Chapter III: Part 3

You are at liberty to dispose of this paper as you shall think proper. I am,

Reverend Sir,
Your respectful and most humble Servant,
J. Johnstone.

Kidderminster, Sept. 11. 1757.

THO’ it is now pretty well known, that colicky and icteric diseases often arise from gall-stones generated in the bilious receptacle, and obstructing its canals; yet an example of one, of such enormous size, voided into the _duodenum_ from the _ductus communis_, as happened in the first of the following cases, is a very rare, if not intirely an unexampled occurrence. It will encourage us not too easily to despair of the expulsion of the largest _calculi_ from the gall-bladder; and will teach us, that all violent attacks of pain about the stomach are not owing to gout reflected upon that organ: it will make us more cautious of giving drastic cathartics, heating and inflaming medicines, upon such a vague presumption; and ought to dispose those, who are trusted with the lives of their fellow-creatures, to a nicer observation of even the minutest symptoms and circumstances, which may occur in diseases.

The second case points out, under certain circumstances, the practibility of extracting, by incision into the gall-bladder itself, those _calculi_, which, from their figure, or other impediments, cannot be voided in the natural way. The method of performing this unusual operation, and some instances of its success, have already been made public in the Memoires de l’Acad. de Chirurg.

1. Mrs. F----, a sedentary corpulent old lady, had been much subject to colicky complaints, without jaundice, in the vigour of life. The seat of the pain was chiefly under the right _hypochondrium_, as high as the stomach. She had been tolerably free from it for at least eight years past. December 5, 1753, about eleven o’clock in the evening, she was suddenly seized with a violent pain, extending from that part of the stomach lying under the right side, thro’ to her back. She compared it to a sword driven in that direction. This pain continued not only with unremitted violence, but even increased, till seven o’clock in the morning: all this time she vomited and strained almost incessantly; but after her stomach was emptied of its contents, nothing came up besides clear slime, streaked with blood. About seven o’clock in the morning she felt her pain fall or move lower, as she expressed it, and from that time became remarkably easier. Soon after this change, she became extremely sick, and vomited up, for the first time, a prodigious quantity of greenish yellow bile. She had not before this seizure been remarkably costive; and in her pain had a free motion to stool with effect; but during the remainder of the (6th) day had none, tho’ all this time emollient clysters were injected; and she took regularly every two hours a powder of _magnes. alb. terr. fol. tartar. tart. vitriol. ana_ ℈j. _ol. nuc. mosch. gutt._ j. with a draught of the _succ. limon. & sal. absinth_. But in the middle of the night, and all day (the 7th), she had an abundant discharge of loose bilious stools. She had continued free from excessive pain since the morning of the former day, only now and then complained of uneasiness sometimes in one, sometimes in another, part of her bowels. About twenty-four hours after her first seizure, she felt a great pain striking towards the bottom of her back, and one hour after voided the extraordinary _calculus_, of which the figure and description are subjoined. Some time after pieces of skins were voided by stool, which were evidently of the texture and appearance of the internal villous coat of the intestines and gall-bladder. The above medicines were the only ones she used, by my direction, under her painful complaint, excepting an external fomentation, and bleeding, which the hardness and contractedness of her pulse seemed to require. She was ordered to drink plentifully of thin broths, and other soft diluent liquors. During the course of her disorder she had no appearance of jaundice, nor since; and, considering her years, enjoys at present (Sept. 1757) very good health.

This _calculus_, as appears by the figure, was of a pyriform shape, resembling the form of the _cystis fellea_ itself. Its surface was quite smooth and polished, excepting towards the base, at that part marked A, where it was scabrous, as if some other substance had lain contiguous to it. When broken through, it was composed of concentrical laminæ, which were alternately white and ochre-coloured. In length it measured one inch and three tenths; its transverse section measured at least seven tenths of an inch. It had a saponaceous smoothness, like other gall-stones, and floated upon water. It weighed only about 126 grains.

Tho’ it be difficult to conceive, how so bulky a substance, generated in the gall-bladder, could be conveyed along so narrow a passage as the common biliary duct, especially considering the obliquity of its insertion for near half an inch of length betwixt the coats of the _duodenum_; yet there seem sufficient _data_ in the above case to prove, that this animal stone was not formed in the alimentary tube, but (large as it was) had come into it from the _ductus communis choledochus_.

The shape and saponaceous smoothness, and colour of the laminæ, of this substance, shew it was moulded in the gall-bladder, and formed from bilious particles. The severe pain and torture, and enormous vomiting, she underwent, for seven hours after her first seizure, argue, that it must then be lodged in some canal much narrower and straighter than the alimentary canal; for so soon as it dropped into that, the severe pain in a great measure ceased.

But that straight canal, in which it was situated during those seven hours of torture, could be no other than the _ductus communis choledochus_; for, during this space of time, no bile was emptied into the bowels, nor thrown up by the strongest efforts of vomiting. But no sooner had she perceived the cause of her pain to move or drop downwards (a sensation, which points out the precise moment the stone must have dropped into the _duodenum_), than she began to sicken, and instantly after vomited up a vast quantity of bilious matter; which now, from the de-obstructed duct, began to flow freely into the _duodenum_. The obstruction of the _ductus choledochus_ was of too short a duration (only three hours) to occasion any observable jaundice. And it appears by the bloody flesh-like knots, thrown up with phlegm by vomiting, that the passage of the substance was not effected without considerable laceration of the small bilious ducts. And this easily accounts for the separation of the villous coat, which afterwards appeared in this patient’s stools.

