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Massachusetts Board of Retirement v. Murgia/Dissent Marshall

Mr. Justice Marshall, dissenting.

Today the Court holds that it is permissible for the Commonwealth of Massachusetts to declare that members of its state police force who have been proved medically fit for service are nonetheless legislatively unfit to be policemen and must be terminated--involuntarily "retired"--because they have reached the age of 50. Although we have called the right to work "of the very essence of the personal freedom and opportunity that it was the purpose of the [Fourteenth] Amendment to secure," Truax v. Raich, 239 U.S. 33, 41 (1915), the Court finds that the right to work is not a fundamental right. And, while agreeing that "the treatment of the aged in this Nation has not been wholly free of discrimination," ante, at 313, the Court holds that the elderly are not a suspect class. Accordingly, the Court undertakes the scrutiny mandated by the bottom tier of its two-tier equal protection framework, finds the challenged legislation not to be "wholly unrelated" to its objective, and holds, therefore, that it survives equal protection attack. I respectfully dissent.

I
Although there are signs that its grasp on the law is weakening, the rigid two-tier model still holds sway as the Court's articulated description of the equal protection test. Again, I must object to its perpetuation. The model's two fixed modes of analysis, strict scrutiny and mere rationality, simply do not describe the inquiry the Court has undertaken--or should undertake--in equal protection cases. Rather, the inquiry has been much more sophisticated and the Court should admit as much. It has focused upon the character of the classification in question, the relative importance to individuals in the class discriminated against of the governmental benefits that they do not receive, and the state interests asserted in support of the classification. Marshall v. United States, 414 U.S. 417, 432-433 (1974) (Marshall, J., dissenting); San Antonio School District v. Rodriguez, 411 U.S. 1, 98 -110 (1973) (Marshall, J., dissenting); Richardson v. Belcher, 404 U.S. 78, 90 -91 (1971) (Marshall, J., dissenting); Dandridge v. Williams, 397 U.S. 471, 519 -530 (1970) (Marshall, J., dissenting). See also City of Charlotte v. Firefighters, 426 U.S. 283, 286 (1976); Memorial Hospital v. Maricopa County, 415 U.S. 250, 253-254 (1974); Dunn v. Blumstein, 405 U.S. 330, 335 (1972); Kramer v. Union School Dist., 395 U.S. 621, 626 (1969); Williams v. Rhodes, 393 U.S. 23, 30 (1968).

Although the Court outwardly adheres to the two-tier model, it has apparently lost interest in recognizing further "fundamental" rights and "suspect" classes. See San Antonio School District v. Rodriguez, supra (rejecting education as a fundamental right); Frontiero v. Richardson, 411 U.S. 677 (1973) (declining to treat women as a suspect class). In my view, this result is the natural consequence of the limitations of the Court's traditional equal protection analysis. If a statute invades a "fundamental" right or discriminates against a "suspect" class, it is subject to strict scrutiny. If a statute is subject to strict scrutiny, the statute always, or nearly always, see Korematsu v. United States, 323 U.S. 214 (1944), is struck down. Quite obviously, the only critical decision is whether strict scrutiny should be invoked at all. It should be no surprise, then, that the Court is hesitant to expand the number of categories of rights and classes subject to strict scrutiny, when each expansion involves the invalidation of virtually every classification bearing upon a newly covered category.

But however understandable the Court's hesitancy to invoke strict scrutiny, all remaining legislation should not drop into the bottom tier, and be measured by the mere rationality test. For that test, too, when applied as articulated, leaves little doubt about the outcome; the challenged legislation is always upheld. See New Orleans v. Dukes, ante, p. 297 (overruling Morey v. Doud, 354 U.S. 457 (1957), the only modern case in which this Court has struck down an economic classification as irrational). It cannot be gainsaid that there remain rights, not now classified as "fundamental," that remain vital to the flourishing of a free society, and classes, not now classified as "suspect," that are unfairly burdened by invidious discrimination unrelated to the individual worth of their members. Whatever we call these rights and classes, we simply cannot forgo all judicial protection against discriminatory legislation bearing upon them, but for the rare instances when the legislative choice can be termed "wholly irrelevant" to the legislative goal. McGowan v. Maryland, 366 U.S. 420, 425 (1961).

While the Court's traditional articulation of the rational-basis test does suggest just such an abdication, happily the Court's deeds have not matched its words. Time and again, met with cases touching upon the prized rights and burdened classes of our society, the Court has acted only after a reasonably probing look at the legislative goals and means, and at the significance of the personal rights and interests invaded. Stanton v. Stanton, 421 U.S. 7 (1975); Weinberger v. Wiesenfeld, 420 U.S. 636 (1975); United States Dept. of Agriculture v. Moreno, 413 U.S. 528 (1973); Frontiero v. Richardson, 411 U.S., at 691 (Powell, J., concurring in judgment); James v. Strange, 407 U.S. 128 (1972); Weber v. Aetna Casualty & Surety Co., 406 U.S. 164 (1972); Eisenstadt v. Baird, 405 U.S. 438 (1972); Reed v. Reed, 404 U.S. 71 (1971). See San Antonio School District v. Rodriguez, supra, at 98-110 (Marshall, J., dissenting). These cases make clear that the Court has rejected, albeit sub silentio, its most deferential statements of the rationality standard in assessing the validity under the Equal Protection Clause of much noneconomic legislation.

But there are problems with deciding cases based on factors not encompassed by the applicable standards. First, the approach is rudderless, affording no notice to interested parties of the standards governing particular cases and giving no firm guidance to judges who, as a consequence, must assess the constitutionality of legislation before them on an ad hoc basis. Second, and not unrelatedly, the approach is unpredictable and requires holding this Court to standards it has never publicly adopted. Thus, the approach presents the danger that, as I suggest has happened here, relevant factors will be misapplied or ignored. All interests not "fundamental" and all classes not "suspect" are not the same; and it is time for the Court to drop the pretense that, for purposes of the Equal Protection Clause, they are.

