-5): 
1-221 |34-0 | 41° | 
1-224 |38 °3 | 44 0/35 °5} 
1:245 |36 ‘8 | 41 -5| 35 °5/| 
1-255 |41 6 | 45-0 37° 
1338 38 5 [425 37° 


Ronmwnww| H—Fwewe 
wUNNHonere 
ARDDSODSHWSTARAR 
Fs 

oo 


JANUARY 31, 9 P.M. | Marca 18, 9 a. M. 


Wind. | | Wind. | 
Barom. i Manes) Mins” || _— | Barom: Therm.| Cloud. 


|| Direction. | Force) * || Direction. Force, | 
1-440 | 40°-7 | 44°-0 | 30°-0 | | 1-395|42°9| 10 
1-484 | 34 8/41 -0| 33 -0| 1:373|41 6| 10 
|1:441/ 40 -9|44 0/31 5 1:475| 44 10 
|1°525) 36 5/43 3/34 8) W.N.W.) 4 | 1:325| 41 — 
|1-485| 32 6/40 -8)31-0|| S.E. | 3:5| 1-328) 45 10 

1-460) 34 -4|44 -0 : 1-460 | 45 10 
1:531| 35 3/42 °1 1-331) 45 

1-366 47 
1:381 | 50 
| 1-460 50 
1-465 44 
1-504 48 
1-458} 48 - 
| 1523 50° 


Station. | ] | 


Portrush, ... 
Buncrana,.. . 
Donaghadee, . 
Killybegs,. . . 
Armagh, ... 
Killough, ... | 
Markree, ... 
Westport,. .. 
Dublin, ... 
Courtown, 
Karsh sire 
Dunmore,... 
Cahirciveen, 
Castletownsend, 


mm OO 


1382 40-0 44:8 
1-288 40 7/44 5|: 
1-380 38 8/440 
|1-258/ 41 8/44 0 
1-268) 42 -4/ 46 -2 
1243/43 -5 48-0 


NERO RW] WOROwWH ND 


Cr RB OOo & OO 


AN DarAsdAwWHUAR 


REMARKS. 


Jan. 30, 9 p.u.—Lightning at Markree and Buncrana. Rain, snow, and hail in west. 

Jan, 31, 9 a. M.—Lightning observed in north in the evening. Light rain on west coast. 
Hail and sleet in some places. 

March 18, 9 a. m-—Rain throughout island, south-eastern quarter excepted. 


VOL. XXII. 3R 


484 


The Rev. H. Luoyp on the Meteorology of Ireland. 


Taste X XXIII. (continued). 


SELECTED OBSERVATIONS. 


} Marcu 18, 9 P.M. Marca 19, 9 A.M. 
pee | Wind. 
| Direction. | Force Barom.| Therm.| Max. | Min. \| Direction. | Force Barom.| Therm.) Cloud. | Rain. 
Portrush,. .. | S.W. | 3 |1:371|42°-4|49°0|39°0 | S.W. | 3 |1-449|44°3| 4 | -46 
Buncrana,... | W.S.W.| 3 1°376 | 41 +1/50 -0|40°0 | Ss. W. 2 |1:395 46 “6 5 31 
Donaghadee, . | W. 3 | 1-454) 41 4/50 5/41 5 |W.S.W.| 2 |1520/ 44 -4 9 46 
Killybegs,... |  W- 5 | 1-408 45 0 49 5/41 -0 |W. S.W.| 0 |1:450|47 -1) — | *00 
Armagh, . || S.S.W. | 2:5 |1-470 40 -8 | 49 5 | 40 -0 S. 2 |1:-487/44-5) 10 | -25 
Killough,... | S. W. 3 |1500 43-3) 50-0} 41 -0 Vis 3 |1510? 44-5 2 | 18 
Markree, ...|| S.E. | 3 |1-465|42°7/48-7|/39-5|| S.E. 2 |1°386|46 3! 10 | :14 
Westport,... || W. | 5 |1495)47-0/ —/} — | 5S. 2 |1-428|/47-0| — | -14 
Dublin, .... | S.S.W.| 3 |1:557|43 -7 | 54-3) 41 5 || S. E. 0 (1518 )46°5|} 10 | -03 
Courtown, .. || S. W. 1 |1-608| 41 -2/55 -0)41°5]|_ ~‘S. 1 |1:534/46-5| 10 | -00 
Kilrush,.... | W. | 4 |1-608)46-8 48-5|40-5] S.E, | 2 |1-411|46°8) 10 | 06 
Dunmore,... | W. 3 |1:634| 45 -3)57 -5| 43 0}| S.S.W. | 2 |1:°504/47 3) — | -16 
Cahirciveen, . ||W.S.W.| 3 /1:671/45 6/51 -0|46 4] E.S.E.| 1 |1°345|46 4) 10 | -32 
Castletownsend,| W. 3 |1662)47 5 53 0) 46°5|| S.W. | 5 |1°393/47 5} 10 | -10 
Marcu 19, 9 p. uM. Marcu 25, 9 A.M. 
Sao Wind. Wind. 
|| Direction. | Force Barom.| Therm.| Max. | Min |SDiraRtfon.|| Fores Barom.| Therm.| Cloud. | Rain. 
Portrush,... 8. E. 3 | 1-121) 44°-1|51°0|40°0}) S. E. 3 |1:611|44°2| 10 ‘01 
Buncrana,.. . Ss. 3 |1:112| 44 -4/52 0/41 -0 Ss. 3 |1:579| 45 -4 9 “00 
Donaghadee, . | Ss. 3 | 1170) 45 -4|50 °3/40-5||S S.E.| 3 |1676|45 -4| 10 00 
Killybegs,.. . || S.S.E.| 6 |0-953|45 -3|50 3/423] S.E. | 3 |1-437/46-0| — | +10 
Armagh, ...|| ‘8S. 2°8 |1:108| 43 -0/49 5/39 -0|| S.E. |25 1590/45 5) 10 | ‘01 
Killough, . . S. 3 | 1240/45 -4/51 0/41 0) Ss. 2 '11:677|/46 -4' 10 | -00 
Markree, ... Ss. 5 |0:900! 41 :3|47 6/38 -0||\W.S.W.| 4 |1:-444/46 -2| 10 | -20 
Westport,... || S.W. | 6 |0°773)45 0) — | — W. 3 |1:408)50-0| — | °35 
Dublin, .... Ss. 3 |1:143) 44 -5|49 -5|42-0] S.E. 2 |1°592|)45 -9|} 10 | :25 
Courtown, . S.S.W.| 3 |1°180]45 8/51 5/39 -8]| S.E. 3 |1599|47-0] 10 | :34 
Kilrush, S. W. 5 |1:014] 43 8/52 -0| 44 5 ||W.S.W.| 3 |1:513/50°3| 10 | -34 
Dunmore,. . S.S.W. | 4 | 1-207) 46 -8|50 5] 47 5?) S.S.W.| 1 |1:487/}49 8) — | -56 
Cahirciveen, . |\W.S.W.| 4 | 1:069| 45 653 4/45 -2)) W. 3 |1:460)51°8| 9 | -68 
Castletownsend,| W. 5 }1:129] 48 5/52 -5|46-0|) S.W. | 3 |1:520/52°5| 10 | -30 
REMARKS. 
March 18, 9 p. u.—Lightning observed at Markree, Buncrana, and Donaghadee. Rain in 


the north-west. 


Lunar halo observed at Armagh. 


March 19, 9 a. m—At 2 p.m. the wind shifted to S.S. E. at Donaghadee, and to E. S. E. 
at Killybegs; the shift being followed by a gale. 
served at Armagh, 

March 25, 9 a. M.—Light rain throughout, south-western quarter excepted. 


Rain in the south. Solar halo ob- 


The Rev. H. Luoyp on the Meteorology of Ireland. 485 


TaBLE XXXIII. (continued). SerectED OBSERVATIONS. 


JuNE 11,9 P Mm. JUNE 12, 9 A.M. 


Wind. Wind. 
lnpireeGioni| Rosca Barom.| Therm.) Max. OM || ipareaitons | Wonts Barom.| Therm. 
|1-748| 51°-3| 56°-0 | 460 | N. E. 1-455 |49°1 
|1689 51 -6 | 63 -0 1-466 52 6 
1-806) 50 -6 | 59 5 | 1-425 |57 
1683 49 +2 67-0 1:443|56 - 
1-710 48 “5 | 60 -0 1-407 55 
1-760 | 52 -7 | 64 -0 | 1531 54 
'1-523) 48 -0|61 +4 1-381 57 
1614/54 1-396 54 
1-675 49 1-401 66 
1695 49 1-445 59 
1-463 54° 1-347 57 
1556 53° 1-440 56 
1412/56 -4) — | 1-348 57° 
1493/55 ‘0 57-0 41° 1378 56 ° 


Portrush, ... 
Buncrana,.. . 
Donaghadee, . 
Killybegs, .. . 
Armagh, : 
Killough,... 
Markree, ... 
Westport, .. . 
Dublin, . 

Courtown,.. . 
Kilrush,.... 
Dunmore,.. . 
Cahirciveen,. . 
Castletownsend, 


AA A Ny 
Zon C 

pe Sam 
~ Orn 


65 °7 
61-0 
59 “0 
57 5 


SROBDAHSSAANAD 
SAKWDSKSAKUADR 


WHNNWREKNW 


AWANn Pr RW RWWaAN Wh 


P DAD » 
| sca 


JUNE 12, 9 P.M. 


Station. Wind. 


Direction. | Force’ 


Barom. .| Max. 


|| Direction. | Force’ 


1558 57°-0 | 46°-0 | 
1593 | 59 0 46 0 
Donaghadee, . 1510) 59 6| 48 -0| 
Killybegs, . . . |] 5 1624 58 °8| 47 0 | 
Armagh,.... | N.N. W.) 05 | 1:557 58 0/47 -0 
Killough, . . . 3 1-474 65 -0| 46-0, 
Markree, | 1-622} 59 -0| 48 6 
Westport, . . . 1-676 — | — 

Dublin, . 1-479 66-7) 48 °5 
Courtown,. . . 1-487 61 5 \ 49 °3 
Kilrush, .... | 1563 65 0) 45 °5 

Dunmore,.. . || 1521 57 °5| 50 °5 |} 
Cahirciveen,. . 1-625 — 1/49 -2)) 
Castletownsend, | 1555 /61 5 | 49 0 


Portrush, ... 
Buncrana,... 


NwWNre 


ASDHDSARSATAANH 
CR HR CUO Cr 09 & OD DO 
ARKHDKSASHADANYAREH 


NWN NNR ww 


REMARKS. 


June 11, 9 p. m.—Heavy rain throughout the island, 

June 12, 9 a.m.—Light rain at most of the stations. 

June 12, 9 Pp. w.—Rain at Armagh, Killough, and Castletownsend; light rain 
naghadee and Killybegs. 

June 15, 9 a. M—Rain throughout the island; heavy rain in south-west. 


3 Rie 


486 The Rev. H. Liuoyp on the Meteorology of Ireland. 


Taste XXXIII. (continued). SELecTED OBSERVATIONS. 


JunE 15, 9 P.M. June 16, 9 A.M. 
Station. | Wind. | Wind. 

lipireeHiona| Ronee Barom.| Therm.| Max. | Min. | Divcouions Force Barom. Therm.| Cloud. | Rain. 
Portrush, ... S. W. 3 |1:586 | 53°-9 |61°0|51°-0 W. 5 11:727|53°-7 9 | 14 
Buncrana,... || W. 4 |1:565 |53 -9 |62 0/52 0 | N.W 5 |1:785 | 55 *4 8 | :04 
Donaghadee, . | W.S. W.| 3 |1°635 |54 “6/61 -4/52 5 || N. W. 5 |1-742|57 -4 Cy Poti 
Killybegs,. . . || S. W. 5 |1:658)54 -5|61 2/524 || W. 5 |1:870)56 -7| — | -10 
Armagh, ... S. W. | 2°8 |1-655 | 54 -9 | 63 -4|52 -5 W. 3°5 |1°824|56°1 7 | 08 
Killough, ... S. 3 \1°9302!52 -8|64-0/51°0 | S. W. 3 |2:1672155 -7 4 | :10 
Markree, ... W. 3 11679 |52-8 62 -4|52 -4 W. 4 |1911|56°7} 9 | 01 
Westport,... W. ay |Pesil |a5-<0) |) — W. 5 |1:909|55 -0; — | :02 
Dybline 28 sree S. W. 3 |1°730 | 55 :0| 64 -2/53 -0 S. W. 3 {1881/59 1] 10 | 16 
Courtown, .. |\W.S.W.) 2 |1°779|55 -5|64 0/54 °5 | W. 4 |1:890 | 57 °5 4 | 22 
Kilrush,.... VW 4 |1°814/|53 -8|58 0/50 °5 | W.N.W.) 5 |1°813|55 -8 4 | 00 
Dunmore,. .. || W.S. W.| 2 |1:826/54 3/60 -0/55 0 || W. 2 |1:978|59 -3| — | -26 
Cahirciveen, . W. 3/182] |56 -0'}) — |53)-4 W. 3 |2:048 |57 °3 2 | :08 
Castletownsend,|| S. W. | 4 |1:872|56 -0|60-0)53 0 | W.S.W.) 4 |2°023|59°0| 7 | -42 

duty 13, 9 a. M. JuLy 13, 9 P.M. 
Siation. Wind. | Wina. 

ipmerannel orca Barom.| Therm.| Cloud | Rain. ‘Direction. | Force Barom.| Therm.) Max. | Min 
Portrush, ... Ss. 3 | 1:503)}60°3| 10 | 08 || S. W. ay | 1:038 | 59°°9 | 66°-0 | 54°°0 
Buncrana,... || S.W. | 5 |1-474/61-1| 10 | -15 |W.S.W.| 5 |1-075/58-°6| — |56°5 
Donaghadee, . | Ss. W. 2 |1°613|64-4) 10 | 05 | S. W. 3 /|1:143|59 -9| 67 -0 )o8 6 
Killybegs,.. . || 8.S.W.] 5 |1:501/60:0| — | -14 S. W. 5 |1:042/58-1| — — 
Armagh, ... | S.W. 3 | 1568/62 °7| 10 | 15 |) S.S.W.| 4 |1:091/59 0/65 °3|58 6 
Killough, .. . | S. W. 3 WA T6NSiK Ol |e LOe |) SS Wer 116 — |54-4/68 -0'51°0 
Markree, ... |S. S.W.| 4 1-479 61 1) 10) 303 Ss. 4 |1:032!57 -0'65 -8 58-4 
Westport, . . S. W. 6 | 1460630) — | 25 W. 6 |1:082/58-0| — ; — 
Dublin, ... Ss. 4 |1-656|70 -6 7 | :00 Ss. W. 3 |1:209/62 °5|73°2 60°5 
Courtown, . S. W. 1 | 1721/66 °5 200 S. W. 4 |1:311|61°3|)69 5 59-5 
Kilrush,.... Ss. W. 5 |1:590|/62°8} 10 | 00 || S. W. 5 /|1:308 59 °8|64-0 56 °5 
Dunmore,... || S. W. | 2 |1°756/65 -8 | — | :00 S.W. | 3 |1:345|/60-8/62 0 59 -5 
Cahirciveen, . || S.W. | 3 | 1:664/62-2/ 10 | -00 W. 5 |1:349|59 -2| — 60-4 
Castletownsend, | S. W. 3 |1°779/63 -0} 10 | :00 W. 5 |1-423)58 -5|65-°0 59 -0 

REMARKS. 


June 15, 9 p. Mm—Light rain, chiefly in north-west. 

July 13, 9 a. ma—Rain in north and north-west. 

July 13, 9 rp. m.—Gale highest at 1 p.m. at Cahirciveen, and at 2 p.m. at Donaghadee. 
Rain at Portrush, Buncrana, Killough, and Westport; light rain at Dublin and Dun- 


more. 


The Rev. H. Luoyp on the Meteorology of Ireland. 487 


Taste XXXIII. (continued). SrLrectED OBsERVATIONS. 


JuLy 14, 9 a. M. JuLY 27, 9 a.M. 
Station. | | | 


Wind. | | | 
ice Cloud. | Rain. || —=——.—,, — Barom. | Therm. Cloud. | Rain. 


Barom. 


| Direction. Force | | | Direction. Force 


| °56 

ea ea 
36 

| -36 
AT 


| -04 
24 
| -02 

‘09 
00 
‘01 
“02 
10 
00 
‘00 
05 
00 
14 
23 


Portrush, ... 
Buncrana,. .. 
Donaghadee, . | 
Killybegs,.. . | 
Armagh,.... 
Killough, . 
Markree, . 
Westport, . 
Dablin;,.< .. 
Courtown,. . 
Kilrush,.... 
Dunmore,. . 
Cahirciveen,. . 
Castletownsend,| 


ARWARANARW AA AL 
AR DHODSDSHWSGAKES 


SSHDSHSHAWARA 


—_ 
WwWNNRKWNO.> 


JuLy 27, 9 P.M. ILY 28, 9 aA. M. 


Station. Wind. | 


Barom., Therm. Max. 


F 


a SET Barom. Therm. 
Direction. | Force’ 


Direction. | Force 


Portrush, ... . E. 2 |1:626 56°3 66°0 
Buncrana,... || S.S.E.| 2 |1:578/56 6| — 
Donaghadee, . 1671 55 0 65 °5 
Killybegs, . . . 1594 59 °3| 
Armagh, - 1-607 57 - 
Killough,... 1-747 55 ° 
Markree, ... 1-559 | 57 - 
Westport,... 1-583 61 ° 
Dublin, ... 1664) 63 - 
Courtown,. . - 1-713) 61 ° 
Kalrush;. 7. 1630) 61 ° 
Dunmore,... 1707/61 - 
Cahirciveen,. . 1595/61 ° 
Castletownsend, 1446 61: 


mn 
“33? 
Pa Se SS) 


1553) 60°9 
1551| 62 
1603) 63 
1613) 61 
1585 | 61 
|1-625 | 60 
|1579 | 65 
158059 
1634/70 
1-662 | 64 
1597/61 
1:671| 62 
1597 | 62 
1631/62 


Ann 
on 
at ae 
Agr: 
4 
a 
ee 
nr 


A PAR 


Andsnanred 


aa 


n 
nm 


DPR AMON HD 
o 
nRrns 


an 
<5 gle 
"S83 

Or Go bo DS GO DY OO bY OO 


Cr Go Go DD OO DD WO BD 
OoOMdDONNO=I 
KR) SEB] s 
S ASwWA : 
aa 
n 

nanwaas 
ARDOANNSNHAKRARA 

= || — 
©coolaan| oawl Saw 


4 


REMARKS. 


July 14, 9 a. m—Rain throughout the north, 

July 27, 9 a. w.—Rain along west coast. Arch in N. W. observed at Markree. 

July 27, 9 ep. m.—Lightning seen in north-west at Donaghadee. Rain throughout island. 

July 28, 9 a. m—Solar eclipse in the afternoon of this day; clouds of slate colour, as ob- 
served at Markree, at time of greatest obscuration. Showers on west coast. 


488 The Rev. H. Luoyp on the Meteorology of Ireland. 


Taste X XXIII. (continued). SELEcTED OBSERVATIONS. 


| 
| AuvcustT 23, 9 P.M. Aucust 24, 9 A.M. 
Station. zs | | Wind 
ane Barom.|Therm.| Max. | Min. ||__""“"_| Barom.| Therm.| Cloud. | Rain. 
Direction. | Force’ Direction. | Force 
} | 
Portrush, ... || S. W. 2 1-684 54°9 64°-0 55°:0 || S. E. 1 |1-°593| 52°4| 10 14 
Buncrana, .. ||W.S.W.| 3 |1°663/55 6) — |56-0 S. 1 |1:°587|53 +1] 10 18 
Donaghadee, . ||W.S.W.) 2 |1°717 54 9/67 0/55 0) E.S.E.| 3 (1545/52 9) 10 59 
Killybegs, .. W. Ae (2Shon ee) — = N. 3 |1:584)47 -7| — 41 
Armagh, ... || S.W. !1°6 /1°746 53 °1|66 4/55 -1|| N.E. | 2-2 |1-439|50 “(he AKG) “30 
Killough, ... S.W. | 3 |1:772 57 -4/63 -0'56-0)| S.E. 3 |1°7372157 -0| 8 “62 
Markree, ... || S.S.E.| 1 |1°736)|51 -2|65 -5|53 -2||N.N.W.| 2 |1:539 | 46 6} 10 88 
Westport,... W. 3 11:'747/58 :0| — = N.W. | 2 {1603/53 0) — TT 
Courtown, ..- || S. W. 1 /1°815|56 5) 73 -3)54°3]] S.W. | 4 |1:523/59-2}; 5 30 
Kealirnshier iene W. 3 |1:850|54 8/63 -0|57-5]| N.W. | 5 |1:630)51°8/ 10 ys 
Dunmore,.. - W. 1 |1°845 | 56 ‘8/60 °5|57 :0 Whe 5 |1:588/59-8) — 37 
Cahirciveen, . W. 2 |1-827|57 -2| — |58-5/W.N.W.) 4 |1°700/57-4| 4 “88 
Castletownsend,, S. W 5 | 1°860 57 0) 68 -0| 59 °5 W. 5 |1:677|57 -5| 5 35 
AvucusT 24, 9 P.M. SEPTEMBER 29, 9 A. M. 
Station. | Wind. Wind. 
| een Roos Barom.| Therm.| Max. | Min. linameetionll |Korce Barom.| Therm.| Cloud. | Rain. 
Portrush, .. . | N. 2 1823 | 55°1 57°-0 |49°-0 || S. E. 2 |1:531 | 52°2| 10 |, 02 
Buncrana, .. | N. 2 (1-772) 53 6] — |51,:0 Ss. 4 |1-482/51 6} 10 | -14 
Donaghadee, . |W.N.W.) 2 |1-773)|50 2/61 -3/50°0] 8.S.E.| 3 |1:577|}53 -9| 10 | 03 
Killybegs,.-. || N. W. | 2 |1:890 | o00) — S. E. 5 {1373/52 -0| — | 06 
Armagh, ...|| W. 1 |1-838 | 50 -8/57 -2 49 7;| S.W. | 3 {1485/51 °3] 10 | -09 
Killough,...{|} N. 3 |1°817/ 52 -7 64 -0/49-0| S.E. 6 !1:244?'48 -4' 10 | -08 
Markree, ... || N.W. | 2 |1:922/50-5/60-0|50°2]) S.E. 5 |1:286)51-0} 10 | -16 
Westport,...|| N. 3 |1:896/57 -0) — | — || SE. | 5 |1-215/54-0| — | -70 
Dublin, . — —}|—;}]—]—]— S. E. 2 |1:478|}52-7| 10 | 05 
Courtown, ..|W.S.W.| 2 /1:851|54 -5/63 -0/50-0]| S.E. 5 |1°518)53 5} 10 | 11 
Kilrush, ... || N.W. | 3 |1:946) 54 8/62 °0 | 46 -5 Ss. 5 |1:109 |) 58 8 6 | 04 
Dunmore,. . . || W.N.W.| 2 |1:914 156 3/72 52155 -0 Ss. 5 |1:349|/56 3} — | -25 
Cahirciveen, . || N. W. | 2 |1:988\57 6} — |53 6 Ss. 5 |1:082 59 °5| 10 | 93 
Castletownsend,! W. 2 |1-:921/57 5|66 0/55 -0|/ S.W. | 5 /1:120,60°5| 10 | -40 
REMARKS. 


Aug. 23, 9 p. m—Lightning observed throughout the eastern coast during the day. Rain 
at Killough and Castletownsend; showers at Killybegs, Westport, and Courtown. 
Aug. 24, 9 a. m.—At Courtown gale commenced at 5 A.M., and ended at 2P.m. Rain 

throughout island, but chiefly in north. 
Aug. 24, 9 p.m.—Aurora observed at several places. Showers in north. 
Sept. 29, 9 a. m.—Gale highest in the south-west at 3 a.m. Rain throughout the island. 


The Rev. H. Luoyp on the Meteorology of Ireland. 489 


Taste XXXIII. (continued). SrLectED OBsERVATIONS. 


SEPTEMBER 29, 9 P. M. SEPTEMBER 30, 9 A. M. 
Sun Wind. | l Wind. | | 

——— ROMs | Meri) ise ea MRS pe cee ~ | Barom. Therm. Cloud. | Rain. 

Direction. | Force I Direction. | |Force | 
Portrush, ... S.E. 2 | 1-271) 54°0 | 58°-0 48°-0 | Ss. 2 |1:020/56°4| 10 16 
Buncrana,... | 8S. 5 |1:287)53 6| — |49-0|/W.S.W.| 3 |1:056/56 1} 10 “59 
Donaghadee, . | S.E. | 5 |1:315/51 0/60 0/50 -0||S.S.W.| 3 (1106/57 -8| 10 | -25 
Killybegs,. .. ||N.N.E.| 5 |1°162/54:1) — | — |[W.N.W.) 5 |1:148/55 -9} — | 1:02 
Armagh,.... || S.E. | 3:5 | 1178) 53 8) 54 3/49 5) S.W. |2°5 |1°107|55 0; 10 50 
Killough,... |, S. 6 |1:149 48 -1/57 -0|45 -0 S. 2 |1:157|55-0) 8 37 
Markree,. ... N. E. 1 |1:030 54 -5| 56 -3) 46 ‘8 W. | 4 /1:200|52-9|] 10 ‘79 
Westport, .. . N.E. 3 |1:132/56 0/57 0/50 -0|) N. W. | 5 |1:265/55-0| — “30 
Dublin, 4.4% S. E. 4 |1:134|55 -9|58 0/51 -5]/ S. W. | 3 /1°209/55 -6] 10 ‘78 
Courtown,... || S.S.E.| 5 |1:147/56 5/58 5/46 -0|W.S.W.) 2 |1:270|/56-5| 8 ‘48 
Kilrush,.... ||N.N.W.| 4 |1:138/57 -8|63 -0/50°5|| N. W. | 4 |1:402/53 8] 10 03 
Dunmore, . . . S. 3 |1-089/58-3| — |50-0] W. | 2 |1°325/57-3| — | -20 
Cahirciveen, . || N.W. | 3 |1:225'56 6/61 -4|52-2|) N.W. | 2 |1-400|/54-6| 6 35 
Castletownsend,/W.S. W.) 3 |1:194 57-5 63 -0| 51-0 } S.W. | 3 |1°374)55-5) 6 | -00 

SEPTEMBER 30, 9 P. M. OcTosER 1, 9 A. M. 
Sra, Wind. | Wind. | 

DiecGo |Force| Bare hen Max. | Min. Direchons kos BBO NC Cloud. | Rain. 
Portrush, ... Ss. 1 |1:178|50°-2|59°-0|50°0}| S. E. 3 |0°855/54°4! 10 28 
Bunerana,... || S.W. | 3 |1185/51-1} — |50-0// S.S.E.| 1 |0-889|50 6| 10 | -45 
Donaghadee, . | S.S.W.| 1 |1-240|51 -8|59 5/53 -0|| S.S.E.| 4 |0.936 54-9) 10 07 
Killybegs,. . . || E.S. E.| 5 (0973/53 -3) — | — ||W.N.W. 3 |0:873 52-7) — .03 
Armagh, ... Ss. 2 |1:189|49 -8|57 -3|50-8||S.S. W.| 2°5|0°846 52-0) 10 72 
Killough, . . Ss. 3 1-172 55 1|59 0 47 0 Ss. 6 — 5644! 10 AT 
Markree,.... S. E. 4 |1:048/ 50 -0|57 -6| 53 -2 W. 0 |0°834 53-0) 10 ‘ll 
Westport,. .. Ss. 3 | 1062) 56 -0|57 ‘0 53 0 N. 2 |0°882 52:5) — “30 
Dublin;y..- °. Ss. 2 |1-231)51 -4/58 -7| 52 -2| 8. 0 0°8388 54-0} 10 33 
Courtown, .. Ss. 1 |1-275| 52 -2/59 -7 53 3 Ss. 1 |0°844 52-0} 10 | 1:03 
Kilrush,....||S.S.E. | 3 |1:142/53 8/58 -0/47 -5||N.N. W.) 2 |0-912 49:3) 5 O8 
Dunmore,.. .- aoe — || — |) —. 600156 -0)'S.S:W.| 1 0-831) 53-8] — 1:97 
Cahirciveen,. . a 3 |1:094/56 -3)58 6 52 -2)N.N. W.) 2 |0:923 51-4] 10 ‘79 
Castletownsend,|| S. W. 5 1173 57 0/62 5 52°5|) W. 2 |0°892 54°5| 5 82 

REMARKS. 


Sept. 29, 9 p.w.—Wind fell at 7 p.m. at Markree. Aurora. Rain throughout, except 
south-western quarter. 

Sept. 30, 9 a.».—Rain, for the most part light, at Buncrana, Killough, Armagh, Mark- 
ree, and Kilrush. 

Sept. 30, 9 p. m.—Gale commenced at 8 p.m. at Markree. Rain in south-west. 

Oct. 1, 9 a. m—Rain, chiefly in north and east. 


490 The Rey. H. Luoyp on the Meteorology of Ireland. 


Taste XXXII. (continued). SrtecTED OBSERVATIONS. 


| OcroBer 1, 9 P. M. OcToBER 4, 9 A. M. 
Sipe Wind | Wind. 

Tinionl Roses Bam, Therm.| Max. | Min. \niraciansll Morea Barom. Therm.) Cloud. | Rain. 
Portrush, ... |] W. 2 (0:853 | 49°9 | 56°-0| 47°-0 | S. W. 2 |1:309 | 50°-0 1 10 
Buncrana,... ||\W.S. W.| 2 0898 49 6] — |44:°0)W.S. W.) 3 1314/50 °6] 3 15 
Donaghadee, . | S. W. 1 (0901/48 9 |57 -3|50 -5 |W. S. W.| 1 |1-472?/51 -2} 1 13 
Killybegs,. .. |W.N.W.) 2 0°916|49 ‘7 | — — |\S.S. W.| 3 11347153 :0)|. — 30 
Armagh, ... S. W. 1 |0°927|45 -0 |52 ‘7 |49 7) S. W. 2 |1:270/50-2) O ‘ll 
Killough, .. . || W. 2 | — |53-7 |58 0/480) _ S. 2 |1°386/51-7| 7 04 
Markree, Ss 3 |0:900|50 -37)55 -0|49 -3//S.S. W.| 4 |1:304/51°8| 3 13 
Westport,..- || W. 5 |0-912|52 -5 |56 -0|50°0|| S. W. 5 |1°304|52 5) — 50 
Dabliye. <1 real | ave 2 |0-980/44 -1 | 57 -0|53 -2|) S. W. 2 |1-406\51°9| 0 25 
Courtown, 5 Wir 1 {1-:012/48 -0 [55 -0/}51 -7|| S. W. 2 |1480/50°3/ 2 14 
Kilrush,.. . . ||W.N.W.) 4 |1-045/49 °8 |56 0/45 -5|| S.W. | 5 |1-468|49-8|. 8 | 48 
Dunmore,... || W.N.W.| 1 /|1:081/48 3 | — |54-0|))W.S. W.| 2 /|1-4772)53 3) — 35 
Cahirciveen.. . || W. 2 |1-056/49 -6 | 55 4/50 O|}W.S. W.| 4 11-457 | 52-2) 5 27 
Castletownsend,|| S.W. | 2 |1:092/48 -5 |61 -0 | 49 °5|| W. 5 1600/58 -5| 5 25 

| , OcToBER 4, 9 P. M. | OcToBeEr 5, 9 A. M. 

