Chapter VIII: Part 8

_Gen tchis khan_, or _Temoug in_, the founder of the dynasty _Yuen_, is the dynasty of the Mongol or Mogol Tartars. Besides the founder of this dynasty, there are ten other emperors of this dynasty, whose memory is honoured in the _Ti ouang miao_. The four first emperors of this dynasty, _viz. Gen tchis khan_, _Ogo tay_, _Kouey yevou_, and _Meng ko_, reigned in the northern provinces, and had not conquered all China. The emperor _Cobilay_, or _Koublay_, in Chinese _Yuen chitsou_, completed the conquest of China.

The founder of the dynasty _Ming_, and the eleven emperors of this dynasty.

The emperor _Ogo tay_, the second of the dynasty _Yuen_, completed the destruction of the dynasty of the eastern Tartars, called _Kin_. It reigned to the north as long as the dynasty _Song_ reigned to the south. In the _Ti ouang miao_ is honoured the memory of the founder of this dynasty _Kin_, and four other emperors of it.

The founder of the Tartar dynasty _Kin_ destroyed the dynasty of the Tartars _Ki tan_, called _Leao_, which conquered a great part of North China and Tartary.

In the _Ti ouang miao_ is honoured the memory of this Tartar dynasty _Leao_, and five other emperors of the Tartars _Ki tan_, whose country was in that of Parin in Tartary, among the Mongou or Mogols.

_Continuation of the Remarks on the_ Ti ouang miao.

2. In the palace of Peking, and elsewhere, there are great halls, in which honours are paid to the memory of the deceased emperors of the reigning dynasty of the _Mantcheou_. The first and second emperor reigned in East Tartary. The emperor _Chun tchi_ began to reign in China. If we reckon the present emperor in the number, there are six emperors _Mantcheou_. Father Couplet, and others, are mistaken in reckoning one more. This error was occasioned by the years of the reign of _Tay hong_, the second emperor, having had two names. Father Couplet, and others, took the two names of the years of the reign for the name or title of the two emperors.

3. In the _Ti ouang miao_ is honoured the memory of some illustrious persons in the different dynasties. The same is done in the hall, where honour is paid to the memory of the deceased emperors _Montcheou_: and there are there tablets for so many illustrious persons among those emperors.

4. In the _Ti ouang miao_ are placed none of the emperors of the dynasty _Hin_ before Christ, nor any of those between the dynasties _Tang_ and _Han_, nor of those of the five small dynasties after that of _Tang_. Besides, in each dynasty there are some emperors, whose tablets are not placed in the _Ti ouang miao_. The reigning dynasty has not thought it a duty to pay honours to those emperors, but considered them as unworthy the pompous title of _Tin tse_, or _Sons of Heaven_.

5. The Tartars _Sien pi_, who came from the confines of _Leao tong_ and Mongol or Mogol Tartary, had hords named _To pa_. One of these hords made themselves masters of Tartary _Leao tong_, and of several northern provinces of China. This Tartar power has the Chinese name of _Ouey_. It has produced several great princes. The year of Christ 386 is reckoned the first of that dynasty[153], which reigned above 180 years. I do not know why the reigning dynasty has not placed the name of any of these emperors in the _Ti ouang miao_.

6. If we suppose, first, that all the books of the history of China should be lost, or the contents of them should not be known in Europe; and secondly, that the catalogue of the emperors, who are mentioned in the _Ti ouang miao_, should fall into the hands of some European critics; it is probable, that such a catalogue would occasion many false reasonings with relation to the succession of the emperors, who have reigned in China.

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._

[Read June 8, 1758.]

SIR,

THE reverend and ingenious Dr. Hales, from whom mankind has received such benefit by his useful application of ventilators, being inclined to extend its use to those, who work in mines at great depths under ground, where the lives of many are lost by damps and noxious vapours, occasioned by the want of a free circulation of air; and finding by experience, that ventilators worked by wind do not operate above one third part of the year, and in calm hot weather, when most wanted, do not operate at all; did me the honour of applying to me for assistance in contriving a machine to work the ventilator, by the help of the fire-engine, which is now generally used in all mines for drawing off the water; and which I have accordingly attempted, and hope it will answer the purpose.

As the lever of the fire-engine works up and down alternately, and performs at a common medium about a dozen strokes in a minute, it was necessary to contrive some way to make the beam, tho’ moving alternately, to turn a wheel constantly round one way, and also to increase the number of strokes to fifty or sixty in a minute.

The model of a machine for this purpose is composed of four wheels of different sizes, two clicks, three pinions, and a fly; which is put into motion by the part of a wheel fixed to the arch of the lever of the fire-engine.

The wheel, which is turned by the lever, or rather moved up and down by it, is loose on its arbor; and likewise one of the rochets, and the wheel next to it. The outside rochet and outside wheel are fixed on the arbor.

There are two pinion-wheels fixed on the arbor; one on each side, near the edge of the wheel moved by the lever, which turns them.

There are also two clicks; one fixed to the great wheel, the other to the frame. These exclusive of the wheel that moves the fly.