II
The danger of the Court's verbal adherence to the rigid two-tier test, despite its effective repudiation of that test in the cases, is demonstrated by its efforts here. There is simply no reason why a statute that tells able-bodied police officers, ready and willing to work, that they no longer have the right to earn a living in their chosen profession merely because they are 50 years old should be judged by the same minimal standards of rationality that we use to test economic legislation that discriminates against business interests. See New Orleans v. Dukes, supra; Williamson v. Lee Optical Co., 348 U.S. 483 (1955). Yet, the Court today not only invokes the minimal level of scrutiny, it wrongly adheres to it. Analysis of the three factors I have identified above--the importance of the governmental benefits denied, the character of the class, and the asserted state interests--demonstrates the Court's error.

Whether "fundamental" or not, "'the right of the individual...to engage in any of the common occupations of life'" has been repeatedly recognized by this Court as falling within the concept of liberty guaranteed by the Fourteenth Amendment. Board of Regents v. Roth, 408 U.S. 564, 572 (1972), quoting Meyer v. Nebraska, 262 U.S. 390, 399 (1923). As long ago as Butchers' Union Co. v. Crescent City Co., 111 U.S. 746 (1884), Mr. Justice Bradley wrote that this right "is an inalienable right; it was formulated as such under the phrase 'pursuit of happiness' in the Declaration of Independence.... This right is a large ingredient in the civil liberty of the citizen." Id., at 762 (concurring opinion). And in Smith v. Texas, 233 U.S. 630 (1914), in invalidating a law that criminally penalized anyone who served as a freight train conductor without having previously served as a brakeman, and that thereby excluded numerous equally qualified employees from that position, the Court recognized that "all men are entitled to the equal protection of the law in their right to work for the support of themselves and families." Id., at 641.

"In so far as a man is deprived of the right to labor his liberty is restricted, his capacity to earn wages and acquire property is lessened, and he is denied the protection which the law affords those who are permitted to work. Liberty means more than freedom from servitude, and the constitutional guarantee is an assurance that the citizen shall be protected in the right to use his powers of mind and body in any lawful calling." Id., at 636.

See also Arnett v. Kennedy, 416 U.S. 134 (1974); Perry v. Sindermann, 408 U.S. 593 (1972); Bell v. Burson, 402 U.S. 535 (1971); Keyishian v. Board of Regents, 385 U.S. 589, 605-606 (1967); Schware v. Board of Bar Examiners, 353 U.S. 232, 238-239 (1957); Slochower v. Board of Higher Education, 350 U.S. 551 (1956); Wieman v. Updegraff, 344 U.S. 183 (1952); Truax v. Raich, 239 U.S., at 41. Even if the right to earn a living does not include the right to work for the government, it is settled that because of the importance of the interest involved, we have always carefully looked at the reasons asserted for depriving a government employee of his job.

While depriving any government employee of his job is a significant deprivation, it is particularly burdensome when the person deprived is an older citizen. Once terminated, the elderly cannot readily find alternative employment. The lack of work is not only economically damaging, but emotionally and physically draining. Deprived of his status in the community and of the opportunity for meaningful activity, fearful of becoming dependent on others for his support, and lonely in his new-found isolation, the involuntarily retired person is susceptible to physical and emotional ailments as a direct consequence of his enforced idleness. Ample clinical evidence supports the conclusion that mandatory retirement poses a direct threat to the health and life expectancy of the retired person, and these consequences of termination for age are not disputed by appellants. 324*324 Thus, an older person deprived of his job by the government loses not only his right to earn a living, but, too often, his health as well, in sad contradiction of Browning's promise: "The best is yet to be,/The last of life, for which the first was made."

Not only are the elderly denied important benefits when they are terminated on the basis of age, but the classification of older workers is itself one that merits judicial attention. Whether older workers constitute a "suspect" class or not, it cannot be disputed that they constitute a class subject to repeated and arbitrary discrimination in employment. See United States Department of Labor, The Older American Worker: Age Discrimination in Employment (1965); M. Barron, The Aging American 55-68 (1961). As Congress found in passing the Age Discrimination in Employment Act of 1967:

"[I]n the face of rising productivity and affluence, older workers find themselves disadvantaged in their efforts to retain employment, and especially to regain employment when displaced from jobs[.]

"[T]he setting of arbitrary age limits regardless of potential for job performance has become a common practice, and certain otherwise desirable practices may work to the disadvantage of older persons[.]

"[T]he incidence of unemployment, especially long-term unemployment with resultant deterioration of skill, morale, and employer acceptability is, relative to the younger ages, high among older workers; their numbers are great and growing; and their employment problems grave[.]" 81 Stat. 602, 29 U.S.C. § 621 (a) (subsection numbers omitted).

See also ante, at 317 n. 11.

Of course, the Court is quite right in suggesting that distinctions exist between the elderly and traditional suspect classes such as Negroes, and between the elderly and "quasi-suspect" classes such as women or illegitimates. The elderly are protected not only by certain anti-discrimination legislation, but by legislation that provides them with positive benefits not enjoyed by the public at large. Moreover, the elderly are not isolated in society, and discrimination against them is not pervasive but is centered primarily in employment. The advantage of a flexible equal protection standard, however, is that it can readily accommodate such variables. The elderly are undoubtedly discriminated against, and when legislation denies them an important benefit--employment--I conclude that to sustain the legislation appellants must show a reasonably substantial interest and a scheme reasonably closely tailored to achieving that interest. Cf. San Antonio School District v. Rodriguez, 411 U.S., at 124-126 (Marshall, J., dissenting). This inquiry, ultimately, is not markedly different from that undertaken by the Court in Reed v. Reed, 404 U.S. 71 (1971).

Turning, then, to appellants' arguments, I agree that the purpose of the mandatory retirement law is legitimate, and indeed compelling. The Commonwealth has every reason to assure that its state police officers are of sufficient physical strength and health to perform their jobs. In my view, however, the means chosen, the forced retirement of officers at age 50, is so overinclusive that it must fall.