TEU: Wind | Wind. 

Direction. |Foree Barom. Therm.| Max. | Min. iparectioni oe Barom.! Therm.| Cloud. | Rain. 
Portrushyy-) .per||eenss i | 1-182 | 46°-2 58°-0|47°-0 || W. 4 |1:346/51°-0| 10 40 
Buncrana,... || S.W. | 2 |1:201\/47 6] — |47°0!| N.W. | 5 |1°391|51 :1 8 | 57 
Donaghadee, . || S. W. 1 |1:286)48 -9 |57 -4/49 5 |W.N.W.| 2 |1:371|49 4) 10 08 
Killybegs,. . . ||W.N.W. 4 | 1208/51 0} — — ||W.N.W.| 6 |1458/53-1| — | -43 
Armagh, ... |S. S. W.|0°5/1-:225|47 -2 56 3/46 8 W. 1:5) 1-439 | 50-8 8 22 
Killough,... S. 3 (1418/49 0 57 :0|47 0 Wwe 2 |1:573/51 -7 4 20 
Markree, ... Wit. || 24 1 245 46 6 | 54 2/44 6 Ww: 8 |1:528/48 6 3 86 
Westport,... N. 6 |1:276 | 53 0/54 0/51 0}/ N. W. | 6 |1:520)53 5} — 56 
Doblins rere S.W. | 3 |1:260/48 -0|59 -2)49 -0 W. 2 |1:502|49 4 4 14 
Courtown,. .. ||W.S. W.| 1 |1:345/48 0157 -0|46 -5|| S. W. 2 |1:574|49 -5 u( ‘ll 
Kalrush;y-, », ie |W: N.W.| 5 |1:423/46 -8 | 54 0/43 5 || N. W. 5 |1:720/47°8 8 32 
Dunmore,... || W. 2 |1:380 51 -3/58 0} — ||W.S. W.| 2 |1:633)/51 -8) — 25 
Cahirciveen,. . | W. 3 |1-461 51 -6|54.8!50 -2 W. 3 1:728]52 0 9 43 
Castletownsend,| W. 5 |1-426 53 -5|57 0/49 0] W. 3 1-691)57 -5| 10 “40 


REMARKS. 


Oct. 1, 9 vp. m—Aurora observed in several places. Rain, chiefly in south-west. 

Oct. 4, 9 a. M.—Rain, chiefly in south-west; hail and rain at Castletownsend. 

Oct. 4, 9 p. M—Lightning observed throughout Ireland during this day. Rain at Kil- 
rush and Dunmore; hail and rain at Westport and Castletownsend. 

Oct. 5, 9 a. mu—Lightning observed at Cahirciveen. Showers, chiefly on west coast. 


The Rev. H. Luoyp on the Meteorology of Ireland. 491 


Taste XXXIII. (continued). SELEcTED OBSERVATIONS. 


DECEMBER 7, 9 A.M. DECEMBER 7, 9 P.M. 
Station. Wind. Wind. | 

Direchionly| Force Barom.) Therm.) Cloud. | Rain. | Direction. | Force yn Seca Max. | Min. 
Portrush, . . . S. 2 |1-940/51°3| 10 | 02 | Ss. 4 |1-364 | 49°-5 | 53°-0 | 46°-0 
Buncrana, | S.W. | 3 |1-906/51-1| 9 | -00 || S.S.W.] 5 |1-494/49 6] — |46-0 
Donaghadee, . || S.S.W.| 2 |1:970/50-4| 10 | 00 | S.S.W.| 5 |1-541/50 -4|52 0/47 -0 
Killybegs, S)We 52) 11-902)61 283i! —- || -10 1) SAS5W. |) 6 |1-225 52) -9)| ==) 
Armagh, . | S.W. [8:5 |1-941/51 0] 10 | -01 Ss. 6 |1-423 | 50 0 |52 5/46 -4 
Killough,... || S.W. | 2 /2:031/50-4} 6 |-05 || S.W. | 6 !1:570|49 -2'52 -0!46 0 
Markree, | 8.8. W.! 3 [1852/50 -6| 10 | 03 || S.S.W.| 6 |1-274|51 -5|53 -3|47 -4 
Westport,..- | SW. 5 1815/55 -0| — | 07 | S.W. | 6 {1301257 -0 58 0/51 -0 
Dublin, ....||S.S.W.} 2 |1-997/51-6| 6 | -00 = 3 |1-560 |52 8 57 0/48 °8 
Courtown, S.S.W.| 3 |2:058]51-0| 10 | -01 S. 5 |1666 50 5 540/48 0 
Kilrush,. ... || S.S.W.| 3 |1:966]51-8| 10 | -03 || S.S.W.| 5 |1-448/53 -8/55 0/51 5 
Dunmore,.. . || S.S.W. | 3 |2-016|50-8| — | -03 S. 5 1638/50 8 |52-5| — 
Cahirciveen, s. 4 |1-962| 52-3] 10 | -20 w. 4 /1-603 | 53 0 |55 -4|50°8 
Castletownsend,| S.W. | 5 2033 51°5| 10 | 11 S.S.W.| 5 1579 53 5 |57 5/50 0 

| DECEMBER 9, 9 A. M. | DEcEMBER 9, 9 P.M. 

5 | | 
Station. Wind. | Wind. 
Direction! |Reresl Barom, Therm. Cloud. | Rain. Direction. [Force Se Therm. Max. | Min. 
Portrush, .. . S. 3 |1-781/52°0/ 10 | -10 || S. 3 |1:667|55°5 | 58°-0 | 41°-0 
Buncrana,... || S.W. | 3 /1761/53°6) 9 | 06 | S.W. | 4 /1677/55-1| — |43-0 
| Donaghadee, . || S.S.W.| 3 |1-895/49 9] 10 | 05 || S.S.W.| 3 |1-760|52-9| — |42-4 
Killybegs, S.W. | 5 /1-762/54:0) — | 18 || S.W. | 5 /1667/54°5) — | — 
Armagh, .. . || S.S.W.|4°5 |1-767/58 1; 10 | -11 S: 4 |1-726) 54 -5 |57 4/418 
Killough,...'| W. 2 |1-747/48 -7| 3 | -04 8.W. | 2 |1-787| 47 4/50 0/45 -0 
Markree, ... || S.W. | 4 |1-770|54°6| 10 | -05 ||S.S.W.] 4 |1-625|55 -0| 55 -7|41 -7 
Westport,. . . s.W. | 5 1696/58 0); — | 04 W. 6 |1:604| 58 -0 | 59-0) 49 -0 
Dublin,.... ||S.S.W.| 2 |1-885/57-5] 10 | 01 ||S.S.W.| 2 |1:834]55 -8 | 59 -6| 45 -0 
Courtown, . . || 8.S.W.| 3 /1-970/53 3) 10 | 02 | S.S.W.| 4 |1:867|53 5 |56 -0/37 5 
Kilrush, W.S.W.| 4 |1:893|55 -8|} 10 | -00 S.W. | 4 |1-750/54 8/57 -0|48 5 
Dunmore,... || S.S.W.]} 2 /1-997|52 8) — | 03 | S.S.W.| 5 /1883)52 8|53-5) — 
Cahirciveen, S. W. | 4 /1-:913/56 2) 10 | 25 || S.S.W.] 6 |1-780/55 -4 | 57 -4|49 -0 
Castletownsend,) S.W. | 5 1-980/54-0) 10 | 04 S.W. | 5 {1865/54 -0 |53 0/45 -0 
REMARKS. 


Dec. 7, 9 4.M.—Rain at Killough; light rain at Markree and Kilrush. 

Dec. 7, 9 p.M.—Storm lasted from 6 P.M. to 9 P.M. in the south; least pressure at 7 P.M. at 
Cahirciveen. Lightning observed at Buncrana in south-west. Rain at most of the stations. 

Dec. 9, 9 A.m.—Light rain, chiefly on west coast. 

Dec. 9, 9 p.m.—Lunar halo observed at Donaghadee. Light rain, chiefly on west coast. 


VOL. XXII, 


38 


492 The Rev. H. Luoyp on the Meteorology of Ireland. 


Taste XXXIIL. (continued). SrrectED OBSERVATIONS. 


| Decemper 20, 9 A.M. 


DEcEMBER 20, 9 P.M. 


. | 
Station. i Wind. | Wind. | | 

Direction. [iroree|2at™- Therm.| Cloud. | Rain. | Direc Gan wlonce Barom:| ‘Therm. Max. | Min. 
Portrush,... {| S.. | 8 |1:676 | 49°:8 92:00" is, oS: 3 | 1-442 51°-4 | 54°-0 | 38°-0 
Buncrana,. . . ||S.S.W.| 4 |1°717/51 +1} 10 | -00 ||S.S.W.] 5 |1-472|53 6] — | 42-0 
Donaghadee, . || S.S.W.| 3 |1:982 49 6| 10 “00 Ss. W. 4 |1-°580/51 :0| — |42°0 
Killybegs,. . . S.S.W.| 5 |1641 |53 4) — | -00 N. 4 |1-470|46 3) — | — 
Armagh, 7 Ss. 4 |1:788,;50 -2 9 02 | bs) 4:5 |1-480) 52 0/58 6) 38 -0 
Killough, .. . s. 6 |1:667'|48 -7| 5 | 07 || ‘S. 6 11-642) 48 -7|51 0/420 
Markree, ... || S.S.W.| 4 [1644 |51 10 | ‘01 || N.W. 2 1:459|44 -6| 54 0) 40 -2 
Westport,.. . Ss. W. 6 |1:590|58 -0| — | -05 || Ss. 0 |1:491) 48 0) 59 0 | 47 0 
Dabliny 3G 7 i) 1 |1:812|52-1! 10 | -00 S. 3 | 1-578] 52 -8|57 0/35 5 
Courtown,. . . |) 8. | 3 |1:882/51°5} 10 | -02 S. 4 |1617|52 -5|53 -7|45 -0 
(Kalnashy <7]: 3 1-712 |53 -8| 10 03 N. W. 2 (1525/46 -8 49 0 46 ss) 
Dunmore,... | S.S.W.| 5 (1847/51 3) — | 02 | S.S.W.] 5 (1550/52 3/52 5) — 
Cahirciveen,.. || S. | 6 |1°762|54-5| lu | -25 | S.W. | 2 |1580|/48 6/51 8/49 8 
Castletownsend,|, S. W. 5 |1°8387 |52 0; 10 10 S. W. 5 |1:559)51 +5 [55 0/48 ‘0 


REMARKS. 


Dec. 20, 9 A. M—Rain throughout the island, but chiefly on west coast. 
Dec. 20, 9 Pp. Ma—-Wind veered from S.S. W. to N. W. at 7"°30”™ p.m. at Markree. Rain 
throughout the island. 


Notr.—At Armagh the velocity of the wind is recorded, in miles per hour, 
by means of Robinson’s anemometer. The numbers so given are, in the preceding 
Table, reduced to the scale (0 - 6) employed at the other stations. The velocity 
of the wind was also occasionally observed at Portrush, Markree, Dublin, and Cour- 
town, by means of small anemometers constructed on the same principle. 


The Rev. H. Luoyp on the Meteorology of Ireland. 493 


Taste XXXIV. Hovurtry Osservarions. 


CAHIRCIVEEN. . ARMAGH. 


Lat.=51° 56. Long.=10° 13. Height = 52 feet. Lat. =54° 21’. Long.=6° 39’. Height =211 feet. 
Barometric Correction =+ 0-081. Barometric Correction = + 0°273. 
Force of Wind expressed in terms of scale (0 — 6). Velocity of Wind expressed in feet per second 


Therms. Wind. Therms. Wind. Cloud. 
Hour. | Barom. Barom. = 
Dry. | Wet. | Direction. | Force Dry. | Wet. | Direction. . | Amt. Form. 


Or 
° 

° 
for) 


_ 
© 
DRSODBNASSSHSOHDASHNNSCHHDANSSG 


S.W. | 3 |/0:801/ 39%9 | 38°5 
0-786 41 3) 40 
0°769 | 44 0 | 42 
0°755| 46 -3| 43 
0°732| 46 -7| 44 
0705) 47 +1) 45 
0:686| 47 -5| 44 
0-659| 47 -1| 45 
0°627 | 48 -2| 45 
0-600| 48 -3 | 45 
0:584| 46 -3| 44 
0:571| 45 -5| 43 
0:566| 45 -1}-43 - 
0-570) 44 -2/ 42 - 
0°577| 44 -2| 42 
0°585| 43 -g| 42 
0°595| 43 0/41 
0-606 42 9/41 
0:607 | 42 5 40 
0611 41-5 39 
0°608 | 40 -2/ 38 
0:605| 40 8 38 
0614/40 -8|38 
0617/40 -3| 38 
625 40-248 


Mar. 21,| 6 a.m. /0°879 
1 0°878) - 

0870 

0°848 

0-780 

O777 

0-780 

«|0°847 
0-866 
0862 | 4 
0-873 
0-864 
0°863 
0:868 
0-856 
0865 
0861 
0-860 
0°850 
. |0°786 
0-779 
0-753 
0-793 
0:753 
0-755 


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REMARKS. REMARKS. 


The observations of temperature were taken, Squally throughout the day. 

by mistake, with one of the registering ther- March 22, 0 a. m.— Wind unsteady. 

mometers. Raining, with little interruption, from March 
Cloudy for the most part throughout the day. 21, 10 a.m. to March 22, 2 a.mM.; amount 
Heavy showers from March 21, 6 a. M. to 3 P.M. = 0°235 inch. 


Bye 


494 The Rev. H. Luoyp on the Meteorology of Ireland. 
Taste XXXIV. (continued). Hourty OpsERvATions. 
CourToWN. MARKREE. 
Lat. = 52° 39’. Long. = 6°13. Height = 34 feet. Lat. = 54° 14. Long. =8° 28. Height = 132 feet. 
Barometric Correction =+ *036. Barometric Correction = + 0°161. 
Velocity of Wind expressed in feet per second. Velocity of Wind expressed in feet per second. 
Therms. Wind. Therms. Wind. Cloud. 
Day. Hour. | Barom. - \Baom|| |, 
Dry. | Wet. | Direction. | Force! Dry. | Wet. | Direction. | Force. | Amt. | Form. 
Mar. 21,| 6 A.at. |1°042 | 419-2 | 41°2)/S.S. W.] 13 || 0-782 41°-0| 40°3 | S.S. E.}| 25 9 N. 
if 1:030 | 43 ‘8 43 5 Ss. 14 |0-776) 41 7 41 0| S.S.E.| 27 | 10 N. 
8 1-023 | 44 *8| 43 -0 Ss. 17 | 0:758| 43 6/42 6| S.S.E.| 29 | 10 N. 
9 1-013 | 45 *2) 44 +2 S. 22 ||0-738) 45 2 43°7| S.E. 22 9 N, K 
10 0:994 | 47 -0| 46 ‘0 S. 35 ||0°711| 46 -4 44 °6| S.E. 32, i) LOW WANS KS 
11 0-980 | 48 -8| 46 -5|S.S. W.| 35 ||0°691|47 5 45 °3|) S.S.E.| 27 | 10 |K,N,S 
12 0:970 | 49 °8|46 -5|S.S. W.| 43 | 0:657| 46 -7 44-7) S.S.E.| 26 | 10 |N,S,KS 
1 p.m. |0°959 |50 -0| 46 8) S.S. W.| 43 0°615| 47 3 46 -2| S.S.E.] 25 | 10 N 
2 0-955 |50 -8|47 0} S.W. | 43 0560/45 -1 44-9) S.S.E.| 35 | 10 N 
3 0:942 | 50 -2/46 8] S.W. | 58 ||0°528) 47°5 46 9 S. 29 | 10 N 
4 0-934 |50 0/46 -0| S.W. | 43 ||0°528|48 -7 47 :1|S.S.W.} 28 | 10 N 
5 0:930 |47 8) 45 -0| S.W. | 38 |0:555) 47-0 45 -7| S. W. 19 | 10 N 
6 0-933 |47 -0|44 0) S.W. | 35 |\0°563/ 46 ‘0 45 °-1/S.S.W.| 26 | 10 N 
7 0-942 45 -8|43 -0) S.W. | 31 ||0°583/45 1 44°5 8.5. W.| 15 | 10 N 
8 0952 |45 5/43 -0| S.W. | 29 |0597\ 44-3 43 -4)S.S.W.} 22 9 N,S 
9 0-956 | 43 -2 42 -0| S.W. | 29 | 0-600) 43-4 42:9) §. 20 3 N 
10 0-957 | 43 -2|41 -2) S.W. | 17 ||0°613) 43 ‘8 43 3 S. 23 7 N 
11 0-956 | 43 -0)41 0} S.W. | 17 0619 43 3 48 -0 S. 16 9 N,S 
Mar. 22,| 0 10-956 | 42 0 | 40-0} S.W. | 15 ||0617) 42 9) 42 3 S. 20 9 | N,KS 
1 a.m. [0943 |41 -2/39 -0| S.W. | 14 ||0°635 43 -4;43:0|S.S.E.| 16 | 10 | N,KS 
2 0-936 | 41 :0|40 -0| S.S. W.| 13 ||0°637 429/424) SS. 18 | 10 | N,K,S 
3 0:925 | 41 0/40 0| S.W. | 13 ||0°640 42 -4| 42-1 S. 16 7 N,S 
4 0913 |40 0/39 0} S.W. | 12 |\0642 42 ‘0 41 ‘7 S. 15 9 N,S 
5 0-902 | 38 2/38 0| S. W. 7 |\\0645 41-5) 41 -4 Ss. 14 9 |S, KS, 
6 0°894 | 38 aie 0| S.W. | 7 |/0654 41 ue {8/0 IS 14 8 N 
REMARKS. REMARKS. 
Mar. 21.—Intermittent sunshine; partially over- Mar. 21, 6 a. mM. to 12 Pp. M.— Moderate gale; at 
cast, with cumulus. 2 p.M. strong gale. 
3 p. m—Squall, with drops of rain. Rain began at 0 30 P.M., and continued until 
5 p.m.—Halo round sun. 7 e.M.; amount=0:102. Light rain at 10 
Mar. 22, 2 a.m. & 3 a.M.—Halo round moon. and 1] p.m. 
4 p.M.—Clouds very dense in W. and N. W. 


The Rev. H. Luoyp on the Meteorology of Ireland. 495 


Taste XXXIV. (continued). Hourry Osservarions. 


Dunmore East. PortTRUsSH. 
Lat. = 52° 8. Long.= 6° 59. Height = 66 feet. Lat. = 55° 13. Long. = 6°41’. Height = 29 feet. 
Barometric Correction = + 0°091. Barometric Correction =+ 0-082. 
Force of Wind expressed in terms of scale (0 — 6). Velocity of Wind expressed in feet per second. 
Therms. Wind. Therms. Wind. Cloud. 
Day. Hour. | Barom. Barom. — 
Dry. | Wet. | Direction. | Force Dry. | Wet. | Direction. | Force, | Amt Form. 
Mar.21,| 64. m.|0-964| 45°-0|43°5| S. | 3 |/1-:011/40°8/39°9| SE. | 18 | 5] N 
7 0:954|45 -0|43 5/S.S.W.| 4 ]0°998)40 6/39 7] S.E. Nfs) 2 N 
8 0:951| 46 0/44 -5|S.S.W.| 3 |]0:988| 42 -8/41-8] S.E. | 25 | 6 N 
9 0945) 47 5|46 -0/S.S.W.| 3 0971/45 4/43 9) S.E. SOM ae N 
10 0°885| 48 0/47 -0| S.S.W. | 4 ||0°945|47 -4|45 4] S.E. 30 | 8 N 
ll 0881) 48 -5|47 -0| S.S.W. | 4 |/0°923) 49 5/46 9] S.E. S50} 6 N 
12 0-881) 48 5/47 -0|S.S.W.| 4 |/0°901\49 1/46 -5|) S.E. 35 6 N 
lp. m. |0:907| 49 0/47 -5|S.S.W.| 4 ||0°878|48 -6|46-1| S.E. 43 | 6 N 
2 0-913) 49 5|47 -0|S.S.W.| 4 |0°844/49 ‘9/47 5) S.E. 41 | 6 N 
3 0:901| 49 -0|47 -5|S.S.W.| 5 |}0°819/48 5/45 -7| S.E. Som) el N 
4 0:905| 47 5) 45 -0|/W.S. W.| 5 ||0°793/48 -4|46 -0| S.E. 39 | 8 N 
5 0-905) 48 -5|/46 0] S. WwW. 5 ||0°765) 47 9/45 6] S.E. 35 9 N 
6 0:909| 47 -5|45 -0/W.S. W.| 5 ||0°765|46 6/44 -6| S.E. 30 | -9 N 
7 0-914| 46 -0|44 -0|W.S. W.| 5 ||0°744) 45 -7 |43 -8 Ss. 37 | 9 N 
8 0919/45 5/43 -5|W.S. W.| 3 |}0°727) 45 5/43 -7 S. 39 9 N 
9 0:905| 45 6/43 -0/W.S. W.| 4 |0°787| 45 3) 43 -7 S. 36 9 N 
\10 0:905| 44 -5|42 5) S.W. 3 ||0°744| 45 1/48 6 S: 48 8 N 
ill 0-903 | 44-042 -5| S. W. 3 ||0°752| 44 -9 | 43 -3 Ss. 37 if N 
Mar. 22, | 0 0:882| 45 -0/43 -0} S. W. 4 ||0°760) 44 -4|42 -8 Ss. 39 9 N 
1 a. M./0°883/ 45 -0/43 -0/S.S. W.| 4 ||0°764) 44 0/42 -4 Ss. 37 9 N 
2 0°881| 45 -0/43 0} S. W. 3 ||0°770| 43 6 | 42 -0 Ss. 36 10 — 
3 0°855| 44 5/425) S. W. 3 ||0°728) 43 0/41 -0 Ss. 29 10 — 
4 0-830) 43 -5|/41 5) S. W. 2 ||0°764) 42 1/40 6 Ss. 39 9 N 
| 5 0811) 43 0/41 5 S. 2 ||0°776 41 -9| 40 -4 Ss. 35 |} 9 N 
| 6 0-811) 438 -0 41 °5 Ss. — ||0°780 41 -9/40 -5 Ss. 35 | 9 N 
| | | 
REMARKS. REMARKS. 
Mar. 21.—Squally throughout day, and for the Faint sunshine until 4 p. M.; afterwards over- 
most part clouded. cast and misty. 
2 p. m—Heavy shower. Noon. —Light showers. 
Greatest force of wind from 3 P.M. to 5 P.M; 6 v. m—Continued rain. 
amounted to 8 lbs. on the square foot. 9 P. M.—Showers. 


496 The Rev. H. Luoyp on the Meteorology of Ireland. 
Tasre XXXIV. (continued). Hourty OssErvarions. 
CAHIRCIVEEN, | ARMAGH. 
Lat.= 51°56. Long.= 10°13. Height = 52 feet. | Lat. = 54°21. Long.= 6°39. Height = 211 feet. 
Barometric Correction = + 0°081. Barometric Correction = + 0-273. 
Force of Wind expressed in terms of scale (0 — 6). Velocity of Wind expressed in feet per second. 
= 7 | 
| Therms. Wind. | Therms. Wind. Cloud. 
Day. Hour. | Barom. 7 Barom 7 
Dry. | Wet. | Direction. | Force Dry. | Wet. | Direction. | Vel. | Amt. Form. 
June 21,) 6 a.m. |1:757|55°6 |. . S.W. | 1 |1584)57°2|54°6| 5.5. Ww. i 10 s 
7 1-743 | 58 -2 1580/58 °7|55 -3|S.W.08.) 13 5 5, C 
8 1:734) 59 -0 1577 | 60 4/56 ‘8|/S.W.0S., 18 56 |5,C,K 
9 1734/59 6} . S.W. | 1 {1549/61 8/57 -3|S.W.2S.) 17 | 10 KS 
10 1-724 61 -0 1:530/63 3/58 3/S.W.OS.| 12 | 10 bs) 
11 1-721, 60 6 | 1517 65 1/59 °3|S.W.dS.| 14 10 KS 
i2 1713/61 -0| . W. | 2 |/1505|/65 7/59 -0/S.W.5S. 21} 10] KS 
1 P.M. |1°718) 62 4 1-498 | 64 9/60 -0|S.W.0S.) 17 10 K 
2 1-719 58 6 |1-480 | 62 -9/61 -1)S.W.88.| 18 10 | KS,N 
3 1:724| 57 4]. N.W. | 3°||/1467/62 2/58 6|S.W.6W.| 16 | 10 | KS,S 
4 1-726) 56 -4 \1-455|61 3/583} S.W. | 14 | 10 | KS,S 
5 1-730 56 8 /1:469|55 9 |53 9 W.N.W.| 10 10 | KS,S 
| 6 1:751| 56 ‘8 N.N. W.| 2 |/1-476|/53 7/51 -1|W ON.| 8 | 10 | N,KS 
7 1-762 | 56 -2 | 11-474|53 2/517} W. a) SLOP ate Ke 
8 1:773'55 “6 | 1-484,53°9|/51°6, W. 8 3 K 
9 |1-792)54 8]. N.W. | 2 ||1-495/50 6/48 6| W.0N. 6 1 KS 
10 1805 54 4 1-498 50-1 48 +1 W. 9 1 KS 
11 1808 54 :2| 1:509|50 1/48 -2| W. 6 7 K 
June 22,| 0 |1:815| 54 -0 1524|50 -8|48-9| W.5S. | 10 | 7 K 
| Lam, |1°835/53 8... ./W.N.W.) 2 [1522/49 0/47 -6/W.0N.| 5 | 4] CK 
| 2 1851|53 -4|....] N.W. | 2 1529/49 -0|47°3) W DP isis 
| 3 11:866|53 -4|.. N.N. W. /1:533|49 4/47 °3| W. 7 a CK 
|}4 |1:884/53 6 | 1548/51 2/488}  W. 9} |) 9) REGEN 
5 1911 53 4) 1583/50 5|48 -9| W.ON. 8 | 10 K 
6 1937/53 4). N.N.W.| 2 |/1:604)51 9/49 0} N.W. | 17 9 K 
i | } | | 
REMARKS. | REMARKS. 
The observations of temperature were taken, by | June 21.—Rain from 2 p.m. to 6 P.M.; amount 
mistake, with one of the registering thermo- || = 0:076. 
meters. | June 22, 4 a.m, 6 4.m—Drizzling rain. 
June 21, 22.—Clouded throughout day. | 
June 21, 2 p. m—Drizzling rain. | 
June 22, 0 a.m.—Showers; 2 A. M. ditto. 


The Rey. EH. Luoyp on the Meteorology of Lreland. 497 


Taste XXXIV. (continued). 


Hourty OsseRvATIONS 


CourtTown. MARKREE. 
Lat. = 52° 39. Long. = 6°13. Height = 34 feet. | Lat. = 54°14. Long. = 8° 28. Height = 132 feet. 
Barometric Correction = + 0°036. | Barometric Correction = + 07161. 
Velocity of Wind expressed in feet per second. Velocity of Wind expressed in feet per second. 
Therms. Wind. | Therms. Wind. Cloud. 
Day. Hour. | Barom. oe --- Barom. : = 
Dry. | Wet. | Direction. | Vel. | Dry. | Wet. | Direction. | Vel. | Amt. | Form. 
June 21,| 6 a. m.!1-864/59°-0/58°0| — 0 |/1-668 | 56°-1|54°9| S.S.E.| 9 | 10 | S,KS 
7 1851/60 0/58 -0| S.E. | 5 /|1652/57-0/55-4| S.S.E.| 9 | 10 | N,S 
8 |1839|61 -2|59 -2| S.E. 8 ||1-650/ 58 -8|56 -1/S.S.W.| 8 | 10 | N,S 
9 1-804|63 8/61 -2} S.E. | 12 |/1-623/59 5/56 -9/S.S.W.| 13 | 10 | N,S 
10 1°794|64 2/61 2] S.E. | 11 |/1-607|61 0/57 -2/S.S.W.| 9 | 10 | S,KS 
11 1-778|64 -8|61 0) S.E. | 12 |/1-607/62 -6/58-2|S.S.W.] 16 | 10 | N,K 
12 1-767| 67 0/63 0) SE. 9 ||1:599| 63 -4/58 -6|S.S.W.| 12 | 10 h 
1 pu. |1°738) 67 -2163 0) S.E. | 11 1/1593)57-5|55-0) N.W. | 12 | 10 | N,S 
2 1:718|63 -8|60 0) — 0 |/1-611/52-8/51 -9|N.N.W.| 12 | 10 | N 
3 1698/63 0/605) — 0 1/1618) 53 -2|/53 6|W.N.W., 2 | 10 N 
4 1680/65 5|63 5 | W.S.W.| 14 ||1600|54 -1|53-4| N.wW. | 3] 10 | N,K,S 
5 1668/64 0/60 5 |W. N.W.| 17 |\1:586| 57 0/53 -1| N.W. | 14 4 v, K 
6 1668] 63 -2|60 -0|W.N.W.) 17 |/1:596|55 0/52 -1|W.N.W.| 11 9 | NUK 
7 1676|61 -2|57 0) N.W. | 14 |/1-612/55 -2|51 -9|W.N.W| 13 3 N, K 
8 1695/60 0/570) N.W. | 29 ||/1-624/52-9/50-0| W. TON LON) Kee 
9 1726] 56 5 | 53:2) N.W. | 19 |/1-631}51 1/49 -7| W. 14 4 |K,KS 
10 1740|56 0/53 0) N. W. | — |]1:645|50 6|50-0| W. 92 OR EN GEK 
11 1:754| 54 8/502) N.W. | — ||1-645|49 -4/49 -0|W.N.W.| 13 7 |N,KS 
June 22,) 0 1773/52 -2|49 2) N. Ww. | — |1-649/ 50 -2|49 -8|wW.N.W.) 14 SENS 
1a. w./1-786/51 8) 49-0} — | 0 ||1:663/49-9|49 9|W.N.W.| 11 | 10 N 
2 1791|51 2/49 °0| — 0 |\1-680|50 -4|50-3| WwW. | 14 | 10 N 
3 1:805|50 -2|48 -2| Ww. 5 ||1-693| 49 -1|49 -4|N.N.W.| 10 | 10 N 
4 182550 0/48 0| W.S.W.| 5 ||1-717| 48 -7|47 -7| N.N.W,) 14 4 |CS,CK 
5. |1846|52 -8|51 -2 s. 6 1/1641] 51 9/50 -1|N.N.W.| 12 9 | N,CS 
6 1857/53 0/510} W. 7 \1-779) 51 ig -°8|N.N.W.| 19 3 | KN 
REMARKS. REMARKS. 
June 21, 1 p.m@—Overcast. Thunder, followed June 21, 6 a. m—9 a. u.—Light rain. 
by heavy drops of rain; air sultry. 3 ep. m.—Heavy rain; amount = ‘060. 
10 vp. m—Heavy shower. 
June 22,10 a. m.—Moderate rain. 


