Chapter I: Part 1

Transcriber’s Note

Variable spelling and hyphenation have been retained. Minor punctuation inconsistencies have been silently repaired. The Errata of the original edition have been corrected. Other changes made can be found at the end of the book. Formatting and special characters are indicated as follows:

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PHILOSOPHICAL
TRANSACTIONS,
GIVING SOME
ACCOUNT
OF THE
Present Undertakings, Studies, _and_ Labours,
OF THE
INGENIOUS,
IN MANY
Considerable Parts of the WORLD.

VOL. L. +PART II.+ For the Year 1758.

_LONDON_:

Printed for +L. DAVIS+ and +C. REYMERS+,
Printers to the +ROYAL SOCIETY+,
against _Gray’s-Inn Gate_, in _Holbourn_.

M.DCC.LIX.

THE
CONTENTS
TO
PART II. VOLUME L.

LIX. _AN Account of the Effects of Electricity in paralytic Cases.
In a Letter to_ John Pringle, _M. D. F.R.S. from_ Benjamin Franklin,
_Esq; F.R.S._ p. 481.

LX. _Observations on the late Comet in_ September _and_ October
_1757; made at the_ Hague _by Mr._ D. Klinkenberg: _In a Letter to
the Rev._ James Bradley, _D. D. Astronomer Royal, and F.R.S. and
Member of the Royal Academy of Sciences at_ Paris. _Translated from
the_ Low Dutch. p. 483.

LXI. _Remarks on the different Temperature of the Air at_ Edystone,
_from that observed at_ Plymouth, _between the 7th and 14th of_ July
_1757. By Mr._ John Smeaton, _F.R.S._ p. 488.

LXII. _An Account of the Earthquake felt in the Island of_ Sumatra,
_in the_ East Indies, _in_ November _and_ December _1756. In a
Letter from Mr._ Perry _to the Rev. Dr._ Stukeley, _dated at_ Fort
Marlborough, _in the Island of_ Sumatra, Feb. _20. 1757. Communicated
by the Rev._ Wm. Stukeley, _M. D. F.R.S._ p. 491.

LXIII. _Concerning the Fall of Water under Bridges. By Mr._ J.
Robertson, _F.R.S._ p. 492.

LXIV. _An Account of the Earthquake in the West Parts of_ Cornwall,
July _15th 1757. By the Rev._ William Borlase, _M. A. F.R.S.
Communicated by the Rev._ Charles Lyttelton, _LL. D. Dean of_ Exeter,
_F.R.S._ p. 499.

LXV. _Some Observations upon the Sleep of Plants; and an Account
of that Faculty, which_ Linnæus _calls_ Vigiliæ Florum; _with an
Enumeration of several Plants, which are subject to that Law.
Communicated to_ Wm. Watson, _M. D. F.R.S. by Mr._ Richard Pulteney
_of_ Leicester. p. 506.

LXVI. _An Account of the Case of a Boy troubled with convulsive Fits
cured by the Discharge of Worms. By the Rev._ Richard Oram, _M. A.
Chaplain to the Lord Bishop of_ Ely. p. 518.

_An Account of the same Subject, in a Letter from Mr._ John Gaze,
_of_ Walket, _in the County of_ Norfolk, _to Mr._ Wm. Arderon,
_F.R.S. Communicated by Mr._ Henry Baker, _F.R.S._ p. 521.

LXVII. _An Account of the extraordinary Heat of the Weather in_ July
_1757, and of the Effects of it. In a Letter from_ John Huxham, _M.
D. F.R.S. to_ Wm. Watson, _M. D. F.R.S._ p. 523.

LXVIII. _An Account of the fossile Thigh-bone of a large Animal, dug
up at_ Stonesfield, _near_ Woodstock, _in Oxfordshire. In a Letter to
Mr._ Peter Collinson, _F.R.S. from Mr._ Joshua Platt. p. 524.

LXIX. _A Discourse of the Usefulness of Inoculation of the horned
Cattle to prevent the contagious Distemper among them. In a Letter
to the Right Hon._ George _Earl of_ Macclesfield, _P. R. S. from_
Daniel Peter Layard, _M. D. F.R.S._ p. 528.

LXX. _Trigonometry abridged. By the Rev._ Patrick Murdoch, _A. M.
F.R.S._ p. 538.

LXXI. _An Account of Two extraordinary Cases of Gall-Stones. By_
James Johnstone, _M. D. of_ Kidderminster. _Communicated by the Rev._
Charles Lyttelton, _LL. D. Dean of_ Exeter. p. 543.

LXXII. _A remarkable Case of Cohesions of all the intestines_, &c.
_in a Man of about Thirty-four years of Age who died sometime last
Summer, and afterwards fell under the Inspection of Mr._ Nicholas
Jenty. p. 550.

LXXIII. _Of the best Form of Geographical Maps. By the Rev._ Patrick
Murdoch, _M. A. F.R.S._ p. 553.

LXXIV. _A short Dissertation on Maps and Charts: In a Letter to the
Rev._ Thomas Birch, _D. D. and Sec. R. S. By Mr._ William Mountaine,
_F.R.S._ p. 563.

LXXV. _Cases of the remarkable Effects of Blisters in lessening the
Quickness of the Pulse in Coughs, attended with Infarction of the
Lungs and Fever: By_ Robert Whytt, _M. D. F.R.S. Fellow of the Royal
College of Physicians, and Professor of Medicine in the University
of_ Edinburgh. p. 569.

LXXVI. _A remarkable Instance of Four rough Stones, that were
discovered in an human urinary Bladder, contrary to the received
Opinion; and successfully extracted by the lateral Method of Cutting
for the Stone. By Mr._ Joseph Warner, _F.R.S. and Surgeon to_
Guy’s-Hospital. p. 579.

LXXVII. _Observations on the_ Limax non cochleata Purpuram ferens,
_The naked Snail producing Purple. By_ John Andrew Peyssonel, _M. D.
F.R.S. Translated from the_ French. p. 585.

LXXVIII. _New Observations upon the Worms that form Sponges. By_ John
Andrew Peyssonel, _M. D. F.R.S. Translated from the_ French. p. 590.

LXXIX. _Account of an Experiment, by which it appears, that Salt of
Steel does not enter the Lacteal Vessels; with Remarks. In a Letter
to the Rev._ Thomas Birch, _D. D. Secret. R. S. By_ Edward Wright,
_M. D._ p. 594.