All potential officers must pass a rigorous physical examination. Until age 40, this same examination must be passed every two years--when the officer re-enlists--and, after age 40, every year. Appellants have conceded that "[w]hen a member passes his re-enlistment or annual physical, he is found to be qualified to perform all of the duties of the Uniformed Branch of the Massachusetts State Police." App. 43. See id., at 52. If a member fails the examination, he is immediately terminated or refused re-enlistment. Thus, the only members of the state police still on the force at age 50 are those who have been determined—repeatedly—by the Commonwealth to be physically fit for the job. Yet, all of these physically fit officers are automatically terminated at age 50. Appellants do not seriously assert that their testing is no longer effective at age 50, nor do they claim that continued testing would serve no purpose because officers over 50 are no longer physically able to perform their jobs. Thus the Commonwealth is in the position of already individually testing its police officers for physical fitness, conceding that such testing is adequate to determine the physical ability of an officer to continue on the job, and conceding that that ability may continue after age 50. In these circumstances, I see no reason at all for automatically terminating those officers who reach the age of 50; indeed, that action seems the height of irrationality.

Accordingly, I conclude that the Commonwealth's mandatory retirement law cannot stand when measured against the significant deprivation the Commonwealth's action works upon the terminated employees. I would affirm the judgment of the District Court.


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 At the time of the Roman conquest, the province was inhabited by the Vettones and Callaici; it afterwards formed part of Hispania Tarraconensis. Among the Christian kingdoms which arose in Spain as the Moorish invasion of the 8th century receded, Leon was one of the oldest. The title of king of Leon was first assumed by Ordoño in 913. Ferdinand I. (the Great) of Castile united the crowns of Castile and Leon in the 11th century; the two were again separated in the 12th, until a final union took place (1230) in the person of St Ferdinand. The limits of the kingdom varied with the vicissitudes of war, but roughly speaking it may be said to have embraced what are now the provinces of Leon, Palencia, Valladolid, Zamora and Salamanca. For a detailed account of this kingdom, see : History. The captaincy-general of the province of Leon before 1833 included Leon, Zamora and Salamanca. The Leonese, or inhabitants of these three provinces, have less individuality, in character and physique, than the people of Galicia, Catalonia or Andalusia, who are quite distinct from what is usually regarded as the central or national Spanish type, i.e. the Castilian. The Leonese belong partly to the Castilian section of the Spaniards, partly to the north-western section which includes the Galicians and Asturians. They have comparatively few of the Moorish traits which are so marked in the south and east of Spain. Near Astorga there dwells a curious tribe, the Maragatos, sometimes considered to be a remnant of the original Celtiberian inhabitants. As a rule the Maragatos earn their living as muleteers or carriers; they wear a distinctive costume, mix as little as possible with their neighbours and do not marry outside their own tribe.  LEON, an episcopal see and the capital of the Spanish province of Leon, situated on a hill 2631 ft. above sea-level, in the angle made by the Torio and Bernesga, streams which unite on the south, and form the river Leon, a tributary of the Esla. Pop. (1900) 15,580. Leon is on the main railway from Madrid to Oviedo, and is connected with Astorga by a branch line. The older quarters of the city, which contain the cathedral and other medieval buildings, are surrounded by walls, and have lost little of their beauty and interest from the restoration carried out in the second half of the 19th century. During the same period new suburbs grew up outside the walls to house the industrial population which was attracted by the development of iron-founding and the manufacture of machinery, railway-plant, chemicals and leather. Leon thus comprises two towns—the old, which is mainly ecclesiastical in its character, and the new, which is industrial. The cathedral, founded in 1199 and only finished at the close of the 14th century, is built of a warm cream-coloured stone, and is remarkable for simplicity, lightness and strength. It is one of the finest examples of Spanish Gothic, smaller, indeed, than the cathedrals of Burgos and Toledo, but exquisite in design and workmanship. The chapter library contains some valuable manuscripts. The collegiate church of San Isidoro was founded by Ferdinand I. of Castile in 1063 and consecrated in 1149. Its architecture is Romanesque. The church contains some fine plate, including the silver reliquary in which the bones of St Isidore of Seville are preserved, and a silver processional cross dating from the 16th century, which is one of the most beautiful in the country. The convent and church of San Marcos, planned in 1514 by Ferdinand the Catholic, founded by Charles V. in 1537, and consecrated in 1541, are Renaissance in style. They are built on the site of a hostel used by pilgrims on their way to Santiago de Compostela. The provincial museum occupies the chapterhouse and contains some interesting Roman monuments. The lower part of the city walls consists of Roman masonry dating from the 3rd century. Other buildings are the high school, ecclesiastical seminaries, hospital, episcopal palace and municipal and provincial halls.

Leon (Arab. Liyun) owes its name to the Legio Septima Gemina of Galba, which, under the later emperors, had its headquarters here. About 540 Leon fell into the hands of the Gothic king Leovigild, and in 717 it capitulated to the Moors. Retaken about 742, it ultimately, in the beginning of the 10th century, became the capital of the kingdom of Leon (see : History). About 996 it was taken by Almansur, but on his death soon

afterwards it reverted to the Spaniards. It was the seat of several ecclesiastical councils, the first of which was held under Alphonso V. in 1012 and the last in 1288.

 LEONARDO DA VINCI (1452–1519), the great Italian painter, sculptor, architect, musician, mechanician, engineer and natural philosopher, was the son of a Florentine lawyer, born out of wedlock by a mother in a humble station, variously described as a peasant and as of gentle birth. The place of his birth was Vinci, a castello or fortified hill village in the Florentine territory near Empoli, from which his father’s family derived its name. The Christian name of the father was Piero (the son of Antonio the son of Piero the son of Guido, all of whom had been men of law like their descendant). Leonardo’s mother was called Catarina. Her relations with Ser Piero da Vinci seem to have come to an end almost immediately upon the birth of their son. She was soon afterwards married to one Accattabriga di Piero del Vacca, of Vinci. Ser Piero on his part was four times married, and had by his last two wives nine sons and two daughters; but he had from the first acknowledged the boy Leonardo and brought him up in his own house, principally, no doubt, at Florence. In that city Ser Piero followed his profession with success, as notary to many of the chief families in the city, including the Medici, and afterwards to the signory or governing council of the state. The son born to him before marriage grew up into a youth of shining promise. To splendid beauty and activity of person he joined a winning charm of temper and manners, a tact for all societies, and an aptitude for all accomplishments. An inexhaustible intellectual energy and curiosity lay beneath this amiable surface. Among the multifarious pursuits to which the young Leonardo set his hand, the favourites at first were music, drawing and modelling. His father showed some of his drawings to an acquaintance, Andrea del Verrocchio, who at once recognized the boy’s artistic vocation, and was selected by Ser Piero to be his master.