The effect is, When the lever moves the wheel downwards, its click forces the rochet fixed on the arbor to move along with it, and the other wheels the same way. When it moves upwards, the click fixed on the frame stops the larger rochet, and the wheel next to it, which are pinned together. This wheel being stopped, and the great wheel carried upwards by the lever, the pinion towards the edge of the great wheel is forced round it, and moves the pinion on the other side the great wheel; which pinion moves the wheel fixed on the arbor, the contrary way to the great wheel, which is carried upwards by the lever. By which means, the arbor is constantly turned the same way, when the lever of the fire-engine is moved either upwards, or downwards.

Upon the arbor there is also another great wheel fixed, which turns a pinion: on the arbor of which pinion is a crank to move the ventilator, and also a fly fixed to the end, to help the motion of the crank, which in the model is turned three times for each stroke of the lever, and may be increased or diminished, according to the number of teeth in the pinion.

The number of teeth in the great wheel moved by the lever is sixty-six; but need not have teeth above half way round.

The wheel fixed to the rochet has thirty-three teeth, and its pinion eleven.

The wheel fixed on the arbor, on the outside, has twenty-four teeth, and its pinion sixteen.

The wheel, which turns the fly, has ninety teeth, and the pinion turn’d by this wheel ten.

The greater the number of teeth in the rochets, the better.

This machine may also be applied to other useful purposes at mines; and it may be easily made to turn a mill to grind corn; or to turn a wheel to raise coals, or whatever else is wanted to be raised from the mines. As I have not met with any thing of the kind described, I take the liberty of desiring you to lay it before the Society; and I hope it may be made some way useful to the public.

I am, Sir,

Your most obedient humble Servant,
Kea. Fitz-Gerald.

Poland-Street, June 7th, 1758.

_Explanation of the Three Tables._

The wheel A (_Tab. 26._), which is turned by the lever B (_Tab. 27._), or rather moved up and down by it, is loose on its arbor; and likewise one of the rochets C (_Tab. 26._), and the wheel next to it D. The outside rochet E, and outside wheel F, are fixed on the arbor.

There are two pinion-wheels G and H fixed on one arbor; one on each side, near the edge of the wheel A, moved by the lever.

There are also two clicks _a_ and _b_; one _a_ fixed to the great wheel A, the other _b_ fixed to the frame. These exclusive of the wheel I, that moves the pinion _c_, on the arbor of which, the crank _d_, and fly _e_, (_Tab. 27._) are fixed.

The effect is, when the lever B moves the wheel A downwards; its click _a_, forces the rochet E, fixed on the arbor K, to move along with it, and the other wheels the same way. When it moves upwards, the click _b_ fixed to the frame, stops the larger rochet C, and the wheel D next to it, which are pinned together; and as the wheel A is carried upwards by the lever, the pinion G towards the edge of it, is forced round the wheel D, and moves the pinion H, on the other side the great wheel A, which moves the wheel F fixed on the arbor K, the contrary way to the wheel A. By which means, the arbor K is constantly turned the same way, when the lever of the fire-engine moves either upwards, or downwards.

The pinion G, by being made proportionally smaller than the pinion H, keeps the arbor K in the same swiftness of motion, when the lever is moved upwards, as downwards.

_J. Mynde sc._]

_J. Mynde sc._]

_J. Mynde sc._]

The great wheel I, fixed on the arbor K, turns the pinion _c_, on the arbor of which the crank _d_ (to move the ventilator), and the fly _e_ (to help the motion), are fixed. The pinion _c_, is turned three times by each alternate motion of the lever; which may be increased, or diminished, according to the number of teeth in the pinion _c_.

The number of teeth in the wheel A is sixty-six, but need not be toothed above half way. Instead of this wheel there might be a barrel, with a chord round it, fixed at each end of the arch of the lever, and projecting somewhat from it; which, by the motion of the lever, would work in the same manner in other respects, and be easier made, and at less expence.

The wheel D fixed to the rochet C has thirty-three teeth, and its pinion G eleven.

The wheel F fixed on the arbor K has twenty-four teeth, and its pinion H sixteen.

The greater the number of teeth in the rochets, the better.

_Tab. 26._ contains the plan (in parts) of the whole machine, except the lever B and fly _e_, which are in _Tab. 27._

_Tab. 27._ also contains the elevation of the arbor, with its different fixtures; _viz._

_Fig. 1._ The rochet C and wheel D (_Tab. 26._) fixed together.

2. The outside wheel F that works the pinion-wheel H (_Tab. 26_).

3. The two pinion-wheels H and G (_Tab. 26._) fixed on their arbor.

4. The same fixed to the wheel A (_Tab. 26._) by means of two cocks
_u_ and _w_ (_Tab. 26._).

5. The arbor, with the wheel L and rochet E fixed; _t_ the place,
where the wheel A is fixed.

6. The elevation of the whole arbor.

_Tab. 28._ The elevation of the whole machine, the lever B (_Tab. 27._) working the wheel A (_Tab. 26_).

_s_ (_Tab. 26._) a thin piece of metal screwed to the wheel A, to
keep it in its place _t_ on the arbor K (_Tab. 27._)

_u_ (_Tab. 26._) the cock, that fastens the pinion G, to the inside
of the wheel A.

_w_ (_Tab. 26._) the cock, that fastens the pinion H on the outside
of the wheel A.

_x_ (_Tab. 27._) the arbor, on which the pinions G and H are fixed.