LXXX. _A Dissertation on the Antiquity of Glass in Windows. In a
Letter to the Rev._ Tho. Birch, _D. D. Secret. R. S. By the Rev._
John Nixon, _M. A. F.R.S._ p. 601.

LXXXI. _An Account of an extraordinary Case of the Efficacy of the
Bark in the Delirium of a Fever. By_ Nicˢ. Munckley, _M. D. Physician
to_ Guy’s-Hospital, _and F.R.S._ p. 609.

LXXXII. _An Account of an Earthquake felt at_ Lingfield _in_ Surrey,
_and_ Edenbridge _in_ Kent, _on the 24th of_ January _1758. By_ James
Burrow, _Esq; R. S. V. P._ p. 614.

LXXXIII. _An Account of the Case of the First Joint of a Thumb torn
off, with the Flexor Tendon in its whole Extent torn out. By_ Robert
Home, _late Surgeon to the Thirtieth Regiment of Foot, and Surgeon
at_ Kingston upon Hull. _In a Letter to_ John Pringle, _M. D. F.R.S._
p. 617.

LXXXIV. _An Account of the late Discoveries of Antiquities at_
Herculaneum, _and of an Earthquake there; in a Letter from_ Camillo
Paderni, _Keeper of the Museum at_ Herculaneum, _and F.R.S. to_ Tho.
Hollis, _Esq; F.R.S. dated_ Portici, Feb. _1. 1758._ p. 619.

LXXXV. _A further Attempt to facilitate the Resolution of
Isoperimetrical Problems. By Mr._ Thomas Simpson, _F.R.S._ p. 623.

LXXXVI. _Observations on the_ Alga Marina latifolia; _The Sea
Alga with broad Leaves. By_ John Andrew Peyssonel, _M. D. F.R.S.
Translated from the_ French. p. 631.

LXXXVII. _An Account of the distilling Water fresh from Sea-Water
by Wood-Ashes. By Capt._ William Chapman: _In a Letter to_ John
Fothergill, _M. D._ p. 635.

LXXXVIII. _Observatio Eclipsis Lunaris facta_ Matriti _a Pª._ Joanne
Wendlingen, _Societatis_ Jesu, _in Regali Observatorio Collegii
Imperialis ejusdem Societatis, Die 30_ Julii _1757_. p. 640.

_Observatio Eclipsis Lunaris, facta ab eodem, eodem modo, eodem loco,
iisdemque instrumentis, Die 24_ Januar. _Anni 1758._ p. 642.

LXXXIX. _Observations upon a slight Earthquake, tho’ very particular,
which may lead to the Knowlege of the Cause of great and violent
ones, that ravage whole Countries, and overturn Cities. By_ John
Andrew Peyssonel, _M. D. F.R.S. Translated from the_ French. p. 645.

XC. _A Catalogue of the_ Fifty Plants _from_ Chelsea Garden,
_presented to the_ Royal Society _by the worshipful Company of
Apothecaries, for the Year 1757, pursuant to the Direction of Sir_
Hans Sloane, _Baronet, Med. Reg. & Soc. Reg. nuper Præses, by_ John
Wilmer, _M. D. clariss. Societatis Pharmaceut._ Lond. _Socius,
Hort._ Chelsean. _Præfectus & Prælector Botanic._ p. 648.

XCI. _An Historical Memoir concerning a Genus of Plants called_
Lichen _by_ Michelli, Haller, _and_ Linnæus; _and comprehended by_
Dillenius _under the Terms_ Usnea, Coralloides, _and_ Lichenoides:
_Tending principally to illustrate their several Uses. Communicated
by_ William Watson, _M. D. F.R.S._ p. 652.

XCII. _An Account of the fossil Bones of an Allegator, found on
the Sea-shore, near_ Whitby _in_ Yorkshire: _In a Letter to_ John
Fothergill, _M. D. from Capt._ William Chapman. p. 688.

XCIII. _De rariori quadam_ Orthoceratitis _Specie, in_ Suecia
_reperta, tractatus: in literis a_ Nicholao de Himsel, _M. D._ Riga
Livono, _ad_ Gul. Watson, _M. D. R. S. S._ p. 692.

XCIV. _A further Account of the Effects of Electricity in the Cure of
some Diseases: In a Letter from Mr._ Patrick Brydone _to Dr._ Robert
Whytt, _Professor of Medicine in the University of_ Edinburgh, _and
F.R.S._ p. 695.

XCV. _An Account of the Black Assize at_ Oxford, _from the Register
of_ Merton College _in that University. Communicated by_ John Ward,
_LL. D. With some additional Remarks._ p. 699.

XCVI. _A Description of the Plan of_ Peking, _the Capital of_ China;
_sent to the Royal Society by Father_ Gaubil, è Societate Jesu.
_Translated from the_ French. p. 704.

XCVII. _An Attempt to improve the Manner of working the Ventilators
by the Help of the Fire-Engine. In a Letter to_ Tho. Birch, _D. D.
Secret. R. S. from_ Keane Fitz-Gerald, _Esq; F.R.S._ p. 727.

XCVIII. _An Account of some Experiments concerning the different
Refrangibility of Light. By Mr._ John Dollond. _With a Letter from_
James Short, _M. A. F.R.S. Acad. Reg. Suec. Soc._ p. 733.

XCIX. _An Account of some extraordinary Effects arising from
Convulsions; being Part of a Letter to_ John Huxham, _M. D. and
F.R.S. from_ William Watson, _M. D. R. S. S._ p. 743.

C. _An Account of an extraordinary Storm of Hail in_ Virginia. _By_
Francis Fauquier, _Esq; Lieutenant Governor of_ Virginia, _and F.R.S.
Communicated by_ William Fauquier, _Esq; F.R.S._ p. 746.

CI. _An Account of an extraordinary Case of a diseased Eye: In a
Letter to_ Matthew Maty, _M. D. F.R.S. By_ Daniel Peter Layard, _M.
D. F.R.S._ p. 747.

CII. _An Account of the Heat of the Weather in_ Georgia: _In a Letter
from his Excellency_ Henry Ellis, _Esq; Governor of_ Georgia, _and
F.R.S. to_ John Ellis, _Esq; F.R.S._ p. 754.