Verrocchio, although hardly one of the great creative or inventive forces in the art of his age at Florence, was a first-rate craftsman alike as goldsmith, sculptor and painter, and particularly distinguished as a teacher. In his studio Leonardo worked for several years (about 1470–1477) in the company of Lorenzo di Credi and other less celebrated pupils. Among his contemporaries he formed special ties of friendship with the painters Sandro Botticelli and Pietro Perugino. He had soon learnt all that Verrocchio had to teach—more than all, if we are to believe the oft-told tale of the figure, or figures, executed by the pupil in the picture of Christ’s Baptism designed by the master for the monks of Vallombrosa. The work in question is now in the Academy at Florence. According to Vasari the angel kneeling on the left, with a drapery over the right arm, was put in by Leonardo, and when Verrocchio saw it his sense of its superiority to his own work caused him to forswear painting for ever after. The latter part of the story is certainly false. The picture, originally painted in tempera, has suffered much from later repaints in oil, rendering exact judgment difficult. The most competent opinion inclines to acknowledge the hand of Leonardo, not only in the face of the angel, but also in parts of the drapery and of the landscape background. The work was probably done in or about 1470, when Leonardo was eighteen years old. By 1472 we find him enrolled in the lists of the painters’ gild at Florence. Here he continued to live and work for ten or eleven years longer. Up till 1477 he is still spoken of as a pupil or apprentice of Verrocchio; but in that year he seems to have been taken into special favour by Lorenzo the Magnificent, and to have worked as an independent artist under his patronage until 1482–1483. In 1478 we find him receiving an important commission from the signory, and in 1480 another from the monks of San Donato in Scopeto.

Leonardo was not one of those artists of the Renaissance who sought the means of reviving the ancient glories of art mainly in the imitation of ancient models. The antiques of the Medici gardens seem to have had little influence on him beyond that of generally stimulating his passion for perfection. By his own instincts he was an exclusive student of nature.

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title: Page:EB1911 - Volume 16.djvu/464


text: 1911 Encyclopædia Britannica/Leon (city)


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User:Cleonis/Sandbox/Heuristic

Maxwell's theory of electromagnetic processes in so-called empty space differs in a profound, essential way from the current theoretical models of gases and other matter. On the one hand, we consider the state of a material body to be determined completely by the positions and velocities of a finite number of atoms and electrons, albeit a very large number. By contrast, the electromagnetic state of a region of space is described by continuous functions and, hence, cannot be determined exactly by any finite number of variables. Thus, according to Maxwell's theory, the energy of purely electromagnetic phenomena (such as light) should be represented by a continuous function of space. By contrast, the energy of a material body should be represented by a discrete sum over the atoms and electrons; hence, the energy of a material body cannot be divided into arbitrarily many, arbitrarily small components. However, according to Maxwell's theory (or, indeed, any wave theory), the energy of a light wave emitted from a point source is distributed continuously over an ever larger volume.

The wave theory of light with its continuous spatial functions has proven to be an excellent model of purely optical phenomena and presumably will never be replaced by another theory. Nevertheless, we should consider that optical experiments observe only time-averaged values, rather than instantaneous values. Hence, despite the perfect agreement of Maxwell's theory with experiment, the use of continuous spatial functions to describe light may lead to contradictions with experiments, especially when applied to the generation and transformation of light.

In particular, black body radiation, photoluminescence, generation of cathode rays from ultraviolet light and other phenomena associated with the generation and transformation of light seem better modeled by assuming that the energy of light is distributed discontinuously in space. According to this picture, the energy of a light wave emitted from a point source is not spread continuously over ever larger volumes, but consists of a finite number of energy quanta that are spatially localized at points of space, move without dividing and are absorbed or generated only as a whole.

Subsequently, I wish to explain the reasoning and supporting evidence that led me to this picture of light, in the hope that some researchers may find it useful for their experiments.

A certain problem concerning the theory of "black body radiation".
We begin by applying Maxwell's theory of light and electrons to the following situation. Let there be a cavity with perfectly reflecting walls, filled with a number of freely moving electrons and gas molecules that interact via conservative forces whenever they come close, i.e., that collide with each other just as gas molecules in the kinetic theory of gases. In addition, let there be a number of electrons bound to spatially well-separated points by restoring forces that increase linearly with separation. These electrons also interact with the free molecules and electrons by conservative potentials when they approach very closely. We denote these electrons, which are bound at points of space, as "resonators", since they absorb and emit electromagnetic waves of a particular period.

According to the present theory of the generation of light, the radiation in the cavity must be identical to black body radiation (which may be found by assuming Maxwell's theory and dynamic equilibrium), at least if one assumes that resonators exist for every frequency under consideration.

Initially, let us neglect the radiation absorbed and emitted by the resonators and focus instead on the requirement of thermal equilibrium and its implications for the interaction (collisions) between molecules and electrons. According to the kinetic theory of gases, dynamic equilibrium requires that the average kinetic energy of a resonator equal the average kinetic energy of a freely moving gas molecule. Decomposing the motion of a resonator electron into three mutually perpendicular oscillations, we find that the average energy $$\bar{E}$$ of such a linear oscillation is

\bar{E} = \frac{R}{N} T , $$

where R is the absolute gas constant, N is the number of "real molecules" in a gram equivalent and T is the absolute temperature. Because of the time averages of the kinetic and potential energy, the energy $$\bar{E}$$ is 2/3 as large as the kinetic energy of a single free gas molecule. Even if something (such as radiative processes) causes the time-averaged energy of a resonator to deviate from the value $$\bar{E}$$, collisions with the free electrons and gas molecules will return its average energy to $$\bar{E}$$ by absorbing or releasing energy. Hence, in this situation, dynamic equilibrium can only exist when every resonator has an average energy $$\bar{E}$$.

We apply a similar consideration now to the interaction between the resonators and the ambient radiation within the cavity. For this case, Planck has derived the necessary condition for dynamic equilibrium ; treating the radiation as a completely random process.