_y_ (_Tab. 26._) a spring, that keeps the click _a_ in its place.

L (_Tab. 26._) a frame-plate with the centers marked.

_z_ The opposite hole enlarged, to admit the pinion _c_ to pass
through.

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._

[Read June 8, 1758.]

_To the Rev. Dr._ Birch, _Secret. R. S._

Dear Sir,

I Have received the inclosed paper from Mr. Dollond, which he desires may be laid before the Royal Society. It contains the theory of correcting the errors arising from the different refrangibility of the rays of light in the object-glasses of refracting telescopes; and I have found, upon examination, that telescopes made according to this theory are intirely free from colours, and are as distinct as reflecting telescopes. I am,

Dear Sir,
Your most obedient humble Servant,
Ja. Short.

Surrey-street, 8th June, 1758.

IT is well known, that a ray of light, refracted by passing thro’ mediums of different densities, is at the same time proportionally divided or spread into a number of parts, commonly called homogeneal rays, each of a different colour; and that these, after refraction, proceed diverging; a proof, that they are differently refracted, and that light consists of parts that differ in degrees of refrangibility.

Every ray of light passing from a rarer into a denser medium, is refracted towards the perpendicular; but from a denser into a rarer one, from the perpendicular; and the sines of the angles of incidence and refraction are in a given ratio. But light consisting of parts, which are differently refrangible, each part of an original or compound ray has a ratio peculiar to itself; and therefore the more a heterogene ray is refracted, the more will the colours diverge, since the ratios of the sines of the homogene rays are constant; and equal refractions produce equal divergencies.

That this is the case when light is refracted by one given medium only, as suppose any particular sort of glass, is out of all dispute, being indeed self-evident; but that the divergency of the colours will be the same under equal refractions, whatsoever mediums the light may be refracted by, tho’ generally supposed, does not appear quite so clearly.

However, as no medium is known, which will refract light without diverging the colours, and as difference of refrangibility seems thence to be a property inherent in light itself, Opticians have, upon that consideration, concluded, that equal refractions must produce equal divergencies in every sort of medium: whence it should also follow, that equal and contrary refractions must not only destroy each other, but that the divergency of the colour from one refraction would likewise be corrected by the other; and there could be no possibility of producing any such thing as refraction, which would not be affected by the different refrangibility of light; or, in other words, that however a ray of light might be refracted backwards and forwards by different mediums, as water, glass, _&c._ provided it was so done, that the emergent ray should be parallel to the incident one, it would ever after be white; and, conversely, if it should come out inclined to the incident, it would diverge, and ever after be coloured. From which it was natural to infer, that all spherical object-glasses of telescopes must be equally affected by the different refrangibility of light, in proportion to their apertures, whatever material they may be formed of.

But it seems worthy of consideration, that notwithstanding this notion has been generally adopted as an incontestable truth, yet it does not seem to have been hitherto so confirmed by evident experiment, as the nature of so important a matter justly demands; and this it was that determined me to attempt putting the thing to issue by the following experiment.

I cemented together two plates of parallel glass at their edges, so as to form a prismatic or wedge-like vessel, when stopped at the ends or bases; and its edge being turned downwards, I placed therein a glass prism with one of its edges upwards, and filled up the vacancy with clear water: thus the refraction of the prism was contrived to be contrary to that of the water, so that a ray of light transmitted thro’ both these refracting mediums would be refracted by the difference only between the two refractions. Wherefore, as I found the water to refract more or less than the glass prism, I diminished or increased the angle between the glass plates, till I found the two contrary refractions to be equal; which I discovered by viewing an object thro’ this double prism; which, when it appeared neither raised nor depressed, I was satisfied, that the refractions were equal, and that the emergent rays were parallel to the incident.

Now, according to the prevailing opinion, the object should have appeared thro’ this double prism quite of its natural colour; for if the difference of refrangibility had been equal in the two equal refractions, they would have rectified each other: but the experiment fully proved the fallacy of this received opinion, by shewing the divergency of the light by the prism to be almost double of that by the water; for the object, tho’ not at all refracted, was yet as much infected with prismatic colours, as if it had been seen thro’ a glass wedge only, whose refracting angle was near 30 degrees.

_N. B._ This experiment will be readily perceived to be the same as
that which Sir Isaac Newton mentions[154]; but how it comes to differ
so very remarkably in the result, I shall not take upon me to account
for; but will only add, that I used all possible precaution and care
in the process, and that I keep the apparatus by me to evince the
truth of what I write, whenever I may be properly required so to do.

I plainly saw then, that if the refracting angle of the water-vessel could have admitted of a sufficient increase, the divergency of the coloured rays would have been greatly diminished, or intirely rectified; and there would have been a very great refraction without colour, as now I had a great discolouring without refraction: but the inconveniency of so large an angle, as that of the vessel must have been, to bring the light to an equal divergency with that of the glass prism, whose angle was about 60 degrees, made it necessary to try some experiments of the same kind, by smaller angles.