498 The Rev. H. Luoyp on the Meteorology of Ireland. 


Taste XXXIV. (continued). Hourty Osservartions. 


Dunmore East. 


Lat. = 52° 8. Long. = 6°59. Height = 66 feet. 
Barometric Correction = + 0°091. 
Force of Wind expressed in terms of scale (0 — 6). 


Portrusz. 


Lat. = 65°13. Long.=6° 41. Height = 29 feet. 
Barometric Correction = + 0°082. 
Velocity of Wind expressed in feet per second. 


Therms. Wind. Therms. Wind. Cloud. 
Date. Hour. | Barom. Barom. | 
Dry. | Wet. | Direction. Force) Dry. | Wet. | Direction. | Vel. | Amt. Form. 

June 21,| 6 a. m.|1°784| 60°5 |57°°0 | S.S.W.| 1/1761) 57°0 | 56°-3 8. 15 | 10 = 
7 1:774|62 0/58 -5| S.S.W.| 2 |/1-744| 57 5 56 6 Ss. 17 10 _ 

8 1:761| 63 -0|60 :0| S.S.W. | 2 111-732) 58 -4\57 °3 S. 17 10 == 

9 1-737|65 :0|60 -5| S.S.W.| 2 111°718] 58 -5 | 57 -4 s: 25 10 — 

10 1:727| 66 ‘0 |62 °5 | 5. 2 |/1°705| 58 °6|56 ‘9 S. 26 10 _ 

11 1-716) 68 -0 |64 5 s. 2 ||1-689| 59 ‘6 |58 -2 5 28 10 —_ 

12 1688 | 69 :0 |64 °5 8. 2 ||1-673| 60 -4|57 ‘7 S. 31 10 — 

1 vp. m.|1°676| 69 -0 |63 -0 Ss. 2 ||1:-667| 61 :0|58 9 8. 35 10 —_— 

2 1:661|67 -0|62 -0|}S.S.W.| 2 |11.655| 60 -4|57 6] S. W. 35 10 _— 

3 1:647| 66 -0 |60 -5 | S.S.W.| 2 ||1-642'60 -4/57:1] S. W. 35 10 — 

4 1-632|65 ‘5 |60 5 |W.S. W.| 1 111-651/| 54 9/53 -2| N. W. 36 10 —_ 

5 1632/63 -0|58 0 |W. N.W.| 1 1-652 52-9 51 5 WwW. |-36 10 — 

6 1-644|62 ‘0/58 0} N. W. 2 |/1-654| 53 -3|51 -0 W. 23 9 N 

it 1-649|61 -0|57 °0| N. W. 2 ||1-655 | 54 -4 |52 °3 W. 17 8 N 

8 1-658|58 5/54 0] N. W. 2 111-659 | 54 ‘2/518 W. 34 4 N 

9 1-667 |56 5 |62 0] N. W. 2 ||1°654|53 1) 51 -0 Ww. 39 4 N 

\10 1-714|54 5 |50 -5| N. W. 2 11-665 | 52 ‘5 |50°8 W. 27 3 N 

11 1:739|53 ‘5/49 5| N. W. 1 ||1:673/52 3 | 513 W. 36 10 —_— 

June 22,| 0 1-749|52 0/49 -0| N. W. 1 |/1-682|52 2/50 -7 AWS 35 4 N 
1 a.M.|1°813]50 ‘5 |47 5 | N. W. 1 ||1-674|52 3/50°8 AWE 37 9 N 

2 1808/48 0/46 -0|W. N.W.| 1 /11:685|52 5 | 50 °8 W. 39 5 N 

3 1'811|48 5 |46 -0/W. N. W.| 1 |/1-693/52 0|50-9| N.W. 4l 10 — 

4 1813/48 0/46 -0|W.N. W.| 1 11-715) 51 9 | 50 3) N. W. 48 8 N 

5 1:813}51 :0/49 -0|/W.N. W.) 2 |/1-748| 51 6 | 48 ‘9 N. W. 48 9 N 

6 1835 | 54 5/52 ‘0/W.N.W.) 2 |/1-760 516 | 48-4) N.W. 48 9 N 

REMARKS. REMARKS. 


June 21,—Cloudy until 10 P.M. Raining from 
4 P.M. to 6 P.M. 
Clear from June 21, 11 p.m. to June 22, 5 a.M. 


June 21.—Overcast until6p.m Light rain 
until 1 P.M. 

June 22, 3 a.m. to 6 A.mM.—Showers with inter- 
mittent sunshine. 


499 


XIX.—Experimental Researches on the Lifting Power of the Electro-Magnet. 
Part II. Temperature Correction; Effects of Spirals and Helices. By the 
Rev. T. R. Rosryson, D.D., President of the Royal Irish Academy, and 
Member of other Scientific Societies. 


Read June 26, 1854. 


ly my former communication on the subject, I examined the relation between 
the lifting power of the electro-magnet and the force of the current which 
excites it; and shewed that the first increases much more slowly than the 
second, so that it cannot pass a limit which depends on the size of the magnet 
by any assignable amount of current force. But besides the magnitude of that 
force, the magnet’s power depends even more on the number and distribution 
of the spires of its helices; we can dispose of a very restricted amount of 
current. The most advantageous mode of employing a given battery is when 


its internal and external resistance are equal, its action therefore = oR This 
vu 


for the Grove’s which I use, exposing 19 inches of platinum, is 6 of my units ; 
and for my Callan’s of 90 square inches is 14.5, the last of which would only 
excite my magnet with a single spire to one-sixtieth of its maximum. But how- 
_ever we increase the number of spires, they have all an exciting power ; and if 
this acted equally for each on the magnet, the effect of the current might be 
increased without limit. It is true that the increased resistance would require 
a larger battery, but this can always be commanded. But this equality of action 
does not exist ; the exterior spires act more feebly on account of their greater 
distance, and those at a distance from the polar surfaces exert little influence 
on them, both from distance and obliquity of force ; and secondly, though they 
do excite fully the parts near their plane, yet the magnetism developed there is 
VOL. XXII. 37 


500 The Rev. T. R. Rostnson’s Experimental Researches on the 

greatly weakened by the induction which transmits it to the poles. As far as I 
know, these disturbing causes have not been studied ; and I hope that the fol- 
lowing results will not be without their value to the construction as well as 
theory of the electro-magnet. 

The electro-dynamic laws, discovered by Ampere, Biot, and others who have 
followed in their steps, may seem suflicient to establish its theory ; and it is 
desirable to ascertain whether they succeed in doing so, for the simple case of a 
circular or helical current. 

Let BEG be a differential slice of the magnet, Z one of its elements, H a 
current element below its 
plane, whose direction is 
perpendicular to the plane 
HAG, the power of H to 
attract and, as we may infer, 
to magnetise / is, as its 
magnitude de, as its energy, a 
uf (F being the force of Part 
the current), as the inverse er 
square of the distance HZ, 
and as the cosine of the an- 
gle CHE; or putting HA ™ 
=z, AC=2, CE=y, DE =r, AD=b, and BDE = 6, the magnetism of E, 


IM’ = bE .dc. E (2? + 2*) 
(ik ye oF 
A difficulty occurs here however. The polarity given to the element £ is 
such, that its axis is perpendicular to HH; but, as in the case before us, the 
current surrounds the magnet, it is evident that unless z = 0, each portion of it 
must produce a different axis. Is this physically possible in the molecules of 
iron? If so, their polarities must be very irregularly distributed. Or do the 
axes coalesce into one resultant, whose intensity may be estimated by the com- 
position of forces? This seems most probable ; and, therefore, assuming it, 
and resolving dM’ in the direction of z, 
IM= meee x e 
(Pe +y? +2)? 


ea 


Lifting Power of the Electro-Magnet. 501 


As the magnet has cylindric arms, BHG isa circle; EL, therefore, = rdrdédl, 
transporting the origin to the centre, we have 


pldedl (b —r cos 6) . rdrdé 1 
(0? + 7° + 2 — 2br cos 0)3* i) 


dM = 


Integrating this for @ from 0 to 2z, and for r from 0 to 7’, we obtain the mag- 
netic force of a slice of the magnet whose thickness = dl, due to the action 
of H. 

This, however, assumes that each molecule is susceptible of magnetism up 
to the full influence of the current on it, which can scarcely be the fact. Those 
nearest the helix being most excited, must tend to induce polarities opposite to 
their own on those next within, on which also the direct action is less ener- 
getic ; and we may, therefore, expect to find a zone of intense magnetism suc- 
ceeded by one weaker, null, or even reversed, followed by a series of similar 
alternations. ‘This does occur in compound magnets to a great extent ; and is 
manifest in those experiments of Pliicker, which prove that a mass of iron is 
less attracted than filings of the same metal, and these less than powder of iron, 
more sparsely distributed by being diffused through lard. Of course the same 
inductive interference occurs in the case before us; but we know too little of 
its laws to be able to introduce it into the calculation. 

The first integral belongs to a class which presents considerable difficulty 
when its modulus is so near unity, as must be the case with the innermost 
spires ; and among the methods of approximation which have been devised by 
Euler and Legendre, none, on the whole, are as convenient for my purpose as 


the common development by the Binomial theorem. Let b?+r°4 2 =’, 


+ 
rdr=udu ; and expanding a , and omitting odd powers of cos @, 


because the terms introduced by their integration vanish between the limits, 
we obtain 


2 2 
be Axa t (Ix wee 1) cos? 6 
ue\4- wu 


267 )rs /9 2? 
uFdedidude } +Cx ( a ( ea 1) cos‘ 0 
; 2b)8r° 13 2B 
+ Ex O(a ae = 1) cos® @ 
+ &e. &e. J 
on2 


dM= 


502 The Rev. T. R. Rozinson’s Experimental Researches on the 


The general term being 
SO. Me 2 — Oo 27 — ly 0) eae Te -C08"O (aS 20° 1) 


Q.4....2n—4. 2n-—2 Te 2n Ww 


When n is even, 


Qn 
{ cos" 6d@ = 27 
0 


See ate bere 
Bap og ae CAPs 
and, therefore, the integral of the corresponding JED is 


ye OO BN 3. In—-1 Loe ts sot=al OP)” (2n+1. Bb 1 
Or ee er ao a 1.235 an x= un? Tarn eo wp 


and it is derived from that which precedes it by multiplying the latter by the 
factor 

2n—3.2n—1_ Br? 

Pr ae (@) 


b  3br? (5B Bad hela ie 
youl 2Qut Gat) + o-3-e ar get) 
3 


Soot Teo Ce a /tsnt 
dM = pF de.dl dum} 2.2.4.4.6.0 (oe) 


we thus obtain 


Oe ae Oe nu 


3.5.7...2n—3.2n-1.0". oe e -1) 


This must now be integrated for r. As rdr= udu, integrating by parts, 


fea —7 nr? n.n—2 7 
um m—1L.u™? m=1.m—3.u" > m=1.m—3.m—5.u” 


&c., 


which must be continued till the exponent of 7 vanishes. Each value of n 
(2n + 1)b° 
nu 


gives two sets of terms on account of the factor —1; if then we 


combine the first set of the n with the second of the (n+2)", we have the 
sun) 
BEX ancl x 
n 
if r” nie n.n—2.7" 4 
\~ e418 OFT. nT IFT. MNT. Bn 3a 
|+ prt? 7 nr" -2 


— ke. 


n+2. west ona. mri + In+1. on — yn + &c. 


Lifting Power of the Electro-Magnet. 5038 


which destroy each other, except the term 


LEV GaSe Ne gp 
Nm. +2 .unrs 9 


which belongs to the exponent n+2. If the term of n= 7, 
Por. 7" 


P= nT oP 
and the next, 
2n+1.2n—1.b?.1 


Te saa 
Bea t n.n+2.ut , 


(3) 
from which the successive terms of the integral (which all vanish when r=0) 
are easily formed. We thus find, calling the section of the magnet ar*dl= A 
Us De MS Soe? aoe 
Dui * 2.2.4.0 © 2.2.4.4. 6.00 
Wee Oo fewhe lilt 13 .b'.r 
ae oe ETL +6 


This converges sufficiently, unless b is nearly =r ; then, notwithstanding the 
simplicity of the law of continuation, the computation is tedious. But as soon 


=pFA x de. (4) 


+ 


as n is so large that 


= : may be neglected, it can be much simplified ; for 
2,2 n+ 2n 


calling s =p, (3) becomes 
(Spas Pas Ta p+ sj 
and « being the number of steps, 
eaters p +e (5) 


Even this is too slow ; but it enables us to compute « terms per saltum. The 
sum of them is (m=4n), 


m "Mm em 7m 
} pm_ | p p Hall 


“Um+1°om+2°>m4+3°°° ° mt+ey’ 
E : ; 1 : 
or developing and arranging according to the powers of = and putting 
ptp..-- nee © — p*)=A, 


p+2p+....4+ap= —(e+1) p?+ap {=B, 


Be Be 
(ae 


504 The Rev. T. R. Rosinson’s Experimental Researches on the 


p+4p+9p’.. $a aE [lp (a4) F424 2e—1) aig} = ; 
S(Lnoi++: Toure) = Tod 24 5h 


a (6) 
which is sufficient for practice. I take 2=10 or 20, and thus obtain the value 
of the integral very rapidly. This must now be integrated for c, which admits 
of two cases. In the first the current is a circle whose radius = 0, therefore 
{de =2xb ; and if S = the sum of the series in (4), the action of a single ring or 
convolution of a spiral, whose plane is perpendicular to the axis. 


M=pF.A. Sx 2Qab. (7) 


No sensible error can arise from considering it a circle ; and I have computed 
the following table of the coefficient of »./.A for the magnet and spirals 
which I use, in which r = 1, and the least value of b=1.13. 


Taste I. 


b z=0. z2=2). z2=4!0. z=6'-0. z=8'0. | z=10'-0. 


1:13 | 464861 | 0:27331 | 0:05165 | 0:01904 | 0:00738 | 0:00390 
elaaee nating 0-06874 | 0:02306 | 0-01019 | 0:00541 
ee ee pease 0-08722 | 0:02971 | 001325 | 000703 
1-73 see 0:45736 | 0-10757 | 003720 | 001671 | 0-00887 
1:93 vesiaa | cose] Wipes! oases baapls 0-01093 
2:13 161455 0°53619 | 0-14628 | 0:05351 | 0:02457 | 0:01313 
ba | ee OSes 0:16393 | 006206 | 0-02890 | 0:01552 
o-63 | 1.39285 | 057794 | o-1s1a4 | o-o70es | 0-03349 | o-01810 
2°73 Serie cveaeae llorieeil) OUTase onc oaente 
2-93 bare 0'59570 | 021376 | 0-08832 | 0-04286 | 0-02349 
3:13 ieee 0°59226 0-22864 | 0:09676 | 0:04762 | 0:02632 
3:33 o-gri26 0:58978 , 0:24042 | 0:10541 | 0-05268 | 0-02941 
3:53 | 091764 | osease | 0-25166 | 0-11340 | o0s764 | 0-03253 
3-73 | o-senoo | os7aes | 026148 | 0-12155 | 0-06261 | o-03555 
3:93 ove2ia5 | 056522 |-0-27009 | 012913 0:06756 | 0-03870 


Lifting Power of the Electro-Magnet. 505 


It 4ppears from the second column of this table that the power of a ring 
decreases with an increase of its diameter, very rapidly at first, but more slowly 
afterwards, so that its action continues sensible to a considerable distance. But 
out of its plane the case is different, the total effect is much less ; but if z 
have any considerable magnitude, it increases with the diameter of the ring. 

The case of a spiral is, however, not that of most ordinary occurrence, the 
wire being generally disposed in a helix. To obtain its effect on the magnet’s 
element A, we substitute for de in (4) the differential of the helix. In this 


curve if e = the slope of the wire, 


d 
=b0x tane, dene 
sin @ 


as, however, the curve is inclined and its induction is in a plane perpendicular 
to it, de must be resolved in the direction of its base, and we have 


2 St 
Me BF. ee hs Bt) alder &e.} 


d tan é Quast 2.9.4.0" 


Putting 6? +r? =#’, the integral consists of a series of terms, 


1 rf 2n—4 
2n—3.0.u"™ 3° In-—3.2n— See 


n-1 
fo ET gy: Sia 


which vanish with z, and therefore require no constant. 
The series terminates when 7 =n, and its last term is 


gn Uf 2.4.6... 4.1 
ce. == 3.5....2n—5. = 

ae 
a the next 


The term preceding this is obtained by multiplying it by 5 


oe — -—5.t? 
by the additional factor ——,, and so on till the last factor is —————. 
4.u 2n—4.u? 
Having obtained Q,, the next term, 
Qn BAR 2n—2.2n mee 


Qn+1.2%n— ie ee 


506 The Rev. T. R. Rosryson’s Experimental Researches on the 


and as each term of (4) has a coefficient, whose law of derivation is 
2n+1.2n—1 


ae , we have 


nm—1_ 4rb? 


Qnea = Qy X 5X a 


’ 


so that the successive integrals can be computed with facility. This expression, 

however, is not so well adapted as that for a spiral, to the process of summary 
computation which becomes desirable when 6 is near r. The (m+ 2x)” term 
4dr” n—-1.n4+1...n4+2a-—3 

Quste= Qu x n+2.n+4...n4+20 ’ 


4hr? 


pS 


3 3 
log Quine = Qa-+og px 2+ 10g (1-25) +log (1 - ri) SAT ete 


3 


Developing the logarithms, and stopping at = this becomes 


whence, putting as before p= 


cz 8a i Ns 
log. Qri22=log. (Q, x p”) — modulus —— (22-1) +3 (4a? — 3” + 2)f, 


which for 2 =10 or 20 is sufficiently rapid. 
The intermediate terms in this instance are more easily obtained by the 


n+ 22 
method of quadratures, their sum being | Q,dz. This process gives 


Bo 
Poh Ose bide ama + Qunj= Qf 4'- 45h, (9) 
in which 


P + &e. 


v log 
ee loge — 


2 


B’ = {+3422 log p} 


8 


= = j= 3 —2zrlog p+10z}, 


Lifting Power of the Electro-Magnet. 507 


p 
lo 


sufficiently exact, and easier for computation than their true values, &e. 
In practice I found it best to take « =— 4 and +5. ‘i 

Having obtained the sum of any number of the terms Q, the sums of the 
preceding terms are successively obtained by the factors already given, and the 
multiplication must be continued till the products are certainly of an order that 
may be neglected. 


If the sum of all these integrals = S’, 


Fee ee pA x bos’, 


tan e 
and as @=2z x number of spires in helix (=s), 
M=pFA x 2nbS’. (10) 


The computation of S’ is much facilitated by the terms Q containing only 
the inverse first power of w as a factor, so that when their sum is once got for 
any values of z, it is known for any other with a given 6. The terms derived 
from Q are similarly computed in sum. 

I have tabulated a few values of it, which will suffice to make an approxi- 
mate comparison of this theory with observation. 


Taste II. 


| 
1-130 | 2:1902 | 1-3456| 0:9580| 0-7367| 05976 | 0:5017 | 0:4320| 0:3791 | 0:3377 | 0°3044 
1-564 | 1-9663 | 1-3382| 0-9798 | 0°7670 | 0°6280 | 05294 0°4574 | 0-4023 | 0:3589 | 03242 
1-998 | 1:4987 | 1:1642| 08800 | 0:7052| 0:°5845 | 0-4973 | 0-4318]| 0:3811 | 0°3409 | 0:3081 
2-432 | 13014} 1:0418| 0-8142 | 06516 | 0:5598 | 0:4817 | 0°4207 | 0°3727 | 0:°3343 | 0°3042 
2-866 | 1:1040 | 0°9206 | 0°7676 | 0-6443 | 0°5485 | 0-4749 | 0-4172) 0°3712| 0°3339 | 0°3031 


For any point within or without the helix, 
gi S# Suze 
Bp l 
It is useless to pursue the analytic part of the inquiry further at present, 
because the distribution of the magnetism excited by the spires ina closed cir- 
cuit (which is quite a different problem from that of a magnetic bar) depends 
VOL. XXII. 3 U 


508 The Rev. T. R. Rosryson’s Experimental Researches on the 


on the law of induction from molecule to molecule, which is altogether unknown. 
Sir W. S. Harris has inferred, in the case of a permanent magnet inducting at 
a distance, that this law is the inverse of the distance. Without, however, 
inquiring how far his observations justify this conclusion, it manifestly cannot 
apply in the present instance, as the facts rather indicate an exponential func- 
tion. If the coercive force of the metal did not interfere, the negative logarithm 
of the induction through iron should be proportional to the distance ; but the 
law of this force also is unknown.* 

In examining the action of spires, and, still more, facts of induction, it is 
necessary tohave a magnet of variable length, as no satisfactory conclusion can 
be drawn if several be employed, owing to the various qualities of iron. It is 
almost impossible to get two pieces of equal power, since the slightest diffe- 
rence in forging, turning, or planing, influences this property. That which was 
used in these experiments is of the same dimensions as the one described in 
my former paper, differing in being solid, and having its base of brass. The 
cylinders are connected by a slide, composed of two pieces of the same iron, 
each one and a quarter by two inches in section, in which semicircles are cut out 
to receive them ; and by steady-pins and screws it can be firmly attached at any 
height. From the excellence of the fitting the contact is very close ; and ex- 
perience shows that it makes no interruption of the magnetic circuit. Setting 
it to leave four inches of each cylinder, I found that with 0°85 current force, and 
helices (/’) containing 641 spires, the lift of the magnet is 817 lbs., when the 
screws are tight, and 800 when they are slackened, and the contact maintained 
by the attraction alone. If we allow for the decrease of magnetism mentioned 
in my first paper, these two may be considered identical. The sufficiency of 
the contact may also be inferred, from the parts of the cylinders below the slide 
showing no free magnetism. I found this to be the case even when this magnet 
was excited to the highest power which I have yet obtained with it I may 
add, that no part of the lifting power is due to the action of the spires on the 
keeper or slide : when the helices, even excited to the great power mentioned 


* Bringing into contact with my magnet’s N pole an iron tube, three-quarters of an inch in 
diameter, and nine feet long, seven feet of it are N, and the remaining two 8. 

+ The cylinders were 2°1 long, the helices those already mentioned, and y = 3005-04, T'= 81°-8, 
LT! was 1374:17. 


Lifting Power of the Electro-Magnet. 509 


in the note, were laid on the keeper in the same position as they had on the 
magnet, its extremities would neither attract a small key nor hold a horse-shoe 
keeper. 

I have already pointed out the gradual decrease of the magnet’s power 
during a series of experiments, and the fact that this decrease is prevented by 
continually reversing the current. On this plan most of the experiments whose 
results follow were conducted. It is made more effectual by exciting the 
magnet, and, without disturbing the keeper, suddenly reversing. It seems that 
the abrupt change of magnetic tension keeps the molecules of the iron in a state 
of neutrality, which prevents them from assuming permanent polarity.* To 
perform this easily, a commutator is attached to the magnet, and each set con- 
sists of six, half direct and half reverse. By this method the results have 
become far more consistent. The rest of the apparatus is unchanged except 
the rheometer, which is now on the construction discovered by M. GauGatn, 
and demonstrated by M. Bravais.t Six rings, the largest 19° in diameter, 
are placed parallel on a frustum of a cone, whose base is four times its axis: 
the centre of the needle is in the vertex of the cone, the needle is three inches 
long. This arrangement has the advantage of giving the proportionality of the 
force to the tangent of deflection—a far wider range than in the ordinary con- 
struction, and enabling to measure much higher currents. For such the largest 
ring alone is used ; for small currents the whole six. A set of fifteen obser- 
vations with the voltameter gives for its constants in the first case, 


F=tan ¢ x log! (0°58298) {1 + log"! (6°7607) x (sin? @— # sin‘ ¢)}, 


which will serve for any instrument of the same dimension. 

In comparing the efficiency of different arrangements of spires or magnets, 
the most obvious method is to excite them till the lifts of the magnet are the 
same, when the mean efliciency of each spire, = a, must be inversely as ¥, the 
product of the force and number of spires. It would, however, involve an 
immense waste of time to ascertain this equality, and therefore it is better to 
refer them to acommon standard. That which I have chosen is the action of 


* This has been so effectual that the residual magnetism is insensible, though the number of 
times that it has been excited exceeds 1200. 
+ Comptes rendus, Jan., 1853. 
3U 2 


510 The Rev. T. R. Rosinson’s Experimental Researches on the 


a pair of spirals (A), possessing a definite character, and acting on the magnet 
under the most favourable circumstances, namely, when its cylinders are reduced 
so as merely to lodge the wire, in which case the action with a given > is the 
greatest possible. With these I obtained a series of values of Z and the cor- 
responding y’, from which can be found, by interpolation, the y’ correspond- 
ing to any L. If that Z is obtained by any other spirals, helices, or altered 
length of the magnet, we have, assuming the mean efficiency of (A) = 1, 


p=. 
¥ 
As, however, in using different currents, the magnet is unequally heated, it is 
necessary, in the first instance, to determine 


THE TEMPERATURE CORRECTION. 


In my former paper I investigated the correction by heating the magnets to 
about 70° and 170°; and, assuming that the decrease was uniform throughout 
this interval, I deduced the coefficient of decrease = 0:00033. The experi- 
ments of Dr. Luoyp on the temperature change of the magnetism induced by 
the earth on soft iron have led me to doubt the correctness of this assumption, 
and institute further experiments, which show that the law is much more com- 
plicated in the case of the electro-magnet, and that the coefficients which ex- 
press it vary with the nature of the magnet. The magnet used in the first 
instance is one belonging to Mr. Brrarn’s collection (to whom I am indebted 
not only for the use of much valuable apparatus, but for still more valuable 
assistance in these researches), extremely convenient for the work. The cylin- 
ders are five and a half inches diameter, their centres six asunder; they are 
hollow, their thickness being half an inch ; they are eight inches long, and the 
base and keeper have a section equal to theirs. The helices are those desig- 
nated (J). The balance used with it is well worth notice. It has only one 
lever (whose ratio is 11625), the longer arm of which carries a platform, on 
which weights, multiples of 30lbs., can be placed: below the platform is sus- 
pended, by a spring balance, a tin vessel, into which shot is poured, whose 
weight is seen by the index up to 30lbs., the limit of the spring. If this be 
not sufficient, the shot is permitted to escape by a valve at the bottom of the 
vessel, another weight is set on the platform, and the process is repeated. The 


Lifting Power of the Electro-Magnet. . Se 


manipulation is easier than in mine, and the accuracy superior, but the concus- 
sion is greater. The hollow cylinders receive copper vessels, which may be 
filled with hot water or ice, and their magnitude is sufficient to preserve a 
nearly uniform temperature for some time. The experiments were, unfortu- 
nately, much disturbed by the perpetual passage of carriages through the street, 
which caused the loss of many results ; indeed we could only work during the 
night, and even then had much disturbance. The temperature was measured in 
the middle of the keeper, the middle of the base, and the top of the cylinders, 
and the mean taken. J’ was kept at 0:4734, giving ¥=143-91; Tis the mean. 


Taste III. 

\| No 

Tr E. | 0-C. Obs. 

1 Roa aree| _ 29-68 | 6 
2| 53-56 | 876 -48 || + 19-49 | 8 
3 | 58-07 | 859 -25 | + 12-85 | 6 
4 | 64-78 | 842 23) + 7-67 | 5 
5 | 78-41 | 812-48 || — 13-11 | 8 
6 | 76-83 | 822 36] + 1-42 | 9 
7 | 81°85 |823 61||+ 078] 8 
8 | 87°62|818:05|| — 4:73] 8 
9 | 92-38 | 822 -74|| — 3:44 | 9 
10 | 96°56 | 826 -72|| — 4:20 | 6 
11 | 102 68 | 831 99 | - 3:23 | 6 
12 | 107 -40 | 855 -17 || + 13-98 | 6 
13 | 111 -89 | 854-83 || + 7-48 | 9 
14 | 116-14 845 53 | —- 813) 5 
15 | 121 -85 | 856 -82 || — 5:91 | 5 
16 | 127 -44| 876 68 || + 4-74 | 8 


The third column shows that the value of Z diminishes as the temperature 
increases ; becomes a minimum at about 75°; it then increases to the highest 
temperature in the Table ; after that it would certainly again decrease ; but 
we could not easily, with this arrangement, pass 127°. If there be no subse- 
quent maxima and minima, these facts imply a formula such as 


L=L'\1—at+be—ct*}, 
which, in fact, is the form given when the coefficients are determined by 
Caucuy’s method of interpretation. 
By this, reckoning ¢ from 60’, is derived 


Ov 
—_ 
bo 


The Rev. T. R. Ropinson’s Experimental Researches on the 


L =842.54 {1 —tx log?(7:35439) + @ x log?(5-78313) 


i 
—t x log (3-46064)}. Gy 


The fourth column contains the difference between the observed LZ and 
that calculated by this formula; the discordance is considerable, especially in 
the three first, but not greater than might be expected under the circumstances, 
and the errors being often effected with contrary signs shows that they are 
casual. I may also remark, that the current was not reversed in these obser- 
vations. The difference between the correction given by this formula, and the 
change of Z which I had obtained with the hollow two-inch magnet, showed 
the necessity of instituting similar experiments for that which I was using in 
the present series; and*I found that by surrounding it and its slide with a 
covering of thick cloth, and the keeper with a similar one, I could raise the 
temperature to 220°, the limit of the thermometer which I used, by placing a 
gas flame on the base. The slide is the hottest; but its temperature, that of 
the cylinders at their top, and that of the keeper, were taken, and the mean 
deduced by giving each weight as the length of the piece. 

The first was with the cylinders =0*15, and the spirals (A) with y=170-79. 
I obtained 


Taste IV. 


No. Te 


17 | 69°-6 | 615-90 | + 2°89 | 18 
18 | 81 -0| 603-44 | — 3°84 6 
19 | 100 5 | 601-40 | + 0-94 | 12 
20 | 130 0 | 59889 | + 3:14 | 12 
21 | 161 -7| 59153 | — 4:08 | 12 
22 | 207 -4| 598-90 12 


whence I similarly deduce 


L =618-96 {1 —£. log? (703890) +22. log" (499503) 


— 1° log (2°43656)}. on 


Secondly. With the cylinders=2"1, the helices (B) and y= 553°75. 


Lifting Power of the Electro-Magnet. 513 


TaBie V. 


No. 