He found:

\bar{E}_{\nu} = \frac{L^{3}}{8 \pi \nu^{2}} \rho_{\nu}. $$

Here, $$\bar{E}_{\nu}$$ is the average energy of a resonator of eigenfrequency ν (per oscillatory component), L is the speed of light, ν is the frequency, and ρνdν is the energy density of the cavity radiation of frequency between ν and ν + dν.

If the net radiative energy of frequency ν is not to continually increase or decrease, the following equality must hold

\frac{R}{N} T = \bar{E} = \bar{E}_{\nu} = \frac{L^{3}}{8 \pi \nu^{2}} \rho_{\nu}, $$

or, equivalently,

\rho_{\nu} = \frac{R}{N} \frac{8 \pi \nu^{2}}{L^{3}} T. $$

This condition for dynamic equilibrium not only lacks agreement with experiment, it also eliminates any possibility for equilibrium between matter and aether. The wider the range of frequencies of the resonators is chosen the bigger the radiation energy in the space becomes, and in the limit we obtain:

\int_{0}^{\infty} \rho_{\nu} \, d\nu = \frac{R}{N} \frac{8 \pi}{L^{3}} T \int_{0}^{\infty} \nu^{2} \, d\nu = \infty \. $$

Planck's Derivation of the Fundamental Quantum
In the next section we want to show that the determiniation that Mr. Planck gave of the elementary quanta is to some extent independent of the "black body radiation" theory that he created.

The Formula by Planck for ρν that suffices for all experiments so far goes

 * $$\rho_{\nu} = \cfrac{\alpha \nu^3}{e^{\cfrac{\beta\nu}{T}}-1}, $$

where

 * $$ \alpha = 6.1 \cdot 10^{-56},$$
 * $$ \beta = 4.866 \cdot 10^{-11}.$$

In the limit of large values of T/ν, that is for large wavelengths and radiation densities this formula approaches the form:

 * $$ \rho_{\nu} = \frac{\alpha}{\beta}\nu^2T. $$

One recognizes that this formula is the same as the one that was derived from Maxwell theory and electron theory. Equating the coefficients of the formula's:

 * $$\frac{R}{N}\frac{8\pi}{L^3} = \frac{\alpha}{\beta} $$

or

 * $$N = \frac{\beta}{\alpha}\frac{8 \pi R}{L^3} = 6.17 \cdot 10^{23},$$

that is, a hydrogen atom weighs 1/N gram = 1.62·10-24g. This is precisely the value found by Mr. Planck, which is in satisfactory agreement with values obtained in other ways.

This brings us to the conclusion: the larger the energy density and the wavelength of radiation the more suitable the theoretical basis that we used; but for small wavelengths and low radiation densities the basis fails completely.

In the following the "black body radiation" is to be considered in terms of what is experienced, without forming a picture of the creation and propagation of the radiation.

The Entropy of Radiation
The following discussion is contained in a famous work of Mr. Wien, and is only included here for the sake of completeness.

Let there be radiation taking up volume v. We assume that the observable properties of the radiation are determined completely when the radiation densities ρ(ν) are given for all frequencies. Since we can regard radiations of different frequency as separable without doing work or transferring heat the entropy of the radiation can be expressed in the form

 * $$ S = v \int\limits_0^{\infty}\phi (\rho, \nu) d\nu $$

where φ is a function of the variables ρ and ν. φ can be reduced to a function of only one variable by expressing that the entropy of radiation between reflecting walls is not changed by adiabatic compression. We won't go into that however, but investigate right away how the function φ can be obtained from the radiation law of the black body.

In the case of "black body radiation" ρ is such a function of ν that for a given energy the entropy is a maximum, that is, that

 * $$ \rho \int\limits_0^{\infty}\phi (\rho, \nu) d\nu = 0, $$

When

 * $$ \rho \int\limits_0^{\infty}\phi \rho d\nu = 0. $$

From this it follows that for any choice of δρ as function of ν

 * $$ \int\limits_0^{\infty} \left(\frac{\partial\phi}{\partial\rho} - \lambda \right) \delta\rho d\nu = 0, $$

Where λ is independent of ν. Thus $$\partial\phi / \partial\rho$$ is independent of ν

For the temperature increase of dT of a black body radiation of volume v = 1 the following equation is valid:

 * $$ dS = \int\limits_{\nu=0}^{\nu=\infty} \frac{\partial\phi}{\partial\rho} d\rho d\nu,$$

or, since $$\partial\phi / \partial\rho$$ is independent of ν:

 * $$ dS = \frac{\partial\phi}{\partial\rho}dE.$$

Since dE is equal to the transferred heat, and the process is reversible we also have:

 * $$ dS = \frac{1}{T}dE.$$

Equating formula's gives:

 * $$ \frac{\partial\phi}{\partial\rho} = \frac{1}{T}.$$

This is the black body radiation law. So it's possible to determine the black body radiation from the function φ. Conversely, through integration one can obtain φ from the black body radiation law keeping in mind that φ vanishes for ρ = 0.

Limiting law for the entropy of monochromatic radiation at low radiation density
Admittedly, the observations of "black body radiation" so far indicate that the law that Mr. Wien originally devised for the "black body radiation"

 * $$ \rho = \alpha\nu^3 e^{-\beta\tfrac{\nu}{T}} $$

is not exactly valid. However, for large values of ν/T experiment completely confirmes the law. We shall base hour calculations on this formula, keeping in mind that the results will be valid within certain limitations only.

First, we get from this equation:

 * $$ \frac{1}{T} = -\frac{1}{\beta\nu}\lg\frac{\rho}{\alpha\nu^3} $$

and then, using the relation obtained in the preceding section:

 * $$\phi(\rho,\nu) = - \frac{\rho}{\beta\nu} \left\{ \lg\frac{\rho}{\alpha \nu^3} - 1\right\} .$$

Let there be a radiation of energy E, with a frequency between ν and ν + dν. Let the radiation extend over volume v. The entropy of this radiation is:

 * $$S = v \phi(\rho,\nu) d\nu = - \frac{E}{\beta\nu} \left\{ \lg\frac{E}{v \alpha \nu^3 d\nu} - 1\right\} .$$

We will limit ourselves to investigating the dependency of the radiation's entropy on the volume that is occupied. Let the entropy of the radiation be called S0 when it occupies the volume v0, then we get:

 * $$S - S_0 = \frac{E}{\beta\nu}\lg\left(\frac{v}{v_0}\right).$$

This equation shows that the entropy of monochromatic radiation of sufficiently low density varies with volume according to the same law as the entropy of an ideal gas or that of a dilute solution. In the following the equation just found will be interpreted in terms of the principle introduced by Mr. Boltzmann that says that the entropy of a system is a function of the probability of its state.