I ground a wedge of common plate glass to an angle of somewhat less than 9 degrees, which refracted the mean rays about 5 degrees. I then made a wedge-like vessel, as in the former experiment, and filling it with water, managed it so, that it refracted equally with the glass wedge; or, in other words, the difference of their refractions was nothing, and objects viewed thro’ them appeared neither raised nor depressed. This was done with an intent to observe the same thing over again in these small angles, which I had seen in the prism: and it appeared indeed the same in proportion, or as near as I could judge; for notwithstanding the refractions were here also equal, yet the divergency of the colours by the glass was vastly greater than that by the water; for objects seen by these two refractions were very much discoloured. Now this was a demonstration, that the divergency of the light, by the different refrangibility, was far from being equal in these two refractions. I also saw, from the position of the colours, that the excess of divergency was in the glass; so that I increased the angle of the water-wedge, by different trials, till the divergency of the light by the water was equal to that by the glass; that is, till the object, tho’ considerably refracted, by the excess of the refraction of the water, appeared nevertheless quite free from any colours proceeding from the different refrangibility of light; and, as near as I could then measure, the refraction by the water was about ⁵⁄₄ of that by the glass. Indeed I was not very exact in taking the measures, because my business was not at that time about the proportions, so much as to shew, that the divergency of the colours, by different substances, was by no means in proportion to the refractions; and that there was a possibility of refraction without any divergency of the light at all.

Having, about the beginning of the year 1757, tried these experiments, I soon after set about grinding telescopic object-glasses upon the new principles of refractions, which I had gathered from them; which object-glasses were compounded of two spherical glasses with water between them. These glasses I had the satisfaction to find, as I had expected, free from the errors arising from the different refrangibility of light: for the refractions, by which the rays were brought to a focus, were every-where the differences between two contrary refractions, in the same manner, and in the same proportions, as in the experiment with the wedges.

However, the images formed at the foci of these object-glasses were still very far from being so distinct as might have been expected from the removal of so great a disturbance; and yet it was not very difficult to guess at the reason, when I considered, that the radii of the spherical surfaces of those glasses were required to be so short, in order to make the refractions in the required proportions, that they must produce aberrations, or errors, in the image, as great, or greater, than those from the different refrangibility of light. And therefore, seeing no method of getting over that difficulty, I gave up all hopes of succeeding in that way.

And yet, as these experiments clearly proved, that different substances diverged the light very differently, in proportion to the refraction; I began to suspect, that such variety might possibly be found in different sorts of glass, especially as experience had already shewn, that some made much better object-glasses, in the usual way, than others: and as no satisfactory cause had as yet been assigned for such difference, there was great reason to presume, that it might be owing to the different divergency of the light by their refractions.

Wherefore, the next business to be undertaken, was to grind wedges of different kinds of glass, and apply them together, so that the refractions might be made in contrary directions, in order to discover, as in the foregoing experiments, whether the refraction and divergency of the colours would vanish together. But a considerable time elapsed before I could set about that work; for tho’ I was determined to try it at my leisure, for satisfying my own curiosity, yet I did not expect to meet with a difference sufficient to give room for any great improvement of telescopes; so that it was not till the latter end of the year that I undertook it, when my first trials convinced me, that this business really deserved my utmost attention and application.

I discovered a difference, far beyond my hopes, in the refractive qualities of different kinds of glass, with respect to their divergency of colours. the yellow or straw-coloured foreign sort, commonly called Venice glass, and the English crown glass, are very near alike in that respect, tho’ in general the crown glass seems to diverge the light rather the least of the two. The common plate glass made in England diverges more; and the white crystal or flint English glass, as it is called, most of all.

It was not now my business to examine into the particular qualities of every kind of glass that I could come at, much less to amuse myself with conjectures about the cause, but to fix upon such two sorts as their difference was the greatest; which I soon found to be the crown, and the white flint or crystal. I therefore ground a wedge of white flint of about 25 degrees, and another of crown of about 29 degrees, which refracted nearly alike; but their divergency of the colours was very different. I then ground several others of crown to different angles, till I got one, which was equal, with respect to the divergency of the light, to that in the white flint: for when they were put together, so as to refract in contrary directions, the refracted light was intirely free from colour. Then measuring the refractions of each wedge, I found that of the white glass to be to that of the crown nearly as 2 to 3; and this proportion would hold very nearly in all small angles. Wherefore any two wedges made in this proportion, and applied together, so as to refract in a contrary direction, would refract the light without any difference of refrangibility.

To make therefore two spherical glasses, that shall refract the light in contrary directions, it is easy to understand, that one must be concave, and the other convex; and as the rays are to converge to a real focus, the excess of refraction must evidently be in the convex; and as the convex is to refract most, it appears from the experiment, that it must be made with crown glass, and the concave with white flint glass.

And further, as the refractions of spherical glasses are in an inverse ratio of their focal distances; it follows, that the focal distances of the two glasses should be inversely as the ratio’s of the fractions of the wedges: for being thus proportioned, every ray of light, that passes thro’ this combined glass, at whatever distance it may pass from its axe, will constantly be refracted, by the difference between two contrary refractions, in the proportion required; and therefore the different refrangibility of the light will be intirely removed.

