the name given to a Greek version of the books of the Old Testament, from its being supposed to be the work of seventy-two Jews, who are usually called the seventy interpreters, because seventy is a round number.

The history of this version is expressly written by Aristeas, an officer of the guards to Ptolemy Philadelphus, the substance of whose account is as follows: Ptolemy having erected a fine library at Alexandria, which he took care to fill with the most curious and valuable books from all parts of the world, was informed that the Jews had one containing the laws of Moses, and the history of that people; and being desirous of enriching his library with a Greek translation of it, applied to the high-priest of the Jews; and to engage him to comply with his request, set at liberty all the Jews whom his father Ptolemy Soter had reduced to slavery. After such a step, he easily obtained what he desired; Eleazar the Jewish high-priest sent back his ambassadors with an exact copy of the Mosaic law, written in letters of gold, and five elders of each tribe, in all seventy-two; who were received with marks of respect by the king, and then conducted into the isle of Pharos, where they were lodged in a house prepared for their reception, and supplied with everything necessary. They set about the translation without loss of time, and finished it in seventy-two days; and the whole being read in the presence of the king, he admired the profound wisdom of the laws of Moses; and sent back the deputies laden with presents, for themselves, the high-priest, and the temple.

Arystobulus, who was tutor to Ptolemy Philostratus, Philo who lived in our Saviour's time, and was contemporary with the apostles, and Josephus, speak of this translation as made by 72 interpreters, by the care of Demetrius Phalereus in the reign of Ptolemy Philadelphus. All the Christian writers, during the first fifteen centuries of the Christian era, have admitted this account of the Septuagint as an undoubted fact. But since the reformation, critics have boldly called it in question, because it was attended with circumstances which they think inconsistent, or, at least, improbable. Du Pin has asked, why were 72 interpreters employed, since 12 would have been sufficient? Such an objection is trifling. We may as well ask, why did king James I employ 54 translators in rendering the Bible into English, since Du Pin thinks 12 would have been sufficient?

1. Prideaux objects, that the Septuagint is not written in the Jewish, but in the Alexandrian, dialect; and could not therefore be the work of natives of Palestine. But these dialects were probably at that time the same, for both Jews and Alexandrians had received the Greek language from the Macedonians about 50 years before.

2. Prideaux farther contends, that all the books of the Old Testament could not be translated at the same time; for they exhibit great difference of style. To this it is sufficient to reply, that they were the work of 72 men, Septuagint, each of whom had separate portions assigned them.

3. The Dean also urges, that Aristeas, Arystobulus, Philo, and Josephus, all distinctly tell us, that the law was translated without mentioning any of the other sacred books. But nothing was more common among writers of the Jewish nation than to give this name to the Scriptures as a whole. In the New Testament law is used as synonymous with what we call the Old Testament. Besides, it is expressly said by Arystobulus, in a fragment quoted by Eusebius (Prep. Evang. i. i.), that the whole Sacred Scripture was rightly translated through the means of Demetrius Phalereus, and by the command of Ptolemy Philadelphus. Josephus indeed, says the learned Dean, affirms, in the preface to his Antiquities, that the Jewish interpreters did not translate for Ptolemy the whole Scriptures, but the law only. Here the evidence is contradictory, and we have to determine, whether Arystobulus or Josephus be most worthy of credit. We do not mean, however, to accuse either of forgery, but only to inquire which had the best opportunities of knowing the truth. Arystobulus was an Alexandrian Jew, tutor to an Egyptian king, and lived within 100 years after the translation was made, and certainly had access to see it in the royal library. Josephus was a native of Palestine, and lived not until 300 years or more after the translation was made, and many years after it was burnt along with the whole library of Alexandria in the wars of Julius Caesar. Supposing the veracity of these two writers equal, as we have no proof of the contrary, which of them ought we to consider as the best evidence? Arystobulus surely. Prideaux, indeed, seems doubtful whether there was ever such a man; and Dr Hody supposes that the Commentaries on the five books of Moses, which bear the name of Arystobulus, were a forgery of the second century. To prove the existence of any human being, who lived 2000 years before us, and did not perform such works as no mere man ever performed, is a task which we are not disposed to undertake; and we believe it would not be less difficult to prove that Philo and Josephus existed, than that such a person as Arystobulus did not exist. If the writings which have passed under his name were a forgery of the second century, it is surprising that they should have imposed upon Clemens Alexandrinus, who lived in the same century, and was a man of abilities, learning, and well acquainted with the writings of the ancients. Eusebius, too, in his Prep. Evang. quotes the commentaries of Arystobulus. But, continues the learned Dean, "Clemens Alexandrinus is the first author that mentions them. Now, had any such commentaries existed in the time of Philo and Josephus, they would surely have mentioned them. But is the circumstance of its not being quoted by every succeeding author a sufficient reason to disprove the authenticity of any book?" Neither Philo nor Josephus undertook to give a list of preceding authors, and it was by no means the uniform practice of these times always to name the authors from whom they derived their information."

