Part 23

Exhibeat sphærois oblonga ADC_d_ (_Fig._ 7.) terram fluidam, cujus centrum T, AC axis transversus jungens centra terræ et solis vel lunæ, D_d_ axis minor, EO diameter æquatoris, et XZ axis motûs diurni. Centro T et radio TD describatur circulus BD_d_ secans axem transversum AC in B, et agatur BK perpendicularis in TE: tum ex quovis circuli puncto P ductâ PM ad axem XZ normali quæ secet TA in H, sit P_pr_ circumferentia circuli quam punctum P rotatione suâ diurnâ describit, ad cujus quodvis punctum _p_ ducatur T_p_ et producatur donec occurrat superficiei sphæroidis in _q_; deinde demissâ _p_G perpendiculari in PM, et GF perpendiculari in TA, si per puncta A_q_C transire intelligatur ellipsis ellipsi ADC similis et æqualis, erit ex naturâ curvæ, quia sphærois nostra parùm admodùm differt à sphærâ, _pq_ = AB × ((TF)² ⁄ (TP)²) quamproximé. Jam designet U velocitatem particulæ in terræ æquatore revolventis motu diurno circum axem XZ ad distantiam semidiametri TP, eritque ((U × PM) ⁄ TP) velocitas particulæ P circulum P_pr_ describentis, et cum sit TF =(((GM - HM) × TK) ⁄ TP) + TH, erit motus totius lineolæ _pq_ æqualis _pq_ × ((U × PM) ⁄ TP) = ((U × AB × PM) ⁄ (TP)³) × (((GM - HM) × (TK)²) ⁄ TP) + TH, adeoque summa horum motuum in circuitu circuli P_pr_, hoc est, motus superficiei inter circulum P_pr_ et sphæroidem in directione T_p_ contentæ, æquabitur circumferentiæ hujus circuli ductæ in ((U × AB × PM) ⁄ (TP)³) × (((TK)² × (PM)²) ⁄ 2(TP)²) + ((TK)² × (HM)²) ⁄ (TP)²) - ((2TK × HM × TH) ⁄ TP) + (TH)²) sive quia est HM. TM ∷ TK. BK, et TH. HM∷ TP. TK, scribendo D pro circumferentiâ circuli BD_d_, æquabitur ille motus quantitati ((U × AB × D) ⁄ 2(TP)⁶) × ((TK)² × (PM)⁴ + 2(BK)² × (TM)² × (PM)²). Deinde horum motuum summa in toto circuitu globi collecta, hoc est, motus totius materiæ globo BD_d_ incumbentis prodibit æqualis ((U × AB × DD) ⁄ 32) x ((3(TP)² - (BK)²) ⁄ (TP)²). Ubi planeta in plano æquatoris consistit, fit BK = 0, et motus prædictus æqualis ((U × 3AB × DD) ⁄ 32). Motus autem globi QPR circa eumdem axem est (uti facilé demonstratur) ((U × TP × DD) ⁄ 16), adeoque motus terræ totius fit ((U × TP × DD) ⁄ 16) + ((U × AB × DD) ⁄ 32) × ((3(TP)² - (BK)²) ⁄ (TP)²), qui cum idem semper manere debeat, denotet V velocitatem in superficie æquatoris terrestris ubi planeta versatur in plano æquatoris, eritque ((U × TP × DD) ⁄ 16) + ((U × 3AB × DD) ⁄ 32) = ((U × TP × DD) ⁄ 16) + ((U × AB × DD) ⁄ 32) × ((3(TP)² - (BK)²) ⁄ (TP)²); unde scribendo 1 pro TP quatenùs est radius ad sinum BK anguli BTK, habetur V. U∷ TP + (3AB ⁄ 2) - ((AB × (BK)²) ⁄ 2). TP + (3AB ⁄ 2), indeque, quia minima est altitudo AB respectu semidiametri TP, U - V. V∷ AB × (BK)². 2TP, et U - V = V × ((AB × (BK)²) ⁄ 2TP): pro V autem patet scribi posse velocitatem angularem terræ mediocrem quia ab eâ differt quam minimé et ducitur in quantitatem perexiguam ((AB × (BK)²) ⁄ 2TP), et quia tempora revolutionum terræ circa centrum suum sint reciprocé ut motus angulares U, V, fiet differentia revolutionum terræ ubi planeta æquatorem tenet et ubi ab æquatore distat angulo BTK, æqualis 23ʰ 56´ × (AB × (BK)²) ⁄ 2TP. Quoniam igitur est acceleratio horaria ad motum terræ horarium mediocrem circa centrum suum ut AB × (BK)² ad 2 TP sive (quia est sinus _p_ inclinationis eclipticæ ad æquatorem ad radium 1 ut sinus BK ad sinum distantiæ planetæ ab æquinoctio, quem sinum dico K) ut AB × _p_² × K² ad 2 TP; adeoque acceleratio horaria rotationis terræ crescit in ratione duplicatâ sinûs distantiæ planetæ à puncto æquinoctii, et summa omnium illarum accelerationum, quo tempore transit planeta ab æquinoctio ad solstitium, est ad summam totidem motuum horariorum mediocrium, hoc est, acceleratio tota eo tempore genita est ad tempus illud ut summa quantitatum omnium AB × _p_² × K² in circuli quadrante ad summam totidem 2TP, id est, quia summa omnium K² in circuli quadrante dimidium est summæ totidem quadratorum radii, ut AB × _p_² ad 4 TP. Quamobrèm, si denotet P quartam partem temporis planetæ periodici circa terram, erit acceleratio tota motûs terræ circum axem suum in transitu planetæ ab æquinoctio ad solstitium genita æqualis (AB × P × _p_²) ⁄ 4TP, atque eadem erit retardatio in transitu planetæ à solstitio ad æquinoctium. Unde sponte nascitur hoc Theorema: _Est quadratum diametri ad quadratum sinûs obliquitatis eclipticæ ut quarta pars temporis periodici solis vel lunæ ad tempus aliud_; deinde, _est semidiameter terræ ad differentiam semiaxium ut tempus mox inventum ad accelerationem quæsitam_.