CIII. _The Invention of a General Method for determining the Sum of
every 2d, 3d, 4th, or 5th_, &c. _Term of a Series, taken in order,
the Sum of the whole Series being known. By_ Thomas Simpson, _F.R.S._
p. 757.

CIV. _Observatio Eclipsis Lunæ Die 30_ Julii _1757. habita_
Olissipone _à_ Joanne Chevalier, _Congregationis Oratorii Presbytero,
è Regiâ_ Londinensi _Societate. Communicated by_ Jacob de Castro
Sarmiento, _M. D. F.R.S._ p. 769.

CV. _Singular Observations upon the_ Manchenille Apple. _By_ John
Andrew Peyssonel, _M. D. F.R.S. Translated from the_ French. p. 772.

CVI. _Abstract of a Letter from Mr._ William Arderon, _F.R.S. to Mr._
Henry Baker, _F.R.S. on the giving Magnetism and Polarity to Brass.
Communicated by Mr._ Baker. p. 774.

CVII. _An Account of the_ Sea Polypus, _by Mr._ Henry Baker, _F.R.S._
p. 777.

CVIII. _A Description of the fossil Skeleton of an Animal found in
the Alum Rock near_ Whitby. _By Mr._ Wooller. _Communicated by_
Charles Morton, _M. D. F.R.S._ p. 786.

CIX. _A Dissertation on the_ Phœnician _Numeral Characters antiently
used at_ Sidon. _In a Letter to the Rev._ Tho. Birch, _D. D. Secret.
R. S. from the Rev._ John Swinton, _M. A. of_ Christ-Church, Oxon.
_F.R.S._ p. 791.

CX. _Of the Irregularities in the Motion of a Satellite arising from
the Spheroidical Figure of its Primary Planet: In a Letter to the
Rev._ James Bradley, _D. D. Astronomer Royal, F.R.S. and Member of
the Royal Academy of Sciences at_ Paris; _by Mr._ Charles Walmesley,
_F.R.S. and Member of the Royal Academy of Sciences at_ Berlin, _and
of the Institute at_ Bologna. p. 809.

CXI. _Some Observations on the History of the_ Norfolk Boy. _By_ J.
Wall, _M. D. In a Letter to the Rev._ Charles Lyttelton, _LL. D. Dean
of_ Exeter. p. 836.

CXII. _Observations upon the_ Corona Solis Marina Americana; _The_
American Sea-Sun-Crown. _By_ John Andrew Peyssonel, _M. D. F.R.S._
p. 843.

CXIII. _An Account of several rare Species of Barnacles. In a Letter
to Mr._ Isaac Romilly, _F.R.S. from_ John Ellis, _Esq; F.R.S._
p. 845.

CXIV. _A further Account of the poisonous Effects of the_ Oenanthe
Aquatica Succo viroso crocante _of_ Lobel, _or Hemlock Dropwort. By_
W. Watson, _M. D. F.R.S._ p. 856.

CXV. _Extract of a Letter to_ John Eaton Dodsworth, _Esq; from Dr._
George Forbes _of_ Bermuda, _relating to the_ Patella, _or_ Limpet
Fish, _found there_. p. 859.

CXVI. _A Discourse on the_ Cinnamon, Cassia, _or_ Canella. _By_
Taylor White, _Esq; F.R.S._ p. 860.

LIX. _An Account of the Effects of Electricity in paralytic Cases. In a Letter to_ John Pringle, _M. D. F.R.S. from_ Benjamin Franklin, _Esq; F.R.S._

[Read Jan. 12, 1758.]

SIR,

THE following is what I can at present recollect, relating to the effects of electricity in paralytic cases, which have fallen under my observation.

Some years since, when the news-papers made mention of great cures performed in Italy or Germany, by means of electricity, a number of paralytics were brought to me from different parts of Pensylvania, and the neighbouring provinces, to be electrised; which I did for them at their request. My method was, to place the patient first in a chair, on an electric stool, and draw a number of large strong sparks from all parts of the affected limb or side. Then I fully charged two six-gallon glass jars, each of which had about three square feet of surface coated; and I sent the united shock of these thro’ the affected limb or limbs; repeating the stroke commonly three times each day. The first thing observed was an immediate greater sensible warmth in the lame limbs, that had received the stroke, than in the others: and the next morning the patients usually related, that they had in the night felt a pricking sensation in the flesh of the paralytic limbs; and would sometimes shew a number of small red spots, which they supposed were occasioned by those prickings. The limbs too were found more capable of voluntary motion, and seemed to receive strength. A man, for instance, who could not the first day lift the lame hand from off his knee, would the next day raise it four or five inches, the third day higher; and on the fifth day was able, but with a feeble languid motion, to take off his hat. These appearances gave great spirits to the patients, and made them hope a perfect cure; but I do not remember, that I ever saw any amendment after the fifth day: which the patients perceiving, and finding the shocks pretty severe, they became discouraged, went home, and in a short time relapsed; so that I never knew any advantage from electricity in palsies, that was permanent. And how far the apparent temporary advantage might arise from the exercise in the patients journey, and coming daily to my house, or from the spirits given by the hope of success, enabling them to exert more strength in moving their limbs, I will not pretend to say.

Perhaps some permanent advantage might have been obtained, if the electric shocks had been accompanied with proper medicine and regimen, under the direction of a skilful physician. It may be, too, that a few great strokes, as given in my method, may not be so proper as many small ones; since, by the account from Scotland of a case, in which two hundred shocks from a phial were given daily, it seems, that a perfect cure has been made. As to any uncommon strength supposed to be in the machine used in that case, I imagine it could have no share in the effect produced; since the strength of the shock from charged glass is in proportion to the quantity of surface of the glass coated; so that my shocks from those large jars must have been much greater than any, that could be received from a phial held in the hand.

I am, with great respect,

SIR,
Your most obedient Servant,
R. Franklin.

London, Dec. 21, 1757.

LX. _Observations on the late Comet in_ September _and_ October 1757; _made at the_ Hague _by Mr._ D. Klinkenberg: _In a Letter to the Rev._ James Bradley, _D. D. Astronomer Royal, and F.R.S. and Member of the Royal Academy of Sciences at_ Paris. _Translated from the_ Low Dutch.

[Read Jan. 12, 1758.]