Molecular Theoretical investigation of the Volume Dependence of the Entropy of Gases and Dilute Solutions
In calculating Entropy on the grounds of molecular theory the word "probability" is often used in a meaning that isn't covered by the definition in probability theory. Especially the "cases of equal probability" are often set by hypothesis, where the applied theoretical representation is sufficiently definite to deduce probabilities without fixing them by hypothesis. I will show in a separate work that in considerations of thermal processes one obtains a complete result with the socalled "statistical probability". This way I hope to remove a logical difficulty that is in the way of fully implementing Boltzmann's principle. Here however only its general formulation and application in quite specific cases will be given.

When it's meaningful to talk about the probability of a state of a system, and additionally every increase of entropy can be described as a transition to a more probable state, the entropy S1 of a system is a function of the probability W1 of its instantaneous state. In the case of two systems S1 and S2, one can state:

\begin{align} S_1 & = \phi_1(W_1), \\ S_2 & = \phi_2(W_2). \\ \end{align} $$

If one considers these systems as a single system with entropy S and probability W, then:

 * $$S = S_1 + S_2 = \phi(W) $$

and

 * $$W = W_1 \cdot W_2.$$

The latter equation expresses that the states of the two systems are independent.

From these equations it follows:

 * $$\phi(W_1 \cdot W_2) = \phi_1(W_1) + \phi_2(W_2)$$

and hence finally

\begin{align} \phi_1(W_1) & = C \lg(W_1) + const. \, \\ \phi_2(W_2) & = C \lg(W_2) + const. \, \\ \phi(W)    & = C \lg(W) + const. \end{align} $$

The quantity C is also a universal constant; it follows from kinetic gas theory, where the constants R and N have the same meaning as above. Denoting the entropy at a particular starting state as S0, and the relative probability of a state with entropy S as W we have in general:

 * $$S - S_0 = \frac{R}{N}\lg W.$$

We now consider the following special case. Let a number (n) of movable points (for example molecules) be present in a volume v0, these point will be the subject our considerations. Other than these, arbitrarily many other movable points can be present. As to the law that describes how the considered points move around in the space the only assumption is that no part of the space (and no direction) is favored over others. The number of the (first-mentioned) points that we are considering is so small that mutual interactions are negligable.

The system considered, which can be for example an ideal gas or a diluted solution, has a certain entropy. We take a part of the volume v0 with a size of v and we think of all n movable points displaced to that volume v, with otherwise no change of the system. Clearly this state has another entropy (S), and here we want to determine that entropy differencen with the help of boltzmann's principle.

We ask: how large is the probability of the last-mentioned state relative to the original state? Or, what is the probability that at some point in time all n independently moving points in a volume v0 have by chance ended up in the volume v?

For this probability, which is a "statistical probability" one obtains the value:

 * $$W = \left( \frac{v}{v_0} \right) ^n \ ;$$

one derives from this, applying Boltzmann's principle:

 * $$S - S_0 = R \left(\frac{n}{N}\right)\lg\left(\frac{v}{v_0}\right).$$

It's noteworthy that for this derivation, from which the Boyle-Gay-Lussac law and the identical law of osmotic pressure can be easily derived thermodynamically, there is no need to make any assumption regarding the way the molucules move.

Interpretation of the Volume Dependence of the Entropy of Monochromatic Radiation using Boltzmann's Principle
In paragraph 4 we found for the dependence of Entropy of the monochromatic radiation on volume the expression:

 * $$S - S_0 = \frac{E}{\beta\nu}\lg\left(\frac{v}{v_0}\right).$$

This formula can be recast as follows:

 * $$S - S_0 = \frac{R}{N}\lg\left[ {\left(\tfrac{v}{v_0}\right)}^{\tfrac{N}{R}\tfrac{E}{\beta\nu}} \right]

$$

Comparing this with the general formula that expresses Boltzmann's principle

 * $$S - S_0 = \frac{R}{N}\lg W,$$

we arrive at the following conclusion:

If monochromatic radiation of frequency ν and energy E is enclosed (by reflecting walls) in the volume v0, then the probability that at a arbitrary point in time all of the radiation energy located in a part v of the volume v0 is:

 * $$ {\left(\tfrac{v}{v_0}\right)}^{\tfrac{N}{R}\tfrac{E}{\beta\nu}} \ .$$

Subsequently we conclude:

In terms of heat theory monochromatic radiation of low density (within the realm of validity of Wien's radiation formula) behaves as if it consisted of independent energy quanta of the magnitude Rβν/N.

We also want to compare the average magnitude of the Energyquanta of the "black body radiation" with the mean average energy of the center-of-mass-motion of a molecule at the same temperature. The latter is 3/2(R/N)T, and for the average energy of the Energy quanta Wien's formula gives:

 * $$\frac{\int\limits_{0}^{\infty} \alpha\nu^3e^{-\frac{\beta\nu}{T}}d\nu }{\int\limits_{0}^{\infty} \frac{N}{R\beta\nu} \alpha\nu^3e^{-\tfrac{\beta\nu}{T}}d\nu } = 3 \frac{R}{N}T.$$

The fact that monochromatic radiation (of sufficiently low density) behaves as regards to dependency of entropy on volume like a discontinuous medium that consists of energy quanta of magnitude Rβν/N suggests we should investigate whether the laws of generation and transformation of light are what they must be if light consisted of such energy quanta. In the following we will address that question.