Ascensus aquæ AB vi solis debitus est duorum pedum circiter, existente semidiametro terræ mediocri TP = 19615800, unde prodit per theorema acceleratio terræ circa centrum suum gyrantis facta quo tempore incedit sol ab æquinoctio ad solstitium, æqualis 1´´´ 55ⁱᵛ in partibus temporis; et si vi lunæ ascendunt aquæ ad altitudinem octo pedum, acceleratio revolutionis terræ inde orta, quo tempore luna transit ab æquatore ad declinationem suam maximam, erit 34ⁱᵛ: et summa harum accelerationum, quæ obtinet ubi hi duo planetæ in punctis solstitialibus versantur, cum non superet duo minuta tertia temporis cum semisse sive 37 minuta tertia gradûs, vix observabilis erit. _Q. E. I._

Cùm igitur tantilla fit hujusmodi variatio in hypothesi sphæricitatis terræ; qualis evaderet, terrâ existente sphæroide oblatâ, frustrà quis inquireret.

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.

[Read Dec. 14, 1758.]

SIR,

THE history of the Norfolk Boy, which, you inform me, has been communicated to the Royal Society, seems to deserve a place in the memoirs of that illustrious body, as well on account of its utility, as its singularity.

The symptoms in this case most evidently arose from worms in the intestines; which often occasion unaccountable complaints, and frequently elude the most powerful medicines, as they did in the instance before us, till at last they were dislodged by the enormous quantity of oil-paint, which the poor boy devoured; and the cause being thus removed, all the effects ceased.