23 
24 
25 
26 
27 


giving 
L =911°85 {1 —t. log? (7:09736) + #. log? (508868) 
—t’. log (2°61666)}. 
Thirdly. With the cylinders = 10-1, with the helices (B), (J), (K), (ZL) 
and (J), containing 1002 spires, and with y= 553-75, I obtained,* 


(13) 


Taste VI. 


giving 
L= 73569 \1—t. log" (7°30919) +? . log (540470) 


14 
—t°. log? (2:98826)}. Oa 


It must be remembered, that these equations are mere formule of interpo- 
lation, and not the actual functions expressing the change due to temperature ; 
yet there is an evident correspondence between them and the forces which are 


* As the slide was at the bottom of the magnet, the plan of heating it, used for the others, 
was not available ; but by placing a brass curved funnel over a double argand gas-burner, a stream 
of heated air was thrown within the covering of the magnet; and by placing its orifice so that 
part impinged on the slide, while the rest circulated within the confined space, I insured the same 
temperature in the slide and cylinders. 


514 The Rev. T. R. Ropinson’s Experimental Researches on the 


concerned. They all comprise three terms affected with ¢, and, of course, show a 
decrease at first toa minimum, then an increase to a maximum, and a subsequent 
decrease. Now, as I formerly noticed, the Z represents the polarity at the 
contact surfaces of the magnet and keeper: this depends on, first, the polari- 
zation of those molecules which are excited by the helices; secondly, on that of 
the remainder of the magnetic circuit, and therefore its amount depends on the 
intensity of these polarizations, and on the facilities with which their influence 
is transmitted by induction. The intensity, again, depends on the suscepti- 
bility of the molecules directly, and inversely as the coercing force. Now each 
of these may be expected to change with the temperature. The correlation 
of heat with other molecular forces is such that, d priori, we would anticipate 
its lessening such forces as we are considering ; and we find that at a red heat 
even iron is scarcely attracted by the most powerful magnets, which must de- 
pend on the molecules ceasing to be excitable. A diminution of this power, 
and of that which transmits the magnetism from one particle to another, must 
lessen Z, while a contrary effect will arise from the diminution of the coercing 
force. All these influences will be functions of the lengths of the magnetic 
current, and of the excited cylinders ; and accordingly we find that the co- 
efficients in (12), (13), and (14), increase with the latter. Calling them a, £, 
and y, and the length of the cylinder z, the three values of vy are exactly repre- 
sented by the formula a+ bz, and those of a nearly by a’ + 6’; from which one 
might infer that y corresponds to that part of the change which belongs to the 
excitabiles, and @ to the conduction. I have not found any simple expression 
for B, but since it gives the intermediate increase of magnetic attraction, which 
(as I hope to show in a future communication) depends on the coercive force, 
we may refer it to that. 

I did not think it necessary to investigate these corrections for the other 
lengths of cylinder, as these three give sufficient data for interpolation, and 
from them,* 


* Although it is not safe to interpolate beyond the limits of the observations, yet, computing 
from these the constants for twelve-inch cylinders, and reducing by them the temperature ex- 
periments with my first magnet, I find the higher gives in each pair an Z/ less than that of the 
lower by 7:56, 6°92, 4:44, 6-24, or in the mean 6-29 for a difference of temperature=101°6. This, 
therefore, shows both that the same law holds in this magnet, though hollow, and that these con- 
stants will serve to reduce the observations made with it. 


Lifting Power of the Electro-Magnet. 51: 


or 


a=0°001094 + = x log (617319) += x log” (4:90309). 
B= 000000989 +< x log” (434242) + 7 x log” (325527). 
y = 000000002733 + = x log (2°14768). 


The case is, however, very different if those parts of the circuit, which are 
not directly excited, be lengthened. With the cylinders = 10-1, and the helices 
(B), two inches high, placed in contact with the keeper, I got with y=544'83: 


Taste VII. 


33 | 64°41} 806-70 | — 0-71 | 12 
34 | 119 -2| 772:97 | — 0-15 | 12 
35 | 161 -1 | 752-33 | + 0:25 | 12 
36 | 197 -9 | 732-81 | — 0:08 | 12 


These give 
L=810°84 {1 —t. log” (6-99120) + #. log” (462797) , 
—# log (2-21015)}, ae 
when the coefficients are less than even in (12), but the law is the same as 
in the rest. The places of the minimum and maximum are much higher, and 
the change of Z is greater than in any of the others. 

The terms within the brackets in these expressions are, I think, indepen- 
dent of y-; for in my former paper it is shown that, with the magnet there used, 
the decrease of Z for a given difference of ¢ is the same, with very considerable 
variations of the current. 


ACTION OF SPIRALS. 


I. In the first instance, I give the Table already referred to of the spirals 
(A), which I assume as my standard. Their constants are 
b= 114 b= 2805 s=40. 
Their external diameter was intended to be as large as the distance of the 
cylinders would admit, and the cylinders themselves are shortened to 0-15, 
VOL XXII. 3x 


516 The Rev. T. R. Rosryson’s Experimental Researches on the 


giving the greatest number possible of spires, and the shortest magnet. The 
observed values of Z are reduced to 60° by the coefficients of (12). 


Taste VIII. 


0°34503 
0:67322 
0°42218 
0:30301 
0:38538 
023523 
0-19900 


a ep ee Ye eS) 


0-16252 


As higher values could not easily be obtained without some risk of destroy- 
ing the spirals by the evolved heat, I use, when necessary, the numbers of Table 
xt. obtained with the helices B, whose ratio to A is known. 


IJ. We can now compare spirals of different diameters, and thus ascertain 
how far the preceding theory agrees with experiments. The cylinders were 
set to 0°6, which permits the use of spirals 75 diameter by overlapping 
them. The spirals are made of flatted copper wire 0:2 by 0:05, to enable the 
employment of powerful currents with such batteries as I possess;* but 
experience makes me regret this arrangement, for it requires a greater length 
of cylinder, and the action of the current is probably not quite uniform 


* The current employed with (C) would evolve in a voltameter 18 cubic inches of mixed gases 


per minute. 


Lifting Power of the Electro-Magnet. 517 


through the section of the wire. The error, however, must be trifling. Their 
constants are 

(C) b=1:135. 8 =1:905. s=18. 

(Dy): Te -1120; » 2770: » 40. 

(4). -,, 14150. » 3873. » 60. 


I obtained with them 
Tasre IX. 


| Theoretic | Ni 
No. | Spiral. | 7. L. » || Wee BOTS NG: 
0. | Spira | | v | v | # pe | Obs. 
| | | 


69° | 641-86 | 187-32 | 17863 | 09684 | 1-3772 | 12 
66 -0 | 598°85 | 18802 | 156-12 | 0-8303 | 1-0000 | 12 
66 2 606-07 | 19378 | 15827 | 08167 | 0-8229 | 12 


L is reduced by (12), as from the shortness of the cylinders it must nearly be 
exact for them also. These results are in a ratio so different from what I anti- 
cipated, that I suspected some error was produced by the overlapping of the 
spirals Z. I therefore repeated the experiments with one of Mr. Bergin’s 
magnets, in which the distance of the axes is 7°5, and the length of the cylin- 
der 0°5 ; but it gave similarly 


Tasie X. 


Spiral. T. L. | wb. | W. pe ae 


(D) | 64°3 
(E) | 63-2 | 


(C) ne 502-32 | 19338 | 195-69 | 06497 “srr 


05624 


457-56 | 18914 | 107-53 | 05685 | 1-0000 
| 0:8229 


458°38 | 191-74 | 107°84 


Both sets agree in showing that the power of a spire does not decrease nearly 

so fast by an increase of diameter as the equation (7) assigns. In both the 

is diminished relatively to that of A by the greater length of the cylinder, and 

(in the second) of the entire magnet and its keeper, as will be more evidently 

shown hereafter. As, however, ()) is almost identical in its diameter with A, 

by taking it as unit, we get a more distinct comparison of the relative values of y. 
3x2 


518 The Rey. T. R. Rozrson’s Experimental Researches on the 


Taste XI. 


Tab. 1x. | Tab. X. | Theoretical, 


| | 

C | 1:1663 | 1:1428 | 1:3772 
D 1:0000 | 1:0000 1:0000 
E | 0°9836 | 0:9893 | 0°8229 


The formula gives more power to the spires of C, less to those of the zones 
D—C and E—D than is observed: if, in fact, we determine what parts of the 
effect of H belong to them, we find for 

C effect = 10-4967 = 9 x 1:1663. 
Dero ss 95033 = 10 x 09508. 
E-D , 95080 = 10 x 0:9508. 

It appears probable, from Table 1., that the two or three innermost spires act 
much more powerfully than the rest; and therefore it seems that, from them 
to a considerable distance, the exciting force of the others is constant. The dis- 
crepancy between the computed and observed yu is far too great to be caused 
by error of observation ; for again taking D as the standard, the theoretic p will 
give L’ 48 greater for C, and 61 less for H, than the true values, while the 
probable errors of the latter are only 2:04 and 1:99. 


ACTION OF HELICES. 


Here also the discrepancy between theory and observation is considerable, 
independent of the interference of induction. This is shown, even without mea- 
sures, by some striking facts; for instance, the helices (/’) being placed above the 
polar surfaces of the cylinders set to 4:1, but separated by plates of zinc =, thick, 
and excited to have y= 552, the magnetism produced was scarcely sensible 
when a keeper was applied across the cylinder, immediately below them ; I had 
no means of measuring it, but its attraction was not more than a pound or two. 
Had the helices been on the cylinders, Z would be 850. If one of these 
helices be placed in the same way above one polar surface, there is scarcely any 
attractive power developed at the other: in this case, however, as the magnetic 
circuit is incomplete, the force is much less; but I expected to find 30 or 40 
pounds at least. Similar results were obtained with a magnet, the upper two 


Lifting Power of the Electro-Magnet. 519 


inches of whose cylinders are iron, the rest brass. When the helices were on 
the brass, just below the iron, the lift was but 0-18 of its amount when they 
were on the iron. At the extremity of the helix, the exciting force might be 
supposed to be little less than in its interior. The constants of the helices 
which I used are 


(BB) b=1-180: b’ = 1-965. Z—ES No. layers=8. s=214. 
(A). a 1-130: » 2°866. eal S, ieee 20 » 641. 
(Cie e100: AE Oy aa fie} 5 B24. 
(H) ,, 1-650. » 1750. TG > 2. , 320. 
(1), 2°890. 2990. » 76. Beet) » 804. 
(J) ] * 8. n, bo2. 
a | The same dimensions as (B). : : ‘ a 
(i) | a 8. 225. 


(@), (#7), and (J) are from Mr. Bergin’s collection ; the two last were 
kept concentric with the magnet by wooden framing, though a considerable 
error in this respect seems to have little effect. 

The results obtained with (B) are given in a separate Table, as they were 
intended to be used for interpolation beyond the range of Table vnr., and, 
therefore, the first differences are included in it. JL’ is reduced by (13), the 
cylinders being 2:1. 


TaBieE XII. 


Li. 


ae = 
| 
52 | 68°1 | 1098-90 


53 | 69-1 | 1035-43 | 
| 124:55 | | 201991 
23 | 69-2) 910:88 552°53 16 

96:25 1-36820 
54 | 64:4] 814-63 420-84 12 
111-22 1-25265 
55 | 64:2| 703-41 281-52 12 
114-74 0:70865 | 
56 | 65 °4| 588°67 200-21 jee 
| 110-80 0°44052 | 
57 |62-6| 477-87 151-40 | 12 
14503 0:34793 


332°84 


520 The Rev. T. R. Rozinson’s Experimental Researches on the 


The four last are comparable to Table vu, and give for p, 


07571 
0-7606 
0-7577 
0:7498 


mean = log (9:87912)=0:7570 


The others are given in 


Taste XIII. 
No. Helices. ai Tis w. wv. fe Cale. p. oa | ae 
a ) se) Coaeges leeteutee | cae esa NOLO On| OS2889) 2:1 )/r48 
59 | (F) 71:4 | 874:96 | 550-72 | 380:42 | 06927 | 0-°7038 | 2°1 | 10 
60 | (B+J) | 67-0 | 848-91 | 544-20 | 353-21 | 0:6490 | 05452 | 4:1] 11 
61 | 60+(K) | 66:9 | 810°70 | 547-78 | 318-61 | 05816 | 0:4073 | 6:1 | 17 
62 | (@) 63-5 | 767-41 | 547-19 | 27253 | 0:4981 | 0:°3280| 8-1 j 11 
63 | (HZ) 63-2 | 747-34 | 541°89 | 249-41 | 0-4603 | 03211 | 81 | 11 
64 | (J) 616 | 737°58 | 543-49 | 240-74 | 0-4430 | 02695 | 81 | 11 
65 | 61+(L) | 67-4 | 765-12 | 547-65 | 270-35 | 0:4937 | 0:3228| 81 | 11 
28 | 65 + (JZ) | 64-4 | 733-44 | 553-75 | 237-48 | 0:4289 | 0:2552 | 10-1 | 12 
33|B 64-4 | 810713 | 544:83 | 314-12 | 05765 | .... | 10-1 | 12 
66 | F 71-7 | 797-39 | 548-04 | 301°56 | 05502 | .... | 101 | 10 
et 


Here also the difference between the theory and observation is considera- 
ble; more so than appears at first sight. The computed values of « given in the 
eighth column assume that the intensity in every part of the magnetic circle is 
equal ; or, in fact, that magnetism is transmitted by induction without any 
diminution. That this is not the case is evident from comparing Nos. 55, 58, 
and 33, in which the difference of sixteen inches in the two cylinders of the 
magnet reduces the actual efficiency of the spires of B from 0:757 to 0-5765. 
Therefore, all these calculated values are much too great, and yet all of them, 
except the first, are less than those given by observation, while in the spirals 
they are greater. 

The decrease of efficiency depending on an increase of the spire’s diameter 
is less than that assigned by theory, still more than in the spiral. In (#’) and 
(BL), which are nearly of the same radii as (D) and (C), the ratio of pu is 0915 


Lifting Power of the Electro-Magnet. 521 


with the cylinders 2-1, and 0-954 with 10-1 (which case does not properly be- 
long to this part of my subject, but is given for the comparison), instead of 
0°849. 

This discrepancy is still more evident with the cylinder 8:1, where ((@), 
(#7), and () are mere cylindric annuli, but where the ratio of (I) to (@) is 
found to be 0°8894 instead of 0:8217. 

The same is the case with respect to the influence of the cylinder’s length ; 
as is shown in the following Table of the ratio of the observed to the theoretic 
a, for helices equiradial to (B) ; in which I have also given it for the spirals 
and three helices. 


Taste XIV. 
| | | 
- Obs. be i M Di Obs. a ; 
‘y] rs | ie .| Mean jameter |= =!" P lL 
Cylinder. Cale. Helices, ci Spiel, |Calejs Spira 


This divergence was not expected by me ; for the principles on which the 
equation (1) is founded have been found to give correctly the action of helical 
currents on each other, and their deflection of a magnetic needle. There is, 
however, one marked difference between these and the case of the electro-mag- 
net. The polarities of two currents cannot be in any way altered by their 
mutual action ; those of the molecules of the needle are kept nearly permanent, 
both in intensity and direction, by the coercive force of the hard steel ; so that 
the ordinary methods of statics ‘apply with certainty to them. In the case of 
soft iron, both these vary with the condition of the current, and according to 
laws which I do not think are fully known. From the excess of activity of the 
outer and lower spires, I am inclined to suspect that the resolution of the ex- 
citing power in the direction of x and zis the main cause of error, though some 
of it, as I have already indicated, must also belong to the mutual induction of 
the molecules. 


522 The Rev. T. R. Rozinson’s Experimental Researches on the 


Some practical inferences may be drawn from these experiments, for the 
construction of electro-magnets intended to act with a closed magnetic circuit. 

1. The nearer the spires can be kept to the polar surfaces, the better, for 
their activity is much diminished as they recede from it: the great superiority 
of spirals over helices shows this. Thus, the efficiency of (A) is 1:4436 times 
that of the equiradial (/’) ; their mean distances from the poles being 0:07 and 
1:07. 

2. The very small decrease caused by increasing the diameter (at least, as 
far as 7°5, and probably beyond it to an extent not likely to occur in practice) 
leads to the conclusion that the helices should be as wide as the distance of the 
cylinders permits, or that b’ shall be half that distance ; 6 will, of course, be as 
nearly as possible the radius of the cylinders. 

3. The height of the helices and cylinders should be as little as is consistent 
with lodging a sufficiency of wire to employ to the best advantage the power of 
the battery which is used. 

4. This height = z may be determined thus :— 

Let Hand F& be the constants of the batteries; d=the diameter of the wire ; 
d +c that of it when covered with thread (c being in my wire = 0°03) ; 2s = 
the number of spires in the helices ; and p’ their resistance. We have 


22 (bb), _8p. (b+) (8 —b) xz 
(ieee 2 d(d+c) . 


23S 


: : : 4 
p being a constant, such that the resistance of a unit of the wire = aa : for 
7 


copper I find p=log! (571018). Then we have for the exciting power with 
a unit current, 
_ 2spE pe EEO pz : 
ae oe oy gana (dc)? + 8pz (0 +b) (bb)? 
Rd? 


or, putting me ie a fg =p 


_2E (bb) | pz 
(dt+ey +5 


pyr 


Lifting Power of the Electro-Magnet. 523 


If in this we consider d and z as variables, « a function of z, and differentiate 
for the maximum, we obtain the equations, 


o=d' (d+c)—az, 


_ 2dp az (16) 
0= dz {itera rapt tH 
Substituting, in the second, for az its value in (16), 
zdu d 5 
o= TE t+ atte (17) 


When z is determined by any particular condition, (16) gives the most 
advantageous diameter of wire, and vice versd. 

If it be not, and if the relation between it and » be known, the two equa- 
tions give the d and z for the absolute maximum. In the case of my magnet 
(when b’= 3, 6=1:13) Nos. 55, 58, 60, 61, 65, and 28, give the means of ex- 
pressing that relation by an interpolation formula, A —Bz+Cz?— Dz. Sup- 
posing the battery to consist of ten Groves’ such as I use, R= 47, with these 
I obtain 


Z— 8:39 
d= 014725, or nearly No. 9 of the wire gauge, 
= CS) 

pvr = 2780°29. 


A much higher power, however, would be obtained if the ten cells were 
grouped as five double cells, and the helices made to suit this condition. In 
this case R=11:75 ; and we find for the best arrangement, 


Zi Oroe 
d= 0-2106, a little more than No. 6, 
$= 53818, 

par = 8549-60. 


5. I suppose the current to traverse the helices consecutively; but they are 
frequently used collaterally with the notion of obtaining a more powerful cur- 
rent. This is not to be recommended in ordinary cases. If the numbers of 
the spires be s’ and s”, and their resistances p’ and p”, 

VOL. XXII. 3Y 


524 The Rev. T. R. Rozryson’s Experimental Researches, §c. 


The ay 


SOS p Rapti" 


ao ell 
pte Pees 
p+p" 


consecutive y-: collateral y,,:: s’+s 


If, as is usual, s‘=s’’, p' =p”, the ratio becomes 
Vv: Weiss 2R+ p': ifjae 2p'. 

When p’ is greater than # the collateral arrangement is best, but then it 
must be observed, the expenditure of zinc and acid is twice as great as in the 
ordinary arrangement. 

In these experiments the cylinders were entirely covered aah spires; when 
this is not the case, and particularly when the helices are at a distance from the 
polar surfaces, the action is diminished, because it is imperfectly transmitted by 
induction. Such observations seem calculated to advance our knowledge re- 
specting that power, and I hope soon to submit to the Academy those which I 


have made with this view; and some respecting electro-magnets of hard steel 
and cast iron. 


XX.—Some Account of the Marine Botany of the Colony of Western Australia. 
By W. H. Harvey, M.D., M.R.I. A., Keeper of the Herbarium of the Uni- 
versity of Dublin, and Professor of Botany to the Royal Dublin Society, &e. 


Read December 11, 1854. 


Tue land vegetation of Western Australia is now tolerably well known, 
chiefly through the labours of Mr. James Drummonp and of Dr. L. Pretss, who 
have separately explored almost all the settled districts; and the former has 
also pushed his researches far to the northward and eastward, beyond the range 
of any colonist’s settlement. Lesser collections of land plants have been made 
by Baron Hucet, Captain Manctes, the late Mrs. Mottoy, Mr. J. S. Roz, and 
other amateurs. 

The vegetation of the seaboard of the colony is much less known. Our 
earliest acquaintance with West Australian Alga is derived from small but in- 
teresting collections, made by some of the early French exploring expeditions ; 
and by Dr. Rogert Brown, who accompanied Frrypers. Many of the less com- 
mon species of these collections are only known to botanists by description or 
figures. By far the largest series of Alge brought from this coast is that pro- 
cured during four years’ exploration of the colony by Mr. L. Pretss, to whom 
great credit is due for having collected 141 species, as, from the nature of his 
engagements, but little time could be devoted to this branch of botany. We 
owe to Dr. SonpEr, of Hamburgh, a very able analysis and description of PrEtss’s 
Algz; and the Dublin University Herbarium is indebted to the liberality of 
Senator Biyper, of the same free city, for a tolerably perfect set of these Alge. 
I have thus had the great advantage of examining authentic specimens of most 
of the new genera and species discovered by Preiss, and described by SonprEr. 
A parcel containing between sixty and seventy species of Western Australian 

3y¥ 2 


526 Dr. W. H. Harvey's Account of the Marine Botany of 


Algz, collected by Mr. Mytye, was presented to me by the late Dr. CHARLEs 
Lemany, of London, and is now incorporated with the Dublin University Her- 
barium. This series, though small, contains several not ascertained by Pretss, 
and the specimens are generally more copiously collected, and in better order. 
I have received a few others from my friend J. Backuouss, of York, who pro- 
cured them at Fremantle, during his visit to the colony. Collections of Alge, 
I am informed, have been repeatedly made in this colony by amateurs, chiefly 
ladies; but respecting their contents the botanical world is no wiser, as they 
have been dispersed hither and thither among friends at home. 

This is all the information I possess respecting previous algological re- 
searches in Western Australia. My own observations were made between 
January and August, 1854, at a few widely separated points on this extensive 
coast ; not, perhaps, at the best possible collecting stations, but at those which 
were most accessible. ‘These were King George’s Sound and Cape Riche, on 
the southern coast; and Fremantle, Garden Island, and Rottnest Island, all in 
the immediate vicinity of Swan River, on the western coast. I shall briefly 
describe the features of the coast of these places. 

I landed at King George’s Sound in January, and remained till the end of 
February ; and I revisited this shore in August. My head-quarters were at the 
little town of Albany, situated on the shores of Princess Royal Harbour, an 
oval, land-locked, lake-like basin, with a very narrow entrance; and I made fre- 
quent excursions on foot to the coasts in the vicinity, chiefly to Middleton Bay, 
distant about three miles; and also dredged repeatedly in various parts of the 
Sound between Bald Head and the opposite shores. The vegetation of the 
enclosed harbour is, as might be expected, very different from that of the more 
exposed Sound. Its shores are generally sandy, shoaling to a considerable 
distance from the margin, leaving a very broad marginal belt of less than two 
fathoms in depth at high water, and in many places of less than one fathom. 
The tides rise and fall very irregularly, being much influenced by the wind. 
The rise varies from two to four feet; and there is generally but one tide in the 
twenty-four hours. Now and then, however, I have observed two tides. The 
depth of the central basin varies from five to seven fathoms. About the entrance 
the shores are rocky and rather steep, the rocks being coarse granites perhaps 
the least adapted of any to the growth of Algw. In all the shallow water round 


the Colony of Western Australia. 527 


the northern and north-eastern beaches grows abundance of Polyphysa peniculus, 
a very remarkable little Alga, known only in this locality, where it was detected 
by Dr. R. Brown. It is invariably found attached to dead shells, chiefly to the 
separated valves of acommon Venus (like V. awrea ?), and is very frequently in- 
fested by a peculiar Polysiphonia (P. infestans H.), which I have found nowhere 
else. Hormosira Labillardieri, a fucoid plant, resembling strings of beads, and 
the only representative of the littoral fuci which I have met with, occurs on 
rocks near high-water mark, and extends to half-tide level. All the other fucoid 
plants of this coast commence at low-water mark, and are rarely left dry, even 
at the greatest recess of the tide. The deeper parts of the harbour appear to 
be occupied by immense strata of Dictyota furcellata, a slender, excessively 
branched species ; and of Stilophora Lyngbyci, with a liberal sprinkling of Hyp- 
nec, and of a very luxuriant variety of Spyridia jilamentosa. On the leaves of 
Zostera, and on the stems of Caulinia antarctica, both which form vast meadows 
in water from two to six feet deep, grows a profusion of small parasites, and on 
scattered stones, in the same zone of depth, Lawrencia Tasmanica, and Cysto- 
phyllum muricatum, flourish abundantly. 

At Middleton Bay is an extensive strand, some miles in length, reaching to 
the entrance of Oyster Harbour, and a narrow belt of rocky shore at the southern 
end, where, at the low-water of spring tides, many interesting species of the La- 
minarian zoné may be gathered. Ecklonia radiata, the only laminarioid plant of 
this coast, fringes the whole of these rocks, and extends some distance within the 
heads of Princess Royal Harbour. Outside the heads, in the more open bay, 
the leaves are generally rough with prickles, and the whole plant grows stronger, 
being the state described by authors as L. biruncinata or E. exasperata ; while 
in the tranquil water of the harbour the surface of the fronds is generally smooth, 
being the £. radiata of Agardh. From personal observations I conclude that 
these supposed species are not distinct, as originally stated by Turner. In 
summer time the rocks at Middleton Bay, between high and low water, are 
either completely bare, or produce a scanty vegetation of obscure Calothrices ; 
or of a very minute Polysiphonia, with starved varieties of Gelidium corneum ; 
the power of the sun being probably too great to admit of the growth of a 
fucoid vegetation, such as clothes rocks similarly exposed in colder climates. 
But in winter these same rocks are all densely covered with Chorda lomentaria 


528 Dr. W. H. Harvey's Account of the Marine Botany of 


and Eetocarpus siliculosus, two plants of rapid growth, and both belonging to 
forms which are rare in the warmer, and abundant in the colder waters of the 
sea. Just above the laminarian belt, and extending into it, several social Lau- 
rencie, both here and on other parts of the coast, cover the rocks, often in very 
wide patches. 

Nothing of any interest was collected in Oyster Harbour ; nor was dredging 
in the Sound attended with any very remarkable result. Very little of the 
amount dredged had been detached by the dredge; the greater portion con- 
sisted of drifting plants, collected by currents and eddies on various parts of 
the sandy bottom. The deepest fucoid plant, observed in situ, was Scaberia 
Agardhii, which abounds on every part of the coast explored by me in 2-5 fa- 
thom water. Wherever Caulinia antarctica can find a footing, its wiry stems, 
but rarely its leaves, are generally found covered with parasites, many of which 
(such as Thuretia, Halophlegma, and various Dasya) are very curious and beau- 
tiful. The parasites on Zostera, on the contrary, usually grow on the leaves, 
not on the stem; and here are found Chondrie, Griffithsie, Callithamnia, 
Wrangelie, Crouanie, &e. 

I spent the month of March at Cape Riche, a bold promontory, about 60 
miles by compass, and 70 or 80 by land, to the east of King George’s Sound; 
and famous for the beauty and variety of flowering plants found on the hills in 
its neighbourhood. Here I was the guest of Grorcr Curyne, Esq., who has 
a farm and sheep-run at the Cape. The dry season had advanced too far to 
permit my seeing this beautiful district to the best advantage, or to allow of 
my making an extensive gathering of land plants; and the sea-shore proved to 
be singularly barren in Alge. The ordinary Pucoidew (Sargassa and Cysto- 
phore), with Ecklonia radiata, chiefly occupy the laminarian zone; and the 
smaller Rhodospermea, scattered among them, are few, and of little interest. 
Here, nevertheless, I collected a new Genus (Lasiothalia), and a remarkably 
fine Liagora (L. Cheyniana). 

Early in April I started, overland, for Swan River, and on the 21st reached 
Fremantle, where I remained till the 21st of May; and returned again for the 
first fortnight in July. At this place the algologist must depend, either on the 
dredge, or on the western gales, which frequently throw drifted plants ashore. 
The coast at both sides of the town, which is built on a little calcareous pro- 


the Colony of Western Australia. 529 


montory, consists of long, sandy beaches that extend for many miles. On these, 
in stormy weather, many beautiful plants are cast up; but, owing to the fine- 
ness of the weather during nearly the whole of my stay, my success must have 
fallen far short of that of a collector in average seasons. I am convinced of 
this from the reports I heard from many persons at Fremantle; and also from 
the fact that thirty of the species found by Preiss were not ascertained by me. 
Nevertheless, I more than doubled my previous list, finding very many species 
not in Pretss’s collection. Some of these were dredged in the bay, in 5 or 6 
fathoms water, but the greater number were picked up on the beach. Amongst 
the most remarkable of the Fremantle plants are Claudea elegans (found by 
Grorce Cuirron, Esq.), and Kallymenia cribrosa. Halophlegma: Preissii is 
very common; so also is Dasya tenera, which, in a very few minutes after it has 
been removed from the water, melts into a rose-coloured, gelatinous mass. 
Halosaccion jirmum and H. Hydrophora, apparently identical with the Kam- 
tchatkan plants, are also very frequent ; and Hucheuwma speciosum, the jelly 
or blanc-mange weed of this colony, floats on shore in great abundance after 
winter gales. 

Whilst residing at Fremantle, I made three excursions to Garden Island, 
distant about nine miles ina 8. W. direction, landing each time on the northern 
and north-eastern beaches. On all these excursions I made very considerable 
collections of drifted plants, finding several species not seen or very rarely met 
with elsewhere. Among these the most remarkable were Sarcomenia deles- 
serioides and S. hypneeoides; and Lenormandia spectabilis, which is here ex- 
tremely abundant, varying greatly in size, and in the breadth of the frond. I 
noticed that several species found at this island were much more luxuriant than 
individuals of the same kind collected at Rottnest Island, a few miles to the 
north. This is especially the case with Grifithsia Binderiana,—the specimens 
from Garden Island being four, times the size of those from Rottnest. This I 
attribute to the fact, that at Rottnest this species always grows on Zostera; 
whilst at Garden Island it attaches itself to various Algz; and the observation 
(coupled with other similar ones elsewhere made), seems to render it probable 
that Algw really derive nourishment from the soil on which they grow. 