2. In February 1752. I was called to relieve a poor woman of this place, Sarah Ewdall, aged 30 years and upwards, and the mother of several children. She laboured under the jaundice, and complained of a severe acute pain striking thro’ from the right _hypochondrium_ to her back, with frequent vomitings. A præternatural hardness, of a compass not exceeding the hollow of the hand, was then plainly to be felt at the pit of the stomach, or a little nearer to the right _hypochondrium_. When that particular part was pressed, she complained of great pain. The pain at this part was always increased by attempting to lie upon the left side. She was blooded, fomented externally, had emollient saponaceous clysters injected, and a nitrous apozem, and pills composed of _galban. & sap. Castillens._ and soon after recovered. She had frequent returns of the same complaint after this; but I saw her not again till Jan. 1755, when she lay insensible in a fit, which for several days deprived her of the use of her speech and of all her senses, only she tossed her limbs about. About a quarter of a year after she had recovered from this fit, Mr. Cooper of this place, her apothecary, informed me, that from a small sore at the pit of her stomach, which came since her last illness, she had voided several gall-stones. Curiosity prompted me to inquire into the matter of fact from herself. She shewed me the sore, which was now almost cicatrized. She said, that soon after her last illness a little pimple arose upon that part of the pit of the stomach, which had been hard ever since she had been subject to the jaundice. This pimple broke, ran matter, and at different times the _calculi_, which she shewed me, had come out with the matter. Her stomach had been somewhat painful before it broke, but was now easy. The _calculi_, which she shewed me, had the appearance of being fragments of larger ones, and some were almost dust; tho’ she assured me they all came from the sore in that condition. Of these fragments I have two or three of the largest now in my custody: they are light, swim on water, smooth like soap; are of a yellow colour, and in some parts brown like snuff; and consist of similar concentrical layers. The poor woman has since then been troubled with returns of pain and jaundice, in the intervals of which her skin is perfectly clear and white. She is still alive, and ready to attest the truth of this narrative.

J. Johnstone.

Kidderminster, Sept. 11th, 1757.

LXXII. _A remarkable Case of Cohesions of all the Intestines_, &c. _in a Man of about Thirty-four Years of Age, who died some time last Summer, and afterwards fell under the Inspection of Mr._ Nicholas Jenty.

[Read Feb. 9, 1758.]

THE subject was tall, and partly emaciated. I found nothing externally but a wound in the left side, which seemed to me to have been degenerated into an ulcer. As I did not know the man when he was alive, and had him two days after his decease, I cannot give an immediate account of the cause of his death. But in opening his abdomen, I found the epiploon adhering close to the intestines, in such a manner, that I could not part it without tearing it. It felt rough and dry. And as I was going to remove the intestines, to examine the mesentery, I found them so coherent one with the other, that it was impossible for me to divide them without laceration. Then I inflated the intestinal tube, for the inspection of this extraordinary phænomenon; but, to my great surprize, all the external parts of the intestines appeared smooth; very few of the circumvolutions were seen, occasioned by the strong lateral cohesions of their sides with each other. The substance of the intestines was rough, and a great many pimples, as big as the head of a pin, appeared in them, and were almost free from any moisture. It is proper to observe, that these pimples have been taken for glands by the late Dr. James Douglas, and others; whereas they are in reality nothing else but the orifices of the exhaling vessels obstructed, and are not to be met with except in morbid cases.

After having made incisions in that part of the _colon_ next to the _rectum_, I found the _peritonæum_, or external membrane which invests the intestines, and the _viscera_ of the _abdomen_, to be of the thickness of a six-pence; and I fairly drew all the intestines from their external membrane without separating their cohesions; the _peritonæum_, or external membrane, afterwards appearing like another set of intestines. I found a fluid in the intestines; and I will not take upon me to say, how the peristaltic motion must have been performed. And afterwards I parted the stomach from its external tunic, as I had done the intestines. I found no obstruction in the mesenteric glands; but every evolution of the mesentery firmly cohered together. The liver also adhered closely to the diaphragm, and its adjacent parts: and in the _vesicula fellis_ I found the bile pretty thick, neither too green nor too yellow, but a tint between both. I met with nothing remarkable in the other parts of the _abdomen_. In opening the _thorax_, I found the lungs closely adhering to the ribs laterally, and posteriorly and interiorly close to the _pericardium_. In making an incision to open the _pericardium_, I found it so closely adhering to the heart, that I could not avoid wounding that organ, and with much difficulty could part it from it. I met with no fluid in the _pericardium_. The heart was small; and in the internal side the pores of the _pericardium_ appeared so large, that one might have insinuated the head of a middling pin into them. They have been described by some anatomists, who have met with cases somewhat similar to this, but without such universal adhesions; and they have been supposed to have been glands. The same pores likewise appeared on the heart; which, in my opinion, are nothing but the extremities of the exhaling vessels. In removing the heart, I found the _dorsal_, and other lymphatic glands above the lungs, quite large, indurated, and of a dark greyish colour. Nothing remarkable appeared in the lungs; only, that the portion of the _pleura_, which invests the lungs, and is generally thin, was here thick and rough; and thro’ a glass it appeared as if covered with grains of sand; and might in several places have been easily torn from the lungs.