4. Prideaux farther contends, that the sum which Ptolemy is said to have given to the interpreters is too great to be credible. If his computation were just, it certainly would be so. He makes it £2,000,000 Sterling, but other writers reduce it to L. 85,421, and some to L. 56,947; neither of which is a sum so very extraordinary in so great and magnificent a prince as Philadelphus, who spent, according to a passage in Athenaeus (lib. v.), no less than 10,000 talents on the furniture of one tent; which is five times more than what was spent in the whole of the embassy and translation, which amounted only to 1552 talents.

5. Prideaux says, "that what convicts the whole story of Aristeas of falsity is, that he makes Demetrius Phalerus to be the chief actor in it, and a great favourite of the king; whereas Philadelphus, as soon as his father was dead, cast him into prison, where he soon after died." But it may be replied, that Philadelphus reigned two years jointly with his father Lagus, and it is not said by Hermippus that Demetrius was out of favour with Philadelphus during his father's life. Now, if the Septuagint was translated in the beginning of the reign of Philadelphus, as Eusebius and Jerome think, the difficulty will be removed. Demetrius might have been librarian during the reign of Philadelphus, and yet imprisoned on the death of Lagus. Indeed, as the cause of Philadelphus's displeasure was the advice which Demetrius gave to his father, to prefer the sons of Arsinoë before the son of Berenice, he could scarcely show it till his father's death. The Septuagint translation might therefore be begun while Philadelphus reigned jointly with his father, but not be finished till after his father's death.

6. Besides the objections which have been considered, there is only one that deserves notice. The ancient Christians not only differ from one another concerning the time in which Aristobulus lived, but even contradict themselves in different parts of their works. Sometimes they tell us, he dedicated his book to Ptolemy Philometer, at other times they say, it was addressed to Philadelphus and his father. Sometimes they make him the same person who is mentioned in 2 Maccabees, chap. i., and sometimes one of the 72 interpreters 152 years before. It is difficult to explain how authors fall into such inconsistencies, but it is probably occasioned by their quoting from memory. This was certainly the practice of almost all the early Christian writers, and sometimes of the apostles themselves. Mistakes were therefore inevitable. Josephus has varied in the circumstances of the same event, in his antiquities and wars of the Jews, probably from the same cause; but we do not hence conclude, that every circumstance of such a relation is entirely false. In the account of the Marquis of Argyle's death in the reign of Charles II., we have a very remarkable contradiction. Lord Clarendon relates, that he was condemned to be hanged, which was performed the same day: on the contrary, Burnet, Woodrow, Heath, Echard, concur in stating, that he was beheaded; and that he was condemned upon the Saturday and executed upon the Monday. Was any reader of English history ever sceptic enough to raise from hence a question, whether the Marquis of Argyle was executed or not? Yet this ought to be left in uncertainty according to the way of reasoning in which the facts respecting the translation of the Septuagint is attempted to be disproved.

Such are the objections which the learned and ingenious Prideaux has raised against the common account of the Septuagint translation, and such are the answers which may be given to them. We have chosen to support that opinion which is sanctioned by historical evidence, in preference to the conjectures of modern critics however ingenious; being persuaded, that there are many things recorded in history, which, though perfectly true, yet, from our imperfect knowledge of the concurrent circumstances, may, at a distant period, seem liable to objections. To those who require positive evidence, it may be stated thus. Aristeas, Aristobulus, Philo, and Josephus, assure us, that the law was translated. Taking the law in the most restricted sense, we have at least sufficient authority to assert, that the Pentateuch was rendered into Greek under Ptolemy Philadelphus. Aristobulus affirms, that the whole Scriptures were translated by the 72. Josephus confines their labours to the books of Moses. He therefore who cannot determine to which of the two the greatest respect is due, may suspend his opinion. It is certain, however, that many of the other books were translated before the age of our Saviour; for they are quoted both by him and his apostles; and, perhaps, by a minute examination of ancient authors, in the same way that Dr Lardner has examined the Christian fathers to prove the antiquity of the New Testament, the precise period in which the whole books of the Septuagint were composed might, with considerable accuracy, be ascertained.