From Fremantle I moved to Rottnest Island, about the end of May, and re- 
mained till the end of June, a period of six weeks. This little island is situated 


530 Dr. W.H. Harvey's Account of the Marine Botany of 


about twelve miles W. by N. from Fremantle; and its land Flora is remarkable 
for the total absence of Proteacew and of grass trees (Xanthorrhea), and for the 
paucity of Myrtacee, Epacridee, and Leguminose (with the exception of Tem- 
pletonia, and two or three Acacias). It is seven miles long, and about three 
wide; it contains several large lakes of salt water, and is indented with many 
small bays, some of them with sandy beaches, and others rocky. Almost the 
whole island is surrounded by limestone reefs, at greater or less distances from 
the shore. The limestone seems of very recent formation, and is of similar 
character to that at Arthur’s Head, and in other localities near Fremantle, al- 
ready described by several geologists. It is remarkable for very fantastic and 
diversified forms. The reefs are generally flat-topped, but the surface is very 
rough, either thickly bristling with sharp points, a few inches high; or broken 
into miniature mountains and valleys,—strongly recalling to mind the raised 
map of Switzerland. Other reefs are ridged; the ridges parallel to each other, 
but variously directed towards the shore. The outer face of the bordering 
reef is generally very steep, often perpendicular or overhanging; and frequently 
it goes down, like a quay wall, into two or three fathoms water. At the N.E. 
angle of the island, a very remarkable quay-like reef, called the “ Natural 
Jetty,” runs out many hundred yards into the sea. Its surface is laid bare, at 
low-water, of spring tides, which rise and fall from 2 to 33 feet. Many of the 
detached reefs are shaped like round tables, or mushrooms, being fixed on a 
slender central stalk, often only a few feet in diameter; the horizontal ledge, or 
table, spreading out to many yards on all sides. Sometimes two or three of 
these tables are joined together by narrow stone bridges; and sometimes large 
holes, through which you can look down two or three fathoms into the clearest 
water, are found in the table; and the swells rise through them, and flow over. 
I often wondered how these jiligree reefs could so long withstand the beating 
of the waves in winter storms. Almost all of them offer good harvests to the 
algologist; and beautiful pictures to any one who can appreciate the loveliness 
of living vegetable forms. The surfaces of most are well clothed with the 
smaller Rhodospermece (Laurencie, Hypnee, Acanthophora, &c.); and thickly 
studded with a Caulerpa (C. latevirens, Mont?) with short stems, clothed with 
brilliant club-shaped leaves, resembling miniature clusters of grapes. At every 
few yards, deep basin-like hollows, of greater or lesser size, break the surface 


the Colony of Western Australia. 531 


of the reef, and afford well-sheltered nooks for a variety of beautiful Alow. The 
water in these basins is always intensely transparent; the bottom frequently of 
white sand; and the steep and craggy sides clothed with Algze vegetation, in 
which the brightest tints of green, purple, carmine, and olive, and the most grace- 
ful waving forms, are mingled in rich variety. Here is the favourite locality of 
some eight or ten species of Caulerpa, of several very distinct forms, and every 
one a beautiful object. All these are green; but the tints vary from the darkest 
bottle-green to the pale, fresh green of an opening beech leaf. Some resemble 
soft ostrich feathers; others, branches of the Norfolk Island pine ; others, strings 
of beads; others, squirrels’ or cats’ tails; and C. scalpelliformis is like a double 
saw. Under the shelter of the Cauwerpe the smaller Rhodosperms (such as 
Dasye and Callithamnia) are often found. But these are most numerous on 
the perpendicular sides of the border reefs, where also rich meadows of Cau- 
lerpe are seen waving in the clear water, from a foot beneath the surface to a 
considerable depth. Various Mucoidee and Ecklonia radiata are scattered here 
and there through the deeper pools, and on the sides of the reef. None of these 
are ever left dry at low water. In many places a profusion of a Bryopsis (B. 
Australis) enlivens the rocks with its silky tufts of green, each tuft separate 
from its neighbour. Some of the shallower reefs, near high-water mark, are 
partially covered with sand: and this is the habitat of Penicil/us arbuscula, a little 
green Alga, which may be compared either to a miniature tree, or to a shaving- 
brush. Sérwvea plumosa abounds on all the reefs, at about half tide level, ge- 
nerally growing on the very edges of the rock-pools and border-reefs. I obtained 
from Mr. Sanrorp, Colonial Secretary, a specimen of a new Struvea, sent by 
Mrs. DrumMonpd from Champion Bay, differing from S. plumosa in its vastly 
larger size, and more compound network. The specimen has been bleached 
white, and in this state strongly resembles a beautiful pattern of old point-lace, | 
and might be made into ladies’ collars, as it is of a tough substance. 

I shall conclude this summary with a few remarks on the geographical dis- 
tribution of the species collected. 

The annexed descriptive catalogue contains 352 species: of which 277 are 
(so far as we yet know) peculiar to the Australasian Flora, and 75 belong 
either to pelagic species, or to more or less distant botanical regions. They 
are grouped as follows:— 

VOL. XXII. 3Z 


532 Dr. W. H. Harvey's Account of the Marine Botany of 


Whole number collected. Australian. 
Ser. 1. Melanospermem; sae) 42 eine iin st ated BEE 
PR NNR 3 DOR Ge SB UIE 
3, Chlorospermedy ir sn (AD) “16 eee shal aol BD 
352 277 


These numbers do not show the whole of the JMfelanospermee observed ; 
some 15 or 20 species of Sargassum and Cystophora not having been exa- 
mined, and having therefore been omitted from the list. 

Still, the great preponderance of Rhodospermee is a remarkable feature. 
But the most singular fact is the proportion between the Australian and pelagic 
species of Chlorospermece, a group whose species are, generally speaking, much 
less local than those of either of the other divisions. The comparatively great 
number of Siphonee in Australia is one reason of this anomaly ; another may 
be, that I have not yet minutely examined the species of Cladophora and Calo- 
thrix. Nevertheless, there is a marked deficiency in W. Australia of the com- 
mon littoral Chlorosperms. 

The Pelagic species, or those which inhabit many very distant places and 
dissimilar climates, are :— 


Chorda lomentaria. Plocamium coccineum. Gracilaria confervoides. 
Dictyota dichotoma. Spyridia filamentosa. Codium tomentosum. 

A sperococcus echinatus. Centroceras clavulatum. | Ulva latissima. 
Ectocarpus siliculosus. Ceramium rubrum. Enteromorpha compressa. 
Gelidium corneum. ——— fastigiatum. 


Species showing affinity with the vegetation of the Red Sea and Indian 
Ocean, are :— 
Turbinaria vulgaris. Leveillia jungermanni- | Callithamnion — thyrsige- 
Cystoseira prolifera. oides. rum. 
Dictymenia fraxinifolia. | Dasya Lallemandi. 

Connecting the W. Australian with the Flora of the South Pacific, are :— 

Dictyota Kunthii ; Rhodymenia corallina ; Ceramium miniatum. 
The Cape of Good Hope is represented by,— 
Martensia elegans ; Dasya pellucida ; and Halophlegma. 


the Colony of Western Australia. 533 


Of Antarctic species are Callithamnion simile and Delisia pulchra, both found 
by Dr. Hooxer at Kerguelin’s Land. 

Representing the North Pacific, from S. Francisco to Kamtchatka, are Halo- 
saccion firmum and H. hydrophora, identical, so far as my judgment goes, with 
the specimens from high northern latitudes. 

The characteristic vegetation of the Mediterranean Seas (of Europe and 
Mexico) is more largely developed, as shown by the following list :— 


Dietyota ciliata. Polysiphonia Havanensis. | Liagora distenta. 
Hydroclathrus cancella- | — obscura. viscida. 
tus. pennata. Halymenia Floresia. 
Asperococcus sinuosus. Dasya mollis. Dudresnaia coccinea. 
Chondria sedifolia? Wrangelia penicillata. Crouania attenuata. 
Polysiphonia breviarticu- | Peyssonelia rubra. Halimeda macroloba. 
lata. Helminthora divaricata. 


The following 27 are natives of the coasts of the British Islands, as well as 
of those of W. Australia :-— 


Chorda lomentaria. Champia parvula, Ceramium fastigiatum. 
Dictyota dichotoma, Laurencia obtusa. —— _gracillimum. 
Stilophora Lyngbyci. Gracilaria confervoides. | Dudresnaia coccinea. 
Asperococcus Turneri. Gelidium corneum. Crouania attenuata. 
echinatus. Helminthora divaricata. | Callithamnion sparsum ? 
Sphacelaria cirrhosa. Plocamium coccineum. Codium tomentosum. 
Ectocarpus siliculosus. Rhodophyllis bifida. Ulva latissima. 
Chondria dasyphylla. Spyridia filamentosa. Enteromorpha compressa. 
Polysiphonia obscura. Ceramium rubrum. Calothrix coespitula? 


I hope this outline may prove not uninteresting to botanists, and trust to 
be permitted, after my return to Europe, to lay before the Academy a more 
full memoir on this subject, accompanied by copious descriptions of the new 
species, and plates illustrative of the new genera, and some of the more remark- 
able species. 

W. H. HARVEY. 


MELBourneE, September 11, 1854. : 
3z 2 


534 Dr. W. H. Harvey’s Account of the Marine Botany of 


CataLocus of Marine Alge, collected by Dr. W. H. Harvey in Western Aus- 


12. 


tralia, from January to August, 1854; with short Descriptions of the New 
Genera and Species. 


Nore.—The Numbers between parentheses ( ) in this List are those under which the Species stand in a running 
Catalogue, kept by Dr. H., as the Collection proceeds. 


Series — MELANOSPERME 2. 
Orver I.—FUCACE. 


SARGASSUM, eae species of these genera have been collected and packed away without 


CysTOPHORA, examination, and are not now accessible. 


. Tursinarta vulgaris, J. Ag. Fragments on the beach, Fremantle (288). 
. SerrorHatta dorycarpa, Grev. Rocks below low-water mark, common. King George’s 


Sound, and Rottnest (300). 


. ScyToTHALIA dorycarpa PB. xiphocarpa; S. xiphocarpa, J. Ag. Thrown up from deep water 


at King George’s Sound and Cape Riche. I consider that the characters which distinguish 
this plant from the preceding depend on depth of water, and exposure to currents (301). 


. Scaperia Agardhii, Grev. Very common everywhere, in 2-3 fathoms (83). 
. CysToPHYLLUM muricatum, J. Ag. Common in Princess Royal Harbour, King George’s 


Sound; and in the Swan River, from Perth to Fremantle (73). 


. Crstoseira prolifera, J. Ag. A single specimen on the beach, Fremantle, after a gale (287). 
- Hormosira Labillardieri, Bory. Common near high-water mark, and at half-tide, in Princess 


Royal Harbour, King George’s Sound. Rare at Cape Riche. Not seen elsewhere (76). 


. CARPOGLOSSUM quercifolium, Kiitz. Rottnest, on the reefs (_ ). 
. CARPOGLOsSUM angustifolium, Sond. Cast ashore at Cape Riche and Fremantle (_ ). 
. MyriopEesma serrulatum, Dne. A few specimens picked up at Cape Riche and Fremantle, after 


storms (159). 


. Myrropesma Jatifolium, n. sp.; on the beach at Fremantle (278). My specimens not being at 


hand, I cannot at present further characterize this new species than by saying that it has 
the ramification of JZ. serrulatum, but the segments are an inch broad, densely dotted with 
innumerable scaphidia. It is quite different from JZ. quercifolium, Bory. 

Norueta anomala, Bail. and Harv. Harv. in Hook. Fl. Nov. Zel. cum icone. Parasitical on 
Hormosira in Princess Royal Harbour. 


Orper II. _SPOROCHNACE&. 


. Sporocunvs comosus, Ag.(?) King George’s Sound and Fremantle, two or three feet long, 


and much stouter and more rigid than S. pedunculatus (13). 


14. 


15. 
16. 


17. 


18. 


19. 


20. 


21. 
22. 
23. 


24. 


the Colony of Western Australia. 535 


Srorocunus sp. Fremantle (157). Being uncertain whether this or the preceding be Agardh’s 
plant, I defer the description of either, 

Sporocunus radiciformis, Ag. Fremantle and Cape Riche (156). 

SPorocanvs scoparius, n. sp.; fronde tereti rigida crassa dendroidea (2-3 pedali); caule strato 
velutino vestito; ramis creberrimis undique egredientibus decomposito-pinnatis angulatis 
glabris, minoribus erectis strictis sparsé spinosis subalternis; receptaculis ovalibus v. ob- 
longis pedicellum ipsis multiplo longius coronantibus. At Cape Riche, and Garden and 
Rottnest Islands (248). I collected this at first as Fucus inermis, R. Br., or IF. caudatus, 
Lab.; but my plant is a true Sporochnus, and not always unarmed. 


Orper III._LAMINARIACE®. 


Ecxtonta radiata, Turn. JL. radiata and EL. exasperata, J. Ag. Lining most of the rocky 
shores at extreme low-water mark. Examination on the sea shore disposes me to unite these 
two supposed species. They vary extremely in roughness and smoothness, and in the com- 
parative length of the rachis, all the forms imperceptibly running together (75). 

Cuorpa lomentaria, Lyngb. Clothing tidal rocks, in winter, at King George’s Sound. My spe- 
cimens are not fully grown, being in the state called Asp. castaneus, Carm. (323). 


Orper IV.—DICTYOTACEZ. 


Hauiseris Mullert, Sond.; stipite elongato ramoso; fronde dichotoma y. suppressione ramorum 
alterné ramosa, sinubus obtusiusculis, segmentis erectis latis linearibus integerrimis sepé 
alterné divisis; lamina crassiuscula enervi; antheridiis sparsis. King George’s Sound, Cape 
Riche, and Fremantle (102). Much larger and thicker in substance than H. polypodioides 
with rounded sinuses. 

Hautseris pardalis, n. sp.; stipite brevi; fronde dichotoma, sinubus rotundatis, segmentis 
patentibus linearibus integerrimis repetite furcatis subundulatis obtusis; lamina tenui-mem- 
branacea enervi; soris dispositis in lineas recuryas é costa ad marginem proficiscentibus. Fre- 
mantle, rare (155). A beautiful and distinct species, elegantly marked in dotted lines like 
a leopard’s skin. 

Papina Frazeri, Grev. Fremantle and Rottnest, common (158). 

Zonania nigrescens, Sond. Rocky shores, common (49). Very near Z. variegata, if distinct. 

Zonanta interrupta, Ag. var. spiralis; segmentis spiraliter tortis. Cape Riche and Rottnest (295). 

MerTacnroma, noy. gen. Caulis basi radicans, cartilagineus, tereti-compressus, alterné ramosus, 
Rami inferné costati, lineares, pinnatifidi, lacinulis bicuspidatis. Spore (?) per superficiem 
laciniarum sparse, prominentes, intra perisporum hyalinum singule nidulantes. Alga Aus- 
tralasica radice ramoso-fibrillosa, caule ramosissimo, ramis spiraliter tortis, laciniis tortione 
spurié trifariis. 

Meracnroma thuyoides, n. sp.; Middleton Bay, King George’s Sound; and Cape Riche at low- 
water mark (21). Frond 12-18 inches long, much branched. The generic name alludes to 
a remarkable change of colour, from olive to verdigris green, when thrown into fresh water, 


536 Dr. W. H. Harvey's Account of the Marine Botany of 


25. 
26. 
27. 


28. 


37. 


38. 


39. 
40. 


41. 
42. 


Dictyota Kunthii, Ag. Key West and Rottnest (81 and 225). 

Dieryora fastigiata, Sond. Abundant at Cape Riche and Fremantle (167). A true Dictyota. 

Dicryora radicans, n. sp.; fronde estuposa stipitata basi fibris crassis sparsis é stipite et lamina 
emissis radicante dichotomo-pinnatifida, segmentis cuneatis, lateralibus erectis, sinubus 
angustis, apicibus obtusissimis; soris effusis in medio parte frondis collectis. Rottnest and 
Garden Island (184). This species is readily marked by its rooting by a few rope-like fila- 
ments, 


Dietyora paniculata, J. Ag. Common (14). If Irightly understand this plant it varies much 
in breadth and degree of ramification, 


. Dicryora furcellata, Ag.? D. minor, Sond. Excessively common in Princess Royal Harbour, 


King George’s Sound, and elsewhere. In summer it comes ashore in vast banks, and is often 
the only plant raised from the bottom, by the dredge or hooks, in shallow water (24). 


30. Dicryora dichotoma. King George’s Sound and Rottnest (15). 
. Dicryora ciliata, J. Ag.? Carnac and Rottnest Islands, on shallow reefs, growing with D. 


dichotoma, from which its greener colour and ciliate margins best distinguish it (154). 


. Stitornora Lyngby, J. Ag. Princess Royal Harbour in summer, very common (25). 

. HyprocLaturus cancellatus, Bory. Cape Riche, Fremantle, and Rottnest (183). 

. AsPEROCOCCUS sinwosus, Ag. King George’s Sound and Rottnest, &c. (27). 

- AspErococcus Turneri, Hook. A. bullosus, Auct. King George’s Sound and Fremantle (26). 
. AsPEROCcoccus échinatus, Lx. King George’s Sound (_ ). 


Orver V.—CHORDARIACEZA. 


CLaposirHon? sp.... King George’s Sound (17). This has the habit of Mesogloia virescens, 
and I should so name it, but that the frond is certainly hollow, which character would put 
it in Cladosiphon. Iam by no means, however, satisfied that this isa character of any generic 
importance in these plants. 


Mesoctora filum, n. sp.; fronde simplici vy. ramo uno v. altero donata, basi et apice attenuata. 
King George’s Sound (82). 


Orper VIL.—ECTOCARPACE. 


SPHACELARIA paniculata, Suhr. Cape Riche (297). 

SpHaceLaria Nove Hollandie, Sond. Cape Riche, on rocks and shells in shallow water, com- 
mon. Dredged at Fremantle (296). 

SPHACELARIA cirrhosa, Ag. On Zostera leaves, Fremantle, common (153). 

Ecrocarpvs siliculosus, Lyngb. Very abundant at King George’s Sound, in winter. Just 
commencing at Rottnest in June; and at Cape Riche in March (322), 


43. 
44. 


45. 


46. 


47. 
48. 


49. 


50. 


51. 


the Colony of Western Australia. 537 


Serres IIL—RHODOSPERME 2. 


Orper IL.—RHODOMELACE. 


Craupea elegans, Ag. Fremantle, very rare, June, Geo. Clifton, Esq. (276). 

Marrensia elegans, Her. MZ. Brunonis, Harv. MS. Garden Island and Rottnest, rare, May 
and June. My specimens seem identical with the South African ones (170). 

Marrenst denticulata, n. sp.; frondibus sessilibus cxspitosis tenui-membranaceis repetité di- 
chotomis, laciniis cuneatis ultimis non raro flabelliformibus; margine crispato denticulato; 
fenestro apice ciliato y. lobato, lobulis demum elongatis fenestratisque. Species valdé vari- 
abilis. Garden Island and Rottnest, on reefs near low-water mark, June (171). 

Martensia Australis, n. sp.; stipite cartilagineo brevi in frondem multilobatam membranaceam 
basi incrassatam desinente, margine hic illic minutissimeé denticulato; fenestro apice angustis- 
simé marginato denticulato. King George’s Sound, rare, February (88). 

TuoreTIA quercifolia, Dne. King George’s Sound and Garden Island (65). 

Sarcomenta delesserioides, Sond. Garden Island and Fremantle (130). Three varieties occur 
together, viz.: a. latifolia, phyllodiis lato-lanceolatis; £8. lancifolia, phyllodiis lineari-lanceo- 
latis; y. cérrhosa, phyllodiis angustissimis, supremis spits cirrhiferis. The plant described 
by me in Ner. Austr. as S. delesserioides is a Delesseria, namely, D. corifolia, H. I have now 
gathered Sonder’s plant in abundance. 

SaRcoMENIA hypneoides, n. sp.; fronde lineari angustissima compressa distiché ramosissima, 
ramis ramulisque oppositis attenuatis acutis basi nec angustatis; stichidiis lanceolatis spar- 
sis v. fasciculatis. Garden Island and Fremantle. Certainly a congener with the preceding, 
to which it bears precisely the same relation that Desmarestia viridis does to D. ligulata. 
Both this and the preceding species are gray and iridescent when living, but turn a bril- 
liant rosy red after afew minutes’ exposure to the air, and this colour is preserved in drying 
(276). 

LENOoRMANDIA spectabilis, Sond. Garden Island, abundant; rare at Rottnest (113). JZ. latifolia, 
Harv. Ner. Austr. is only a broad-leaved variety. This plant varies extremely in size. 

JEANNERETTIA frondosa, n. sp.; caule dichotomo cartilagineo alato v. denudato; phyllodiis cune- 
atis dichotomis crispatis, costa infra medium lamine evanescente; fasciculis stichidiorum 
sparsis. Garden Island, rare(112), This plant is intermediate in character between Jean- 
nerettia and Pollexfenia. : 


. PoLLEXFENIA pedicellata, Harv. Ner. Austr., t. 5. King George’s Sound, Garden Island, and 


Rottnest, common (33). . multipartita; fronde angustiore, regulariter dichotoma (100). 
P. multipartita, Harv. in Herb. T.C. D. Having collected both these forms in abundance, 
I am forced to unite them under one specific name. 


. PotypHacum proliferum, Ag. King George’s Sound and Fremantle (89). 
54. 
55. 


THAMNOCLONIUM proliferum, Sond. King George’s Sound, cast ashore (318). 
Tuamnocionium flabelliforme, Sond. Fremantle, in fragments only (319). 


538 Dr. W. H. Harvey’s Account of the Marine Botany of 


56. THamnoctonium Lemannianum, n, sp.; caule corneo crasso (pedali et ultra) echinulato in- 


ferné tereti superné alato ramoso; ramis quoquoversum directis alatis phyllodia proliferé 
ferentibus; phyllodiis furcatis v. dichotomis costatis basi cuneatis apice obtusis, segmentis 
lateralibus erectis plus minus incisis. Fremantle, cast ashore in July (320). I first received 
this truly noble species in a collection of Western Australian Alge, made by Mr. Mylore, 
and presented to Herb. 7. C.D. by my late lamented friend Dr. Cuartes Lemann, of Lon- 
don, to whose memory this plant is now consecrated. 


57. Dictymenta frazinifolia. Fucus fraxinifolius, Turn. Rottnest, rare (241). I abandon the 


genera Epineuron and Spyrymenia as not being distinguishable from Dictymenia. 


58. DicryMEntA jimbriata, Grey. Garden Island, rare (110). 
59. Dicrymenta tridens, Grev. Garden Island, Rottnest, and King George’s Sound (111). 
60. Dicrymenta spiralis, Sond. Common everywhere (20). 


61 


. Dicrymenta pectinella, n. sp.; fronde inferné valdé costaté superné sub-costata lineari distiché 
ramosa plana; ramis erecto-patentibus oppositis v. abortu alternis linearibus obtusis tenuis- 
simeé costatis ciliato-fimbriatis; ciliis oppositis arguté pectinato-pinnatifidis involutis; anthe- 
ridiis magnis ovalibus ad apices ciliarum fasciculatis. Garden Island, very rare (290). A 
very distinct and beautiful species. 


62. Kurzinera canaliculata, Sond. Abundant everywhere. Often 2 or 3 feet in length (61). 
63. Ktrzine1a angusia, n. sp.; fronde inferné costa cartilagined percursd decomposité pinnata; 


ramis anguste-linearibus planis, superioribus tenuissimé costatis v. ecostatis; ramulis oppo- 
sitis erecto-patentibus obtusis apice involutis. Rottnest, rare (242), A very much smaller, 
narrower, and thinner plant than K. canaliculata, of which it has the structure. 


64. Kurzineta serrata, n.sp.; fronde basi cartilagined denudata vy. alato-marginata bi-tripinnati- 


lor} 


5 


66. 


67 
68 


fida et 6 costa primaria prolifera; laciniis membranaceis planis tenuissimé costatis, juniori- 
bus, lacinulisque arguté serratis. Rottnest, very rare (291). 
RywiruLxa Australasica, Mont. King George’s Sound, common. Rare at Garden Island (31). 
Rytieuixa elata. (Rhodomela elata, Sond.!) dendroidea (1-2 pedalis) ; caule tereti crassis- 
simo (2-3 lineas diametro) opaco ramoso; ramis decomposito-ramosissimis di-tri-chotomis v. 


vagé divisis, minoribusramulisque patentibus transversim striatis; striis approximatis; axillis 
latissimis; ceramidiis ovatis pedicellatis; stichidiis ad latera ramulorum fasciculatis; sipho- 
nibus primariis 5-6 magnis, strato crasso cellularum minutarum corticatis, Cast ashore at 
Fremantle (304). A gigantic species, quite unlike any known to me. 

. Tricenta Australis, Sond. Cast ashore in July, Fremantle (292). 

. AcanrHorHoRA dendroides, n. sp.; caule incrassato indiviso inferné nudo superné ramis alternis 
spiraliter evolutis vestito; ramis decompositis circumscriptione lanceolatis; ramulis spinosis, 
spinulis solitariis sparsis. Rottnest on the reefs, near low-water mark (224). Much the 
largest and most robust of the genus. 


9. AtstDIuM? spinulosum, n. sp.; fronde tereti crassA dendroided decomposité ramosissima; ramis 


ramulisque erectis quoquoversum sistentibus; ramulis spineformibus sparsis; ceramidiis 
ramulos terminantibus. Garden Island, Rottnest, and Cape Riche (180). Primary tubes in 
the stem, 5, very large, and full of granular endochrome. 


70. 
71. 


72. 


le 


75. 


77. 
78. 


79. 
80. 
81. 
82. 


83. 


84. 


the Colony of Western Australia. 539 


Cuonpria dasyphylla, Ag. King George’s Sound, August (293). 

Cuonpria sedifolia, Harv. Ner. Bor. Amer. C. zostericola, and C. Curdicana, Harv., MS. 
Common on Zostera leaves, King George’s Sound, and Rottnest (29). 

CxHonprIA corynephora, n. sp.; fronde tereti succosa siccitate rosea robusta quoquoversum ramo- 
sissima; ramis indivisis patentibus é latere bis terve ramosis; ramulis oppositis, fasciculatis, 
v. sparsis, sepius incurvis cylindraceis basi constrictis obtusissimis. Cape Riche and Garden 
Island (114). Much more robust than C. dasyphylla. It soon breaks to pieces in fresh water, 
by which character and others it is readily known from the following. 

Cuonprta verticillata, n. sp.; fronde tereti succosa siccitate badia bis-terve umbellatim divisa; 
ramulis fasciculato-verticillatis saccatis oblongis obtusissimis basi constrictis; tetrasporis in 
ramulis nidulantibus. Garden Island, rare (273). 


. CHonpria Umbellula, n. sp.; fronde pusillé (4-1 unciali) simplici saccato-clavata apice ramulis 


5-10 conformibus umbellatim coronata; ramulis nunc apice umbellulatis; ceramidiis ovatis 
sessilibus; tetrasporis sparsis (190). Rottnest, on Zostera leaves. A very curious and pretty 
little species. 

Cuonpria lanceolata, n. sp.; fronde pusillé (1-2 unciali) compressa cartilaginea alterné ramosa 
sub-disticha; ramis ramulisque alternis basi et apice attenuatis acutis; ceramidiis ovatis 
pedicellatis; tetrasporis sub apicibus ramulorum congestis. Rottnest, on Zostera leaves 


(191). 


. LEVEILLIA jungermannioides. L. Schimperi, and L. gracilis, Dne. Abundant on a variety of 


Alge at Fremantle, Garden Island, and Rottnest (123). 

Poxyzon1a Sonderi, Hary. Ner. Austr. Garden Island, on Pucoids (284). 

Poryzonta flaccida, n. sp.; caule primario repente; ramis erectis simplicibus ramosisve tenuis- 
simis flaccidis oligosiphoniis; foliis (v. ramulis) alternis pectiniformibus, pectinis lacinulis 
5-6 filiformibus articulatis monosiphoniis acutis; stichidiis arcuatis rostratis. On Fucoids, 
King George’s Sound, Garden Island, and Rottnest. Much more slender, and of softer tex- 
ture than P. Sonderi, and readily known by its one-tubed lacinule (34). 

Potysipuonia Hystrix, Harv. Ner. Austr., t. 14. Cast ashore, Garden Island (121). 

PotysrPHontA Mallardie, Harv. Ner. Austr., t.13. With the preceding (117). 

Porysrpnonta breviarticulata, Ag. Abundant on the reefs, near low water, Rottnest (188). 

PorysipHonta Havanensis, Mont.(?) With the preceding, profusely common. More robust 
than the American plant, but otherwise very similar (118). 

POLYSIPHONIA infestans, n. sp.; pallida, siccitate fuscescens; frondibus (2-3 uncialibus) carti- 
lagineis charte arcté adherentibus setaceis sursum attenuatis pellucidé articulatis ramosis- 
simis; ramis patentibus pluries alterné v. vagé divisis ramulisque conspersis; ramulis capil- 
laribus simplicibus patentibus; axillis latis; articulis 4~siphoniis subtorulosis, inferioribus 
diametro brevioribus, superioribus zqualibus v. sublongioribus. Common on Polyphysa 
peniculus, at Princess Royal Harbour, King George’s Sound. It has the habit of P. fibrillosa, 
but is more nearly allied to P. Harveyi and P. Binneyi than to any other that I remember 
(22). 

PotysipHonta mollis, Hary. Ner. Austr. On Zostera, at Fremantle (120). 

VOL. XXII. 4A 


540 Dr. W. H. Harvey’s Account of the Marine Botany of 


85. PoLysrpHonta mutabilis, n. sp.; mollis, aére cito deliquescens, versicolor, siccitate rosea, frondi- 
bus aggregatis (2-3 uncialibus) tenuissimé corticatis articulatis superné ecorticatis dicho- 
tomis ramosissimis; ramis minoribus subalterné divisis erecto-patentibus; ramulis sparsis 
basi et apice attenuatis acutis; articulis 6-siphoniis, ramorum diametro equalibus, ramu- 
lorum brevioribus. On Zostera, at Fremantle (116). Pale brown when fresh, but almost 
instantly changing to rose red, and soon decomposing. I have neglected to make a section 
of the living stem, and it is impossible to cross-cut the dried frond, and very difficult to 
remove from the paper the smallest scrap for examination. Three primary tubes are seen 
in the front view of each articulation; and in most of the branches a series of external, 
shorter, secondary cells appear, being the commencement of a cortical layer, which is more 
evident in the lower parts of the frond. 

86. PotysirHontA Roeana, n. sp.; punicea; frondibus (3-6 uncialibus) cespitosis capillaribus 
mollibus charte arcté adherentibus decomposité ramosissimis; ramis alterné compositis sepé 
subsecundis pluries divisis; ramulis ultimis filiformibus elongatis sparsis omnibus eximié 
patentibus; axillis latissimis; articulis pellucidé 4-siphoniis, inferioribus diametro 4-6-plo, 
superioribus duplo, ramulorum sesqui-longioribus. Dredged at Fremantle in 4-5 fathoms 
(119). A beautiful species, allied to P. formosa, but quite distinct. I name it in honour 
of J. S. Roz, Esq., Surveyor-General of the colony, from whom I received much kind 
attention during my stay at Perth, and who, though not a botanist, never neglects an 
opportunity of promoting the science. 

87. PorysipHonta rufolanosa, n. sp.; siccitate rosea; frondibus pusillis (vix uncialibus) densissimeé 
intertextis arachnoideis dichotomis ramosissimis suffastigiatis; ramis ramulisque patentis- 
simis divaricato-squarrosis crispisque ; axillis distantibus; articulis 4—siphoniis diametro 
sesquilongioribus. On the stems of Caulinia antarctica, Princess Royal Harbour, King 
George’s Sound (39). To the naked eye this little plant looks like a small Callithamnion, or 
like delicate flocks of fine crimson silk. The stems are about <4; of an inch in diameter. 