SIR,

I Hope you will be pleased to excuse the liberty, which I take, of troubling you with my observations on the comet, which made its appearance here, and in other parts of Europe, in the months of September and October last; and which, according to the news-papers, was first observed the 11th September by Mr. Gartner, at Dorlkeurtz near Dresden; then, by me, on the 16th of the said Month, here in the Hague; and afterwards in different places. As I find, that you have observed the comet, I doubt not but that you have done it in the most accurate manner; and my great love for this science induces me to beg, that I may have the happiness of knowing some of your observations. My good friend Mr. Struyk at Amsterdam wrote me some time ago, that he intended to ask the same favour of you; but I have not since heard any further from him. I observed this comet from Septemb. 16th in the morning, until Octob. the 11th in the morning; and found its situations, according to my method, as follows:

_Longit._ _Latit._
1757. ° ´ ° ´
Sept. 16. at 4 h. ante mer. The comet in ♋ 10 15 with 10 10 North.
17 -- 3 -- -- -- -- -- ♋ 14 7 ---- 9 38
18 -- 3¾ -- -- -- -- -- ♋ 18 10 ---- 8 57
19 -- 4 -- -- -- -- -- ♋ 22 1 ---- 8 17
22 -- 2¾ -- -- -- -- -- ♌ 3 46 ---- 6 15
23 -- 4 -- -- -- -- -- ♌ 7 36 ---- 5 24
25 -- 4¼ -- -- -- -- -- ♌ 14 50 ---- 4 6
28 -- 4 -- -- -- -- -- ♌ 24 22 ---- 1 41
Oct. 1 -- 4¾ -- -- -- -- -- ♍ 2 46 ---- 0 12 South.
4 -- 4½ -- -- -- -- -- ♍ 9 45 ---- 1 30
9 -- 4½ -- -- -- -- -- ♍ 20 20 ---- 2 40
11 -- 5 -- -- -- -- -- ♍ 24 46 ---- 3 9

But the two last observations will, in my opinion, differ the most; because, when I made them, I was in some doubt about the adjustment of my instruments; and the comet was then far advanced into the morning rays. I have, since the month of February last to the end of May, made sundry observations on fixed stars, with a telescope of 16 inches, made by Mr. Short; and with a pendulum clock, made after the manner of Mr. Graham, by Mr. Vryhthoff of this place. In the months of February and March, by a medium of eight observations, I found, that by the clock, the star Rigel, in every daily revolution, passed 4 min. 2⁴⁄₉ seconds of time earlier, in the telescope; and in the latter end of May I found, by six observations, (the clock not in the least changed or altered) on the star Spica Virginis, that that star, in every revolution, passed 4 min. 5¹⁄₂₀ sec. earlier, in the same telescope; which intervals differ pretty nearly 2⅗ seconds of time from one another. Whether this difference arises from any defect in the clock, or whether it proceeds from any small difference of velocity of the earth’s motion round its axis, I would have been very glad to have endeavoured to find out by farther inquiry, had not the death of Mr. S. Koenig intervened, and I thereby hindered from continuing my observations. The above observations were taken in the observatory of his illustrious Highness the minor Prince of Orange and Nassau, _&c. &c._ under the direction, and with the approbation of the aforesaid Mr. Koenig. After the death of that gentleman, I petitioned her Royal Highness the Princess Governess of these Provinces, _&c._ that I might have leave to continue my astronomical observations; but as yet I have not been able to obtain her Royal Highness’s permission: otherwise I would have observed this last comet with more exactness. Had I been able to pursue the above-mentioned observations, I would, for the greater certainty in regard to the pendulum, have made use of a farther precaution. By means of a stove, with the help of a thermometer, I would have endeavoured to have kept the room (in which the clock stood) in the winter, and at all times, in the same degree of heat it had at the time I made the observations in the summer. I would also have daily observed and noted the moon’s place, at the time of the observations. Tho’ this is but a slight observation of mine; yet I make no doubt, but that in case, by the different distances of the earth from the sun, and the different distances and situations of the moon with respect to the earth, and the respective effects produced by these causes, any inequality arises in the velocity of the diurnal motion of the earth on its axis, you (who have made the most sublime observations on the aberration of the fixed stars, and more than any mortal ever did before) must have discovered, and are well acquainted, with the same.

As my above-mentioned observations on the comet appeared too incorrect to undertake a calculation for the ascertaining of its path from the theory, I contented myself with effecting it by a construction. By this means I found, on a figure, whose globular or spherical diameter was 13½ Rhineland inches, as follows:

That the comet was in its perihelion the 21st of October, at two of the clock in the afternoon: the place of the perihelion 3 degrees in Leo. The comet’s distance in the perihelion from the sun was about 34 parts, whereof 100 make the mean distance between the sun and the earth. The inclination of the comet’s orbit with the ecliptic 13 degrees; and the southern latitude of the perihelion also 13 decrees: the ascending or north node ☊ 4⅓ degrees in Scorpio; and the comet’s motion direct, or according to the order of the signs of the zodiac. On this supposition I have, for some of the times of observations, estimated the apparent places of the comet, and found them as follows:

_Long._ _Latit._
Sept. 18, at 3¾ ante merid. In ♋ 18¹⁄₁₂ and 9 deg. North.
19 -- 4 -- -- -- ♋ 22 ---- 8⅖
22 -- 2¾ -- -- -- ♌ 3⅝ ---- 6¼
23 -- 4 -- -- -- ♌ 7⅗ ---- 5½
25 -- 4¼ -- -- -- ♌ 14⅔ ---- 4
28 -- 4 -- -- -- ♌ 24⅓ ---- 1¾
Oct. 4 -- 4½ -- -- -- ♍ 9⅓ ---- 2 ---- South.
9 -- 4¾ -- -- -- ♍ 19⅔ ---- 3⅖
11 -- 5 -- -- -- ♍ 23⅛ ---- 3⅘

The observations, which I have taken, to ground the measurement on, are those of the 16th and 23d of September, and of the 1st of October. It appears very evident, not only from this rough calculation, but every other circumstance of this comet, that it is not the same with that in the year 1682: which, on certain accounts, is very desirable to be known; for both here, and in other parts of the Netherlands, there have been some people, who have published mere conjectures; and have ventured (very minutely and exactly, as they pretended) about the time that this comet first made its appearance, to predict the return of the comet of the year 1682. But by the above, the weakness of their pretensions is very evident to all the world: whereas, if this had proved to be the expected comet, they would have assumed to themselves much undue praise, and have pretended to knowlege even superior to the every-where much celebrated Newton and Halley.