For 400 years this translation was in high estimation with the Jews. It was read in their synagogues in preference to the Hebrew; not only in those places where Greek was the common language, but in many synagogues of Jerusalem and Judea. But when they saw that it was equally valued by the Christians, they became jealous of it, and at length, in the second century, Aquila, an apostate Christian, attempted to substitute another Greek translation in its place. In this work he was careful to give the ancient prophecies concerning the Messiah a different turn from the Septuagint, that they might not be applicable to Christ. In the same design he was followed by Symmachus and Theodotion, who also, as St Jerome informs us, wrote out of hatred to Christianity.

In the mean time, the Septuagint, from the ignorance, boldness, and carelessness of transcribers, became full of errors. To correct these, Origen published a new edition in the beginning of the third century, in which he placed the translations of Aquila, Symmachus, and Theodotion. This edition was called Tetrapla, the translations being arranged opposite to one another in four columns. He also added one column, containing the Hebrew text in Hebrew letters, and another exhibiting it in Greek. In a second edition he published two additional Greek versions; one of which was found at Nicaopolis, and the other at Jericho: this was called the Hexapla. By comparing so many translations, Origen endeavoured to form a correct copy of the Scriptures. Where they all agreed, he considered them right. The passages which he found in the LXX, but not in the Hebrew text, he marked with an obelisk: what he found in the Hebrew, but not in the LXX, he marked with an asterisk. St Jerome says, that the additions which Origen made to the LXX, and marked with an asterisk, were taken from Theodotion. From this valuable work of Origen the version of the LXX was transcribed in a separate volume, with the asterisks and obelisks. Septuagint obelisks for the use of the churches; and from this circumstance the great work itself was neglected and lost.

About the year 300 two new editions of the LXX were published; the one by Heirychius an Egyptian bishop, and the other by Lucian a presbyter of Antioch. But as these authors did not mark with any note of distinction the alterations which they had made, their edition does not possess the advantages of Origen's.

The best edition of the LXX is that of Dr Grabe, which was published in the beginning of the present century. He had access to two MSS, nearly of equal antiquity, the one found in the Vatican library at Rome, the other in the Royal library at St James's, which was presented to Charles I. by Cyril, patriarch of Alexandria, and hence is commonly called the Alexandrine MS. Anxious to discover which of these was according to the edition of Origen, Dr Grabe collected the fragments of the Hexapla, and found they agreed with the Alexandrian MS but not with the Vatican where it differed with the other. Hence he concluded that the Alexandrine MS was taken from the edition of Origen. By comparing the quotations from scripture in the works of Athanasius and St Cyril (who were patriarchs of Alexandria at the time St Jerome says Hesychius's edition of the LXX was there used) with the Vatican MS he found they agreed so well that he justly inferred that that MS was taken from the edition of Hesychius.

This version was in use to the time of our blest Saviour, and is that out of which most of the citations in the New Testament, from the Old, are taken. It was also the ordinary and canonical translation made use of by the Christian church in the earliest ages; and it still subsists in the churches both of the east and west.

Those who desire a more particular account of the Septuagint translations may consult Hody de Bibliorum Textibus, Prideaux's Conclusions, Owen's Inquiry into the Septuagint Version, Blair's Lectures on the Canon, and Michaelis's Introduction to the New Testament, last edition.

**Septuagint Chronology**, the chronology which is formed from the dates and periods of time mentioned in the Septuagint translation of the Old Testament. It reckons 1500 years more from the creation to Abraham than the Hebrew bible. Dr Kennicott, in the dissertation prefixed to his Hebrew bible, has shown it to be very probable that the chronology of the Hebrew scriptures, since the period just mentioned, was corrupted by the Jews, between the years 175 and 200, and that the chronology of the Septuagint is more agreeable to truth. It is a fact, that during the second and third centuries the Hebrew scriptures were almost entirely in the hands of the Jews, while the Septuagint was confined to the Christians. The Jews had therefore a very favourable opportunity for this corruption. The following is the reason which is given by oriental writers: It being a very ancient tradition, that the Messiah was to come in the fifth chiliad, because he was to come in the last days (founded on a mystical application of the six days creation), the contrivance was to shorten the age of the world from about 5500 to 3760; and thence to prove that Jesus could not be the Messiah. Dr Kennicott adds, that some Hebrew copies having the larger chronology were extant till the time of Eusebius, and some till the year 700.