88. PotysipHonta scopulorum, n. sp.; badia; frondibus pusillis (vix uncialibus) cxspitosis basi 
radicantibus rigidulis capillaribus tetragonis erectis parce ramosis infra simplicibus supra 
ramis lateralibus plus minis onustis; ramis sepé secundis erectis simpliciusculis vel ramu- 
liferis; ramulis paucis consimilibus; axillis angustissimis; articulis diametro subduplo-lon- 
gioribus, superioribus equalibus; ceramidiis ovatis sessilibus. On littoral rocks, Rottnest, 
common (187). Allied to P. rudis, but smaller. It slightly adheres to paper in drying. 

89. PorysipHonta implera, Hook. and Harv. Nov. Zel. Parasitic on Corallines and on Caulinia at 
King George’s Sound (79). 

90. PotystPHonta prostrata, n. sp.3 parasitica, omnino prostrata, discis rameis prorepens, rubra, 
siccitate fuscescens; frondibus pusillis (1-2 uncialibus) é centro radiantibus subparallelis 
secundé ramosis; ramis filiformibus simplicibus repentibus apice involutis; ramulis liberis 
paucissimis brevissimis; articulis 4-siphoniis diametro subduplo-brevioribus ; ceramidiis 
ovatis longiusculé pedunculatis (ramos v. ramulos terminantibus). Parasitical on the fronds 
of Zonaria nigrescens, which it sometimes completely covers over with cobweb-like threads, 
Fremantle, rare (305). 


91. 


92. 


93. 


94. 
95. 


the Colony of Western Australia. 541 


PotysieHonta neglecta, MS. Sand-covered rocks, at Middleton Bay, King George’s Sound, 
mixed with P. pennata and Callith. cymosum. I have not fully determined this species, 
which requires a careful comparison with some others of similar habit (11). 

PotysiPHontA forcipata, n. sp.; pallida, siccitate purpureo-nigrescens; frondibus subsolitariis 
(2-3 uncialibus) crassis cartilagineis pellucidé articulatis repetite dichotomis y. abortu scor- 
pioideo-secundis; ramulis ultimis bis terve furcatis apice forcipatis! articulis 6—siphoniis 
diametro brevioribus; ceramidiis ovatis sessilibus. On Zostera at Rottnest and King George’s 
Sound (186). A distinct species, looking like a Ceramium to the naked eye. 

PotysipHontA cancellata, Harv. Ner. Austr., t. 15. King George’s Sound, common (35). 

PoLysirHonia nigrita, Sond. Garden Island and Rottnest (122). 

PoLysIPHoNIA aurata, n. sp.; fusco-rubra, madefacté aurea; frondibus cespitosis (2-3 uncia- 
libus) capillaribus cartilagineo-membranaceis articulatis decomposité ramosis; ramis dicho- 
tomis alternisve erecto-patentibus; ramulis alternis v. secundis apice furcellatis; articulis 
10-siphoniis inferioribus diametro 2—3-plo-longioribus, superioribus equalibus; septis angus- 
tissimis; ceramidiis ovatis sessilibus; tetrasporis magnis subsolitariis. King George’s Sound, 
rare (307). Allied to P. furcellata in ramification, and to P. versicolor in substance and colour. 


. PotysrpHonta versicolor, Harv. Ner. Austr., t. 16. King George’s Sound (36), var. B. tenuior. 


With the preceding (37). 


- PotysipHonia rostrata, Sond. On Caulinia, &e, Rottnest and Fremantle (115). 
. PoLysipnonta pennata, Ag. Sand-covered rocks, Middleton Bay, King George’s Sound (12). 
. PoLysiPHonta pectinella, n. spy; siccitate roseo-purpurea; frondibus pusillis (uncialibus) basi 


radicantibus ramosis arachnoideis; ramis paucis alternis vy. sparsis filiformibus simplicibus 
per totam longitudinem pectinatis; ramulis secundis patentissimis simplicibus brevibus ob- 
tusis; articulis 8-siphoniis diametro xqualibus v. duplo-longioribus. On mud, near high- 
water mark, Princess Royal Harbour, King George’s Sound. A larger variety at Rottnest 
(38). Certainly allied to P. Pecten Veneris, but a far more delicate and more brightly coloured 
species. 


100. Poxysipnonta obscura, Ag. Sand-covered rocks at Middleton Bay, King George’s Sound ; 


mixed with P. pennata and P. neglecta (47). 


101. Potysipuonra Calothrix, n. sp.; minuta, densé exspitosa, rupestris, badia; surculo prostrato 


radicibus numerosissimis elongatis apice mamilloso-squamosis radicante; ramis erectis se- 
cundis simplicissimis brevissimis approximatis subacutis; articulis 10-12-siphoniis, sur- 
culi diametro duplo-brevioribus, ramorum adultorum sesquiduplo-longioribus; tetrasporis 
paucis in ramis nidulantibus. On rocks at half-tide level, King George’s Sound (337). 
This spreads in wide patches, like those of Calothrix scopulorum, which it so closely resem- 
bles in aspect, that I had actually dried and set it aside for that plant, nor did I discover 
my error till after I had applied the microscope. It is a larger plant than P. prorepens, 
and very much smaller than P. obscura, to which it is allied. 


102. PoLysipHontA prorepens, Harv. Ner. Austr. Parasitical on Dicranema Grevillii, at King 


George’s Sound (306). 


103. PotysipHonta cladostephus, Mont. Garden Island and King George’s Sound (271). 


4a2 


542 Dr. W. H. Harvey's Account of the Marine Botany of 


104, Dasya Gunniana, Harv. Ner. Austr., t. 17. On the reef called ‘“‘ The Natural Jetty,” Rott- 
nest (211). . 

105. Dasya elongata, Sond. Abundant at Fremantle, and Rottnest, and King George’s Sound (59). 

106. Dasya Clifioni, n. sp.; caule elongato (pedali et ultra) tenui flexuoso v. scandente glabro 
omnino corticato subdistiche ramoso bi-tripinnato, pinnis patentibus glabris; pinnulis alter- 
nis remotiusculis ramellosis ; ramellis multoties divaricato-dichotomis vix attenuatis obtusis 
monosiphoniis, articulis cylindraceis, diametro 3-4-plo-longioribus. Dredged in Fremantle 
Harbour, by G. Ciirron, Esq., after whom this beautiful plant is deservedly named. I also 
collected it at Garden Island and Rottnest, and afterwards at King George’s Sound (164). 

107. Dasya frutescens, n. sp.; caule (2-4 unciali) vagé ramosissimo glabro corticato; ramis quo- 
quoversum directis patentibus bis-terve divisis attenuatis, minoribus ramellis vestitis; ra- 
mellis pluries dichotomis vix attenuatis obtusis, segmentis falcato-recurvis y. incurvis, ar- 
ticulis diametro 2—3-plo-longioribus ; ceramidiis sessilibus urceolatis ore porrecto ; stichidiis 
minutis sessilibus oblongis acutis. Rottnest, on Zostera. Something like a small form of 
D. elongata, but with much more slender and longer jointed ramelli. It is perhaps nearer 
to D. arbuscula, with which, however, it does not agree (303). 

108. Dasya proxima, n. sp.; fronde crassa corticata vagé ramosi; ramis elongatis virgatis simpli- 
cibus vel ramos 2-3 consimiles lateraliter ferentibus, ramis omnibus ramulos breves quo- 
quoversum emittentibus; ramulis corticatis simplicibus y. iterum ramosis, junioribus 
ramellis vestitis; ramellis subverticillatis dichotomis é basi lata conspicué attenuatis, axillis 
patentibus, apicibus filiformibus obtusis, articulis diametro 3-4-plo-longioribus; ceramidiis 
ramulos primarios terminantibus urceolatis ore brevi prominulo. Cast ashore at Middleton 
Bay, King George’s Sound, August. Nearly allied to D. elongata, but the ramelli are very 
different, quickly melting in fresh water. It is a much larger plant than D. naccarioides, 
with larger ramelli and longer joints (336). 

109. Dasya collabens, Harv. Ner. Austr., t. 21. King George’s Sound, rare (58). 

110. Dasya Wrangelioides, n. sp.; caule gracili (2~3 unciali) pellucidé articulato 10-12-siphonio 
distiché ramoso omnibus partibus ramellis vestito; ramis patentibus sursum curvatis sim- 
plicibus v, iterum alterné ramosis; ramellis densissimis multoties divaricato-dichotomis 
acutis, articulis diametro sesquilongioribus ; ceramidiis .. . . . . ; stichidiis minutissimis 
oyato-acuminatis, Parasitical on Caulinia antarctica, Fremantle, King George’s Sound, 
and Cape Riche. A very distinct species, named from its external resemblance to Wran- 
gelia velutina (272). 

111. Dasya multiceps, n. sp.; caule subnullo (feré bulboso!) mox in ramos numerosissimos erectos 
diviso; ramis (2-3 uncialibus) simplicibus pellucidé articulatis, articulis diametro subbre- 
vioribus polysiphoniis, pinnatis v. apice bipinnatis, ambitu linearibus v. lineari-spathulatis; 
pinnis oligosiphoniis alternis approximatis brevissimis superioribus sensim longioribus ra- 
mellosis ; ramellis alternis pluries dichotomis parum attenuatis obtusis. On sand-covered 
rocks, half buried in sand, on the Natural Jetty reef, Rottnest, June. The specimens are 
not in fruit, and probably but half grown. There is an evident tendency in the upper 
pinne to lengthen and become compound (251). 


SS 


the Colony of Western Australia. 543 


112. Dasya plumigera, n. sp.; caule elato (pedali et ultra) crasso villis stipato sub-dichotomo, seg- 
mentis ramiferis; ramis secundariis longissimis (1-2 pedalibus) caule multd tenuioribus 
glabris corticatis simplicibus inferné seepé denudatis superné pulcherrimeé plumoso-pinnatis ; 
pinnis alternis crebris horizontalibus plus minus ecorticatis polysiphoniis iterum pinnu- 
latis; pinnulis oligosiphoniis brevissimis ramelliferis; ramellis dichotomis attenuatis obtusis, 
articulis diametro 2—4-plo-longioribus; ceramidiis magnis pedicellatis inflato-ovatis ore pro- 
minulo; stichidiis minutis oblongis acutis. King George’s Sound, and Cape Riche, and 
Garden Island; cast ashore and dredged. Also sent by Dr. Curdie from Cape Northum- 
berland. A superb species, with branches like ostrich feathers (32). 

113. Dasya villosa, Herv. Ner. Austr., t. 20. Garden Island, Rottnest, and King George’s Sound 
(109). Very variable in size and ramification, putting on as many phases as D. elegans, its 
representative species. 

114. Dasya mollis. Harv. Ner. Bor. Amer. King George’s Sound, rare (64). 

115. Dasya Callithamnion. Polysiphonia Callithamnion, Sond.! in Pl. Preiss. Abundant on the 
stems of Caulinia antarctica, &e. Rottnest and Fremantle (106). 

116. Dasya tenera, n. sp.; cartilaginea, mox aére diliquescens, siccitate rosea; fronde tetrasipho- 
nia corticata decomposité ramosissima subdichotoma flexuosa; ramis irregulariter divisis, 
minoribus sepé secundis, ultimis attenuatis acutis, omnibus denudatis v. ramellis tenuissi- 
mis laxé yestitis; ramellis verticillatis basi ramosis subsimplicibus strictis cylindraceis 
obtusis; ceramidiis ovatis pedicellatis; stichidiis sparsis v. fasciculatis lanceolatis ¢ ramulis 
enatis. Very common in May at Fremantle. Dredged in January and February at King 
George’s Sound; and in March at Cape Riche. When growing it is a very pale brown, and 
is then crisp and brittle; but almost immediately it grows flaccid in the air, assumes a bril- 
liant rosy red, and soon melts into a gelatinous mass (78). 

117. Dasya Lallemandi, Mont.! D. gracilis, Harv. MS. Perpendicular sides of the Jetty reef, at 
Rottnest, and rarely on Zostera leaves, June. I have compared my specimens with one 
from the Red Sea, given me by Dr. Montagne, and find them to agree in all essential cha- 
racters. The colour, when growing, is brownish red, becoming purple indrying. Dr. Mon- 
tagne’s specimen is faded (212). 

118. Dasya (Stichocarpus) crassipes, n. sp.; caule incrassato hispido (3-4 unciali) vagé diviso cor- 
ticato ramis articulatis onusto; ramis (2-3 uncialibus) simplicibus glabris plus minus dis- 
tincté articulatis polysiphoniis densissimé pinnatis ambitu linearibus ; pinnis brevissimis 
(2-3 lineas longis) oligosiphoniis dichotomo-multifidis, segmentis ultimis solim monosiphoniis 
acutis, articulis diametro equalibus vel subbrevioribus; ceramidiis magnis inflato-globosis 
pedicellatis. Rottnest, on the perpendicular sides of the Jetty reef, and cast ashore (189). 
It sometimes forms large tufts 6-8 inches in diameter, is very rigid, resists the action of 
fresh water; is carmine when fresh, but becomes brown in drying, and scarcely adheres to 
paper. 

119. Dasya pellucida, Harv. Ner. Austr., t. 27. King George’s Sound, very rare (308). More 
squarrose than the Cape of Good Hope plant, but otherwise the same. 


544 


120. 
12). 


122. 


123. 


124. 
125. 


126. 
127. 
128. 


Dr. W. H. Harvey’s Account of the Marine Botany of 


Orver IL—LAURENCIACEA. 


Deuista pulchra, Grev. Rottnest Island, rare (239). 

AsparaGopsis Sanfordiana, n. sp.; surculo valido ramosissimo repente caules plures emit- 
tente; caulibus erectis simplicibus é basi-longeé nudis supra ramellis thyrsoideo-penicillatis; 
penicillis ramellorum quoquoversum egredientibus eximié obtusis; pinnellis oppositis fili- 
formibus crispato-incurvis; ceramidiis globosis inferné in pedunculo clayato attenuatis. Gar- 
den Island and Rottnest. A very distinct and noble species, much larger and more robust 
than A, Delilei, with which, however, I cannot at present further compare it. The much- 
branched surculi are as thick as crowquills; the stems, equally thick, are 3-8 inches long, 
or more, ending in a very dense, deep purple coma. The fasciculi of ramelli are remark- 
ably obtuse in outline. I name it in honour of W. A. Sanrorp, Esq., Colonial Secretary of 
Western Australia, with whom I had some pleasant sea-side walks, and to whom, during 
my stay in the colony, I am indebted for much kind attention and assistance (124). 

ASPARAGOPSIS armata, n. sp.; surculo ultra-setaceo parum ramoso repente caules plures emit- 
tente; caulibus erectis ramosis usque ad basin ramellis obsitis v. brevissimé nudis; ramis 
secundariis consimilibus ad basin armatis ramulis subternis nudis retrorstiim aculeatis; 
penicillis ramellorum subdistichis ambitu ovatis acutis; pinnellis oppositis; ceramidiis glo- 
bosis; pedunculo cylindraceo. Garden Island and King George’s Sound(193). Also from 
Tasmania, R. Gunn, Esq. Whether this be what I have figured for A. Delilei, in Ner. Austr., 
t. 35, I cannot at present say, not having the book at hand. If not, I at least confounded it 
with that species. It differs from the European plant in having branched stems, feathered 
with ramelli nearly to the base; and in having two or three naked branchlets armed with 
reflexed prickles issuing from the lower side of every main branch, near the base. The frond 
is from 6-10 inches long, twice as thick as hog’s bristle, and of a pale red colour. 

Lavrencia Forsteri, Grev. On Caulinia stems, &c., very common (103 and 126). No. 126 
is var. 8. elata, Sond. A much larger and stronger form than the common one. 

Lavrenct obtusa, Lx. King George’s Sound and Rottnest, on Alge (67). 

Lavrencia sp.... Onvrocks, King George’s Sound and Rottnest, near low-water (6). Either 
a larger form of Z. obtusa, or a new species. 

Lavrencta affinis, Sond. Cape Riche (310). 

Laurencia arbuscula, Sond. Cape Riche (309). 

LavrEncia cruciata, n.sp.; livido-purpurea, cespitosa; fronde tereti rigida quoquoversum 
ramosi; ramis ramulisque patentissimis oppositis verticillatisve rard alternis, ramulis juni- 
oribus cylindricis truncatis, fructiferis verrucoso-glandulosis. This requires to be compared 
with Z. paniculata, J. Ag., of which I have no specimen, My plant is extremely hard and 
rigid, scarcely adhering to paper after two days’ maceration in fresh water. Agardh com- 
pares his plant with Z. obtusa, with which mine cannot be confounded. On Caudinia stems, 
Rottnest (209). 


. Laurencta heteroclada, n. sp.; densissimé cespitosa, é surculis repentibus orta; fronde livido- 


purpurea tereti rigida tenaci; juniori pluries secundé ramosé, ramis ramulisque erecto- 


130. 


132. 


133. 


134. 


135. 


136. 
137. 


138. 


139. 


140. 


the Colony of Western Australia. 545 


appressis, axillis angustissimis; adulta apice paniculata, ramis quoquoversum egredientibus 
elongatis patentibus, ramulis alternis spiraliter insertis corymboso-multifidis; ceramidiis 
ovatis sessilibus. Clothing the borders of reefs laid bare at low water, and covering wide 
spaces, Rottnest (210). Nothing can be more dissimilar in ramification than the young 
and the full-grown plant. 

LAURENCIA sp.... On rocks near low-water mark, King George’s Sound (7). I have not 
determined this species. 


. Lavrencra Tasmanica, Hook. and Harv. Abundant on stones in shallow water in Princess 


Royal Harbour, King George’s Sound (5). 

Lavrencta elata, Harv. Ner. Austr., t. 33. Garden Island, Rottnest, and King George’s 
Sound (125). 

Lavrencia Grevilleana, n. sp.; purpureo-coccinea; fronde complanata eximié disticha decom- 
posito-pinnata; pinnis in rachide stricta alternis erecto-patentibus; pinnulis oblongis inciso- 
crenatis v. pinnatifidis, inferioribus minutis glandula-formibus, fructiferis... Abundant 
on the under surface of flat-topped reefs, near low-water mark, Rottnest (196). Allied to 
L. pinnatifida, but of softer substance, and very different colour. When fresh it is a beauti- 
ful rosy carmine, partially preserved in drying. I name it in honour of Dr. Grevitte, the 
first reformer of this genus. 

Lavrencia sp.... Rottnest (197). Near L. distichophylla, J. Ag.? It requires further 
examination. Besides these species of Laurencia here enumerated, I have collected two or 
three others in small quantity, which for the present I suppress. 

Lomenrarta zostericola, n. sp.; fronde pusilla (1-2 unciali) paniculatim ramosé ambitu ovata; 
caule basi inconspicué articulato supra toruloso; ramis ramulisque patentibus suboppositis 
v. verticillatis (nunc sparsis) obtusis articulato-constrictis, articulis diametro brevioribus 
v. subeequalibus; ceramidiis globosis sparsis v. aggregatis. On Zostera at Rottnest (195). 
The spores are aflixed to a very large placenta, nearly filling the cavity of the ceramidium. 

Cuampta parvula, Lomentaria parvula, Ag. King George’s Sound and Rottnest (57). 

Cuampia affinis. Lomentaria affinis, Ag. King George’s Sound, Rottnest, and Garden Island 
(194). 

CuampPlA compressa, Harv. Rottnest, rare (245). 


Orper II.—WRANGELIACE. 


WranceLia penicillata, Ag.! W. plumosa, Harv.! Alg. Tasm. On Zostera leaves at Rott- 
nest, abundant (198). Much more robust than a Mediterranean specimen with which I 
have compared it, but very similar to one from Florida. My W. plumosa from Tasmania 
seems to differ solely in being more luxuriant, so far as Ican judge from a very poor speci- 
men now before me. 

Wranceiia? Agardhiana, n. sp.; fronde cartilagined (6-8 unciali) corticata decomposité 
ramosissima; ramis ramulisque dichotomo-alternis pluries divisis patentissimis ad genicula 
verticillatim ramellosis; ramellis minutissimis dichotomo-multifidis obtusis; articulis ramel- 


546 


Dr. W. H. Harvey's Account of the Marine Botany of 


lorum diametro sesquilongioribus. Dredged in 6-7 fathoms in King George’s Sound (40). 
I have seen no fruit, but have little hesitation in referring this fine species to Wrangelia. 
It seems nearly allied to a plant from Cape Northumberland, distributed by me under the 
MS. name of Crouania insignis, but which is perhaps also a Wrangelia. 


141. WranceLt velutina, H. Dasya velutina, Sond.! Common at Rottnest and Garden Island, 


rare at King George’s Sound (108). Ihave found both the cystocarpic and tetrasporic 
fruits, which are exactly as in other species of Wrangelia. 


142. WrancGeELia myriophylloides, n. sp.; fronde rigidiuscula é basi articulata ecorticata inferné 


stuposi pinnatim ramosa; ramis patentibus simplicibus v. iterum pinnatis ad genicula ver- 
ticillatim ramellosis; ramellis pluries trichotomis segmentis patentibus apice trifurcis 
acutissimis; fructu... Parasitical on the larger Fucoids, Rottnest (246). A very distinct 
species. 


143. Wrance.is Witella, n. sp.; fronde membranacea flaccida é basi articulata (articulis diametro 


4-6-plo-longioribus) ecorticataé decomposité pinnata; ramis ramulisque sepits oppositis 
distichis ad genicula verticillatim ramellosis; ramellis di-tri-chotomo-multifidis segmentis 
patentibus acutissimis; tetrasporis globosis ad ramellos sessilibus; cystocarpiis... Cast 
ashore at King George’s Sound and Rottnest, rare (213). Very similar in external habit 
to W. multifida, but much more nearly allied to W. squurrulosa and W. myriophylloides. It 
is a much smaller and more flaccid plant than the latter, and closely adheres to paper in 
drying. Many of the branches, on my specimens, end in nearly naked cirrhose prolon- 
gations, indicating that they come from deep water. 


144. Wrancetia Halurus, n. sp.; rosea, gelatinoso-membranacea (aqua dulci cito deliquescens) ; 


fronde é filo repente orta articulata ecorticata vagé ramosa; ramis elongatis simplicibus 
basi et apice attenuatis ad genicula verticillatim ramellosis; ramellis dichotomo-multifidis 
patentibus obtusis; articulis ramorum diametro 2-3-plo, ramellorum multiplo-longioribus; 
eystocarpiis ramulos abbreviatos coronantibus. On Caulinia stems at Fremantle and King 
George’s Sound (127). Very similar in aspect to Halurus equisetifolius, but much softer, 
of paler colour, and soon decomposing. The cystocarps are those of a Wrangelia. 


145. Wrancetta? abictina, n. sp.; fronde cartilaginea crassi elongata (6-10 uncias longa) corti- 


eata decomposité pinnaté; pinnis pinnulisque alternis distichis subhorizontalibus, ultimis 
subarticulatis tenuiter corticatis, ad genicula verticillatim ramellosis; ramellis dichotomis 
incurvis obtusis; articulis diametro 3-4—plo-longioribus. Garden Island, rare (270). 
Possibly a species of Halurus. 


146. Wrancetra? tenella, n. sp.; pusilla (14 uncialis), cespitosa; fronde tenuissima membranacea 


é basi articulatd ecorticat’ vagé ramos; ramis subsimplicibus nunc iterum ramosis elon- 
gatis virgatis per totam longitudinem bipinnatis; pinnis brevissimis (vix semilineam longis) 
oppositis v. verticillatis, pinnulis 2-3-cellularibus obtusis; articulis ramorum diametro 
4-plo, pinnarum 2-3-plo, pinnularum sesquilongioribus. On the Jetty reef, Rottnest, rare 
(285). Iam doubtful whether to place this species in Wrangelia or Callithamnion; but 
place it provisionally in the former, on account of the tendency to verticillation in the 
pinne and ramelli. 


147. 
148. 


149. 
150. 


151. 


152. 
153. 
154. 
155. 


156. 


159. 
169. 
170. 


the Colony of Western Australia. 547 


Orver IV.—CORALLINACE#., 


Ampuiroa charoides, Lx. King George’s Sound, Cape Riche, and Rottnest, on rocks (9). 

AmpPHiroa intermedia, n. sp.; fronde gracili (biunciali) fastigiata sub-tetrachotom4, ramulis 
stellatim patentibus verticillatis; articulis cylindraceis basi et apice nodoso-incrassatis, 
superioribus diametro 8-plo-longioribus; geniculis angustissimis; ceramidiis ad ramulos 
secundis. On Caulinia stems, Rottnest (282). A much smaller plant than A. charoides; 
and differing from A. stelligera in the shorter nodes, &e, 

Ampninoa stelligera, Dne. On Caulinia, King George’s Sound, and Rottnest, common (4). 

Ampuiroa gracilis, n. sp.; fronde lapidescente di-tri-chotoma fastigiata; articulis cylindraceis 
basi et apice truncatis diametro multoties (10-14-plo) longioribus; geniculis diametro 
equalibus; ceramidiis numerosissimis quoquoversis. King George’s Sound and Rottnest, 
common (218). 

Amuro granifera, n. sp.; fronde lapidescente di-tri-chotoma fastigiata; articulis cylindra- 
ceis, inferioribus basi et apice nodoso-incrassatis, superioribus simplicibus diametro 6-8-plo- 
longioribus; geniculis diametro «qualibus, inferioribus calcareo-granulosis, superioribus 
cartilagineis nudis; ceramidiis ad ramulos secundis. On Caulinia at King George’s Sound 
and Rottnest, common (283). 

Ampuniroa Ephedra, Lx. Fremantle, G. Clifton, Esq. (289). 

AmpHiRoA anceps, Lx. Rottnest, not common (281). 

Ampuiroa australis, Sond. In dark hollows of the reefs, Rottnest (217). 

Ampurroa sp.... Rottnest, growing with A. australis, to which it is allied (219). The 
specimen retained for description has become broken in travelling, and I therefore leave 
this plant undescribed for the present. 

CuEILosporuM pulchellum, n.sp.; fronde pusilla brevi stipitata dichotoma flabelliformi fasti- 
giata; articulis sagittatis medio costatis sepé transversim rugulosis diametro sesquilongi- 
oribus, lobis brevibus acutis erectis; ceramidiis.... At Rottnest, parasitical on Alyce 
(250). A much smaller and more delicate plant than C. sagittatum, and differing from that 
and C. cultratum, to which it is more nearly allied, in the erect, not patent, and shorter lobes 
of the articulations. 

Janta micrarthrodia, Lx. Common on Caulinia and Alga, &e. (58). 


. JANIA affinis, n. sp.; fronde pusilla dichotom4, ramis ramulisque erectis strictiusculis; axillis 


acutis; articulis omnibus cylindraceis diametro triplo-longioribus; ceramidiis parvis urne- 
formibus. Rottnest ( ). The size of J. micrarthrodia, but with much longer joints and 
more erect growth. It may be J. pacijica, Aresch. 

Janta Cuviert, Lx. Many varieties of this species abundant (3). 

Masropnora plana, Sond. Extremely common on rocks, Rottnest (50). 

Mastopuora Lamourouaiit, Dn. King George’s Sound and Cape Riche (_). 


VOL. XXII. 4B 


548 Dr. W. H. Harvey’s Account of the Marine Botany of 


OrpEer V._SPH ZROCOCCOIDE. 


171. Devesseria denticulata, n. sp.; fronde costata dichotom4 rigidiuscula; segmentis lato-lineari- 
bus crispato-undulatis margine denticulatis; costa opaca cartilagined apicem versus evanes- 
cente; membrane cellulis parvis rotundato-hexagonis; venis nullis; soris in sporophyllis 
muricatis é cost’ prorumpentibus. Parasitic on Alg@, Rottnest (235). Of a rigid sub- 
stance, scarcely adhering to paper. 3-4 inches high, the branches 4 inch broad. 

172. DevessertA crispatula, n. sp.; pusilla (1-2 uncialis); fronde costata dichotoma; segmentis 
linearibus integerrimis undulato-crispatis, costa articulata 3-siphonia; venis nullis; soris 
in sporophyllis propriis é costa enatis v. rard in segmentis terminalibus. Fremantle, on 
Caulinia, rare (129). Analogous to D. alata, but differing in the articulated midrib and 
absence of lateral veins. 

173. Devesserta spathulata, Sond.? On Zostera, Caulinia, and various Alge. Rottnest and 
King George’s Sound. I am not quite sure that my plant and Sonder’s are the same. Mine 
is analogous to D. ruscifolia, as the following is to D. Hypoglossum (203). 

174. Detxsseria hypoglossoides, n. sp.; pusilla, decumbens; fronde costata foliolis é costa tenui 
articulata trisiphonié prorumpentibus ramosd; foliolis lineari-lanceolatis planis utrinque 
acutis, venis nullis. In crevices of rocks at Garden Island and Rottnest (172). So like 
D. Hypoglossum as not to be known without microscopic examination. Then indeed the 
articulated midrib at once characterizes it. 

175. Devesserra dendroides, n. sp.; caule elongato nudo carnoso-cartilagineo crassissimo (2-3 lineas 
diametro) apice in frondem ramosissimam desinente; fronde costata foliolis é costa valida 
prorumpentibus ramosa; foliolis geminis exacté oppositis lineari-lanceolatis utrinque acutis, 
adultis costa cartilagineé opaca, junioribus costa articulaté percursis; venis nullis; mem- 
brane cellulis strato unico dispositis magnis oblongis. Fremantle, rare, G. Clifton, Esq. 
(269). A superb species of the Hypoglossum section, resembling a beautiful tree, a foot or 
18 inches high, with a trunk-like stem 6-8 inches long, supporting a large head of branches. 
The ramification is similar to that of D. oppositifolia, but the substance of the leaf is of a 
very different structure. It closely adheres to paper. 

176. DE.eEsserta revoluta, n. sp.; fronde costata foliolis a costa valida infra apicem revolutum pro- 

rumpentibus ramos4; foliolis ovalibus latitudine sesqui vel subduplo-longioribus tenui- 
membranaceis undulatis denticulatis apice obtusé acuminatis revolutis; soris? . On 
other Alge, King George’s Sound, and Rottnest, rare. 2-3 inches high. Very unlike any 
previously described species (311). 


177. DELEssERIA corifolia, n. sp.; fronde costata foliolis a costa crass’ prorumpentibus ramosa; 
foliolis cartilagineo-carnosis crassis opacis lanceolatis basi ovatis obtusis; membrane cellulis 
pluriserialibus, interioribus magnis, superficialibus minutissimis; cystocarpiis sorisque in 
sporophyllis propriis é costa enatis. Garden Island and Rottnest, rare (279). My speci- 
mens are few and far from complete, but sufficient to establish a very distinct species, with 
remarkably thick and densely cellular leaves. It most resembles D. nereifolia, but has a 
very different structure. It was small scraps of this plant which I described in Ner. Austr. 
under Sarcomenia delesserioides. 