The _aorta_ was pretty large; and in that part of it, which runs on the tenth _dorsal vertebra_, I found a _cystis_, as big as an olive, full of _pus_; and lower down, immediately before that vessel perforates the diaphragm, I found another, something less, full of matter likewise; both which portions I have by me. That portion of the _aorta_, where the _cystis_ appeared, was rather thicker than the other, and osseous. In opening the _cranium_, I found in that part of the _cerebrum_, which lies over the _cerebellum_, a table spoonfull of _pus_, of a greenish colour; and examining it thro’ a glass, there was an appearance of _animalcula_ in it.

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

[Read Feb. 9, 1758.]

I. WHEN any portion of the earth’s surface is projected on a plane, or transferred to it by whatever method of description, the real dimensions, and very often the figure and position of countries, are much altered and misrepresented. In the common projection of the two hemispheres, the meridians and parallels of latitude do indeed intersect at right angles, as on the globe; but the linear distances are every-where diminished, excepting only at the extremity of the projection: at the center they are but half their just quantity, and thence the superficial dimensions but one-fourth part: and in less general maps this inconvenience will always, in some degree, attend the _stereographic_ projection.

The _orthographic_, by parallel lines, would be still less exact, those lines falling altogether oblique on the extreme parts of the hemisphere. It is useful, however, in describing the circum-polar regions: and the rules of both projections, for their elegance, as well as for their uses in astronomy, ought to be retained, and carefully studied. As to Wright’s, or Mercator’s, nautical chart, it does not here fall under our consideration: it is perfect in its kind; and will always be reckoned among the chief inventions of the last age. If it has been misunderstood, or misapplied, by geographers, they only are to blame.

II. The particular methods of description proposed or used by geographers are so various, that we might, on that very account, suspect them to be faulty; but in most of their works we actually find these two blemishes, _the linear distances visibly false_, and _the intersections of the circles oblique_: so that a quadrilateral rectangular space shall often be represented by an oblique-angled rhomboid figure, whose diagonals are very far from equal; and yet, by a strange contradiction, you shall see a fixed scale of distances inserted in such a map.

III. The only maps I remember to have seen, in which the last of these blemishes is removed, and the other lessened, are some of P. Schenk’s of Amsterdam, a map of the Russian empire, the Germania Critica of the famous Professor Meyer, and a few more[27]. In these the meridians are straight lines converging to a point; from which, as a center, the parallels of latitude are described: and a rule has been published for the drawing of such maps[28]. But as that rule appears to be only an easy and convenient approximation, it remains still to be inquired, _What is the construction of a particular map, that shall exhibit the superficial and linear measures in their truest proportions?_ In order to which,

IV. Let E_l_LP, in this figure (_See_ TAB. XXI.) be the quadrant of a meridian of a given sphere, whose center is C, and its pole P; EL, E_l_, the latitudes of two places in that meridian, EM their middle latitude. Draw LN, _ln_, cosines of the latitudes, the sine of the middle latitude MF, and its cotangent MT. Then writing unity for the radius, if in CM we take C_x_ = N_n_ ⁄ (L_l_ × MF × MT), and thro’ _x_ we draw _x_R, _xr_, equal each to half the arc L_l_, and perpendicular to CM; the conical surface generated by the line R_r_, while the figure revolves on the axis of the sphere, will be equal to the surface of the zone that is to be described in the same time by the arc L_l_; as will easily appear by comparing that conical surface with the zone, as measured by _Archimedes_.

_J. Mynde sc._]

And, lastly, If from the point _t_, in which _r_R produced meets the axis, we take the angle C_t_V in proportion to the longitude of the proposed map, as MF the sine of the middle latitude is to radius, and draw the parallels and meridians as in the figure, the whole space SOQV will be the proposed part of the conical surface expanded into a plane; in which the places may now be inserted according to their known longitudes and latitudes.

EXAMPLE.

V. Let L_l_, the breadth of the zone, be 50°, lying between 10° and 60° north latitude; its longitude 110°, from 20° east of the Canaries to the center of the western hemisphere; comprehending the western parts of Europe and Africa, the more known parts of North America, and the ocean that separates it from the old continent.

And because C_x_ = N_n_ ⁄ (L_l_ × MF × MT), add these three logarithms.

Log. 0.8726650 (= 50° to radius 1) -1.9408476
Log. MF (sin. 35°) -1.7585913
Log. MT (tang. 55°) 0.1547732
----------
Take the sum -1.8542121
from log. N_n_ (= .6923772) -1.8403427
----------
the remainder -1.9861306
is the logarithm of C_x_. And because 1:
C_x_ ∷ MT : _xt_, to this adding the log. MT 0.1547732
----------
The sum 0.1409038

is the log. of _xt_ = 1.383260; and _x_R (= _xr_ = ½ L_l_) being .4363325, R_t_ will be 0.9469275, _rt_ = 1.8195925. Whence having fixed upon any convenient size for our map, the center _t_ is easily found. As, allowing an inch to a degree of a great circle, or 50 inches to the line R_r_, R_t_ the semidiameter of the least parallel will be 54.255 inches, and that of the greatest parallel 104.255 inches.

Again, making as radius to MF so the longitude 110° to the angle S_t_V, that angle will be 63° 5´ ⅗. Divide the meridians and parallels, and finish the map as usual.

_Note_, The log. MT being repeated in this computation with a
contrary sign, we may find _xt_ immediately by subtracting the sum of
the logarithms of L_l_ and MF from the log. of N_n_.