**Septum**, in anatomy, an inclosure or partition; a term applied to several parts of the body, which serve to separate one part from another; as, septum narium, or partition between the nostrils, &c.

**Sepulchral**, something belonging to sepulchres or tombs: thus a sepulchral column is a column erected over a tomb, with an inscription on its shaft; and sepulchral lamps, those said to have been found burning in the tombs of several martyrs and others. See Lamp.

**Sepulchre**, a tomb or place destined for the interment of the dead. This term is chiefly used in speaking of the burying-places of the ancients, those of the moderns being usually called tombs.

Sepulchres were held sacred and inviolate; and the care taken of them has always been held a religious duty, grounded on the fear of God, and the belief of the soul's immortality. Those who have searched or violated them have been thought odious by all nations, and were always severely punished.

The Egyptians called sepulchres eternal houses, in contradiction to their ordinary houses or palaces, which they called mans, on account of their short stay in the one in comparison of their long abode in the other. See Tomb.

**Regular Canons of St Sepulchre**, a religious order, formerly instituted at Jerusalem, in honour of the holy sepulchre, or the tomb of Jesus Christ.

Many of these canons were brought from the Holy Land into Europe, particularly into France, by Louis the Younger; into Poland, by Jaxa, a Polish gentleman; and into Flanders, by the counts thereof; many also came into England. This order was, however, suppressed by pope Innocent VIII. who gave its revenues and effects to that of our Lady of Bethlehem; which also becoming extinct, they were bestowed on the knights of St John of Jerusalem. But the suppression did not take effect in Poland, where they still subsist, as also in several provinces of Germany. These canons follow the rule of St Augustine.

**Knights of the Holy Sepulchre**, a military order, established in Palestine about the year 1114.

The knights of this order in Flanders chose Philip II. king of Spain, for their master, in 1558, and afterwards his son; but the grand-master of the order of Malta prevailed on the last to resign; and when afterwards the duke of Nevers assumed the same quality in France, the same grand-master, by his interest and credit, procured a like renunciation of him, and a confirmation of the union of this order to that of Malta.

**Sequani**, a people anciently forming a part of Gallia Celtica, but annexed to Belgica by Augustus, separated from the Helvetii by mount Jura, with the Rhine on the east (Strabo), bordering on the Aedui, and Segugiano to the south, and Lingones to the west (Tacitus). Now Franche Comte.

**Sequestration**, in common law, is setting aside the thing in controversy from the possession of both the parties that contend for it. In which sense it is either voluntary, as when done by the consent of the parties; or necessary, as where it is done by the judge. very different from the similar points of the curve expressing the action of a single particle. These last are in the very places where the light sustains the greatest repulsive action of the whole row of particles. In the same manner may a curve be constructed, whose ordinates express the united action of the whole medium.

From these observations we learn in general, that a particle of light within the space of action is acted on with equal forces, and in the same direction, when at equal distances on each side of the surface of the medium.

Of the focal distance of rays refracted by passing out of one medium into another of different density and through a plane surface.

Lemma. The indefinitely small variation of the angle of incidence is to the simultaneous variation of the angle of refraction as the tangent of incidence is to the tangent of refraction; or, the contemporaneous variations of the angles of incidence and refraction are proportional to the tangents of these angles.

Let RV, rV (fig. 10.) be the progress of the rays refracted at V (the angle rVR being considered in its nascent or evanescent state), and VC perpendicular to the refracting surface VA. From C draw CD, CB perpendicular to the incident and refracted rays RV, VF, cutting rV, Vf in d and b, and let Cd, Cb be perpendicular to rV, Vf.

Because the sines of incidence and refraction are in a constant ratio, their simultaneous variations are in the same constant ratio. Now the angle RVR is to the angle FVf in the ratio of BC to DV; that is, of BC to DV; that is, of fin. incid. to fin. refr.; that is, of tan. incid. to tan. refr.

Corollary. The difference of these variations is to the greatest or least of them as the difference of the tangents to the greatest or least tangent.

PROBLEM.

Let two rays RV, RP diverge from, or converge to, a point R (figs. 1, 2, 3, 4.), and pass through the plane surface PV separating two refracting mediums AB, of which let B be the most refracting, and let RV be perpendicular to the surface. It is required to determine the point of dispersion or convergence, F, of the refracted rays RD, PE.