It appears also probable to me, that this comet is none of those already calculated, or brought upon a list, by Messieurs Halley and Struyk. It is somewhat remarkable, that the line of the nodes is almost at right angles with the long axis of the ellipsis; which corresponds nearly with the comets of the years 1580, 1683, and 1686: but those had their perihelions northward of the ecliptic; whereas the perihelion of the last, which we have lately seen, was to the southward of the ecliptic.

I have the honour to subscribe myself, with the most perfect esteem for you, and your sublime studies, very respectfully,

SIR,
Your very humble and obedient Servant,
D. Klinkenberg.

Hague, 13th Dec. 1757.

LXI. _Remarks on the different Temperature of the Air at_ Edystone, _from that observed at_ Plymouth, _between the 7th and 14th of_ July 1757. _By Mr._ John Smeaton, _F.R.S._

[Read Jan. 12, 1758.]

SIR,

ON the reading of Dr. Huxham’s letter at the last meeting, some observations occurred to me, concerning the different temperature of the air, which I had observed at the Edystone, from what had been observed by the Doctor at Plymouth, between the 7th and 14th of July last: which having been desired by some members to be put into writing, I beg leave to trouble you with the following.

Edystone is distant from Plymouth about 16 miles, and without the head-lands of the Sound about 11.

The 7th and 8th were not remarkable at Edystone for heat or cold; the weather was very moderate, with a light breeze at east; which allowed us to work upon the rock both days, when the tide served.

About midnight, between the 8th and 9th, the wind being then fresh at east, it was remarkably cold for the season, as I had more particular occasion to observe, on account of a ship that was cast away upon the rocks. The wind continued cold the 9th all day; which was complained of by some of the shipwrecked seamen, who had not time to save their cloaths; and so fresh at east, as prevented our going near the rocks, or the wreck; and so continued till Sunday the 10th; when, seeing no prospect of a sudden alteration of weather, I returned to Plymouth in a sailing boat, wrapped up in my thick coat. As soon as we got within the headlands, I could perceive the wind to blow considerably warmer; but not so warm as to make my great coat uneasy. Having had a quick passage, in this manner I went home, to the great astonishment of the family to see me so wrapped up, when they were complaining of the excessive heat: and indeed, it was not long before I had reason to join in their opinion.

This heat I experienced till Tuesday the 12th, when I again went off to sea, where I found the air very temperate, rather cool than warm; and so continued till Thursday the 14th.

In my journal for Wednesday the 13th I find the following remarks, _viz._ “This evening’s tide” (from 6 A. till 12 A.) “the wind at east, but moderate, with frequent flashes of lightning to the southward. Soon after we got on board the store-vessel, a squall of wind arose from the south-west on a sudden, and continued for about a minute; part of which time it blew so hard, we expected the masts to go by the board: after which it was perfectly calm, and presently after a breeze returned from the east.”

And in the journal of the 14th is entered, “This morning’s tide” (_viz._ from 1 M. to 1 A.) “the air and sea quite calm.”

Hence it appears, how different the temper of the air may be in a small distance; and to what small spaces squalls of wind are sometimes confined.

It may not be amiss further to observe upon this head, that once, in returning from Edystone, having got within about two miles of the Ramhead, we were becalmed; and here we rolled about for at least four hours; and yet at the same time saw vessels, not above a league from us, going out of Plymouth Sound with a fresh of wind, whose direction was towards us, as we could observe from the trim of their sails; and as we ourselves experienced, after we got into it by tacking and rowing.

I am, Sir,

Your most humble Servant,
J. Smeaton.

Furnival’s-Inn Court, 12th Jan. 1758.

LXII. _An Account of the Earthquake felt in the Island of_ Sumatra, _in the_ East-Indies, _in_ November _and_ December 1756. _In a Letter from Mr._ Perry _to the Rev. Dr._ Stukeley, _dated at_ Fort Marlborough, _in the Island of_ Sumatra, Feb. 20. 1757. _Communicated by the Rev._ Wm. Stukeley, _M. D. F.R.S._

[Read Jan. 12, 1758.]

THE earthquake at Lisbon, which you gave me an account of, was certainly the most awful tremendous calamity, that has ever happened in the world. Its effects are extremely wonderful and amazing; and it seems, as you observe, to have been felt in all parts of the globe. On the 3d day of the same month the earthquake of Lisbon happened, I felt at Manna[1] a violent shock myself; and from that time to the 3d of December following I felt no less than twelve different shocks, all which I took an exact account of in my pocket-bock. Since which we have had two very severe earthquakes, felt, we believe, throughout this island[2]. The walls of[3] Cumberland-house[4] were greatly damaged by them. Salop-house[4], my own (formerly Mr. Massey’s), the houses of Laye[5] and Manna, were all cracked by them; and the works at the sugar-plantation[6] received considerable damage. The ground opened near the _qualloe_[7] at Bencoolen, and up the River in several places; and there issued therefrom sulphureous earth, and large quantities of water, sending forth a most intolerable stench. Poblo Point[8] was much cracked at the same time; and some _doosoons_[9] in-land at Manna were destroyed, and many people in them.

These are all the ill effects, that have come to our knowlege; but, it is reasonable to suppose, not all the damage, that has happened upon the island.

LXIII. _Concerning the Fall of Water under Bridges. By Mr._ J. Robertson, _F.R.S._

[Read Jan. 19, 1758.]

SOME time before the year 1740, the problem about the fall of water, occasioned by the piers of bridges built across a river, was much talked of at London, on account of the fall that it was supposed would be at the new bridge to be built at Westminster. In Mr. Hawksmore’s and Mr. Labelye’s pamphlets, the former published in 1736, and the latter in 1739, the result of Mr. Labelye’s computations was given: but neither the investigation of the problem, nor any rules, were at that time exhibited to the public.