VI. A map drawn by this rule will have the following properties:

1. The intersections of the meridians and parallels will be rectangular.

2. The distances north and south will be exact; and any meridian will serve as a scale.

3. The parallels thro’ _z_ and _y_, where the line R_r_ cuts the arc L_l_, or any small distances of places that lie in those parallels, will be of their just quantity. At the extreme latitudes they will exceed, and in mean latitudes, from _x_ towards _z_ or _y_, they will fall short of it. But unless the zone is very broad, neither the excess nor the defect will be any-where considerable.

4. The latitudes and the superficies of the map being exact, by the construction, it follows, that the excesses and defects of distance, now mentioned, compensate each other; and are, in general, of the least quantity they can have in the map designed.

5. If a thread is extended on a plane, and fixed to it at its two extremities, and afterwards the plane is formed into a pyramidal or conical surface, it may be easily shewn, that the thread will pass thro’ the same points of the surface as before; and that, _conversely_, the shortest distance between two points in a conical surface is the right line which joins them, when that surface is expanded into a plane. Now, in the present case, the shortest distances on the conical surface will be, if not equal, always nearly equal, to the correspondent distances on the sphere: and therefore, all rectilinear distances on the map, applied to the meridian as a scale, will, nearly at least, shew the true distances of the places represented.

6. In maps, whose breadth exceeds not 10° or 15°, the rectilinear distances may be taken for sufficiently exact. But we have chosen our example of a greater breadth than can often be required, on purpose to shew how high the errors can ever arise; and how they may, if it is thought needful, be nearly estimated and corrected.

Write down, in a vacant space at the bottom of the map, a table of the errors of equidistant parallels, as from five degrees to five degrees of the whole latitude; and having taken the mean errors, and diminished them in the ratio of radius to the sine of the mean inclination of the line of distance to the meridian, you shall find the correction required; remembering only to distinguish the distance into its parts that lie _within_ and _without_ the sphere, and taking the difference of the correspondent errors, in _defect_ and in _excess_.

But it was thought needless to add any examples; as, from what has been said, the intelligent reader will readily see the use of such a table; and chiefly as, whenever exactness is required, it will be more proper, and indeed more expeditious, to compute the distances of places by the following canon.

_Multiply the product of the cosines of the two given latitudes by the square of the sine of half the difference of longitude; and to this product add the square of the sine of half the difference of the latitudes; the square root of the sum shall be the sine of half the arc of a great circle between the two places given._

Thus, if we are to find the true distance from one angle of our map to the opposite, that is, from S to Q, the operation will be as follows:

L. sin. 30° = -1.6989700
L. sin. 80° = -1.9933515
2 L. sin. 55° = -1.8267290
----------
-1.5190505 = log. of 0.330408
and 2 L. sin. 25° = -1.2518966 = log. of 0.178606
---------- --------
Log. of the sum 0.509014 is -1.7067297
Whose half is -1.8533648
the L. sin. of 45° 31´, the double of which is 91° 2´, or 5462
geographical miles.

And seeing the lines TS, TQ, reduced to minutes of a degree, are 6255.189 and 3255.189 respectively, and the angle STV is 63° 5´⅗, the right line SQ on the map will be 5594´, exceeding its just value by 132´ or ¹⁄₄₂ of the whole.

7. The errors on the parallels increasing fast towards the north, and the line SQ having, at last, nearly the same direction, it is not to be wondered that the errors in our example should amount to ¹⁄₄₂. Greater still would happen, if we measured the distance from O to Q by a straight line joining those points: for that line, on the conic surface, lying every-where at a greater distance from the sphere than the points O and Q, must plainly be a very improper measure of the distance of their correspondent points on the sphere. And therefore, to prevent all errors of that kind, and confine the other errors in this part of our map to narrower bounds, it will be best to terminate it towards the pole by a straight line KI touching the parallel OQ in the middle point K, and on the east and west by lines, as HI, parallel to the meridian thro’ K, and meeting the tangent at the middle point of the parallel SV in H. By this means too we shall gain more space than we lose, while the map takes the usual rectangular form, and the spaces GHV remain for the _title_, and other inscriptions.

VII. Another, and not the least considerable, property of our map is, that it may, without sensible error, be used as a sea-chart; the rumb-lines on it being logarithmic spirals to their common pole _t_, as is partly represented in the figure: and the arithmetical solutions thence derived will be found as accurate as is necessary in the art of sailing.

Thus if it were required to find the course a ship is to steer between two ports, whose longitudes and latitudes are known, we may use the following

RULE.

_To the logarithm of the number of minutes in the difference of longitude add the constant logarithm[29] -4.1015105, and to their sum the logarithm sine of the mean latitude, and let this last sum be_ S.

_The cotangent of the mean latitude being_ T, _and an arithmetical mean between half the difference of latitude and its tangent being called_ m, _from the logarithm of_ T + m _take the logarithm of_ T - m, _and let the logarithm of their difference be_ D; _then shall_ S - D _be nearly the logarithm tangent of the angle, in which the ship’s course cuts the meridians_.

_Note_, We ought, in strictness, to use the ratio of _tx_ + _x_R to
_tx_ - _x_R instead of T + _m_ to T - _m_; but we substitute this
last as more easily computed, and very little different.

EXAMPLE 1.

Let the latitudes, on the same side of the equator, be 10° and 60°; then the middle latitude and its complement are 35° and 55°, and half the difference of the latitudes is 25°: and the difference of longitude being 110°, the operation will stand as below.