At first sight it appears wonderful, that this immense quantity of white lead did not prove fatal; and that it was not so, could be owing to nothing but the oil, by which it was enveloped, and its contact and immediate action on the coats of the intestines thereby prevented. But the oil did not only obviate the dangerous effects of this mixture, but appears, to me at least, to have been the chief cause of the success, with which it was happily attended. I speak this with some restriction, because the lead, as its stypticity was thus covered, might, by its weight, assist in removing the verminous filth, especially as the bowels were made slippery by the oil.

Oil has long been observed to be noxious to insects of all kinds, so that not only those, which survive after being cut into several pieces, but those also, which live long with very little air, and those, which revive by warmth after submersion in water, die irrecoverably, if they are immerged in, or covered with oil. Rhedi and Malpighi have made many experiments to this purpose; and account for the event very rationally from the oil stopping up all the air-vessels, which in these animalcula are very numerous, and distributed almost over their whole bodies.

On this account oil has been recommended as a vermifuge both by Andry and Hoffmann, though I believe it has been seldom used in practice in that intention; or at least has not been given in quantities sufficient to answer it. Indeed Hoffmann[222] himself seems not to lay much stress on it as an anthelmintic, recommending it only as serving to line the inside of the intestines, and to relax spasms in them; and therefore as a proper preparative to be given before any acrid purgatives are ventured on.

The medicines commonly prescribed, and most depended on, are either of a virulent and drastic nature, or such as are supposed to be able to destroy those animals by some mechanical qualities _e. g._ to cut, tear, or otherwise affect their tender bodies, and yet not have force enough to lacerate or injure the stomach or intestines. Of the former kind are the leaves and juice of helleboraster, the bark of the Indian cabbage-tree, coloquintida, resin of jalap, glass of antimony, and the like; the effects of which are commonly violent and dangerous, and sometimes fatal. Of the latter class are crude mercury, and the milder preparations of that mineral, aloes and other bitters, tin filings, neutral salts, and vitriolic acids. Every one conversant in practice too well knows, how often these medicines are administred ineffectually. When I had therefore attentively considered the history of the Norfolk Boy, I determined to try the efficacy of oil in such cases, as it seemed capable of producing great effects, and yet could not be attended with any hazard or danger.

The first person, to whom it was given, with this view, was ---- ----, a patient of our Infirmary, who was judged to have worms, but had taken several approved medicines for a considerable time without success. In a consultation with the other physicians, the following form was prescribed.

℞. _Ol. Oliv. lb.ss. Sp. vol. aromat. ʒij M. cap. Cochl. iii. mane et H. S._

The volatile spirit was added here to make the oil saponaceous, and by that means more easily miscible with the juices in the stomach and _primæ viæ_. This medicine answered our expectations, and in a few days brought away several worms.

---- Lacy, a poor boy of the parish of Feckenham in this county, aged 13 years, was, as I was informed, about three or four years ago seized with convulsive fits, which gradually deprived him of his senses, and reduced him to a state of idiocy. He had taken several anthelmintics and purgatives, particularly the _Pulv. Cornachin._ but never had voided any worms, though all the symptoms seemed plainly to shew, that they were the cause of his disorder. As he greedily swallowed any thing, which was offered him, without distinction, I at first ordered him a mixture of linseed oil ℥vij _Tinct. sacr._ ℥j: of which he took four large spoonfuls night and morning. He persisted in the use of this one whole week without at all nauseating it, towards the latter end of which time he voided one round worm of a great length. He now began to shew much aversion to the medicine; on which account the _Tinctur. sacr._ was omitted, and he was ordered to take the oil alone in the same quantities. This he continued to do a fortnight longer, during which time he voided 60 more worms, and in a great measure recovered the use of his reason[223]. This account I had from the Apothecary, who, by my directions, supplied him with the medicines.

Soon after this I ordered the same medicine to be given to Elizabeth Abell, a poor girl in the same neighbourhood, reduced by epileptic fits to such a state of idiocy, as to eat her own excrements. It caused her to void several worms, but she did not recover her senses.