Having thus got rid of the principal cause of the imperfection of refracting telescopes, there seemed to be nothing more to do, but to go to work upon this principle: but I had not made many attempts, before I found, that the removal of one impediment had introduced another equally detrimental (the same as I had before found in two glasses with water between them): for the two glasses, that were to be combined together, were the segments of very deep spheres; and therefore the aberrations from the spherical surfaces became very considerable, and greatly disturbed the distinctness of the image. Tho’ this appeared at first a very great difficulty, yet I was not long without hopes of a remedy: for considering, the surfaces of spherical glasses admit of great variations, tho’ the focal distance be limited, and that by these variations their aberrations may be made more or less, almost at pleasure; I plainly saw the possibility of making the aberrations of any two glasses equal; and as in this case the refractions of the two glasses were contrary to each other, their aberrations, being equal, would intirely vanish.

And thus, at last, I obtained a perfect theory for making object-glasses, to the apertures of which I could scarce conceive any limits: for if the practice could come up to the theory, they must certainly admit of very extensive ones, and of course bear very great magnifying powers.

But the difficulties attending the practice are very considerable. In the first place, the focal distances, as well as the particular surfaces, must be very nicely proportioned to the densities or refracting powers of the glasses; which are very apt to vary in the same sort of glass made at different times. Secondly, the centres of the two glasses must be placed truly on the common axis of the telescope, otherwise the desired effect will be in a great measure destroyed. Add to these, that there are four surfaces to be wrought perfectly spherical; and any person, but moderately practised in optical operations, will allow, that there must be the greatest accuracy throughout the whole work.

Notwithstanding so many difficulties, as I have enumerated, I have, after numerous trials, and a resolute perseverance, brought the matter at last to such an issue, that I can construct refracting telescopes, with such apertures and magnifying powers, under limited lengths, as, in the opinion of the best and undeniable judges, who have experienced them, far exceed any thing that has been hitherto produced, as representing objects with great distinctness, and in their true colours.

John Dollond.

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. F.R.S._

6 June, 1758.

[Read June 15, 1758.]

IN the month of January 1757, I was concerned for a young gentle-woman, who, if the number, continuance, and frequency of their returns, be considered, suffered the most violent and severe convulsions I ever knew. At some times the muscular spasms were general; at other times single muscles only, or a number of them, subservient to some particular purpose in the animal oeconomy, were affected. And such was the peculiarity of this case, that after and in proportion as any single muscle, or any determined number of muscles, had been in a state of spasm, a paralytic inability succeeded to those muscles, which very much disordered and impaired, and several times even for no small continuance prevented the patient from performing, several of her necessary functions. When the muscles, for instance, subservient to deglutition had been convulsed, for many hours after the fits had left her, she has not been able to swallow a single drop of liquid: so that when attempts have been made to cause her to drink, unless the liquor was immediately thrown back, there was imminent danger of her being strangled. When her eyes have been affected, several times a compleat _gutta serena_, and total blindness, has ensued; the patient being able to bear the strong day-light with open eyes, without being sensible of its influence, or in the least contracting her widely dilated pupils. After one of these fits the blindness continued full five days; and I began to be in fear for the return of her sight.

You, Sir, who are so excellently well versed in the animal oeconomy, are not to be informed, that vocification is performed in the _aspera arteria_; but that the articulation of sounds into syllables and words is modulated principally by the tongue, and muscles about the larynx. In the case before you, very early in the disease, the spasms seized the muscles about the larynx: the consequence of which was, that after they were over, the patient was unable to utter a word. This faculty however she again once recovered; but it continued a very short time, as the fits returned, which again left her deprived of the power of speech. After having lost her voice a second time, her power of speech did not return, even after she was freed from her convulsions, and her general health restored. Fourteen months passed, whilst this patient continued absolutely speechless; when, after having violently heated herself by four hours dancing, on a sudden her power of speech returned, and it has continued perfectly free ever since.

What is still further remarkable in this case is, that during the whole time of this patient’s continuing speechless, her life was rendered yet more uncomfortable by her having, from the injury to her brain by the spasms, forgot how to write, so as to express her meaning that way: but upon the recovery of her speech, this faculty likewise returned, which she has retained ever since. During the severity of this disease, which continued several weeks, almost every day of which, from the number and violence of the convulsions, I feared would be the patient’s last, nothing was left unattempted, which I imagined could tend to prevent the return of the spasms, or lessen their effects. My endeavours so far happily succeeded, that her fits did not return; but the consequences of them continued, more particularly her inability to speak. After some months however, when she was recruited in her strength, I was desirous of trying the effects of electricity, more particularly applied about her throat. This was accordingly attempted; but such was the state of her nerves, and their sensibility to its effects, that electrizing brought back the fits, which again affected her sight: so that I was compelled to desist, lest, in endeavouring to restore her speech, I might not only fail in this attempt, but might bring possibly on a permanent blindness. I determined therefore to trust the whole to time, which has happily removed all her complaints.

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._

_To the Rev._ Tho. Birch, _D. D. Secret. R. S._

[Read Nov. 9, 1758.]

SIR,

IN a letter I received from my brother, the lieutenant governor of Virginia, he gives an account of a very remarkable storm of hail; which, if you think it worth communicating to the Society, is very much at their service.