178. 


179. 


180. 


181. 


182. 
183. 


184, 


185. 
186. 


187. 


188. 
189. 


190. 


the Colony of Western Australia. 549 


HEMINEURA crispata, n. sp.; fronde pinnatifido-decomposita, lobis oblongis basi et apice angus- 
tatis obtusis oppositis margine subintegerrimis undulato-crispatis demum crispatissimis; 
costa immersa superné evanescente, costulis obsoletis; coccidiis in costa loborum sessilibus 
ore producto rostratis; soris rotundato-hemisphericis convexis secus marginem seriatis. 
Rottnest and King George’s Sound. Sent also by Dr. Curdie from Cape Northumberland 
(312). A smaller plant than H. frondosa. 

NiTorHyLium cartilagineum, n. sp.; fronde sessili avenia cartilagineo-membranacea rigida 
erassa dichotoma; laciniis linearibus pluries divisis crispato-undulatis obtusis patentibus; 
axillis rotundatis; soris minutis impressis per totam frondem sparsis. Garden Island, not 
uncommon (131). ‘Remarkably thick in substance, shrinking in drying, and imperfectly 
adhering to paper. Colour, brownish red. 

Niropnytium fimbriatum, n. sp.; fronde pusilla (1-2 unciali) bifida v. pluries furcata basi 
cuneata stipitata; stipite brevi in costa mox evanescente prolongato; laciniis rotundatis; 
margine processibus minutis ramosis densé fimbriato; soris per totam laminam sparsis. 
Parasitical on Ptilota coralloidea, at Garden Island, rare (268). I suspect my specimens are 
not fully grown, though one of them is in fruit. The elegantly fringed margin at once 
marks the species. 

Nirornytium pulchellum, n. sp.; pusillum (sub-biunciale), tenuissimé membranaceum, roseum, 
cxspitosum; fronde sessili avenid dichotoma fastigiati; laciniis lato-linearibus v. cuneatis 
undulato-crispatis patentibus obtusis; axillis rotundatis; soris rotundatis majusculis per 
totam frondem sparsis. King George’s Sound and Rottnest, on various Alge, Like a 
miniature NV. punctatum, to which species it is perhaps too nearly allied (60). 

NiTopsYLLuM minus, Sond. Garden Island and Rottnest (181). 

NitopHyLuum ciliolatum, n. sp.; fronde cespitosa sessili angusté-lineari dichotoma ramosissima 
ciliolis marginalibus et superficialibus passim echinulatéa. On Caulinia, &c., King George’s 
Sound (30). Very similar to WV. minus, except in the presence of the ciliz, which I find 
constant in very numerous specimens examined. 

Nov. Gen.? My number (141) from Garden Island appears to belong to a new genus, allied 
to Nitophyllum; but without the cystocarpic fruit it is impossible to determine it. 

Puacexocarrus Labillardieri, Endl. Common at Rottnest and Garden Island (134). 

PuaceLocarpus alalus, n. sp.; fronde costata; costa elevaté bené definité utroque latere 
lamina angusta alata; ciliis subulatis distichis. Rottnest (261). Half the breadth of 
P. Labillardiert, with a more strongly defined midrib and less deeply pinnatifid lamina. 
I suspect that several species are confounded under the name Labillardieri. 

Herincia? filiformis, n. sp.; fronde cespitos), é surculis repentibus orta setacea filiformi v. 
apice compressd vage ramosd subdichotoma rigidiusculaé. Garden Island, rare (182). 
Similar to H. mirabilis in structure, but the fruit is unknown. 

Dicranema filiforme, Sond. Garden Island (133). 

Dicranema Grevillii, Sond. King George’s Sound, Cape Riche, Garden Island, and Rottnest 
(97). 

Dicranema revolutum, Ag. On Caulinia, in shallow water. Cape Riche (128). 


4p2 


550 


191. 


192. 


193. 


194. 


195. 
196. 


197. 


198. 


199. 


200. 
201, 


Dr. W. H. Harvey’s Account of the Marine Botany of 


Dicranema pusillum, n. sp.; fronde unciali subdichotoma v. vagé ramosi, apicibus fructiferis 
strictis; tetrasporis in ramulis immutatis sparsis. Dredged near Emu Point, King George’s 
Sound, on Cauwlinia stems. About the size of D. revolutum, but readily known by its straight 
apices, those bearing tetraspores not swollen. The cystocarps are near the tips of the 
branchlets (80). 

CaLuisLerHaris? Preissii, Ag. Garden Island and Fremantle(138). I have not satisfactorily 
ascertained the genus of this plant. 

CALLIBLEPHARIS conspersa, 0. sp.; fronde stipitata cartilaginea simplici vel parcé dichotoma a 
margine pinnata; pinnis varié lobatis et fimbriatis nunc multifidis margine dentato-aculeatis 
ciliatisve; disco aculeis v. lobulis ramosis consperso; coccidiis per totam laminam sparsis. 
Garden Island (132). Like C. ciliata in habit, and very variable in form, and readily 
known by its scattered cystocarps. 

CALLIBLEPHARIS? pannosa, n. sp.; fronde stipitata rubro-sanguinea v. purpurascente carti- 
lagineo-cornea rigidaé dichotom4; laciniis linearibus é margine densissimé pinnato-fimbri- 
atis; pinnis angustissimis patentibus simplicibus y. pinnatim compositis vagé dentatis v. 
ciliatis; coccidiis..... . Abundant on rocks near low-water mark, Middleton Bay, King 
George’s Sound, and at Rottnest, cast ashore (98). I have seen no fruit, but the habit and 
structure agree with those of Calliblepharis. 

Sarcoc.apiA, nov. gen. Frons plana, cartilagineo-carnosa, crassa, multifida, duplici strato 
constituta; stratum interius cribroso-spongiosum é cellulis brevibus anastomosantibus et 
lacunis intercellularibus; exterius é cellulis minutis verticaliter seriatis constitutum. 
Cystocarpia marginalia, elevata, hemispherica, umbilicata; pericarpium cellulosum, cras- 
sum; spore minute in filis é placenta centrali radiantibus seriate. Tetraspore.... Alga 
livido-rubra, siccitate nigrescens, ramosissima, subdichotoma; margine revoluto. 

SaRcOCLADIA obesa, n. sp.; abundant at King George’s Sound and Rottnest (280). 

THYSANOCLADIA oppositifolia, Ag. T. pectinata, Hary.! Ner. Austr. Common at Garden 
Island and Rottnest. Sometiimes two feet long (165). 

Tuysanocianta laxa, Sond.; fronde livido-purpurea siccitate fuscescente plana, inferné medio- 
incrassaté v. subcostata, superné ecostata, distiché decomposito-pinnata; pinnis lato-lineari- 
bus approximatis patentibus suboppositis; pinnulis erectiusculis lato-linearibus planis basi 
angustatis simplicibus vel trifurcis; axillis pinnularum eximié rotundatis; soris tetra- 
sporarum in apicibus dilatatis immersis. Rottnest, rather rare (237). Livid purple, with 
a slight bloom when fresh. Very distinct from 7. oppositifolia. 

THYSANOCLADIA costata, n. sp.; fronde plana costa valida percurs distiche decomposito-pin- 
nata ambitu ovata; pinnis patentibus approximatis suboppositis costatis; pinnulis arguteé 
serratis subcostatis; coccidiis ... Rottnest (260). A very handsome plant, 12-14 inches 
high, readily known by its strong midrib. 

THYSANOCLADIA coriacea, Hary. Ner. Austr., t. 36. Rottnest and Garden Island, common 
(105). The cystocarps are crowded near the ends of the ramuli exactly as in 7. dorsifera. 

GRACILARIA confervoides, Grey. Abundant at Fremantle (166). 

Gracitaria dactyloides, Sond. Garden Island and Rottnest, not uncommon (178). My plant 


202. 


203. 


204. 


205. 


206. 


207. 


208. 


209. 


the Colony of Western Australia. 551 


is a true Gracilaria, but requires to be compared with Sonder’s, which is said to be terete, 
while mine is strongly compressed. 

GRaciLariA fruticosa, n. sp.; fronde rubro-coceined siccitate fuscescente compressa quoquo- 
versum ramosd; ramis crebris patentissimis bis terve divisis; ramulis alternis vy. secundis 
vagé spinoso-armatis acutis; coccidiis .. . Fremantle, rare (179). Nearly allied to G. armata, 
but of softer substance, and compressed. The peripheric cells are in a single row. 

GRracizaria sp... . King George’s Sound (95). Notin fruit. I have’not been able to deter- 
mine this species satisfactorily. 


Orver VI—SQUAMARIEZ. 


PEYssoneLta rubra, Grev.? Rottnest, a solitary specimen (316). If not the same as the 
Mediterranean plant, it is very nearly allied to it. 

Cruorta? australis, n. sp-; fronde pusilla ovali roseA, filis verticallibus simplicibus, articulis 
diametro subduplo-longioribus, cystocarpiis é basi frondis erectis magnis oblongis. Para- 
sitical on Amphiroa australis, at Rottnest (317). I am doubtful of the genus, not having 
found tetraspores on many specimens examined. The filaments most resemble those of a 
Cruoria or Petrocelis; but the habit is that of an Actinococeus, The cystocarps in my plant 
are oblong, consisting of dichotomous strings of spores, either whorled round a vertical 
axis, or proceeding from a central point. 


Orver VII—GELIDIACE®, 


GELIDIUM cornewm, Lx. King George’s Sound, not common (43). Some of the very dwarf 
varieties are frequent, near high-water mark, on all the rocky shores. Near Arthur’s Head, 
Fremantle, grows abundance of what I suppose to be Acrocarpus ramellosus of Pl. Preiss. 
One or two specimens of a dichotomous Gelidium, resembling G. variabile, were gathered at 
Rottnest. 

GeE.ipium proliferum, n. sp.; fronde inferné semiterete crassissima, superné compresso-plan& 
v. applanata decomposité pinnata et prolifera, setis minutis demum foliaceis densissimé 
muricata; pinnis pinnulisque lato-linearibus planis, pinnulis erecto-patentibus; cystocarpiis 
bilocularibus in processis filiformibus simplicibus y. pinnatis é pinnulis emissis immersis. 
Fremantle, thrown up after storms (244). A very distinct species, much the largest of 
the genus. I have long possessed imperfect specimens collected by Messrs. Mylne and 
Backhouse. 

Preroctapra lucida, J. Ag. King George’s Sound and Rottnest (44). The King George’s 
Sound specimens agree closely with those from New Zealand. The Rottnest plant may 
possibly belong to a new species, but requires very careful examination. 

Evcueuma speciosum, J. Ag, Fremantle and Rottnest (232). The Jelly or Blanc-mange weed 
of the colonists. 


552 Dr. W. H. Harvey’s Account of the Marine Botany of 


210. Sorrert australis, n. sp.; fronde dendroidea (1-2 pedali) robusta decomposito-ramosissima ; 
ramis alternis sparsisve approximatis pluries alterné compositis; ramulis ultimis (1-2 unci- 
alibus) linearibus acutis basi setaceo-attenuatis; cystocarpiis in ramulis semi-immersis. 
Fremantle and King George’s Sound (150). A noble species, much more robust and branch- 
ing than S. chordalis, and readily known, even in fragments, by the acute, but not acuminate 
apices. 

211. Hypyea musciformis, Ag. King George’s Sound and Rottnest, common (16). 

212. Hypnea episcopalis, Hook.and Harv. Rottnest, rare (252). My specimens have fruit of both 
kinds, further establishing this species, whose crosier-like tendrils and scarlet colour are 
truly episcopal. 

213. Hypnea seticulosa, J. Ag. Rottnest and King George’s Sound (70). 

214. Hypnea divaricata, J. Ag. King George’s Sound (69). 

215. Hypnea sp.... Rottnest, on the reefs (253). 


Not tained. 
216. Hypnea sp... . Rottnest, on the reefs at aes 


Orver VIII.—_ CH ZTANGIE. 


HENNEDYA, nov. gen, Caulis teres, ramosus; ramis apice in frondem planam dichotomam 
stratis tribus contextam dilatatis; stratum medullare é filis tenuissimis anastomosantibus 
densissimé intertextis; intermedium cellulis magnis vacuis uniseriatis; periphericum cellulis 
minimis verticaliter ordinatis compositum. Cystocarpia hemisphrica, elevata, umbilicata, 
demum poro pertusa, ad apices laciniarum sessilia, fasciculos sporarum secus parietes loculi 
dispositos foventia. Tetraspore... . Alga australis, fusco-rubra, rigidé membranacea, 
multoties dichotoma; laciniis crispatis lato-linearibus apice emarginatis. 

217. Hennepya crispa, n. sp.; Garden Island and Rottnest, abundant (168). Readily known from 
Chetangium by the single row of large cells forming the intermediate stratum of the frond, 
and by the completely external fruit. It grows in large tufts, often a foot in diameter. The 
frond is deep red when growing, and remarkably crisped and curled. The cystocarps are 
formed in a little notch at the extreme end of the lacinie. The generic name is given in 


honour of Mr. Rocer Hennepy, of Glasgow, a most able and indefatigable investigator of 
the Alge of the West of Scotland. 


Orver IX.—HELMINTHOCLADIE, 


218. Hetmintuora divaricata, J. Ag. Rottnest and King George’s Sound in winter, common 
(234). 

219. Liacora viscida, Ag. King George’s Sound and Cape Riche, common (8). 

220. Liacora distenta, Ag. Cape Riche, rare (313). 

221. Liacora Cheyniana, n. sp.; fronde gelatinosA compressa siccitate subcanaliculata dichotoma 
ramosissimé 5. ramis erecto-patentibus argenteis villo purpureo tomentosis, apicibus divari- 
catis; filis periphericis liberis cylindraceis furcatis. At Cape Riche (294). Frond 6-8 


222. 


223. 


224, 


225, 


226. 
227. 
228. 
229. 
230. 
231. 


the Colony of Western Australia. 553 


inches high, nearly a line in diameter, much branched, dichotomous, rarely with lateral 
branches. The peripheric threads extend beyond the calcareous portion, and form a purple 
tomentum to the branches, as in Microthoe. This fine plant is named in compliment to 
GrorGE Cueyne, Esq., of Cape Riche, at whose hospitable house I resided during my resi- 
dence on that part of the coast. 

MicrorHoe lapidescens, Dne.? Galaxaura lapidescens, Lx.? Reefs at Rottnest (221). This 
is certainly a Rhodosperm, and nearly related to Liagora. When living it is clothed with 
dense, dark purple villosity, composed of Callithamnoid filaments. 

MicroTuoe marginata, Dne.? On the reefs, at Rottnest, and cast ashore at King George’s 
Sound (96). Ihave no authentic specimen at hand to compare with. Mine spring from 
short, dichotomous, cylindrical, woolly stems, which, had they been found disconnected, 
would pass for a separate species. The upper frond is flat, slightly inflexed at the margin 
when dry, repeatedly dichotomous, and deep purple red. 


Orver X.—RHODYMENIACEZ. 


Hymenocrapia? divaricata, n. sp.; fronde plana rosea gelatinoso-membranacea decomposite 
pinnata, rachide flexuosa basi et apice attenuata, pinnis pinnulisque lineari-lanceolatis 
attenuatis patentibus, pinnulis ultimis setaceis minutis horizontali-divaricatis; eystocarpiis 
ad discum vel marginem lamine insidentibus sparsis; tetrasporis magnis triangulé divisis 
per ramos majores distributis. King George’s Sound (68). I venture to refer this plant 
to Hymenocladia, J. Ag., a genus founded on Fucus Usnea, R. Br., whose cystocarps are 
unknown, and which is temporarily placed by J. Agardh in Lauwrenciacew. My plant has 
a similar habit and internal structure, and similar tetraspores; but the nucleus of its cys- 
tocarp is formed of strings of cells radiating from a basal placenta; if I mistake not, on the 
plan of those of a Rkodymeniacea, though the spores are of unusually large size in this order, 
and more resemble those of a Spherococcoid plant. The external habit is not unlike that of 
Gigartina Teedit. 

Hymenociapia? Ramalina, n. sp.; fronde plana rosea membranacea ramosissima, ramis sub- 
pinnatim 2—3-divisis alternis oppositisque patentibus basi et apice attenuatis, ramulis ulti- 
mis subulatis v. filiformibus elongatis horizontaliter patentibus; fructu. . . . King 
George’s Sound, rare (87). A less gelatinous plant than the last, imperfectly adhering to 
paper, more irregularly branched, less compounded, and with much longer ramuli. 

Piocamium procerum, Ag. Very common everywhere (94). 

Procamium Mertensii, Grey. Rottnest (140 and 259). 

Procamium Preissianum, Sond. King George’s Sound and Rottnest (86). 

PLocamium coccineum, Lyngb. King George’s Sound and Rottnest (72). 

RuoporHyxuis bifida, Kiitz. Garden Island, rare (145). 

Ruoporxy 11s volans, n. sp.; cespitosa, é filis intertextis orta; fronde membranaced rosea 
subdichotoma vel vagé partitaé, segmentis linearibus patentibus margine simplicibus vel 
sepissimé pinnatis; pinnis ovalibus oblongisve obtusis basi attenuatis subpetiolatis; cysto- 


554 Dr. W. H. Harvey's Account of the Marine Botany of 


carpiis per discum frondis sparsis; tetrasporis in pinnis nidulantibus zonatim divisis. King 
George’s Sound (93) and Rottnest (142). A pretty little species, with the habit of Hemi- 
neura frondosa in miniature; and readily known by its scattered, not marginal, cystocarps. 

232. Ruopymenta corallina, Grey. King George’s Sound and Rottnest (85). 

233. RuopyMeEnta (Acropeltis) australis, Sond. Abundant at Rottnest (144). I have gathered both 
kinds of fruit. The cystocarps are in every respect similar to those of Rhodymenia. 

234. RuopyMenta (Acropeltis) phyllophora, n. sp.; caulescens; stipite alato ramoso, ramis in frondes 
pergamenas crassas inferné costa valida evanescente donatas dichotomo-multifidas abeunti- 
bus; segmentis linearibus cuneatisve, margine incrassato plano; soris maculam depressam 
infra apicem frondis formantibus. Hab. Rottnest (238). Frond 1-2 feet high, much 
branched; segments }-3 inch broad. This is probably the same as Acropeltis phyllophora, 
H. and H., but I have not had the opportunity of comparing it with that plant. 


i) 
vo 
ou 


5. RHODYMENIA élata, n. sp.; caulescens; stipite plano-compresso subcanaliculato ramoso, ramis 
in frondes pergamenas inferné subcostatas pinnato-dichotomas abeuntibus; rachide flexu- 
osa, segmentis alternis linearibus angustis dichotomis erecto-patentibus obtusis, axillis ro- 
tundatis. Rottnest, rare (233). A noble species, two feet high, and much branched, very 
distinct from R. flabellifolia, with which alone it can be confounded. 

236. RuopyMentA? obtusata, Sond. Rottnest and Garden Island, common (143). I have not ex- 

amined the cystocarps minutely, and my specimens are not now accessible. I think it 

scarcely of this genus. 


i) 
vo 
a 


. RHopYMENIA? rosea, n. sp.; stipite brevi compresso mox ampliato, fronde basi cuneata tenui- 
membranacea flaccida rosed subpalmatifida, segmentis lato-cuneatis varie lobatis, lobis acutis. 
Fremantle, G. Clifton, Esq. I have seen only a single immature specimen, sufficient to estab- 
lish a distinct species, but not to fix the genus. It may possibly be a Rhodophyllis. A 
transverse section shows a double row of large empty cells in the medullary layer, and a 
thin cortical layer of minute cellules. 

AREscHoUGIA, nov. gen. (Harv. MS. Herb. T. C.D.) Frons linearis, compressa, immerse 
costata, distiché ramosissima, é filo centrali articulato et stratis tribus cellularum constituta; 
stratum medullare é filis articulatis longitudinalibus anastomosantibus laxé intertextis, inter- 
medium é cellulis rotundis majusculis pluriseriatis, corticale ¢ cellulis minimis verticalibus 
formatum. Cystocarpia fronde immersa, inter fila strati intermedii suspensa, reticulo filo- 
rum velata, carpostomio demum aperta, fila sporifera a placenta centrali emissa continentia; 
spore subrotunde, seriate. Genus Rhabdonie proximum; differt filo centrali articulato, 
et habitu. Dixi in honorem Prof, J. E. Arescaoua, Upsaliensis, Algologi eximii. 

238. ArescHoucta australis. Halymenia australis, Sond. Pl. Preiss. Phacelocarpus australis, Sond. 
Bot. Zeit. 1845, p. 55. Areschougia ligulata, Harv. MS. olim in Herb. T.C. D. Common at 
Rottnest (173). The structure of the frond is very similar to that of Phacelocarpus; that of 
the cystocarp to Rhabdonia. 

239. ArEscHouciA Laurencia, Harv. in Herb. T. C. D. Thamnocarpus ? Laurencia, H. and H. olim. 
Rottnest, rare (236). Ihave seen no fruit; but the structure of the frond nearly agrees 
with that of A. australis, and the habit is not dissimilar. 

240, Ruapponra ? Sonderi, J. Ag. Cast ashore at Fremantle (139). I have not seen fruit. 


241. 


242, 
243. 


246. 


247. 


248. 


249. 


the Colony of Western Australia. 555 


Orprer XI.—CRYPTONEMIACE. 


Mycuopea carnosa, Hook. and Harv. Cape Riche and King George’s Sound (99). The cys- 
tocarps in this and in the following species are external, hemispherical, sessile on the sides 
of the ramuli, by which character, and the very large size of the intermedial cells of the 
frond, this genus differs from Cystoclonium; to which, however, it is closely allied. 

Mycnopra membranacea, H. and H. King George’s Sound (42). 

CaLLoPHYLLis coccinea, H. Garden Island (137). My (263) is probably only a very narrow 
variety of this variable plant. 


. CALLOPHYLLIS sp. . . . . King George’s Sound (151). Delicately membranous, with 


marginal fruit. 


. KALLYMENIA cribrosa, n. sp.; stipite brevi in frondem maximam simplicem vy. bipartitam 


rotundato-reniformem ampliato, lamina basi cordata gelatinoso-membranacea foraminibus 
circularibus crebris pertusi; cystocarpiis sparsis. Fremantle and King George’s Sound, 
rare. June (274). A very remarkable species, elegantly perforated, like an Agarwm. 

GiGarTINA disticha, Sond. Fremantle (262). A solitary specimen only. 

GatTTya, noy. gen. rons membranacea, compressa, disticha, pinnatifida, é filo centrali ver- 
ticillatim ramelloso composita. Ji/um centrale articulatum, callithamnoideum, ad genicula 
fila verticillata dichotoma emittens, ramellorum apicibus in stratum periphericum membra- 
naceum arcté coherentibus. Cystocarpia et Tetraspore ignote. Alga tenella, parasitica; 
structura feré Endocladie; habitu diversissimo; affinitate magis ad Catenellam accedens. 
The generic name is given in honour of Mrs. Marcarer Garry, of Ecclesfield, Yorkshire, 
a diligent explorer of British Alge and Marine animals. 

Gatrya pinnella, n. sp.; parasite on Sarcocladia, and on Corallines, Rottnest (223). A beau- 
tiful little plant, fit to bear a lady’s name, and of a very curious structure. Though the 
fruit is unknown, I have no hesitation in proposing the genus. 

Hore, noy. gen. rons carnoso-membranacea, plano-compressa, é stratis tribus cellularum 
composita; stratum medullare é cellulis maximis inanibus demum sexpé ruptis; intermedium 
cellulis pluriseriatis minoribus coloratis; corticale filis moniliformibus verticalibus dichoto- 
mis muco cohibitisformatum. avellw intra pericarpium proprium apice spinis coronatum, 
poro pertusum, ad placentam basalem aflixe; filis arachnoideis laxé circumdate, sporas 
conglobatas angulares foventes. Tetraspore sparse, cruciatim divise. Alge Australasice, 
rosex, distiché decomposito-pinnate v. dichotome, charte arcté adherentes. The name is 
given in honour of Rev. W. S. Hore, of St. Clement’s, Oxford, an excellent algologist, and 
ardent and successful explorer of the Algz of Plymouth Sound, &e., to whom I am indebted 
for large numbers of beautifully preserved specimens of rare British Alge. 

Hore halymenioides, n. sp.; fronde subdichotoma, segmentis decomposito-pinnatis ambitu 
ovatis, pinnis pinnulisque divaricato-patentibus nunc spurié anastomosantibus attenuatis 
acutis, pinnulis setaceis. Fremantle, common (152). : 

Horea flabelliformis, nu. sp.; fronde flabelliformi subfastigiata dichotoméa, laciniis dichotomo- 


VOL. XXII. 4¢ 


556 Dr. W. H. Harvey's Account of the Marine Botany of 


multifidis margine integris v. parcé lobatis, lobulis deltoideo-subulatis acutis. King George’s 
Sound, rare (341). Frond broader and more dichotomous than in the preceding, spreading 
from a central point like a fan. 

250. CurysymentA olovata, Sond.! King George’s Sound and Rottnest (104). I have seen no 
fruit, and can throw no light upon the genus. But J. Agardh must have got hold of some- 
thing very different, or he would not refer this plant to Rhabdonia, to which it bears nei- 
ther internal nor external resemblance. 

251. Cuyiociapta secunda, Hook. and Hary.! King George’s Sound (340). I have not compared 
with New Zealand specimens; but refer this plant from memory and description. 

252. CHYLOCLADIA opuntioides, n. sp.; fronde (6-10 uncias alta) inferné cartilaginea solidescente 
obsoleté constricta dichotoma, superné di-tri-chotoma articulato-constricté membranacea 
succo aquoso repleta, ramulis ad genicula verticillatis articulatis; articulis ramorum puncto 
affixis (citO in aqua dulci sejunctis) ovali-oblongis basi et apice obtusissimis; cystocarpiis 

Rottnest, Fremantle, and King George’s Sound (192). Either this or the follow- 
ing appears to be the ‘ Ch. articulata” of Australian botanists, but both differ essentially 
from each other, and from the European species so called. The present is remarkable for 
the rapidity with which its branches and ramuli fall to pieces, without dissolving, when 
thrown into fresh water. An hour or two is sufficient to denude a large specimen, leaving 
nothing behind but the cartilaginous main stem. The colour is a beautiful rosy purple. 

253, CuyLociapia Cliftoni, n. sp.; fronde (6-8 uncias longa) tenui membranacea succo gelatinoso 
repleté rosea é basi articulato-constrictaé trichotoma vy. umbellatim ramosa; ramis ternis 
feré ad singula genicula egredientibus; ramulis sepé numerosis; articulis inferioribus cla- 
vatis diametro 4-5-plo-longioribus, superioribus obovatis, ultimis ellipsoideis utrinque 
obtusis. Fremantle, G. Clifton, Esq. (265). A much more delicately membranous plant 
than Ch. articulata, of larger size, closely adhering to paper in drying, and soon dissolving 
in fresh water. It is nearly allied to Ch. Miillert, Sond.! but quite distinct. 

254. Hatosaccion jirmum, Post. and Rup.? Fremantle, common (135, a). 

255. Hatosaccton hydrophora, Post. and Rup.? With the preceding; also at King George’s Sound 
(135, 8). These are very similar in form to the Kamtchatkan plants to*which I refer them; 
but they closely adhere to paper, and are filled, when recent, with very slimy mucus. 
Both produce cystocarps. Iam doubtful, whether as species they are sufficiently distinct 
one from another. 

256. Hatymenta Floresia, Ag. Fremantle (314); also found by G. Clifton, Esq. 

257. Hatymenta Kallymenioides, n. sp.; fronde plana gelatinoso-membranacea foliacea informi 
varié lobata et sinuata, margine glanduloso, laciniis acutis, cystocarpiis sparsis. Cast ashore 
at Fremantle, rare (174). This has the habit of Kallymenia, but exactly the structure of 
Halymenia. 

258. Getiarta ulvoidea, Sond. Fremantle and King George’s Sound (136). The structure, as 
already stated by Kiitzing, is very similar to that of Halymenia. The only difference is, that 
in Gelinaria the peripheric membrane is very thick and fleshy, composed of two or three 
rows of small polygonal cells, protected externally by a thick stratum of vertical, moniliform 


the Colony of Western Australia. 557 


filaments, formed of very minute oblong, cells. The colour, when fresh, is a bright, but 
very fugacious, rosy pink. I have seen no fruit. 

259. Nemastoma? gelinarivides, n. sp.; fronde gelatinoso-carnosA roseA plana decomposito-pinnata, 
pinnis approximatis erecto-patentibus pinnatis v. bipinnatis, segmentis basi parum atte- 
nuatis sublanceolatis acutis, ultimis lato-subulatis acutiusculis. King George’s Sound, 
rare (84). Very like some of the more branching forms of Gelinaria ulvoidea, but of much 
denser and different structure. The structure is as dense as in Schizymenia. 

260. Nemastoma damecornis, n. sp.; fronde gelatinoso-carnosa extereti compresso-plana dichotomo- 
multifida subfastigiata; segmentis patentibus cuneatis, terminalibus filiformibus obtusis ; 
axillis omnibus eximié rotundatis; tetrasporis sparsis cruciatim divisis. At Fremantle and 
Rottnest, rare (315). It requires to be compared with the Mediterranean WN, dichotoma, 
which it closely resembles, and from which it may not be sufficiently distinct. 


Orper XIL—SPYRIDIACEA, 


261. Spyripia jilamentosa, H. Abundant all along the coast (18). 


Orver XIII.—CERAMIACE®. 


262. Cenrrocrras clavulatum, Ag. Common on littoral rocks and on Zostera, &e. (2). 

263. CeRamium rubrum, Ag. Rottnest and King George’s Sound, in winter (258). 

264. Ceramium puberulum, Sond.! C. monile, H. and H.! On Zostera, Rottnest, and King 
George’s Sound (66). 

265. Ceramium isogonum, n. sp.; fronde pusilla (1-2 unciali) subsetaceA dichotoma fastigiata, 
Segmentis erecto-patentibus terminalibus forcipatis; articulis corticatis omnibus diametro 
equalibus linea hyalina centrali notatis medio parumque constrictis; favellis. subterminali- 
bus bilobis ramellis 1-2-fuleratis; tetrasporis..... On Alge, Garden Island (286). 
Quite distinct from any of the rubrum section. 

266. Ceramium miniatum, Suhr.? CG. Filicula, Harv. M.S. ; filo primario repente frondes minutas 
(semiunciales) sparsas erectas emittente; fronde compressa distiché subpinnata, pinnis di- 
chotomo-fastigiatis, Segmentis terminalibus brevissimis dentiformibus, articulis diametro 
brevioribus sacculo roseo coloratis, omnibus nisi supremis interstitiis nudis, tetrasporis 
secus marginem Segmentorum’ utrinque longitudinaliter seriatis. Parasitical on Dictyota 
Kunthii at Rottnest (220). I have little hesitation in referring this to C. miniatum, Suhr. 
(first found on the Peruvian Coast), although Agardh makes no mention of the primary 
creeping filament, and there are some other slight differences in the description. 