In the year 1742 was published Gardiner’s edition of Vlacq’s Tables; in which, among the examples there prefixed to shew some of the uses of those tables drawn up by the late William Jones, Esq; there are two examples, one shewing how to compute the fall of water at London-bridge, and the other applied to Westminster-bridge: but that excellent mathematician’s investigation of the rule, by which those examples were wrought, was not printed, altho’ he communicated to several of his friends copies thereof. Since that time, it seems as if the problem had in general been forgot, as it has not made its appearance, to my knowlege, in any of the subsequent publications. As it is a problem somewhat curious, tho’ not difficult, and its solution not generally known (having seen four different solutions, one of them very imperfect, extracted from the private books of an office in one of the departments of engineering in a neighbouring nation), I thought it might give some entertainment to the curious in these matters, if the whole process were published. In the following investigation, much the same with Mr. Jones’s, as the demonstrations of the principles therein used appeared to be wanting, they are here attempted to be supplied.

PRINCIPLES.

I. _A heavy body, that in the first second of time has fallen the height of a feet, has acquired such a velocity, that, moving uniformly therewith, will in the next second of time move the length of 2 a feet._

II. _The spaces run thro’ by falling bodies are proportional to one another as the squares of their last or acquired velocities._

These two principles are demonstrated by the writers on mechanics.

III. _Water forced out of a larger chanel thro’ one or more smaller passages, will have the streams thro’ those passages contracted in the ratio of 25 to 21._

This is shewn in the 36th prop. of the 2d book of Newton’s Principia.

IV. _In any stream of water, the velocity is such, as would be acquired by the fall of a body from a height above the surface of that stream._

This is evident from the nature of motion.

V. _The velocities of water thro’ different passages of the same height, are reciprocally proportional to their breadths._

For, at some time, the water must be delivered as fast as it comes;
otherwise the bounds would be overflowed.

At that time, the same quantity, which in any time flows thro’ a
section in the open chanel, is delivered in equal time thro’ the
narrower passages; or the momentum in the narrow passages must be
equal to the momentum in the open chanel; or the rectangle under the
section of the narrow passages, by their mean velocity, must be equal
to the rectangle under the section of the open chanel by its mean
velocity.

Therefore the velocity in the open chanel is to the velocity in the
narrower passages, as the section of those passages is to the section
of the open chanel.

But the heights in both sections being equal, the sections are
directly as the breadths;

Consequently the velocities are reciprocally as the breadths.

VI. _In a running stream, the water above any obstacles put therein will rise to such a height, that by its fall the stream may be discharged as fast as it comes._

For the same body of water, which flowed in the open chanel, must
pass thro’ the passages made by the obstacles:

And the narrower the passages, the swifter will be the velocity of
the water:

But the swifter the velocity of the water, the greater is the height,
from whence it has descended:

Consequently the obstacles, which contract the chanel, cause the
water to rise against them.

But the rise will cease, when the water can run off as fast as it
comes:

And this must happen, when, by the fall between the obstacles, the
water will acquire a velocity in a reciprocal proportion to that in
the open chanel as the breadth of the open chanel is to the breadth
of the narrow passages.

VII. _The quantity of the fall caused by an obstacle in a running stream is measured by the difference between the heights fallen from to acquire the velocities in the narrow passages and open chanel._

For just above the fall, the velocity of the stream is such, as would
be acquired by a body falling from a height higher than the surface
of the water:

And at the fall, the velocity of the stream is such, as would be
acquired by the fall of a body from a height more elevated than the
top of the falling stream; and consequently the real fall is less
than this height.

Now as the stream comes to the fall with a velocity belonging to a
fall above its surface;

Consequently the height belonging to the velocity at the fall must be
diminished by the height belonging to the velocity, with which the
stream arrives at the fall.

PROBLEM.

_In a chanel of running water, whose breadth is contracted by one or more obstacles; the breadth of the chanel, the mean velocity of the whole stream, and the breadth of the water-way between the obstacles being given; To find the quantity of the fall occasioned by those obstacles._

Let _b_ = breadth of the chanel in feet.
_v_ = mean velocity of the water in feet per sec.
_c_ = breadth of the water-way between the obstacles.

Now 25: 21∷ _c_: 21 ⁄ 25 _c_ the water-way contracted. _Principle III._

And 21 ⁄ 25 _c_: _b_∷ _v_: 25_b_ ⁄ 21_c_ _v_ the veloc. _per_ sec. in the water-way between the obstacles. _Princip. V._

Also (2_a_)²: _vv_∷ _a_: _vv_ ⁄ 4_a_ the height fallen to acquire the vel. v. I. & II.

And (2_a_)²: (25_b_ ⁄ 21_c_)² × _vv_∷ _a_: (25_b_ ⁄ 21_c_)² × _vv_ ⁄ 4_a_ the height fallen to acquire the vel. 25_b_ ⁄ 21_c_ _v_. I. & II.

Then (25_b_ ⁄ 21_c_)² x (_vv_ ⁄ 4_a_) - (_vv_ ⁄ 4_a_) is the measure of the fall required. VII.

Or ((25_b_ ⁄ 21_c_)² - 1) × _vv_ ⁄ 4_a_ is a rule, by which the fall may be readily computed.

Here _a_ = 16,0899 feet and 4_a_ = 64,3596.

EXAMPLE I. _For London-Bridge._

By the observations made by Mr. Labelye in 1746,

The breadth of the Thames at London-bridge is 926 feet;

The sum of the water-ways at the time of the greatest fall is 236 feet;

The mean velocity of the stream taken at its surface just above bridge is 3⅙ feet _per_ second.

Under almost all the arches there are great numbers of drip-shot piles, or piles driven into the bed of the water-way, to prevent it from being washed away by the fall. These drip-shot piles considerably contract the water-ways, at least ⅙ of their measured breadth, or about 39⅓ feet in the whole.

So that the water-way will be reduced to 196⅔ feet.

Now _b_ = 926; _c_ = 196⅔; _v_ = 3⅙; 4_a_ = 64,3596.

Then 25_b_ ⁄ 21_c_ = 23150 ⁄ 4130 = 5,60532.

And 5,60532² = 31,4196; and 31,4196 - 1 = 30,4196 = (25_b_ ⁄ 21_c_)² - 1.

Also _vv_ = (19 ⁄ 6)² = 361 ⁄ 36; And _vv_ ⁄ 4_a_ = 361 ⁄ (36 × 64,3596) = 0,15581.

Then 30,4196 × 0,15581 = 4,739 feet, the fall sought after.

By the most exact observations made about the year 1736, the measure of the fall was 4 feet 9 inches.