It happened on Sunday the 9th of July, about four o’clock in the afternoon, and was preceded by some thunder and lightning. It was a small cloud, that did not seem to threaten much before its breaking, and did not extend a full mile in breadth. It passed over the middle of the town of Williamsburgh, and the skirts of the town had but little of it. Its course was from N. by W. to S. by E. The hail-stones, or rather pieces of ice, were most of them of an oblong square form; many of them an inch and half long, and about three fourths of an inch wide and deep; and from one side of most of them there proceeded sharp spikes, protuberant at least half an inch. He says he cooled his wine, and froze cream, with some of them the next day; and they were not totally dissolved when he went to bed on Monday night. This storm broke every pane of glass on the north side his house, and destroyed all his garden things intirely.

He mentions likewise the heats to have been rather more than usual in that country this summer; and particularly on the 9th of August his thermometer (which is hung on the outside of his house on the north aspect) was at 97, by Fahrenheit’s graduation, and some other days as high as 94 or 95. I am,

SIR,
Your most obedient humble Servant,
Wm. Fauquier.

Jermyn street, 18 October, 1758.

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._

[Read Nov. 9. 1758.]

Huntingdon, 20th May, 1758.

Dear Sir,

IN October 1755. I communicated to you, and you inserted in the last volume of your _Journal Britannique_, the case of Susannah Earle, of Hemmingford-Grey in this County, who, in consequence of the whooping cough, was afflicted with a protruded eye. The case I now send you, somewhat similar to that young girl’s in its first appearance and progress, but by accident attended with a second disease, will perhaps deserve your attention, and not seem unworthy of being presented to the Royal Society.

John Law, of Fenny-Stanton, also in the County of Huntingdon, a strong and robust lad, thirteen years and six months old, in Easter week 1756, beating dung about a close with unusual force, on a sudden felt a violent pain in his left eye. The pain increased, an inflammation ensued, and the eye grew daily larger. The poor boy’s mother followed the directions, which she received, without the least benefit to her child, after having, besides other expences, been defrauded by a quack of two guineas; a great sum for a poor cottager!

The widow Law, in her distress, heard of Susannah Earl’s cure. She went to see her; and determined to bring her son to Huntingdon, for Mr. Hopkins’s assistance. Accordingly, October the 7th 1756, she came to Mr. Daniel Hopkins, surgeon, in this town; and having desired my opinion, we both examined the eye together.

The left eye was protruded out of its orbit, and hung down over the cheek to the upper lip. The coats were greatly discoloured, all the vessels turgid, the sight totally lost, and the humours appeared like fluctuating pus. We saw the necessity of an immediate extirpation, to save the right eye, already greatly inflamed; and having apprized the mother and boy of the state the eye was in, a consultation was desired with two surgeons of St. Ives. Mr. Dawkes, who was present with Mr. Skeeles at Susannah Earle’s operation, being dead since that time, Mr. Thomas Skeeles and Mr. Thomas Want very charitably met Mr. Hopkins and me the next day, October the 8th, at the widow Law’s cottage.

The eye appeared to these gentlemen as I have related: and upon Mr. Want’s pressing with his finger on the pupil, the globe burst at the edge of the _Iris_, and discharged pus. The extirpation of the eye was unanimously agreed upon, and immediately performed.

Mr. Hopkins made a puncture with a lancet close to the external and small canthus of the eye, and then with a pair of crooked scissars took off all the distended globe close to the eye-lids. He then cleaned the cavity of the purulent humours, and filled it with soft lint, over which he applied bolsters dipped in warm red wine and water, and the _monoculus_ bandage to keep on the whole dressings. The lad was bled in the arm; nitrous medicines, and anodynes, were prescribed, and a suitable regimen. The fever, and inflammation of the eye, gradually decreased; the suppuration of the wound in few days was good, the distended eye-lids contracted, and a cure was soon expected.

But on November the 7th the lad went to open the street-door, and it being a cold and rainy evening, he quickly felt the bad effects of the cold wind, which drove the rain in upon him. That night the wound became again very painful, the eye-lids puffed up, and next day appeared much inflamed, as were all the contents of the orbit. Fungous excrescences soon followed, and an intermittent fever. An emetic being improper, he was purged with rhubarb, and afterwards took the bark infused in red wine. The fever was removed after some time; but the contents of the orbit continued increasing, and the fungous excrescences became so large and spongy, as to be of equal bulk with the diseased eye before extirpation. All topical applications, to contract this fungus, were ineffectual, and the application of caustics or escharotics was prudently avoided, lest they should produce a carcinomatous ulcer. The discharge was chiefly a purulent serum: on which account, ever since the beginning of November he was kept upon a dry diet.

In February 1757. the remaining coats of the eye began to appear at the most prominent parts of the excrescence, and seemed white like a part of the _conjunctiva_. On touching it with the finger, a distinct fluctuation was felt, and an _hydrophthalmia_ perfectly discovered; but neither the thickness of the coats, nor the sensibility of the parts, would permit a puncture to be made, till the cyst, which appeared formed by the distension of one of the coats of the eye, was freer from the fungus.