Stokes' Rule
Let monochromatic light be transformed by photoluminence into light of another frequency, and let it be assumed that according to the result just obtained the generating as well as the generated light consists of energy quanta of magnitude (R/N)βν, where ν is the corresponding frequency. The transformation process can then be interpreted as follows. Each generating energy quantum of frequency ν1 is absorbed and generates—at least with sufficiently small density of the generating energy quanta—by itself a light quantum of of frequency ν2; possibly other light quanta of frequency ν3, ν4 etc. as well as other form of energy (e.g heat) can be generated simultaneously. Through which intermedia processes the final result comes about is immaterial. If the photoluminescing substance isn't a continuous source of energy it follows from the energy principle that the energy of the generated energy quanta are not larger than the generating light quanta; therefore the following relation must hold:

 * $$\frac{R}{N}\beta \nu_2 \leqq \frac{R}{N}\beta \nu_1$$

or

 * $$\nu_2 \leqq \nu_1.$$

As is well known this is Stokes' rule.

Especially noteworthy is that with weak illumination the amount of generated light must, other circumstances being equal, be proportional to the amount of exciting light, since every incident energy quantum will cause one elementary process of the above indicated kind, independent of the action of other exciting energy quanta. In particular there will be no lower limit of the intensity of the exciting light below which the light would be incapable of exciting light.

According to the way the understanding of the phenomena is laid down here deviations from Stokes' rule are conceivable in the following cases:

 * 1) When the number of energy quanta per unit of volume that are simultaneously involved transformation is so large that the energy quantum of the generated light can receive the energy of several exciting energy quanta.
 * 2) When the generating (or generated) light does not have the energy characteristics of "black body radiation" that is in the realm of validity of Wien's law, when for instance the exciting light is generated by a body of such high temperature that for the wavelengths considered Wien's law is no longer valid.

The last mentioned possibility merits special attention. According to the developed understanding it cannot be excluded that a "non-Wienian radiation" would behave energetically differently from Wien's law valid "black body radiation" even in high dilution.

On the Generation of Cathode Rays by Illumination of Solid Bodies
The usual understanding, that the energy of light is distributed over the space through which it travels in a continuous way encounters extraordinarily large difficulties in attempts to explain photo-electric phenomena, as has been presented in the groundbreaking article by Mr. Lenard. .

According to the understanding that the exciting light consists of energy quanta of energy (R/N)βν the generation of cathode rays by light can be conceived as follows. Quanta of energy penetrate the surface layer of the solid, and their energy is transformed, at least partially, in kinetic energy of electrons. The simplest picture is one where the light quantum gives its entire energy to a single electron; we assume that this will occur. However, it must not be excluded that electrons accept the energy of light quanta only partially. An electron that has been loaded with kinetic energy will have lost some of its energy when it arrives at the surface. Other than that we must assume that on leaving the solid every electron must do an amount of work P (characteristic of that solid). Electrons residing right at the surface, excited at right angles to it, will leave the solid with the largest normal velocity. The kinetic energy of such electrons is

 * $$\frac{R}{N}\beta\nu - P.$$

If the body is charged to a positive potential Π and surrounded by conductors with potential zero and Π is just enough to prevent loss of electricity by the body, then we must have:

 * $$\Pi \epsilon = \frac{R}{N}\beta\nu - P ,$$

where ε is the electrical mass of the electron, or

 * $$\Pi E = R \beta \nu - P^\prime \,\! ,$$

where E is the charge of one gram equivalent of a single-valued ion and P' is the potentel of this amount of negative electricity with respect to this body.

If we set E = 9.6·103, then Π·10-8 is the potential in volts that the body will attain when it is irradiated in vacuum.

To see now whether the derived relation agrees with experiment to within an order of magnitude we set P' = 0, ν = 1.03·1015 (corresponding to the ultraviolet limit of the solar spectrum), and β = 4.866·10-11. We obtain Π·107 = 4.3 Volt, which agrees to within an order of magnitude with the results of Mr. Lenard.

As far as I can see no contradiction exists between our understanding and the properties of photo-electric action observed by Mr. Lenard. If each energy quantum of the exciting light releases its energy independently from all others to the electrons, the distribution of velocities of the electrons, which means the quality of the generated cathode radiation, will be independent of the intensity of the exciting light; the number of electrons that exits the body, on the other hand, will, in otherwise equal circumstances, be proportional to the intensity of the exciting light.

We expect that limits of validity of these rules will be similar in nature to the expected deviations from Stokes' rule.

In the preceding it has been assumed that the energy of at least some of the energy quanta of the generating light is transferred completely to a single electron. If one does not start with that natural supposition then instead of the above equation one obtains:

 * $$\Pi E + P^\prime \leqq R\beta\nu.$$

For cathode-luminescence, which constitutes the inverse process of the one just examined, on obtains by way of analogous consideration:

 * $$\Pi E + P^\prime \geqq R\beta\nu.$$

For the materials investigated by Mr. Lenard PE is always significantly larger than Rβν, as the voltage that the cathode rays have had to traverse to generate even visible light is in some cases several hundred, in other cases thousends of volts.

Ionization of Gases by Ultraviolet Light
We have to assume that in ionisation of a gas by ultraviolet light always one absorbed light energy quantum is used for the ionisation of just one gas molecule. Firstly it follows that the ionisation energy (that is, the theoretically necessary energy to ionize) of a molecule cannot be larger than the energy of an absorbed light energy quantum. Taking J as the (theoretical) ionisation energy per gram equivalent, we have:

 * $$R \beta \nu \geqq J.$$

According to Lenard's measurements for air the largest wavelength that has an effect is about 1.9·1012, so

 * $$R \beta \nu = 6.4 \cdot 10^{12}\ \text{Erg} \geqq J.$$

An upper limit for the ionisation energy can also be obtained from the ionisaton voltage in rarefied gases. According to Stark the smallest measured ionisation voltage (for platinum anodes) is for air about 10 volt.

We have thus for J an upper limit 9.6·1012, which is nearly the same as the one just found. There is another consequence that in my mind is very important to verify. If every light energy quantum ionizes one molecule then the following relation must exist between the absorbed quantity of light L and the number j of thereby ionized gram molucules:

 * $$j = \frac{L}{R\beta\nu}.$$

If our understanding reflects reality this relation must hold for every gas that (at the particular frequency) has no absorbtion that isn't accompanied by ionisation.