EXAMPLE II. _For Westminster-Bridge._

Altho’ the breadth of the river at Westminster-bridge is 1220 feet; yet, at the time of the greatest fall, there is water thro’ only the thirteen large arches, which amount to 820 feet: to which adding the breadth of the twelve intermediate piers, equal to 174 feet, gives 994 for the breadth of the river at that time: and the velocity of the water just above bridge (from many experiments) is not greater than 2¼ feet _per_ second.

Here _b_ = 994; _c_ = 820; _v_ = 2¼; 4_a_ = 64,3596.

Now 25_b_ ⁄ 21_c_ = 24850 ⁄ 17220 = 1,443.

And 1,443² = 2,082; And 2,082 - 1 = 1,082 = (25_b_ ⁄ 21_c_)² - 1.

Also _vv_ = (⁹⁄₄)² = ⁸¹⁄₁₆; And _vv_ ⁄ 48 = 81 ⁄ (16 × 64,3696) = 0,0786.

Then 1,082 × 0,0786 = 0,084 feet, the fall sought.

Which is about 1 inch; and is about half an inch more than the greatest fall observed by Mr. Labelye.

LXIV. _An Account of the Earthquake in the West Parts of_ Cornwall, July _15th 1757. By the Rev._ William Borlase, _M. A. F.R.S. Communicated by the Rev._ Charles Lyttelton, _LL.D. Dean of_ Exeter, _F.R.S._

[Read Jan. 26, 1758.]

ON Friday the 15th of July, 1757. a violent shock of an earthquake was felt in the western parts of Cornwall.

The thermometer had been higher than usual, and the weather hot, or calm, or both, for eight days before; wind east and north-east. On the 14th in the morning, the wind shifting to the south-west, the weather calm and hazy, there was a shower. The afternoon hazy and fair, wind north-west. The barometer moderately high, but the mercury remarkably variable.

On the 15th in the morning, the wind fresh at north-west, the atmosphere hazy. Being on the sands, half a mile east of Penzance, at 10 A. M. near low water, I perceived on the surface of the sands a very unusual inequality: for whereas there are seldom any unevennesses there, but what are made by the rippling of the water, I found the sands, for above 100 yards square, all full of little tubercles (each as large as a moderate mole-hill), and in the middle a black speck on the top, as if something had issued thence. Between these convexities were hollow basons of an equal diameter. From one of these hollows there issued a strong rush of water, about the bigness of a man’s wrist, never observed there before nor since.

About a quarter after six, P. M. the sky dusky, the wind being at west north-west, it fell quite calm. At half past six, being then in the summer-house at Keneggy, the seat of the Hon. J. Harris, Esq; near Penzance, with some company, we were suddenly alarmed with a rumbling noise, as if a coach or waggon had passed near us over an uneven pavement; but the noise was as loud in the beginning and at the end, as in the middle; which neither the sound of thunder, or of carriages, ever is. The sash-casements jarred: one gentleman thought his chair moved under him; and the gardener, then in the dwelling house (about an hundred yards distant from us) felt the stone pavement of the room he was in move very sensibly.

In what place the shock began, and whether progressive or instantaneous in the several places where it was felt, is uncertain, for want of accurately determining the precise point of time in distant places.

The shock was not equally loud or violent. Its extent was from the isles of Scilly eastward as far as Liskerd, and towards the north as far as Camelford; thro’ which district I shall trace it, according to the best informations I could procure.

In the island of St. Mary, Scilly, the shock was violent. On the shores of Cornwall, opposite to Scilly (in the parish of Senan, near the Land’s-end) the noise was heard like that of a spinning-wheel on a chamber-floor. Below stairs there was a cry, that the house was shaking; and the brass pans and pewter rattled one against another in several houses in the same parish. In the adjoining parish of St. Just, two young men being then swimming, felt a strong and very unusual agitation of the sea. In the town of Penzance, in one house the chamber-bell rung; in another the pewter plates, placed edgeways on a shelf, shifted, and slid to one end of the shelf: and it was every-where perceived more or less, according as people’s attention was engaged.

At Trevailer, the seat of William Veale, Esquire, about two miles from Penzance, the noise was heard, and thought at first to be thunder: the windows shook, and the walls of the parlour, where Mr. Veale sat, visibly moved. The jarring of the windows continued near half a minute; but the motion of the walls not quite so long: and some masons, being at work on a contiguous new building, the upright poles of the scaffolds shook so violently, that, for fear of falling, they laid hold on the walls, which, to their still greater surprize, they found agitated in the same manner. And a person present, who was at London at the time of the two shocks in the year 1751, thought this shock to resemble the second, both in degree and duration[10].

At Marazion, the next market-town east of Penzance, the houses of several persons shook to that degree, that people ran out into the street, lest the houses should fall upon them.

In the borough of St. Ives, on the north sea, six miles north of Penzance, the shock was so violent, that a gentleman, who had been at Lisbon during several shocks, said, that this exceeded all he had met with, except that on the 1st of November 1755, so fatal to that city.

At Tehidy, the seat of Francis Basset, Esq; the rooms shook, and the grounds without doors were observed to move. The shock was felt sensibly at Redruth, St. Columb, Bodman, _&c._ along to Camelford, which is about 90 miles from the isle of Scilly. From Marazion eastward it was felt at several places in like manner, as far as Lostwythyel; but at Liskerd, about ten miles east of Lostwythyel, it was but faintly perceived, and that by a few persons. It was still less sensible at Loo and Plymouth, “scarcely sufficient to excite curiosity or fear”[11].

The times of its duration were various. At Keneggy we thought the noise could not have lasted above six seconds; at Trevailer, not two miles distant to the west, it was thought to have lasted near half a minute; in the parish of Gwynier half a minute; at Ludgvan, three miles east of Penzance, the noise was rather longer than half a minute; but the shaking felt in the garden, and observed in the houses, short and momentary. In Germo great Pinwork, seven miles east of Penzance, it lasted only a few seconds; but in the isles of Scilly it was computed at 40 seconds.

Thus was this earthquake felt in towns, houses, and grounds adjacent; but still more particularly alarming in our mines, where there is less refuge, and consequently a greater dread from the tremors of the earth.

In Carnorth adit, in the parish of St. Just, the shock was sensibly felt 18 fathom deep; in the mine called Boscadzhill-downs, more than 30 fathom.