The cyst continued daily to extend itself, and to separate the fungous edges; the fluctuation became more manifest, and the membranes thinner. At length, on the 15th of June 1757, Mr. Hopkins opened the cyst with the point of a lancet, and let out a large cup-full of limpid serum, without smell or taste. The boy felt very little pain in this operation. The cavity was filled with dry lint, and compresses dipt in warm red wine and water were applied over it. All the night following, and several days after, a great discharge of serum came away. On the 19th the fungus was considerably lessened. Mr. Hopkins then dressed the wound with warm _unguentum é gummi elemi_, and washed the fungus with a lotion of _aquarum calcis_, _rosarum_, _et tincturæ myrrhæ_. On the 23d, upon his removing the dressings, he saw the cyst loose and collapsed; which he extracted with his forceps, without the least difficulty, or pain to his patient. The fungus daily wasted afterwards, the wound digested well, and the lad was intirely cured on the 7th of August.

His right eye is perfectly strong, and he has been free from complaint ever since. The remainder of the coats of the eye, and of the muscles, bear up the eye-lids, that when uncovered he only seems to have closed the left eye: however, he has wore all the winter a back patch over it, to guard against fresh cold.

The cyst, when first taken away, measured three inches and half in length, one inch and half in diameter, and contained a large cup-full of water. It appeared to be the _tunica sclerotica_, was of a clear pellucid white, and of so delicate a texture, as scarce to admit of being touched without tearing; and when dried with all possible care, became so brittle, that Mr. Hopkins could hardly preserve it in the manner I now send it.

REMARKS.

In both Susannah Earle and John Law’s cases, the eye was distended by the accumulation of the aqueous humour, separated in great quantity by the repeated straining of the blood-vessels in the whooping cough, which might gradually relax and enlarge the aqueous ducts of Susannah Earle’s eye; and possibly by the rupture of those ducts, and of some blood-vessels, at the time John Law exerted himself violently in beating dung about the close: for in either case the _impetus_ of the blood must have been so violent, as to produce those effects. However, from the _hydrophthalmia_ succeeding the operation on John Law, the fungous excrescence, and continual serous discharge during several months from the wound, it plainly appears, that an abundance of aqueous humour was discharged at first by the distention or laceration of the aqueous ducts, and latterly for want of a contraction of those vessels, and of the lymphatics, which were no longer of use.

Both these cases shew the necessity of inquiring particularly into the causes of diseases of the eyes, as well as of other parts of the body; for by barely attending to the symptoms, the disease will not be removed, tho’ the symptoms be alleviated. Bleeding, and moderate evacuations, would certainly have, at first, decreased the tension and pain, and assuaged the inflammation; but both topical applications, and internal medicines, were properly to be adapted, and a suitable diet regulated.

Not to mention the absurd and impertinent abuse of empirics, what benefit could accrue, in both these cases, from unctuous, laxative, or emollient applications, from drastic and mercurial purges? Tho’ such applications might be well intended, to take off the tension and inflammation; yet, as the distension of the blood-vessels only increased gradually, as the globe of the eye was enlarged; so whatever application relaxed the coats of the eye, must infallibly stretch out the vessels yet farther, and cause a greater pain and inflammation; which drastic and mercurial purges would also increase.

The only method then to be pursued in such bad cases would be at first to endeavour to remove the fullness of the blood, and make use of such topical remedies as would contract without irritation. If the cause remains, as the whooping cough in Susannah Earle’s case, no amendment of the eye can be expected, while the patient’s blood-vessels are continually strained by frequent coughing. This illness therefore should be attended to, and removed as soon as possible.

But should the eye be so enlarged, as to protrude itself out of the orbit, there seems no other way to lessen the bulk of the eye, than by making a puncture with a proper instrument, to let out the aqueous humour; and then apply such agglutinant and contracting _collyria_, as may reduce the distended coats and vessels to their former size. This operation should be performed before the humours are vitiated, the sight lost, the vessels in a state of suppuration, and the coats of the eye too far extended; for at that time nothing less than extirpation can be of use.

Professor Nuck, in his _Tractatus de Ductibus Oculorum Aquosis_, p. 120, _& seq._ relates the success he had in curing a young man by five repeated punctures, and a strict observance in a proper use of all the non-naturals.

I am, with the greatest regard and esteem,

Dear Sir,
Your most affectionate Brother,
and very humble Servant,
D. P. Layard.

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._

[Read Nov. 16, 1758.]

Georgia, 17 July, 1758.

Dear Sir,

THO’ some weeks have passed since I wrote to you, yet so little alteration has happened in the state of our affairs, that nothing occurs to me relative to them worth committing to paper. This indeed I need not regret, as one cannot sit down to any thing, that requires much application, but with extreme reluctance; for such is the debilitating quality of our violent heats at this season, that an inexpressible languor enervates every faculty, and renders even the thought of exercising them painful.

’Tis now about three o’ clock; the sun bears nearly S. W. and I am writing in a piazza, open at each end, on the north-east side of my house, perfectly in the shade: a small breeze at S. E. blows freely thro’ it; no buildings are nearer, to reflect the heat, than 60 yards: yet in a thermometer hanging by me, made by Mr. Bird, and compared by the late Mr. George Graham with an approved one of his own, the mercury stands at 102. Twice it has risen this Summer to the same height; _viz._ on the 28th of June, and the 11th of July. Several times it has been at 100, and for many days successively at 98; and did not in the nights sink below 89. I think it highly probable, that the inhabitants of this town breathe a hotter air than any other people on the face of the earth. The greatest heat we had last year was but 92, and that but once: from 84 to 90 were the usual variations; but this is reckoned an extraordinary hot summer. The weather-wise of this country say it forebodes a hurricane; for it has always been remarked, that these tempests have been preceded by continual and uncommon heats. I must acquaint you, however, that the heats we are subject to here are more intense than in any other parts of the province, the town of Savannah being situated upon a sandy eminence, and sheltered all round with high woods. But it is very sufficient, that the people actually breathe so hot an air as I describe; and no less remarkable, that this very spot, from its height and dryness, is reckoned equally healthy with any other in the province.