Since this time I have given the oil to several persons with good success, and therefore I cannot but recommend a further tryal of it; since it is a remedy, which may be used with safety in almost any quantity; a character, which very few of the anthelmintic medicines deserve.

It is probable, that some oils are more destructive to worms than others. Andry (_Traité de la Generation des Vers, cap. 8_) prefers nut oil, and tells us, that a human worm, voided alive, being put into that oil, died instantly; whereas another worm, voided at the same time, lived several hours in oil of sweet almonds, though in a languishing state. This difference he afterwards (_Cap. 9_) endeavours to account for, by supposing, that the oil of almonds is more porous, and consequently less able to preclude the entrance of air into the worms. And indeed there is some reason to conclude, that oils, which dry in the open air, such as nut and linseed oils, are of a closer texture, less mixed with water, and consequently more anthelmintic, than those oils, which freeze by cold, and will not dry in the open air;[224] such as those from olives or almonds. Andry tells us, that at Milan the mothers have a custom to give their children once or twice a week toasts dipt in nut oil, with a little wine, to kill the worms: and I know a lady in the country, who gives the poor children in her neighbourhood the same oil with great success.

I would recommend this remedy to be used in as large doses as the stomach will well bear: to which purpose it may be adviseable to join it either with aromatics, bitters, or essential oils, such as the case may require. Andry orders the oil to be taken fasting, assigning this for a reason, that the stomach being then most empty, it more readily embraces and stifles the worms. During this course it will be necessary, at proper intervals, to give rhubarb, mercurial or aloetic medicines.

I cannot close this paper without observing, that, from the history of the Norfolk Boy, we may learn, in similar cases, where the head is not idiopathic, never to despair absolutely of a cure, notwithstanding the disease has been of very long standing. For in this boy, though the oppression in the brain and nerves had continued many years, and had been so violent, as to deprive him not only of his intellectual faculties, but almost all his sensations; yet were not the organs much impaired thereby, but he recovered all his senses again, as soon as the irritation and spasms in the intestines, which first caused all these terrible symptoms, were removed. The same thing in a less degree was observable in the Feckenham Boy, mentioned before; and we have had two remarkable instances of the same kind at the Worcester Infirmary; where a boy and his sister, of the name of Moyses, received a perfect cure, and recovered the entire use of their senses, after having been rendered idiots (though not in so high a degree as the Norfolk Boy) for more than two years, by epileptic fits proceeding from worms.

J. Wall.

Worcester Dec. 7, 1748.

_P. S._ As the following history has some analogy with the subject we are now upon, I beg leave to subjoin it by way of postscript.

A young girl of the name of Lowbridge, at Ledbury, in Herefordshire, nine years old, had been long troubled with a gnawing pain at the stomach, which growing gradually more violent, I was at last called to her. About a quarter of an hour before I reached the house, she was seized with a violent vomiting, whereby she brought up an amazing number of living animals supposed, to be upwards of a thousand, together with a vast quantity of clear viscid phlegm. In shape they exactly resembled millepedes, except that some of them, being examined by a magnifying glass, appeared to have a small filament, which arose from the middle of the belly, and might probably have served to fix them to their nidus. They were of different sizes, from that of the largest millepede, to some, that were scarce perceptible; so that they appeared to have been generated at different times, and grown in the stomach. As the child was suddenly seized with this effort to vomit, she discharged her stomach on the floor of the parlour where she was sitting. The millepedes, they told me, were at first very lively, and crept briskly different ways; but they did not live long in the open air. They were lying in the slime when I came to her, so that I could not be imposed on as to the verity of the fact. After this evacuation, the child’s stomach grew perfectly easy, and continued so.

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

[Read Dec. 14, 1758.]

I Shall call this insect by this name, because of the resemblance it bears to the flower called _Corona Solis_; since it is, like this, open and spread.