At Huel-rith mine, in the parish of Lannant, people saw the earth move under them, first quick, then in a slower wavy tremor; and the stage-boards of the little winds or shafts 20 fathom deep were perceived to move.

In Herland mine, commonly called the Manor, in the parish of Gwynier, the noise was heard 55 and 60 fathom deep, as if a studdle[12] had broke, and the deads[13] were set a running. It was nothing like the noise of thunder.

In Chace-water mine the same noise was heard, at least 70 fathom under the surface.

At Huel-rith mine, near Godolphin, the noise was seemingly underneath. I felt (says the director of the mine) the earth move under me with a prodigious swift, and apparently horizontal tremor: its continuance was but for a few seconds of time, not like thunder, but rather a dull rumbling even sound, like deads running under ground. In the smith’s shop the window-leaves shook, and the slating of the house cracked. The whim-house shook so terribly, that a man there at work ran out of it, concluding it to be falling. Several persons then in the mine, working 60 fathom deep, thought they found the earth about them to move, and heard an uncommon noise: some heard the noise, and felt no tremor; others, working in a mine adjoining called Huel-breag, were so frightened, that they called to their companions above to be drawn up from the bottoms. Their moor-house was shaken, and the padlock of their candle-chest was heard to strike against the staples. To shew, that this noise proceeded from below, and not from any concussion in the atmosphere above, this very intelligent captain of the mine[14] observes, from his own experience, that thunder was never known to affect the air at 60 fathoms deep, even in a single shaft pierced into the hardest stone; much less could it continue the sound thro’ such workings as there are in this mine, impeded in all parts with deads, great quantities of timber, various noises, such as the rattling of chains, friction of wheels and ropes, and dashing of waters; all which must contribute to break the vibrations of the air as they descend: and I intirely agree with this gentleman’s conclusion, that thunder, or any other noises from above in the atmosphere, could not be heard at half the depth of this mine. This therefore could be no other than a real tremor of the earth, attended with a noise, owing to a current of air and vapour proceeding upwards from the earth.

I do not hear of any person in those parts, who was so fortunate as to be near any pool or lake, and had recollection enough to attend to the motion of the waters; but it may be taken for granted, that during the tremors of the earth the fluids must be more affected than the solids: nay, the waters will apparently be agitated, when there is no motion of the earth perceptible, as was the case of our ponds and lake-waters in most parts of Britain on the 1st of November 1755. Whence this happens is difficult to say: whether the earth’s bosom undergoes at such times a kind of respiration, and alternately emits and withdraws a vapour thro’ its most porous parts sufficient to agitate the waters, yet not sufficient to shake the earth; or whether the earth, during the agitation of the waters, does rock and vacillate, tho’ not so as to be sensible to man; is what I shall leave to future inquiry.

Earthquakes are very rare in Cornwall. This was but of short duration, and did no harm any-where, as far as I can learn; and it is to be hoped not the sooner forgotten for that reason; but rather remembered with all the impressions of gratitude suitable to an incident so alarming and dangerous, and yet so inoffensive.

LXV. _Some Observations upon the Sleep of Plants; and an Account of that Faculty, which_ Linnæus _calls_ Vigiliæ Florum; _with an Enumeration of several Plants, which are subject to that Law. Communicated to_ Wm. Watson, _M. D. F.R.S. by Mr._ Richard Pultney _of_ Leicester.

[Read Jan. 26, 1758.]

ACosta and Prosper Alpinus, who both wrote near the conclusion of the XVIth century, are, I believe, the first, who recorded that nocturnal change in the leaves of plants, which has since been called _somnus_. It is an observation indeed as old as Pliny’s time, that the leaves of trefoil assume an erect situation[15] upon the coming of storms. The same is observable of our wood-sorrel; and Linnæus adds, of almost all plants with declinated stamina[16]. In the _Trifolium pratense album C. B._ or common white-flowered meadow trefoil, it is so obvious, that the common people in Sweden remark, and prognosticate the coming of tempests and rain from it.

The examples of sleeping plants instanced by Alpinus are but few. That author says, it was common to several Egyptian species[17]; but specifies only the Acaciæ, Abrus, Absus, Sesban, and the Tamarindtree. Cornutus some time afterwards remarked this property in the Pseudo-acacia Americana. From that time it has remained almost unnoticed, till Linnæus, ever attentive to nature’s works, discovered that the same affair was transacted in many other plants; and his observations have furnished us with numerous and obvious examples thereof. Mr. Miller mentions it in the _Medicago arborea Lin. Sp. Pl. 778_. and we may add to the list two other common plants not mentioned by Linnæus: these are the _Phaseolus vulgaris_, common kidney-bean; and the _Trifolium pratense purpureum majus_, or clover-grass: in both which this nocturnal change is remarkably displayed. Doubtless the same property exists in numberless other species; and future observation will very probably confirm Dr. Hill’s sentiment, that no “plant or tree is wholly unaffected by it.”

It is now more than twenty years since Linnæus first attended to this quality in plants. In his _Flora Lapponica_, when speaking of the _Trifolium pratense album_, as above-mentioned, he remarks, that the leaves of the Mimosa, Cassia, Bauhinia, Parkinsonia, Guilandina, and others in affinity with them, were subject to this change in the night time: and he had then carried his observations so far, as to find, that heat and cold were not the cause of this quality; since they were alike influenced by it when placed in stoves, where the temperature of the air was always the same.

The merit of reviving this subject is therefore due to the illustrious Swede; and the naturalist is greatly indebted to him for so far extending his observations thereon.

The subject of the _somnus plantarum_ cannot but be highly entertaining to the lovers of natural knowlege: and such, I apprehend, cannot be less entertained with that faculty, which Linnæus calls _vigiliæ florum_; of which we shall give a brief account.

Previous to our explanation of this affair it is proper to observe, that the flowers of most plants, after they are once opened, continue so night and day, until they drop off, or die away. Several others, which shut in the night-time, open in the morning either sooner or later, according to their respective situation in the sun or shade, or as they are influenced by the manifest changes of the atmosphere. There are however another class of flowers, which make the subject of these observations, which observe a more constant and uniform law in this particular. These open and shut duly and constantly at certain and determinate hours, exclusive of any manifest changes in the atmosphere; and this with so little variation in point of time, as to render the phænomenon well worth the observation of all, whose taste leads them this way.