Make VR to VG as the sine of refraction to the sine of incidence, and draw GIK parallel to the surface, cutting the incident ray in I. About the centre P, with the radius PI, describe an arch of a circle IF, cutting VR in F; draw PE tending from or towards F. We say PE is the refracted ray, and F the point of dispersion or convergence of the rays RV, RP, or the conjugate focus to R.

For since GI and PV are parallel and PE equal to PI, we have PF : PR = PI : PR, = VG : VR, = fin. incid. : fin. refr. But PF : PR = fin. PRV : fin. PFV, and RRV is equal to the angle of incidence at P; therefore PFV is the corresponding angle of refraction, FPE is the refracted ray, and F the conjugate focus to R.

Corol. 1. If diverging or converging rays fall on the surface of a more refracting medium, they will diverge or converge less after refraction, F being farther from the surface than R. The contrary must happen when the diverging or converging rays fall on the surface of a less refracting medium, because, in this case, F is nearer to the surface than R.

Corol. 2. Let RP be another ray, more oblique than RP, the refracting point p being farther from V, and let f be the refracted ray, determined by the same construction. Because the arches FI, f, are perpendicular to their radii, it is evident that they will converge to some point within the angle RIK, and therefore will not cross each other between F and I; therefore RF will be greater than RF, as RF is greater than RG, for similar reasons. Hence it follows, that all the rays which tended from or towards R, and were incident on the whole of VPp, will not diverge from or converge to F, but will be diffused over the line GFf. This diffusion is called aberration from the focus, and is so much greater as the rays are more oblique. No rays flowing from or towards R will have point of concourse with RV nearer to R than F is: But if the obliquity be inconceivable, so that the ratio of RP to FP does not differ sensibly from that of RV to FV, the point of concourse will not be sensibly removed from G. G is therefore usually called the conjugate focus to R. It is the conjugate focus of an indefinitely slender pencil of rays falling perpendicularly on the surface. The conjugate focus of an oblique pencil, or even of two oblique rays, whose dispersion on the surface is considerable, is of more difficult investigation. See Gravesande's Natural Philosophy for a very neat and elementary determination (e).

In a work of this kind, it is enough to have pointed out, in an easy and familiar manner, the nature of optical aberration. But as this is the chief cause of the imperfection of optical instruments, and as the only method of removing this imperfection is to diminish this aberration, or correct it by a subsequent aberration in the opposite direction, we shall here give a fundamental and very simple proposition, which will (with obvious alterations) apply to all important cases. This is the determination of the focus of an infinitely slender pencil of oblique rays RP, Rp.

"Retaining the former construction for the ray PF, (fig. 1.) suppose the other ray Rp infinitely near to RP. Draw PS perpendicular to PV, and Rr perpendicular to RP, and make Pr : PS = VR : VF. On Pr describe the semicircle rRP, and on PS the semicircle SfP, cutting the refracted ray PF in r, draw pr, ps, rp." It follows

(e) We refer to Gravesande, because we consider it as of importance to make such a work as ours serve as a general index to science and literature. At the same time we take the liberty to observe, that the focus in question is virtually determined by the construction which we have given: for the points P, F of the line PF are determined, and therefore its position is also determined. The same is true of the position of pf, and therefore the intersection p of the two lines is likewise determined. Refraction follows from the lemma, that if \( \varphi \) be the focus of spherical refracted rays, the variation \( P_{\varphi} \) of the angle of refraction is to the corresponding variation \( PR_{\varphi} \) of the angle of incidence as the tangent of the angle of refraction \( VFP \) to the tangent of the angle of incidence \( VRP \). Now \( P_{\varphi} \) may be considered as coinciding with the arch of the semicircles. Therefore the angles \( PR_{\varphi}, PR_{\varphi} \) are equal, as also the angles \( PR_{\varphi}, PS_{\varphi} \). But \( PS_{\varphi} \) is to \( PR_{\varphi} \) as \( PR \) to \( PS \); that is, as \( VR \) to \( VF \); that is, as the cotangent of the angle of incidence to the cotangent of the angle of refraction; that is, as the tangent of the angle of refraction to the tangent of the angle of incidence. Therefore the point \( \varphi \) is the focus.

Of Refraction by Spherical Surfaces.

General Problem.

To find the focus of refracted rays, the focus of incident rays being given.

Let \( PV \) (figs. 5, 6, 7, 8, 9, 10, 11, 12, 13, 14) be a spherical surface whose centre is \( C \), and let the incident light diverge from or converge to \( R \).