I have frequently walked an hundred yards under an umbrella, with a thermometer suspended from it by a thread to the height of my nostrils, when the mercury has rose to 105; which is prodigious. At the same time I have confined this instrument close to the hottest part of my body, and have been astonished to observe, that it has subsided several degrees. Indeed, I never could raise the mercury above 97 with the heat of my body.

You know, dear Sir, that I have traversed a great part of this globe, not without giving some attention to the peculiarities of each climate; and I can fairly pronounce, that I never felt such heats any-where as in Georgia. I know experiments on this subject are extremely liable to error; but I presume I cannot now be mistaken, either in the goodness of the instrument, or in the fairness of the trials, which I have repeatedly made with it. This same thermometer I have had thrice in the equatorial parts of Africa; as often at Jamaica, and the West India islands; and, upon examination of my journals, I do not find, that the quicksilver ever rose in those parts above the 87th degree, and to that but seldom: its general station was between the 79th and 86th degree; and yet I think I have felt those degrees, with a moist air, more disagreeable than what I now feel.

In my relation of the late expedition to the north-west, if I recollect right, I have observed, that all the changes and variety of weather, that happen in the temperate zone throughout the year, may be experienced at the Hudson’s Bay settlements in 24 hours. But I may now extend this observation; for in my cellar the thermometer stands at 81, in the next story at 102, and in the upper one at 105; and yet these heats, violent as they are, would be tolerable, but for the sudden changes that succeed them. On the 10th of December last the mercury was at 86; on the 11th it was so low as 38 of the same instrument. What havock must this make with an European constitution? Nevertheless, but few people die here out of the ordinary course; tho’ indeed one can scarce call it living, merely to breathe, and trail about a vigorless body; yet such is generally our condition from the middle of June to the middle of September. Dear Sir,

Yours most affectionately,
Henry Ellis.

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._

[Read Nov. 16, 1758.]

AS the doctrine of Series’ is of very great use in the higher branches of the mathematics, and their application to nature, every attempt tending to extend that doctrine may justly merit some degree of regard. The subject of the paper, which I have now the honour to lay before the Society, will be found an improvement of some consequence in that part of science. And how far the business of finding fluents may, in some cases, be facilitated thereby, will appear from the examples subjoined, in illustration of the general method here delivered.

The series propounded, whose sum (_S_) is supposed to be given (either in algebraic terms, or by the measures of angles and ratio’s, _&c._) I shall here represent by _a_ + _bx_ + _cx_² + _dx_³ + _ex_⁴, &c. and shall first give the solution of that case, where every third term is required to be taken, or where the series to be summed is _a_ + _dx_³ + _gx_⁶ + _kx_⁶, &c. By means whereof, the general method of proceeding, and the resolution of every other case, will appear evident.

Here, then, every _third_ term being required to be taken, let the series (_a_ + _dx_³ + _gx_⁶, &c.), whose value is sought, be conceived to be composed of _three_ others.

⅓ × (_a_ + _b_ × (_px_) + _c_ × (_px_)² + _d_ × (_px_)³ + _e_ ×
(_px_)⁴, &c.)

⅓ × (_a_ + _b_ × (_qx_) + _c_ × (_qx_)² + _d_ × (_qx_)³ + _e_ ×
(_qx_)⁴, &c.)

⅓ × (_a_ + _b_ × (_rx_) + _c_ × (_rx_)² + _d_ × (_rx_)³ + _e_ ×
(_rx_)⁴, &c.)

having all the _same form_, and the _same coefficients_ with the series first proposed, and wherein the converging quantities _px_, _qx_, _rx_, are also in a determinate (tho’ yet unknown) ratio to the original converging quantity _x_. Now, in order to determine the quantities of these ratios, or the values of _p_, _q_, and _r_, let the terms containing the same powers of _x_, in the two equal values, be equated in the common way:

So shall,

⅓ _b_ × _px_ + ⅓ _b_ × _qx_ + ⅓ _b_ × _rx_ = 0
⅓ _c_ × _p_²_x_² + ⅓ _c_ × _q_²_x_² + ⅓ _c_ × _r_²_x_² = 0
⅓ _d_ × _p_³_x_³ + ⅓ _d_ × _q_³_x_³ + ⅓ _d_ × _r_³_x_³ = _dx_³
⅓ _e_ × _p_⁴_x_⁴ + ⅓ _e_ × _q_⁴_x_⁴ + ⅓ _e_ × _r_⁴_x_⁴ = 0
&c.

And consequently,

_p_ + _q_ + _r_ = 0
_p_² + _q_² + _r_² = 0
_p_³ + _q_³ + _r_³ = 3
_p_⁴ + _q_⁴ + _r_⁴ = 0, &c.