This insect adheres to the rocks by its basis, which is flat and round; and tho’ this roundness is sometimes mis-shapen, it is only occasioned by the inequalities of the rocks, to which it sticks. Its diameter is about two or three inches, bearing, from the center, certain rays, like white nerves, upon a moist flesh, of a livid violet colour. These rays or nerves pass from the centre to the circumference; they, too, consist of a soft fleshy substance, which resembles bowels or intestines; the whole length of which is covered with glandulous bodies of a dirty grey colour; and all these glands filled up the middle of the fish, making the flowrets, or petals, that form the disk of the flowers. There is an infinite number of these glands attached to those filets or nerves, all very distinct from one another: these filets are well ranged when viewed downwards; but the upper part is covered by these glands, which are placed in a confused manner. These filets pass to the circumference, forming an edge full of rugosities, which leaves the body of the animal full of flaws. These hard bodies, upon which it lives, are not always permanent in the same place, but capable of changing their places from this edge or circumference; like a skin or texture of fibres or flesh, such as the body of the sea snail I have already described; of the same thickness, of a greenish colour, and sometimes of a greenish spotted grey, without shell, bone, or stay. The body or muscular fleshy skin raises itself up perpendicularly to three inches; rounds itself at the top, when it is touched; but it leaves a hole like a sphincter, formed by the reunion of the fleshy body, which enlarges itself again. The base opens to the whole extent of the bottom, makes a reversed prepuce, and immediately brings to view three rows of _papillæ_, which are of a conical figure, of one or two lines long, resembling the glands under the tongues of oxen, and which may here be compared to the demi-flowers or radiated flowers of the _Corona Solis_.

After this threefold ray of conical pointed _papillæ_, there appears a body of a livid violet colour; I took it for a particular substance or body; but having examined it, I observed it was only a pellicle, or membrane, that covered a part of the _papillæ_ I mentioned. This membrane has sixteen separations, which form kinds of purses, and yet leave, in the center of the animal, an empty space, wherein several glands are brought in view. I do not know, whether, in the natural state, these membranes do not retire to the circumference, in order to discover the glands within, which they usually hide, and which fill up all the middle of the crown; but when the fleshy body is gone up again, it covers all the interior parts, closes them in, and preserves them from the touch of any extraneous body. I cannot tell how these fishes live, or what is their mechanism; for I could not distinguish either a mouth, or any _viscera_, nor any other organ serving to their nourishment.

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._

[Read Dec. 21, 1758.]

London, Dec. 21. 1758.

Dear Sir,

THOSE rare and very extraordinary new species of Barnacles, which you have lately received from abroad, are so different from any of the common species, that I have seen, that I was resolved to inquire into the nature of an animal, which, like a Proteus, appears in so many different shapes or coverings in different parts of the world. For this end I have consulted that excellent collection in the British Museum, and some others in the cabinets of my curious friends.

In this inquiry I met with some very rare ones, which have not yet been described, as you will observe in the annexed plate [_See_ TAB. XXXIV.], where I have given exact drawings of yours, as well as the other species of this genus.

This marine animal is called, by writers on natural history, Balanus, and Concha Anatifera: but the celebrated Professor at Upsal, Dr. Linnæus, calls the internal active part, or fish, the Animal Triton, and the covering or testaceous habitation Lepas, which he says is a multivalved shell, composed of unequal valves. The Animal Triton he describes, as having an oblong body, a mouth with a tongue in it, twisted about in a spiral manner; sixteen tentacula or claws: six of the hinder ones on each side, he says, are cheliferous.

This account differing from that given by the ingenious Mr. Turberville Needham, F.R.S. in his Microscopical Essays, I shall give the character of this animal, as it appeared to me from the many observations I made on it, while alive in salt water; and these I compared not only with many dried specimens of other varieties, but likewise with some of yours, that were preserved in spirits; and I found that the parts of the animal agree in all the species.