Solution. Draw the ray \( RC \) through the centre, cutting the surface in the point \( V \), which we shall denote the vertex, while \( RC \) is called the axis. This ray passes on without refraction, because it coincides with the perpendicular to the surface. Let \( RP \) be another incident ray, which is refracted at \( P \), draw the radius \( PC \). In \( RP \) make \( RE \) to \( RP \) as the sine of incidence \( m \) to the sine of refraction \( n \); and about the centre \( R \), with the distance \( RE \), describe the circle \( EK \), cutting \( PC \) in \( K \); draw \( RK \) and \( PF \) parallel to it, cutting the axis in \( F \). \( PF \) is the refracted ray, and \( F \) is the focus.

For the triangles \( PCF, KCR \) are similar, and the angles at \( P \) and \( K \) are equal. Also \( RK \) is equal to \( RE \), and \( RPD \) is the angle of incidence. Now \( m : n = RK : RP = \sin DPR : \sin RKP = \sin DPR : \sin CPF \). Therefore \( CPF \) is the angle of refraction corresponding to the angle of incidence \( RPD \), and \( PF \) is the refracted ray, and \( F \) the focus. Q. E. D.

Cor. 1. \( CK : CP = CR : CF \), and \( CF = \frac{CP \times CR}{CK} \).

Now \( CP \times CR \) is a constant quantity; and therefore \( CF \) is reciprocally as \( CK \), which evidently varies with a variation of the arch \( VP \). Hence it follows, that all the rays flowing from \( R \) are not collected at the conjugate focus \( F \). The ultimate situation of the point \( F \), as the point \( P \) gradually approaches to, and at last coincides with, \( V \), is called the conjugate focus of central rays, and the distance between this focus and the focus of a lateral ray is called the aberration of that ray, arising from the spherical figure.

There are, however, two situations of the point \( R \) such, that all the rays which flow from it are made to diverge from one point. One of those is \( C \) (fig. 5.), because they all pass through without refraction, and therefore still diverge from \( C \); the other is when rays in the rare medium with a convex surface flow from a point \( R \), so situated beyond the centre that \( CV \) is to \( CR \) as the sine of incidence in the rare medium is to the sine of refraction in the denser, or when rays in the rare medium fall on the convex surface of the denser, converging to \( F \), so situated that \( CF : CV = m : n \). In this case they will all be dispersed from \( F \), so situated that \( CV : CF = n : m \), \( CR : CV \) by spherical surfaces.

For fine \( RPC \): fine \( RKC = n : m \), \( CR : CP = \text{fine } RPC : \text{fine } PCR \). Therefore the angle \( PCR \) is equal to \( RKC \), or to \( FPC \) (by construction of the problem), and the angle \( C \) is common to the triangles \( PCR, FPC \); they are therefore similar, and the angles \( PCR, FPC \) are equal, and \( n : m = CP : CF = CK : CR = CR : CP \); therefore \( CP : CK = CP^2 : CR^2 \); but \( CP \) and \( CR \) are constant quantities, and therefore \( CK \) is a constant quantity, and (by the corollary) \( CF \) is a constant quantity, and all the rays flowing from \( R \) are dispersed from \( F \) by refraction. In like manner rays converging to \( F \) will by refraction converge to \( R \). This was first observed by Huygens.

2. If the incident ray \( R'P \) (fig. 5.) is parallel to the axis \( RC \), we have \( PO \) to \( CO \) as the sine of incidence to the sine of refraction. For the triangles \( R'PK, PCO \) are similar, and \( PO : CO = R'K : RP \), \( m : n \).

3. In this case, too, we have the focal distance of central parallel rays reckoned from the vertex \( = \frac{m}{m-n} \times VC \). For since \( PO \) is ultimately \( VO \), we have \( m : n = VO : CO \), and \( m-n : m = VO - CO : VO = VC : VO \), and \( VO = \frac{m}{m-n} \times VC \). This is called the principal focal distance, or focal distance of parallel rays. Also \( CO \), the principal focal distance reckoned from the centre, \( = \frac{n}{m-n} \times VC \).