Log. 6600´ (in 110°) 3.8195439
Constant log. -4.1015105
----------
-1.9210544
Log. sin. 35° -1.7585913
----------
S = ... -1.6796457
Again T = 1.4281480
_m_ = .4513202
---------
Log. (T + _m_) (= 1.8794682) 0.2740350
Log. (T - _m_) (= 0.9768278) -1.9898180
----------
Log. 0.2842170 = D = -1.4536500
----------
S - D (= log. tangent 59° 16´) = 0.2259957
agreeing to a minute with the solution by a table of meridional
parts.

EXAMPLE 2.

The rest remaining, let the difference of longitude be only 40°; then

Log. 2400´ (in 40°) 3.3802112
Constant log. -4.1015105
----------
-1.4817217
Log. sin. 35° -1.7585913
----------
S = -1.2403130
D (as before) = -1.4536500
----------
S - D (= log. tang. 31° 27´ ½) -1.7866630

EXAMPLE 3.

Let the difference of longitude be 40°; but the latitudes 56° and 80°;

And log. 2400´ }
+ log. constant } = -1.4817217
Log. sin. 68° = -1.9671659
----------
S = -1.4488876
T (tang. 22°) = .4040262
_m_ = .2109980
--------
Log. (T + _m_) (= .6150242) -1.7888921
Log. (T - _m_) (= .1830282) -1.2625181
----------
Log. 0.5263740 = D = -1.7212944
----------
S - D (= log. tangent 28° 6´) = -1.7275932
wanting of the true answer no more than 1° 4´.

And in all cases that can occur, the error of this rule will be inconsiderable.

It is not meant, however, that it ought to take place of the easier and better computation by a table of meridional parts: but it was thought proper to shew, by some examples, how safely the map itself may be depended on in the longest voyages; provided it is sufficiently large, and the necessary rumb-lines are exactly drawn[30].

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

[Read April 6, 1758.]

London, March 21. 1758.

SIR,

AMONG the several improvements made in arts and sciences by ingenious men, the construction of _globes_, _maps_, or _charts_, deserves a place: not only on account of the pleasure and satisfaction that arises to speculative minds, in surveying the extent and divisions of this terraqueous globe, but also for their real use and service to navigation, trade, and commerce.

_Globes_ perhaps were first invented, as bearing the nearest semblance to the natural form of the earth and sea, with proper circles thereon described, and the several empires and kingdoms, according to their extent, latitudes, and longitudes, as far as geography and history would admit.

But tho’ these convey the most general and truest ideas of the position and situation of places; yet, as containing but a small surface, they were found not extensive enough to take in particular kingdoms or states, with their subdivisions, cities, and rivers, so as to convey an adequate and sufficient representation. Besides, they were not so portable and commodious in voyages or travels.

_Maps_ and _Charts_ were therefore thought of, as being most convenient for both the purposes above-mentioned; the accuracy of which depends on representing the meridians and parallels in such manner, that when places are laid thereon, according to their latitudes and longitudes, they may have such respect to each other, as they have on the globe itself; and those are either _globular_ or _rectilinear_.

_Globular_, or _curvilinear_, are either general or particular.

_General_, are the hemispheres; for the most part constructed stereographically.

_Particular_, contain only some part of the terraqueous globe; and of this sort there are sundry modes of construction, which for the most part are defective, so as not to be applied with accuracy and facility to the purposes intended, in determining the courses or bearings of places, their distances, or both.

_Rectilinear_ were therefore very early adopted, on which the meridians were described parallel to each other, and the degrees of latitude and longitude every-where equal; the rumbs were consequently right lines; and hereby it was thought, that the courses or bearings of places would be more easily determined.

But these were found also insufficient and erroneous, the meridians being parallel, which ought to converge; and no method or device used to accommodate that parallelism.

Notwithstanding the great deficiency in this plane map or chart, it was preferred, especially in nautical business; and hath its uses at this day in topographic constructions, as in bays, harbours, and very narrow zones.

However, the errors herein were sooner discovered than corrected, both by mathematicians and mariners, as by Martin Cortese, Petrus Nonius, Coigniet, and some say by Ptolemy himself.

The first step towards the improvement of this chart was made by Gerardus Mercator, who published a map about the year 1550, wherein the degrees of latitude were increased from the equator towards each pole; but upon what principles this was constructed, he did not exhibit.

About the year 1590, Mr. Edward Wright, an Englishman, discovered the true principles upon which such a chart should be constructed; and communicated the same to one Jodocus Hondius, an engraver, who, contrary to his honest faith and engagement, published the same as his own invention: This occasioned Mr. Wright, in the year 1599, to exhibit his method of construction, in his book, intitled, _Correction of Errors in Navigation_; in the preface of which book may be seen his charge and proof against Hondius; and also how far Mercator has any right to share in the honour due for this great improvement in geography and navigation.

Blundevill, in his Exercises, page 327, published anno 1594, gives a table of meridional parts answering to even degrees, from 1° to 80° of latitude, with the sketch of a chart constructed therefrom; but this table he acknowledged to have received from Mr. Wright, in the following words, page 326, _viz._ “In the mean time to reform the saide faults,” (in the plane chart) “Mercator hath in his universal chard or mappe made the spaces of the parallels of latitude to bee wider everie one than other from the equinoctial towards either of the poles, by what rule I know not, unless it be by such a table as my friend Maister Wright of Caius-college in Cambridge at my request sent me (I thank him) not long since for that purpose, which table with his consent, I have plainlie set down,” _&c._

About the year 1720, a globular chart was published, said to be constructed by Mr. Henry Wilson; the errors in which were obviated by Mr. Thomas Haselden, in a letter to Dr. Halley; who at the same time exhibited a new scale, whereby distances on a given course may be measured, or laid off, at one extent of the compasses, on Wright’s projection; and was intended to render the same as easy in practice as the plane chart.