267. Ceramium australe, Sond.! Garden Island, rare (285). Near C. Deslongchampsii. 

268. Crramium Jastigiatum, Hary. Parasitical on Zostera, Rottnest, rare (257). 

269. Ceramium gracillimum, Kiitz, Parasite on Alga, on mud-banks, King George’s Sound, 
January (23). 

270. Pritoctapta pulchra, Sond,! Garden Island, rare (147 and 148), 


4c2 


558 Dr. W. H. Harvey's Account of the Marine Botany of 


274. 


bo 
~ 
or 


- Hatopateama Preissi?, Sond.! Very abundant on the reefs at Rottnest; also on Caulinia, 
&e. (63). 

- Hanowra australis, Sond.! Fremantle, rare (56). 

. Hanowia robusta, n.sp.; fronde (vix evoluta) compressa lata; filis setaceis, articulis prima- 
riis oyoideo-cylindraceis ad genicula contractis diametro 2-3-plo-longioribus, endochromate 
ampla. Fremantle, very rare( ), Myspecimensareimmature. The filaments are much 
more robust and more laxly woven than in H. australis. 

Hanow1a arachnoidea, n.sp.; fronde compressa lat furcatd v. dichotom, filis arachnoideis, 
articulis primariis cylindraceis diametro 6-8-plo-longioribus. King George’s Sound, very 
rare (52). Hrond 1-2 inches high, the segments } to } inch broad, compressed. Filaments 
much more slender than in ZH. australis, with much longer joints. 

LASIOTHALIA, noy. gen. rons filiformis, membranacea, ramosa, hirsuta, é filis longitudina- 
libus intertextis anastomosantibus, filoque centrali majori contexta; filis periphericis 
externé fila callithamnoidea subsimplicia horizontalia libera emittentibus. I ructus? 


. Lasioruaria hirsuta, n. sp.; Cape Riche, very rare (321). I found only two or three speci- 


mens. The largest is about 6 inches long, irregularly divided, with lateral branches and 
slender filiform ramuli. Every part of the plant is clothed with short, simple, or slightly 
branched, horizontal, jointed hairs. There is no trace of gelatine, and the plant but slightly 
adheres to paper. 


276. Dupresnata coccinea, Bonn.! King George’s Sound, very rare (325). 

277. Crovanta attenuata, 2. australis. On Zostera, &c., King George’s Sound (62). Much larger 
and less gelatinous than the British plant usually is, but scarcely otherwise different. 

278. CRovantA vestita, n. sp.; fronde ultra-setaced decomposité ramosissimé membranacea (vix ge- 
latinosa), ramis ramulisque patentibus, omnibus ramellis densissimé velatis, ramellis diva- 
ricato-multifidis; favellis solitariis reniformibus in ramulis minoribus inter ramellos im- 
mersis; tetrasporis sphericis triangulé divisis. Rottnest and King George’s Sound, on 
Zostera, &e. (338). Much more robust than C. attenuata, much less gelatinous, and not 
moniliform in any part of the frond. 

279. Dasypuita Preissii, Sond.! On the stems of Fucoidec, Garden Island, common (149). 

280. Pritora coralloidea, J. Ag. Garden Island, Rottnest, and King George’s Sound, common 
(91). 

281. Priora sp. King George’s Sound (92). Possibly only a variety of the last, with articu- 
lated ramelli. 

282. Prinora striata, n. sp.; fronde ancipiti siccitate transversim ruguloso-striaté decomposité 


ramosissima, ramis majoribus sparsis alterné divisis vix pinnatis, minoribus linearibus 
pectinato-pinnatis, pinnulis subulatis alternis simplicissimis; favellis minimis ad latus su- 
perius pinnularum pedicellatis involucratis, involucro é filis callithamnoideis multiseriatis 
composito; tetrasporis ad processos proprios ramosos é lateribus pinnularum emissis. 
Rottnest, not uncommon (240). A most distinct and beautiful species with the habit of 
Phacelocarpus Labillardieri. Yt most resembles P. Rhodocallis, H. (Rhodocallis elegans, 
Kiitz.), but differs essentially from that species in the position and nature of the involu- 


cres, &c. 


the Colony of Western Australia. 559 


283. Prinora siliculosa, n. sp.; fronde complanata costatd decomposité ramosissima, ramis majori- 
bus alternis sparsisve, minoribus linearibus pectinato-pinnatifidis, pinnulis é basi lato sub- 
ulatis alternis simplicissimis; tetrasporis in glomerula siliculiformia é pinnularum latere 
superiore enata congestis, ad fila callithamnoidea brevissima circum axim verticillata affixis. 
Rottnest, rare (243). Very like the preceding in habit; but evidently ribbed, and rather 
inciso-pinnatifid than pinnate, and not obviously transversely striate; and abundantly cha- 
racterized by the strangely metamorphosed fructification. 

284. THamNnocarrus Gunnianus, Harv. Common at Garden Island and Rottnest; but not in fruit 
(169). 

285. GrRirrirusta ovalis, n. sp.; fronde erecta (sub-bi-unciali) di-tri-chotomA subfastigiata crassis- 
sima, segmentis erecto-patentibus, articulis diametro 3-4-plo-longioribus, inferioribus cla- 
vatis, mediis superioribusque obovatis inflatis ad genicula maximé constrictis; fertilibus 
conformibus; involucris tetrasporarum circa genicula involucratis é ramellis minimis con- 
flatis. Parasitical on Zostera, King George's Sound (41). Also sent by Dr. Curdie, from 
Cape Northumberland. Very much more robust than G. corallina, with nodes contracted 
like those of an Opuntia. It is as robust as Chylocladia articulata. 

286. GRIFFITHSIA monilis, n, sp.; fronde basi radicante cxspitosé (1-2 unciali) dichotomé fasti- 
giata crassissima, segmentis erecto-patentibus; articulis diametro sesquilongioribus globoso- 
inflatis siccitate sub-collapsis et ovalibus ad genicula maximé constrictis; fertilibus confor- 
mibus, involucris tetrasporarum circa genicula verticillatis, Parasitical on Alge at Garden 
Island, and on Zostera at Rottnest (326). When fresh it resembles beautiful strings of 
ruby-coloured beads, but fades much in drying. 

287. Grivritusta Binderiana, Sond.! Garden Island on Alga, Rottnest on Zostera (199). 

288. Grirrirusia Teges, MS. Cast ashore at Fremantle (146). I do not describe this species, as 
the fruit is unknown. It forms enormous, coarse, mat-like strata, one or two feet in breadth, 
composed of filaments resembling those of G. secundiflora, but very irregularly branched. 

289. Corynosrora australis, n. sp.; fronde (biunciali) setaceA gelatinoso-membranace4 dichotomo- 
decomposita et alterné ramos’, ramulis pluries dichotomis, articulis longissimis ad geni- 
cula nec contractis, ramellis superioribus tenuissimis dichotomis, apicibus longé filiformi- 
bus arachnoideis; tetrasporis ad genicula ramorum majorum subsessilibus oblongis nucleo 
indiviso. Rottnest, in June, very rare (344). Fremantle, July, G. Clifton, Esq. A very 
distinct species, readily known by its attenuated apices, 

290. CoryNnospora gracilis, n. sp.; fronde pusilla (unciali) tenui alterné ramosa vy. subdichotoma, 
ramulis quoquoversum egredientibus inferioribus furcatis superioribus bis-terve dichotomis, 
apicibus subattenuatis obtusiusculis; tetrasporis... ? Garden Island, rare, July (266). 
The habit and substance of the plant are those of Corynospora. 

291. CALLITHAMNION thyrsigerum, Thw. MS.; filo primario repente, secundariis erectis cespitosis 
eapillaribus (1-14 uncialibus) vagé ramosis, ramis minoribus sepissime secundis filiformi- 
bus simplicissimis acuminatis; articulis diametro 3-5-plo-longioribus cylindraceis; tetra- 
sporis circa genicula suprema ramorum verticillatis pedicellatis, pedicellis ramosulis thyr- 
soideo-paniculatis; favellis in ramulo terminalibus involucratis. On Alge and Zostera 


560 Dr. W. H. Harvey's Account of the Marine Botany of 


King George’s Sound and Rottnest (51). A beautiful and very distinctly characterized 
species of the C. Turneri section, which I first gathered at Belligam Bay, Ceylon, in com- 
pany with my friend G. H. K. Thwaites, Esq., of Peradenia Botanical Gardens. 

292. CALLITHAMNION cymosum, n. sp.; densissimé czespitosum; filis primariis repentibus intricatis, 
secundariis erectis arachnoideis (uncialibus) vagé ramosis, ramis subdichotomis v. alternis 
minoribus filiformibus erectis longé simplicibus obtusis, articulis diametro multoties 
(8-12-plo) longioribus cylindraceis; tetrasporis in cymis veris equalibus y. scirpoideis 
secus ramos evolutis dispositis; favellis ..... ? On sand-covered rocks, Middleton Bay, 
King George’s Sound and Rottnest; often half buried in sand (10). The cymoid inflores- 
cence is very peculiar, and beautifully accurate to the typical cyme. 

293. CALLITHAMNION delicatulum, n. sp.; pusillum, arachnoideum, filo primario repente; secunda- 
riis erectis (vix uncialibus) parum ramosis é quoque geniculo plumulatis, plumulis oppo- 
sitis per paria decussatis infra apicem articuli egredientibus tenuibus laxé pinnatis, pinnulis 
inferioribus spits oppositis reliquis alternis é rachide flexuos4 emissis omnibus attenuatis 
simplicibus v. ramulo uno alterove auctis; fructu..... Parasite on Solieria australis, 
at King George’s Sound. A very delicate and beautiful little plant (339). 

294. CALLITHAMNION gracilentum, n. sp.; minutum (1-2 lineas altum); filo primario repente crasso 
ramos suboppositos liberos emittente; ramis filo primario quadruplo-angustioribus pinnatis, 
pinnis oppositis patentibus simplicibus v. latere inferiori subramellosis subattenuatis obtu- 
siusculis; articulis fili primarii diametro sesqui v. subduplo, ramorum 4-5-plo, ramulorum 
sesquilongioribus. Parasite on Fucoids, Rottnest, rare (327). Apparently nearly allied to 
C. leptocladum, Mont.; but scarcely the same? 

295. CALLITHAMNION aculeatum, n. sp.; filo primario repente; secundariis erectis (sub-uncialibus) 
capillaribus subdichotomis v. alterné ramosis corymboso-fastigiatis; ramis omnium serierum 
quoquoversum egredientibus, minoribus caule duplo-angustioribus, ramulis ad genicula feré 
omnia verticillatis spineformibus patentissimis brevissimis simplicibus subacutis; tetra- 
sporis solitariis ad ramulos lateralibus; articulis ramorum diametro 2—3-plo-longioribus. 
On Zostera, at King George’s Sound, rare (343). 

296. CALLITHAMNION spinescens, Kiitz.?, Cal. tomentellum, Harv. MS. Very common, everywhere 
on Alga, &c. This species is so common that it can hardly have escaped Preiss, and there- 
fore I suppose it the C. spinescens of Sonder’s list. But the ramuli are not whorled ; but 
opposite and decussated ; one pair spreading one way, the next at right angles to them. In 
all my specimens the articulations of the stem are very short. In habit, it has much re- 
semblance to Jungermannia tomentella (48). 

297. CALLITHAMNION horizontale, n. sp.; filis erectis (uncialibus) capillaribus solitariis parum 
ramosis, ramis 3—4-lateralibus simplicibus patentibus cum filo primario é quoque articulo 
opposité plumulatis; plumulis é medio articuli egredientibus subdistichis horizontaliter 
patentibus (latus planum sursum vertentibus) ambitu ovatis pinnatis; pinna infima simplici, 
ceteris furcatis; articulis omnibus diametro equalibus v. sesquilongioribus; apicibus acu- 
tis; tetrasporis solitariis ramulum pusillum pinnarum terminantibus. Parasitic on Grif: 
Binderiana at Rottnest; and on Pol. négrita at Garden Island (254). 


the Colony of Western Australia. 561 


298. CaLLITHAMNION verticale, n. sp.; filis erectis (uncialibus) capillaribus subsolitariis parum 
ramosis, ramis 1-2-lateralibus brevibus cum filo primario é quoque articulo opposite plu- 
mulatis; plumulis é medio articuli egredientibus distichis verticaliter patentibus (latus 
planum ad latera vertentibus) ambitu ovatis pinnatis; pinnis omnibus plus minis furcatis; 
articulis diametro xqualibus v. sesquilongioribus; apicibus acutis; tetrasporis solitariis 
ramulum pusillum pinnarum terminantibus. Parasite on Alge at Garden Island (267). 
Very nearly allied to the preceding; but having a different aspect, from the different direc- 
tion of the flat surface of the plumules, 

299. CaLuitHamNton pulchellum, n. sp-; pusillum (semi-unciale); filo primario ramisque prima- 
riis prostratis repentibus demum ramos secundarios erectos simplices y. parum ramosos 
emittentibus; ramis omnibus @ quoque articulo opposité v. cruciatim plumulatis; plumu- 
lis 2-4 infra apicem articuli egredientibus patentibus ambitu ovatis pinnatis; pinnis 
simplicissimis approximatis obtusis; articulis ramorum diametro 2-4- plo-longioribus, 
pinnarum et pinnellarum diametro brevioribus; favellis simplicibus rachidem plumuli ter- 
minantibus; tetrasporis 4 pinnellis abbreviatis formatis. Parasitic on various Alga; espe- 
cially on Areschougia australis. Rottnest and Cape Riche (230). At first I supposed this 
beautiful little plant to be CG. australe, J. Ag., but on comparison with his description, my 
plant must be different. The plumules on theyounger part of the frond are always opposite and 
vertical ; those on the older erect branches are frequently in fours, cruciate and horizontal. 
Can this be C. Preissii, Sond.? .The specimens with cruciate plumules would be near Son- 
der’s description. 

300. CaLtitHamnton simile, Hook. and Harv. On Fucoidee at King George’s Sound and Rottnest 
(90). Ihave compared the specimens with one from Kerguelin’s Land, and find them to 
agree, 

301. CALLITHAMNION Wollastonianum, n. sp-; fronde ultra-setacea elata (A unciali) basi tenuiter corti- 
cata sursum longé pilis Squarrosis stuposo-hirsuta subdistiché ramosissima; ramis alternis 
decomposito-pinnatis, penultimis distichis pellucidé articulatis alterné plumulatis; plu- 
mulis patentibus longissimis ambitu linearibus; pinnis tenuibus erectiusculis brevibus, 
inferioribus simplicibus, superioribus sepius furcatis v. pinnulatis; tetrasporis solitariis ad 
ramulos brevissimé pedicellatis; articulis diametro 2-4-plo-longioribus. Middleton Bay, 
King George’s Sound, rare in August (329). A very beautiful species, which I-name in 
affectionate regard to the family of AncHDEAcoN Woxxaston, from whom I received unya- 
rying kindness during the whole of my stay at King George's Sound. It is nearly allied to 
C. latissimum, but differs in several respects. 

302. CALLiTHaMNION Brownianum, n. sp.; fronde ultra-setace’ elath (4 unciali) subecorticata 
sursum longé pilis squarrosis Stuposo-hirsuta quoquoversum ramosissimd; ramis pluries 
alterné decompositis, penultimis quoquoversis pellucidé articulatis nodosis (parietibus cel- 
lularum crassis gelatinosis), alterné plumulatis; plumulis quoquoversis brevibus crispis 
pinnatis, pinnis capillaribus longissimis maximé curvatis inflexis; articulis pinnularum 
diametro 4-plo-longioribus; tetrasporis brevissimé pedicellatis solitariis v, geminis ad 
latera pinnularum enatis, On Zostera at Rottnest, Fremantle, and King George’s Sound 


562 


Dr. W. H. Harvey's Account of the Marine Botany of 


(264). Much resembling the last in aspect, but not distichous in any part; and with re- 
markably curled pinnules. I name it in compliment to Mrs. RicHarpD Brown of Fremantle, 
an amateur collector of Alge, from whom and her estimable husband I received much 
kind attention during my stay in their neighbourhood. 


303. CaLuiTHamnNion laricinum, n. sp.; fronde cartilaginea setacea (1-3 unciali) feré ad apices 


ramorum corticataé glabra quoquoversum ramosa ambitu pyramidali; ramis alternis paten- 
tibus superné sensim brevioribus ramulis dichotomo-multifidis undique obsessis; ramulis 
pluries dichotomis, segmentis patentibus, ultimis brevissimis spineformibus; favellis gemi- 
nis oblongis! simplicibus v. furcatis; tetrasporis globosis ad latera ramulorum sparsis. On 
Zostera at Rottnest, common (200). This has the aspect and substance of C. tetragonum; 
but is more nearly related to C. granulatum or C. grande. 


304. CaLLirHAMNION flabelligerum, n. sp.; fronde erecta crassiuscula alterné decomposito-ramosa 


omnin6 ecorticata; ramis ramulisque quoquoversum egredientibus, terminalibus corym- 
boso-flabellatis, ramulis dichotomo-multifidis fastigiatis; apicibus obtusis patentibus; favel- 
lis geminis rotundatis ramulis stipatis (quasi involucratis). On Zostera at Rottnest, and at 
Garden Island on Alge (201). Nearly allied to C. corymbosum, but a more robust, though 
smaller plant; with cells more like those of a Griffithsia than of a Callithamnion. 


305. CALLITHAMNION multifidum, n.sp.; fronde pusilla (unciali) arachnoidea ecorticata densé ces- 


pitosé alterné ramosi; ramis simplicibus ramosisve, ramulis alternis quoquoversis dicho- 
tomo-multifidis; segmentis patentibus obtusis; articulis ramorum basi incrassatis diametro 
4-plo, ramulorum cylindraceis diametro 2—3-plo-longioribus. On sand-covered rocks, half- 
tide level, generally buried in the sand, the grains of which adhere closely to the filaments. 
Reefs at Rottnest, May and June (229). 


306. CALLITHAMNION crispulum, n. sp.; fronde pusilla (4-3 unciali) capillari ecorticata cespitosa 


inferné quoquoversum, superné distiché ramos; ramis superioribus é rachide flexuosa 
alterné plumulatis; plumulis brevissimis alterné pinnatis, pinnis 3-4 simplicissimis filifor- 
mibus elongatis obtusis eximié arcuato-inflexis; articulis omnibus diametro sesquilongiori- 
bus; favellis geminis; tetrasporis ..... In shady crevices of rocks, at half-tide level, 
Rottnest. Near C. Borreri, but a much smaller plant, and sufficiently characterized as 


above (228 a). 


307. Catiirnamion pusillum, n. sp.; fronde pusilla (vix unciali) capillari ecorticata cespitosa in- 


ferné simpliciuscula superné quoquoversum ramos; ramis inferné plumulatis, superné 
alterné ramosis, ramis minoribus é rachide strictiusculaé quoquoversum plumulatis; plu- 
mulis brevissimis vix pinnatis; pinnis 2-3 alternis v. secundis elongatis obtusis arcuatis 
inflexis; articulis omnibus nisi basilaribus diametro 3-plo-longioribus; favellis geminis; 
tetrasporis globosis ad latera pinnarum solitariis. Crevices of rocks, at half-tide, Rottnest 
(228). At first [had this for a variety of C. crispulum, but it differs in not being in any 
part distichous, and in the longer articulations. 


308. CaLuirHamNion Scopula, n. sp.; fronde pusilla (unciali) capillari ecorticata quoquoversum 


ramosi, ramis paucis cum ramulis ambitu clavatis quoquoversum plumulatis; plumulis in- 
ferioribus brevibus, superioribus elongatis pinnatis; pinnis simplicibus filiformibus longis- 


the Colony of Western Australia. 563 


simis arcuato-incurvis obtusis; articulis omnibus diametro 2-3-plo-longioribus; tetrasporis 
ellipsoideis numerosis secus pinnas sessilibus. Crevices of rocks, at half-tide, Rottnest 
(328). This is certainly near C. rosewm in miniature. To the naked eye it looks very like 
Dasya ocellata, or like a bunch of little bottle brushes. 

309. CaLuiTHamnion dedile, n. sp.; fronde pusilla (vix unciali) tenuissima ecorticata cespitosa in- 
ferné quoquoversum superné distiché ramosa; ramis paucisalterné divisis, ramis minoribus 
distiché ramulosis, ramulis patentissimis inferioribus simplicibus spineformibus superioribus 
furcatis v. subpinnulatis; articulis inferioribus diametro 5-8-plo, ramulorum 3-4-plo-longi- 
oribus; tetrasporis solitariis ad ramulos sessilibus. Rottnest, rare (330). Unlike any Aus- 
tralian species; and most like some starved form of ©. polyspermum, but of a very fragile 
substance and pale colour. 

310. CaLiiraamntion radicans, n. sp.; nanum, parasiticum, velutino-cespitosum; fronde minuta 
(2 lineas alta) basi fibrillis crispatis radicante, é basi ramosissima; ramis primariis alternis 
secundisve 2-3-ties decompositis, minoribus ramulisque secundis strictis; articulis cylindra- 
ceis diametro 4—5-plo-longioribus; ramulis fructiferis prope basin ramorum sparsis simpli- 
cibus v. parum ramosis; tetrasporis ellipsoideis terminalibus. On Zostera leaves, Fremantle 
(331). This resembles C. luxurians, J. Ag., externally, but seems sufliciently marked by 
its rooting filaments and longer articulations. 

311. CattirHamnton botryocarpum, n. sp.; nanum, penicillato-cespitosum; fronde minuta (1-14 
lineas alta) é basi ramosissima, ramis alternis v. secundis patentibus flexuosis nunc sub- 
squarrosis; articulis diametro 4-plo-longioribus; tetrasporis magnis triangulé divisis in glo- 
merula ad axiles ramorum densissimé aggregatis; antheridiis, botryoideis 6 quoque feré 
articulo ramorum sepé evolutis. Abundant on Chorda lomentaria, at King George’s Sound, 
in August (324). Externally very like C. Daviesii, but I suppose distinctly characterized 
by its fruit. The tetraspores are very large for this section of the genus. The antheridia 
resemble little clusters of grapes, ranged along the upper branches of fertile specimens. 

312. CaLLiTHAaMNton sparsum, Harv.(?) Parasite on Sporochnus, at Garden Island. This requires 
to be compared with British specimens; and also with Kiitzing’s C. humile from the Cape of 
Good Hope. It is quite different from either of the preceding, very sparingly branched, of 
a deep purple colour, and rather rigid texture, with very short articulations. 


Serres III.—_CHLOROSPERME &. 
Orper J.—SIPHONACEZ. 


313. CauLerpa simpliciuscula, Ag.? On the reefs,'Rottnest. A much dwarfer, and more branching 
form than that figured by Turner, if the same. Possibly my plant may be rather akin to 
C. lentifera, J. Ag. (207). 

314, Cauxerpa letevirens, Mont.? Extremely abundant on the surface of shallow reefs, exposed 
at low water, Rottnest. I have not compared with Montagne’s plant (208). 

315. Cauterra cylindracea, Sond. King George’s Sound, rare (54). 


VOL. XXII. 4D 


564 Dr. W. H. Harvey's Account of the Marine Botany of 


316. CauLerpa tenella, n. sp.; surculo setaceo glabro; frondibus filiformibus simplicibus y. parcé 
ramosis, ramis vagis, foliis spiraliter laxé insertis subtristichis erecto-patentibus subulatis 
brevibus mucronatis lwteviridibus. On the Natural Jetty at Rottnest, very rare (215). A 
slender species, 1-2 inches high. 

317. Cauterra hypnoides, R. Br. Abundant in tide-pools and borders of reefs, at Rottnest and 
Garden Island (185). 

318. Cauterra DMulleri, Sond.! surculo crasso squamulis cylindraceis dichotomis densé muricato; 
fronde erecta stipitata oblonga obtusa pinnata; stipite pinnisque foliolis undique densissimé 
obtectis, foliolis geminis basi unitis cylindraceis obtusis apice bi-mucronulatis erectis im- 
bricatis intense viridibus. On border reefs and sides of deep tide-pools at Rottnest (205). 
Nearly related to C. hypnotdes, but a much stronger and coarser plant, readily known at a 
glance, when the two are seen together, though difficult to characterize. In C. hypnoides 
the sureulus and base of stem are clothed with far more densely set and muricated squame, 
and the folioli are much smaller, softer, more patent, more laxly set, and more acute. 

319, CauLprpa obscura, Sond.! Abundant at King George’s Sound; and in tide-pools, &e., Rott- 
nest (77). The fronds are often 12-18 inches long. 

320. CauLerpa furcifolia, Hook. and Harv. A few fragments cast ashore at King George’s Sound, 
February (_ ). 

321. CAULERPA geminata, n. sp.; surculo glabro; frondibus erectis simplicibus (brevibus) articu- 
lato-constrictis glabris, foliis parvis oppositis ovoideis distichis v. tortione caulis quoquo- 
versum directis. On very shady rocks, usually on the under surface of table-reefs, Rottnest. 
The distichous form is readily distinguishable; but that with leaves turned to all sides 
resembles C. sedoides in miniature; but is readily known by its articulate stem and opposite 
leaves (214). I suspect that it is S. sedoides, of Sonder in P]. Preiss. 

322. CauLerpa corynephora, Mont. King George’s Sound, and in deep tide-pools, Rottnest (101). 

323. Cauerra scalpelliformis, R. Br. King George’s Sound, and on border reefs, Rottnest (206). 

324. Srruvea plumosa, Sond. Abundant on all the shallow reefs at Rottnest, but scarcely in 
season in June, when I visited the island (216). 

325. SrruvEA macrophylla, n. sp.; fronde oblongo-ovali maxima (4-5 uncias longa, 3 uncias lata) 
crenata, tubulis anastomosantibus pluries pinnatis. Champion Bay, Mrs. Drummond, Jun. 
A single specimen, bleached white, was sent by Mrs. Drummond to Mr. Sanford, who kindly 
presented it to me. The frond closely resembles a beautiful structure of ‘old point-lace,” 
and as it is very tough and strong, it might be manufactured into ladies’ natwral-lace collars, 
by merely tacking on a border of net. 

326. Potypuysa Peniculus, Ag. Fucus Peniculus, R. Br. Extremely abundant, at all seasons, in 
Princess Royal Harbour, King George’s Sound, growing on old shells. Not seen else- 
where (1). 

327. Penicittus Arbuscula, Mont.? Abundant, on shallow, sand-covered reefs at Rottnest (204). 
It varies much in size. The stem is sometimes scarcely twice as thick as a hog’s bristle; 
sometimes as thick as a goose-quill. I have not compared with Montagne’s plant. 

328. Hauimepa macroloba, Dne. Cape Riche and Rottnest, on the reefs (226). 

329. Copium tomentosum, Ag. Abundant everywhere (45). 


the Colony of Western Australia. 565 


330. Copium laminaricides, n. sp.; stipite brevi cuneato mox in frondem amplissimam (2-3 peda- 
lem) planam subsimplicem y. parcé lobatam expanso. At Rottnest and King George’s 
Sound, on the under surface of table-shaped rocks. If this be only a form of C. elongatum 
it is indeed an extraordinary one. The undivided frond is often three feet wide by two feet 
long, resembling a piece of green cloth (227). 

331. Copium spongiosum, n. sp.; fronde sessili molli polymorpha varié lobata et spongioidea; filis 
interioribus laxiusculis in gelatinaé immersis, periphericis cylindraceis y. pyriformibus 
obtusis; spermatiis fusiformibus basi et apice acutis. On shells and stones, &c., about low- 
watermark, common(_ ). Ido not wonder that this has not been brought to Europe, 
as it is almost impossible to prevent the spongy mass decomposing (with a very unsavoury 
shell) during the process of drying. 

332. Coprum mamillosum, n.sp.; fronde globosa vel reniformi puncto affixa solida; filis interioribus 
densissimé intertextis arachnoideis gelatina subsolida obvallatis, periphericis maximis in- 
flato-cylindraceis, eorum apicibus ad superficiem frondis quasi mamillis directis, siccitate 
sericeo-nitentibus. Fremantle and King George’s Sound, cast ashore (162). It forms a 
very solid, green, mammillated ball, composed internally of very slender, densely packed 
threads, throwing off to all sides externally, radiating branches, whose apices, closely set 
together, give the mammillated appearance to the surface. 

333. Bryopsts australis, Sond.? Very common on rocks, at Rottnest and Carnac (161). 

334. Bryopsis sp. On Zostera, Rottnest (175). 

335. Bryopsis sp. Perhaps B. foliosa, Sond. On sand-covered rocks, Rottnest (249). 

336. DicryosPH#RIA sericea, n.sp.; fronde umbilicata medifixa varié laceraé (nunquam vesicata) 
sericea; vesiculis minimis globoso-polyhedris. On rocks near low-water mark, King 
George’s Sound, Cape Riche, and Rottnest (160). Very distinct from D. favulosa at all 


ages. 


Orver I].—CONFERVACE. 


337. CLapopHora valonioides, Sond. Common on rocks and in shallow water (54). 

338. CLAabDoPHoRA sp. Sand-covered rocks, King George’s Sound (46). 

339. CLADOoPHORA sp. C. anastomosans, MS. Cast ashore at Fremantle (163). 

340. CLaporHora sp. Fremantle (176). 

341. CLapopnHora sp. Fremantle (177). 

342. CLapopnora sp. Near C. pellucida. Rottnest, on reefs (275). 

343. CLapopHora sp. Allied to C. glaucescens (333). I have neither books nor specimens at hand 
sufficient to determine whether these species have been previously described. 


Orver I1J.—ULVACE. 


344. Paycoseris Ulva, Sond. Garden Island. 
345. Puycosenis /atissima. Ulva latissima, Auct. I cannot say to which of Kiitzing’s species 


566 


346. 


347. 


348. 


Dr. W. H. Harvey’s Account of the Marine Botany, &c. 


these specimens should be referred, but I fear that author has needlessly multiplied the 
names in this genus. 
Enteromorpua compressa. Submerged rocks and woodwork, everywhere. 


Orver IV.—OSCILLATORIACE, 


RivuraRia australis, n. sp.; fronde maxima (fronde 1-14 uncias diametro) solitaria hemisphe- 
rica solid lubrica olivaceo-viridi. On rocks near low-water mark, Cape Riche (298). I 
suppose this belongs to Kiitzing’s genus Ewactis, but I have not minutely examined it. It 
is the largest of the genus known to me. 

Rivurari sp. Near 2. plicata, Carm. Upper end of Princess Royal Harbour, on stones 
and wood in shallow water (19). 


. CALoTHRIX cespitula, Harv.? Parasitical on Alga, in tide-pools at Cape Riche (299). This 


requires to be compared with the European plant, to which, if not the same, it is closely 
related. 


. Catorurix limbata, MS. Littoral rocks, Rottnest (277). 
. CALoTHRIXx sp. Cape Riche (334). 
. CaLoTuRix sp. Cape Riche (335). I cannot at present identify these species; and have be- 


sides two others, collected in smaller quantity. 


At Sea, September 4, 1854. 


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