N. B. When \( m \) is less than \( n \), \( m-n \) is a negative quantity.—Also observe, that in applying symbols to this computation of the focal distances, those lines are to be accounted positive which lie from their beginnings, that is, from the vertex, or the centre, or the radiant point, in the direction of the incident rays. Thus when rays diverge from \( R \) on the convex surface of a medium, \( VR \) is accounted negative and \( VC \) positive. If the light passes out of air into glass, \( m \) is greater than \( n \); but if it passes out of glass into air, \( m \) is less than \( n \). If, therefore, parallel rays fall on the convex surface of glass out of air, in which case \( m : n = 3 : 2 \) very nearly, we have for the principal focal distance \( \frac{3}{3-2} VC \), or \( +\frac{3}{2} VC \). But if it passes out of glass into the convex surface of air, we have \( VO = \frac{2}{2-3} VC \), or \( -\frac{2}{3} VC \); that is, the focus \( O \) will be in the same side of the surface with the incident light. In like manner, we shall have for these two cases \( CO = +\frac{2}{3} VC \) and \( -\frac{3}{2} VC \).

4. By construction we have \( RK : RP = m : n \) by similarity of triangles \( PF : RK = CF : CR \) therefore \( mPR \times CF = nCR \times PF \) and \( mPR : nCR = PF : CF \) ultimately \( mVR - nCR : mVR = VC : VF \)

This is a very general optical theorem, and affords an easy method for computing the focal distance of refracted rays.

For this purpose let \( VR \), the distance of the radiant point, Besides these, the apartments are furnished at each extremity with an elegant European mahogany bedstead, hung with damask, having on it several matresses placed one over the other, which are covered with various coloured silks; but these beds are merely placed there to ornament the room. In all the apartments, without exception, the ceiling is wood, carved and painted. The principal ornaments in some were large and valuable looking-glasses, hung on different parts of the walls. In others, clocks and watches of different sizes, in glass cases, were disposed in the same manner.

The sultana Lalla Batoom and another favourite were indulged with a whole square to themselves; but the concubines were only each allowed a single room.

Each female had a separate daily allowance from the emperor, proportioned to the estimation in which they were held by him. The late emperor's allowance was very trifling; Lalla Douyaw, the favourite sultana, had very little more than half-a-crown English a-day, and the others less in proportion. It must be allowed, that the emperor made them occasional presents of money, drefs, and trinkets; but this could never be sufficient to support the number of domestics and other expenses they must incur. Their greatest dependence therefore was on the presents they received from those Europeans and Moors who visited the court, and who employed their influence in obtaining some particular favour from the emperor. This was the most successful mode that could be adopted. When Mr Lempriere was at Morocco, a Jew, desirous of obtaining a very advantageous favour from the emperor, for which he had been a long time unsuccessfully soliciting, sent to all the principal ladies of the harem presents of pearls to a very large amount; the consequence was, that they all went in a body to the emperor, and immediately obtained the wished-for concession.

The ladies separately furnish their own rooms, hire their own domestics, and, in fact, do what they please in the harem, but are not permitted to go out without an express order from the emperor, who very seldom grants them that favour, except when they are to be removed from one palace to another. In that case, a party of soldiers is dispatched a little distance before them, to disperse the male passengers in particular, and to prevent the possibility of their being seen. This previous step being taken, a piece of linen cloth is tied round the lower part of the face, and afterwards these miserable females cover themselves entirely with their haicks, and either mount mules, which they ride like men, or, what is more usual, are put into a square carriage or litter, constructed for this purpose, which by its lattice-work allows them to see without being seen. In this manner they set off, under the charge of a guard of black eunuchs. This journey, and sometimes a walk within the bounds of the palace, with which they are, however, seldom indulged, is the only exercise they are permitted to take.

The late emperor's harem consisted of between 60 and 100 females, besides their domestics and slaves, which were very numerous. Many of the concubines were Moorish women, who had been presented to the emperor, as the Moors consider it an honour to have their daughters in the harem; several were European slaves, who had either been made captives, or purchased by the emperor; and some were Negroes.

In this group the Europeans, or their descendants, had by far the greatest claim to the character of handsome. There was one in particular, who was a native of Spain, and taken into the harem at about the same age as Lalla Douyaw, who was indeed a perfect beauty. Nor was this lady quite singular in that respect, for many others were almost equally handsome.

The eunuchs, who have the entire charge of the women, and who in fact live always among them, are the children of Negro slaves. They are generally either very short and fat, or else tall, deformed, and lame. Their voices have that particular tone which is observable in youths who are just arriving at manhood; and their persons altogether afford a disgusting image of weakness and effeminacy.

The same gentleman gives us a very curious account of the manners and ignorance of these immured females, from his own observation, when visiting the prince's harem. "Attended by an eunuch (says he), after passing the gate of the harem, which is always locked, and under the care of a guard of eunuchs, we entered a narrow and dark passage, which soon brought us to the court, into which the women's chambers open. We here saw numbers of both black and white women and children; some concubines, some slaves, and others hired domestics.