The above chart was published in opposition to Mr. Wright’s, which that author charged with imperfections and errors, and that it represented places bigger than they are upon the globe.

It is true, the surface is apparently enlarged; but the position of places, in respect to one another, are in no wise distorted; and it may be asserted, with the same parity of reason, that the lines of sines, tangents, and secants, are false, because the degrees of the circle, which are equal among themselves, are thereupon represented unequal.

Yet if a map or chart was so constructed, as to shew the situation and true extent of countries, _&c. primâ facie_ (if I may be allowed the expression), and yet retain all the properties, uses, and simplicity, of Wright’s construction, it would be a truly great improvement; but this seems to be impossible.

The method exhibited by the Rev. Mr. Murdoch, in his paper, read before the Royal Society on the 9th of February last, shews the situation of places, and seems better calculated for determining superficial and linear measures, than any other that has occurred to me.

This Gentleman illustrates his theory with examples justly intended to point out the quantity of error, that will happen in a large extent.

For instance; Between latitudes 10° and 60° N. and containing 110 degrees difference of longitude, Mr. Murdoch computes the distance at 5594 miles; which, upon the arc of a great circle, is found to be 5477, or by other methods 5462; so that the difference is only 117, or at most 132 miles in so great an extent, and to an high latitude; and the higher the latitude the greater the error is like to be, where-ever middle latitude is concerned.

His courses also agree very nearly with computations made from the tables of meridional parts.

In example the first they are the very same:

In example the 2d they agree to half a minute:

In example the 3d they vary 1° 4´, on account of the high latitudes, which extend from 56° to 80° N.

However, I do not esteem this method so simple, easy, and concise, in the practice of navigation, as Mr. Wright’s construction, especially in determining the bearings or courses from place to place: nor will it (I presume) admit of a zone containing both north and south latitude.

Of these inconveniences Mr. Murdoch seems to be extremely well acquainted, when he expresses himself in the following very candid and ingenuous terms, _viz._ “As to Wright’s or Mercator’s nautical chart, it does not here fall under our consideration: it is perfect in its kind; and will always be reckoned among the chief inventions of the last age. If it has been misunderstood or misapplied by geographers, they only are to blame.”--And again, at the end of his nautical examples, he concludes thus, _viz._ “It is not meant, however, that it ought to take place of the easier and better computation by a table of meridional parts.”

I have the honour to be, with the greatest respect,

SIR,
The ROYAL SOCIETY’S, and
_Your_ most obedient Servant,
William Mountaine.

ADDENDA _to Mr._ Murdoch_’s Paper_, Nº. LXXIII.

IF it is required “to draw a map, in which the superficies of a given
zone shall be equal to the zone on the sphere, while at the same time
the projection from the center is strictly geometrical;” _Take_ Cx
_to_ CM _as a geometrical mean between_ CM _and_ Nn, _is to the like
mean between the cosine of the middle latitude, and twice the tangent
of the semidifference of latitudes_; and project on the conic surface
generated by _xt_. But here the degrees of latitude towards the
middle will fall short of their just quantity, and at the extremities
exceed it: which hurts the eye. Artists may use either rule: or, in
most cases, they need only make C_x_ to CM as the arc ML is to its
tangent, and finish the map; either by a projection, or, as in the
first method, by dividing that part of _xt_ which is intercepted by
the secants thro’ L and _l_, into equal degrees of latitude.

Mr. Mountaine justly observes, “that my rule does not admit of a
zone containing N. and S. latitudes.” But the remedy is, _to extend
the lesser latitudes to an equality with the greater; that the cone
may be changed into a cylinder, and the rumbs into straight lines_.

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.

[Read Feb. 16, 1758.]

ONE of the most natural effects of blistering plaisters, when applied to the human body, is to quicken the pulse, and increase the force of the circulation. This effect they produce, not only by means of the pain and inflammation they raise in the parts to which they are applied, but also because the finer particles of the _cantharides_, which enter the blood, render it more apt to stimulate the heart and vascular system.

The apprehension, that blisters must in every case accelerate the motion of the blood, seems to have been the reason, why some eminent physicians have been unwilling to use them in feverish and inflammatory disorders, till after the force of the disease was a good deal abated, and the pulse beginning to sink. However, an attentive observation of the effects, which follow the application of blisters in those diseases, will shew, that instead of increasing, they often remarkably lessen the frequency of the pulse. This I had occasion formerly to take notice of[31], and shall now evince more fully by the following cases.

I. A widow lady, aged about 50, was seized (December 1755) with a bad cough, oppression about her stomach and breast, and a pain in her right side, tho’ not very acute. Her pulse being quick, and skin hot, some blood was taken away, which was a good deal sizy: attenuating and expectorating medicines were also prescribed. But as her complaints did not yield to these remedies, I was called on December 26th, after she had been ill about ten days; at which time her pulse beat from 96 to 100 times in a minute, but was not fuller than natural. I ordered her to lose seven or eight ounces more of blood, which, like the former, was sizy; and next day, finding no abatement of her complaints, I advised a blister to be applied, in the evening, to that part of her right side which was pained. Next morning, when the blister was removed, the pain of her side was gone, and her pulse beat only 88 times in a minute, and in two days more it came down to 78. However, after the blistered part became dry, the pulse rose in one day’s time to 96, and continued between that number and 90 for four days; after which I ordered a large blister to be put between her shoulders. When this plaister was taken off, her pulse beat under 90 times in a minute; and next day it fell to 76, and the day after to 72. The cough and other symptoms, which were relieved by the first blister, were quite cured by the second.