"Upon their observing the unusual figure of an European, the whole multitude in a body surrounded me, and expressed the utmost astonishment at my dress and appearance. Some stood motionless, with their hands lifted up, their eyes fixed, and their mouths open, in the usual attitude of wonder and surprize. Some burst into immoderate fits of laughter; while others again came up, and with uncommon attention eyed me from head to foot. The parts of my dress which seemed most to attract their notice were my buckles, buttons, and stockings; for neither men nor women in this country wear any thing of the kind. With respect to the club of my hair, they seemed utterly at a loss in what view to consider it; but the powder which I wore they conceived to be employed for the purpose of destroying vermin. Most of the children, when they saw me, ran away in the most perfect consternation; and on the whole, I appeared as singular an animal, and I dare say had the honour of exciting as much curiosity and attention, as a lion or a man-tiger just imported from abroad, and introduced into a country town in England on a market-day." Every time I visited the harem, I was surrounded and laughed at by this curious mob, who, on my entering the gate, followed me close to the very chamber to which I was proceeding, and on my return universally escorted me out.

"The greatest part of the women were uncommonly fat and unwieldy; had black and full eyes, round faces, with small noses. They were of different complexions; some very fair, some fayal, and others again perfect Negroes.

"One of my new patients being ready to receive me, I was desired to walk into her room; where, to my great surprize, I saw nothing but a curtain drawn quite across the apartment, similar to that of a theatre which separates the stage from the audience. A female domestic brought a very low stool, placed it near the curtain, and told me I was to sit down there, and feel her mistress's pulse." "The lady, who had by this time summoned up courage to speak, introduced her hand from the bottom of the curtain, and desired me to inform her of all her complaints, which I conceived I might perfectly do by merely feeling the pulse. It was in vain to ask her where her pain was seated, whether in her stomach, head, or back; the only answer I could procure was a request to feel the pulse of the other hand, and then point out the seat of the disease, and the nature of the pain.

Having neither satisfied my curiosity by exhibiting her face, nor made me acquainted with the nature of her complaint, I was under the necessity of informing her in polite terms, that to understand the disease, it was absolutely necessary to see the tongue as well as to feel the pulse; and that without it I could do nothing for her. My eloquence, or rather that of my Jewish interpreter, was, however, for a long time exerted in vain; and I am persuaded she would have dismissed me without any further inquiry, had not her invention supplied her with a happy expedient to remove her embarrassment. She contrived at last to cut a hole through the curtain, through which she extruded her tongue, and thus complied with my injunction as far as it was necessary in a medical view, but most effectually disappointed my curiosity.

I was afterwards ordered to look at another of the prince's wives, who was affected with a scrophulous swelling in her neck. This lady was, in the same manner as the other, at first excluded from my sight; but as she was obliged to show me her complaint, I had an opportunity of seeing her face, and observed it to be very handsome."

It is curious to observe the strange and childish notions of persons who have been totally secluded from the world. All the ladies of the harem expected that our author should have instantly discovered their complaints upon feeling the pulse, and that he could cure every disease instantaneously. He found them proud and vain of their persons, and extremely ignorant. Among many ridiculous questions, they asked my interpreter (says Mr Lempriere) if I could read and write; upon being answered in the affirmative, they expressed the utmost surprise and admiration at the abilities of the Christians. There was not one among them who could do either; these rudiments of learning are indeed only the lot of a few of their men, who on that account are named Talbs, or explainers of the Mahometan law."

It is melancholy to reflect on the situation of these unfortunate women. Being considered as the mere instruments of pleasure, no attention is paid to the improvement of their minds. They have no employment to occupy their time. Their needle-work is performed by Jewesses; their food is drest, and their chambers taken care of, by slaves and domestics. They have no amusement but a rude and barbarous kind of melancholy music, without melody, variety, or taste; and conversation with one another, which must indeed be very confined, uniform, and inanimate, as they never see a new object. Excluded from the enjoyment of fresh air and exercise, so necessary for the support of health and life; deprived of all society but that of their fellow sufferers, a society to which most of them would prefer solitude itself; they are only to be considered as the most abject of slaves—slaves to the vices and caprice of a licentious tyrant, who exacts even from his wives themselves a degree of submission and respect which borders upon idolatry, and which God and nature never meant should be paid to a mortal.