II. John Graham, bookbinder, in Edinburgh, aged 37, of a thin habit of body, formerly subject to coughs, and thought to be in danger of a _phthisis pulmonalis_, having exposed himself unwarily to cold in the night time, was, about the end of January 1756, seized with a bad cough and feverishness; for which he was blooded, and had a diaphoretic julep, a pectoral decoction, and a mixture with _gum. ammoniacum_ and _acetum scilliticum_, given him by Mr. James Russell, surgeon-apothecary in this place. On the 12th of February, after he had been ill above a fortnight, I was desired to visit him. He seemed to be a good deal emaciated; his eyes were hollow, and cheeks fallen in: he was almost constantly in a sweat; coughed frequently, and spit up a great quantity of tough phlegm, somewhat resembling _pus_: his pulse beat from 112 to 116 times in a minute. In this condition I ordered immediately a blister to be applied between his shoulders, which lessened in some degree his cough and spitting, as well as the frequency of his pulse; but the blistered part no sooner began to heal, than he became as ill as before, and continued in this bad way nine or ten days, gradually wasting, with continued sweats, and a great spitting of a thick _mucus_. During this time he used _tinctura rosarum_, and the mixture with _gum. ammon._ and _acet. scillit._ without any sensible benefit, and had six ounces of blood taken away, which was very watery, and the _crassamentum_ was of a lax texture. In this almost desperate condition, another blister, larger than the former, was put between his shoulders, which remarkably lessened his cough and spitting, and in two or three days reduced his pulse to 96 strokes in a minute. After this he continued to recover slowly, without the assistance of any other medicine, except the _tinctura rosarum_ and the mixture with _gum. ammon._ and _acet. scillit._ and at present he enjoys good health.

III. Mrs.----, aged upwards of 40, who had for several years been subject to a cough and spitting in the winter months, was, in October 1756, seized with those complaints in a much greater degree than usual; to remove which, she was blooded, and got some attenuating and pectoral medicines from Mr. John Balfour, surgeon-apothecary in Leith. I was called on November 11th, after she had been ill several weeks, and found her in a very unpromising condition. She had a frequent and severe cough, with great shortness of breath and a wheezing; her lungs seemed to be quite stuffed with phlegm, of which she spit a vast quantity every day, and of such an appearance, that I was apprehensive it was, in part at least, truly purulent. When she sat up in a chair, her pulse beat above 130 times in a minute. She had a considerable thirst, and her tongue was of a deep red colour, with a beginning aphthous crust on some parts of it. She was so weak, and her pulse so feeble, that there was no place for further bleeding: a blister was therefore applied to her back, November 11th, which somewhat lowered her pulse, and lessened the shortness of breathing and quantity of phlegm in her lungs. November 16th, a second blister was laid to her side, which gave her still more sensible relief than the former, and reduced her pulse to 114 strokes in a minute. November 25th, a third blister was applied to her back; by which her cough and wheezing were rendered considerably easier, and the phlegm, which she spit up, lost its purulent appearance, became thinner, more frothy, and was much less in quantity. Her pulse beat now only 104 times in a minute. After this, her cough and spitting increasing again, she had, on the 20th of December, a fourth blister applied to her back, which, like the former, did her great service. Her stomach being extremely delicate, I scarce ordered any medicines for her all this time, except a cordial julep, with _spir. volat. oleos._ tincture of rhubarb as a laxative, and a julep of _aqu. rosar. acet. vin. alb._ and _syr. balsam._ of which last she took two table spoonfuls twice or thrice a day in a quarter of a pint of lintseed tea. After the fourth blister, she drank for some time a cupful of _infusum amarum_ twice a day, and continued to recover slowly: and tho’ during the remaining part of the winter she was, as usually, a good deal troubled with a cough, yet in the spring she got free from it, and is now in her ordinary health.

IV. Christian Mʿewen, aged 21, had laboured under a cough, thick spitting, pain of her breast, and pains in her sides affecting her breathing, for about a twelvemonth: and after getting, by proper remedies, in a good measure free from those complaints, her cough, from catching a fresh cold, increased to a greater degree than ever, became hard and dry, and was attended with a constant difficulty of breathing, pain in her left side, and head-ach. After having been seven or eight days in this condition, she was admitted into the Royal Infirmary, January 9th, 1757. As her pulse was small, tho’ very quick, _viz._ beating 130 in a minute, I thought it unnecessary to bleed her, as from former experience I did not doubt but that blistering alone would relieve her: I ordered, therefore, a large blister to be applied to her left side, where she complained of pain, and prescribed for her the following julep:

℞ _Aqu. menth. simp. spirit. Minderer. ana_ ℥ iij. _acet. scillit._ ℥
i. _sacchar. alb._ ℥ ij. _misce; cap. coch._ ij. _ter in die_.

She was also desired to breathe frequently over the steam of hot water, and to drink lintseed tea.

January 10th. Her pulse beat only 112 times in a minute, and was somewhat fuller than on the 9th. The blister was not removed till late in the evening, and made a plentiful discharge. The cough having been so severe last night, as to keep her from sleep, I ordered her the following anodyne draught:

℞ _Spirit. Minderer._ ℥ ss. _acet. scillit._ ȝ i. _syr. papav. alb._
ȝ vi. _misce; cap. hor. somni._

Jan. 11th. The cough easier last night; difficulty of breathing less; pulse 108 in a minute. Ordered the anodyne draught to be repeated, and the use of the julep, with _acet. scillit._ to be continued.

Jan. 12th. Pulse slower; cough and pain of the side easier; but still complains of a head-ach.

Jan. 13th. Pulse 94 in a minute; cough continues easier in the night, but is troublesome in the day-time.

Jan. 14th. Every way better; pulse only 80 in a minute. As her cough is still bound, ordered her, besides the medicines above-mentioned, a pectoral decoction of _rad. alth._ &c.

Jan. 15th. Cough and other complaints in a great measure removed; pulse 65 in a minute.

From this time her cough gave her little trouble; but on the 18th she complained of a pain in the _epigastrium_, with sickness at stomach, want of apetite, and a giddiness in her head, which were considerably relieved by a vomit, _infusum amarum_, and stomachic purges; and were almost wholly cured by the return of her menses on the 5th of February, after an interval of eight weeks.

V. A girl 21 months old, who had (December 1756) a great load of the small-pox, and not of a good kind, with a cough and obstructed breathing, was, on the seventh day from the eruption, blistered on the back; by which the pulse was lessened from 200 to 156 strokes in a minute. Next day her legs were also blistered, and the pulse thereby fell to 136. But the child’s lungs being much oppressed, and her throat being so full of pustules that she could scarce swallow any thing, she died towards the end of the ninth day.

I could add several other cases of the remarkable effects of blisters in lessening the quickness of the pulse in coughs attended with fever, pain in the side, and pituitous infarction of the lungs: but those above may be sufficient to put this matter out of doubt, as well as to remove any prejudice, that may still remain against the free use of so efficacious a remedy.

In a true peripneumony, especially where the inflammation is great, repeated bleeding is the principal remedy, and blisters early applied are not so proper. But when the peripneumony is of a mixed kind; when the lungs are not so much inflamed as loaded with a pituitous matter; when bleeding gives but little relief; when the pulse, tho’ quick, is small; when the patient is little able to bear evacuations, and the disease has continued for a considerable time; in all these cases blistering will produce remarkable good effects, and, far from increasing, will generally lessen the frequency of the pulse, and fever, more speedily than any other remedy.

On the other hand, when the fever and frequency of the pulse proceed from a true inflammation of the lungs, from large obstructions tending to suppuration, or from an open ulcer in them, blisters will be of less use, nay, sometimes will do harm, except in the last case, where they, as well as issues and setons, are often beneficial, tho’ seldom able to compleat a cure. But as in pituitous infarctions of the lungs, with cough and fever, repeated blisters applied to the back and sides are far preferable to issues or setons, so these last seem most proper in an open ulcer of the lungs. The former make a greater and more sudden derivation, and are therefore adapted to acute cases; the latter act more slowly, but for a much longer time, and are therefore best suited to chronic diseases. Further, while blisters evacuate chiefly the serous humours, issues and setons generally discharge true purulent matter, and on this account may be of greatest service in internal ulcers.

In what manner blisters may lessen the fever and frequency of the pulse attending internal inflammations, I have elsewhere endeavoured to explain[32]; and shall only add here, that in the cases above recited, where the quick pulse and feverishness proceeded more from a pituitous infarction than a true inflammation of the lungs, blisters, by relieving this organ, in some measure, of the load of humours oppressing it, would render the circulation through its vessels freer, and consequently lessen the quickness of the pulse, and other feverish symptoms.

It may not, however, be improper briefly to point out the reason, why blisters, which have been observed to be remarkably efficacious, even when early applied, in pleurisies[33], are less so in true peripneumonies. This difference, I imagine, may be accounted for from there being no immediate communication between the pulmonary vessels and those of the sides and back, to which the blisters are applied; whereas the _pleura_, and intercostal muscles, are furnished with blood-vessels from the intercostal arteries, which also supply the teguments of the _thorax_: so that while a greater flow of serous humours, and also indeed of red blood, is derived into the vessels of the external parts, to which the vesicatories are applied, the force of the fluids in the vessels of the inflamed _pleura_, or intercostal muscles, must be considerably lessened. Further, as the intercostal muscles and _pleura_ are, as well as the teguments of the _thorax_, supplied with nerves from the _true_ intercostals, blisters applied to the back and sides may perhaps, on this account also, have a greater effect in relieving inflammations there than in the lungs, which have nerves from the eighth pair, and from the _intercostals_ improperly so called.

Edinburgh, May 23d, 1757.

_Extract of a Letter from Dr._ Whytt, _Professor of Medicine in the University of_ Edinburgh, _and F. R. S. to Dr._ Pringle, _F.R.S._

Edinburgh, 10 Nov. 1757.

WHAT you remark with regard to blisters being freely used by the physicians at London, in the cases mentioned in the paper I last sent you, is very just, and indeed what I knew; but altho’ their efficacy in such circumstances is now generally acknowleged both in England and Scotland, yet I do not remember that their remarkable quality in lessening the quickness of the pulse has been particularly attended to. This, therefore, I thought it might not be amiss to ascertain by a few careful observations.