Bern, march 17, 1905

title: User:Cleonis/Sandbox/Heuristic


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Page:Elements of the Differential and Integral Calculus - Granville - Revised.djvu/30

A variable is a quantity to which an unlimited number of values can be assigned. Variables are denoted by the later letters of the alphabet. Thus, in the equation of a straight line,$$\scriptstyle{x}$$ and $$\scriptstyle{y}$$ may be considered as the variable coördinates of a point moving along the line.

A quantity whose value remains unchanged is called a constant.

Numerical or absolute constants retain the same values in all problems, as $$\scriptstyle{2,~5,~\sqrt{7},~\pi}$$, etc.

Arbitrary constants, or parameters, are constants to which any one of an unlimited set of numerical values may be assigned, and they are supposed to have these assigned values throughout the investigation. They are usually denoted by the earlier letters of the alphabet. Thus, for every pair of values arbitrarily assigned to $$\scriptstyle{a}$$ and $$\scriptstyle{b}$$, the equationrepresents some particular straight line.

Very often we confine ourselves to a portion only of the number system. For example, we may restrict our variable so that it shall take on only such values as lie between $$\scriptstyle{a}$$ and $$\scriptstyle{b}$$, where $$\scriptstyle{a}$$ and $$\scriptstyle{b}$$ may be included, or either or both excluded. We shall employ the symbol $$\scriptstyle{[a,b]}$$, $$\scriptstyle{a}$$ being less than $$\scriptstyle{b}$$, to represent the numbers $$\scriptstyle{a,b}$$, and all the numbers between them, unless otherwise stated. This symbol $$\scriptstyle{[a,b]}$$ is read the interval from $$\scriptstyle{a}$$ to $$\scriptstyle{b}$$.

A variable $$\scriptstyle{x}$$ is said to vary continuously through an interval $$\scriptstyle{[a,b]}$$, when $$\scriptstyle{x}$$ starts with the value $$\scriptstyle{a}$$ and increases until it takes on the value $$\scriptstyle{b}$$ in such a manner as to assume the value


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 Florence Earle Coates Lyrics 1909 TRP.jpg Electrotyped and printed by H. O. Houghton & Co. Cambridge, Mass., U. S. A.


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Page:The Life of Michael Angelo.djvu/209

 He was as merciless against those who affected a haughty independence as he was full of indulgence and generosity to modest and faithful disciples. Lazy Urbano, "who would not work" —and who was right, for when he did work it was to spoil, irremediably, through carelessness, the "Christ" of the Minerva—was, during an illness, the object of his paternal care. He said that Michael Angelo was as "dear as the best father." Piero di Giannoto was "loved like a son." Silvio di Giovanni Cepparello, who left him to enter the service of Andrea Doria, was disconsolate and begged to be taken back. The touching story of Antonio Mini is an example of Michael Angelo's generosity towards his assistants. Mini, the one among his disciples who, according to Vasari, "was willing but had no aptitude," loved the daughter of a poor widow of Florence. At the request of his parents, Michael Angelo removed him from Florence. Antonio wished to go to France. Michael Angelo made him a royal gift: "All the drawings, all the cartoons, the painting of 'Leda,' and all the models which he had made for that work,


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 whether in wax or in clay." Possessed of this fortune, Antonio set out. But the ill-luck which affected the projects of Michael Angelo pursued those of his humbler friend still more relentlessly. Antonio went to Paris, but Francis I. was absent. So he left the "Leda" in the charge of one of his Italian friends; Giuliano Buonaccorsi, and returned to Lyons, where he had settled down. On returning to Paris a few months later he found that the "Leda" had disappeared; Buonaccorsi had sold it, to his own profit, to Francis. Antonio, wild with grief, without resources, incapable of defending himself, and lost in the foreign city, died of sorrow at the end of 1533.

But, of all his assistants, the one whom Michael Angelo loved the most, and to whom his affection assured immortality, was Francesco d'Amadore, surnamed Urbino, of Castel Durante. He was in Michael Angelo's service from 1530 and worked under his orders on the mausoleum of Julius II. Michael Angelo was anxious as to what would become of him after he had gone.

"'What will you do if I die?' he once said to him.

"'Serve another,' replied Urbino.

"'Poor fellow!' said his master, 'I will protect you from want,' and he gave him 2000 crowns at one time—a present such as only an emperor or a pope could have made."

Urbino was the first to die. The day after his death Michael Angelo wrote to his nephew:

"Urbino died at four o'clock yesterday afternoon. He has left me so afflicted and so troubled that it would


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Rh From Gen. xxviii., 6-11, it appears there existed already in the days of the patriarchs the custom that if a man died without children it was the duty of the next brother to marry the widow of his deceased brother. This ancient custom was afterwards engrafted into the Mosaic code; but as there had already been laid down a law forbidding such a union, the sacred writer assigns the reason why this exception is made, namely: "And it shall be, that the first born which she beareth shall succeed in the name of his brother which is dead, that his name be not wiped out of Israel." Deut. xxv., 6. It is quite plain that the provision was made to guard against the extinction of Hebrew households. Why this should have been so carefully guarded against, as I have already stated, we may probably not understand now in all its bearings. Still, there can be no doubt, that to a great extent it was intended to protect and preserve the agrarian rights of Hebrew families. To preserve as much as possible the equilibration of the portions of landed property as originally allotted when they took possession of the Holy Land.

To this may be added another and even higher motive why this natural desire, inherent in man for the immortality of name, should have existed with the ancient Hebrews to such a very high degree. The promise of the Messiah, the seed of women, who was to bruise the serpent's head, was well calculated to inspire them with an earnest longing for the perpetuating of their families, and may have been the chief cause which led to the promulgating of this provision in order to guard as much as possible against the entire extinction of Hebrew families.

We can, however, easily imagine of many cases arising in which such a marriage would be distasteful

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12 to the brother, and hence the law does not actually compel him, but provides rather an easy mode by which he may free himself from the obligation by merely publicly declaring before the assembled elders that he was not disposed to marry his brother's widow. Such an easy mode of escaping from an unwelcome obligation would have tended to render the injunction to a great extent nugatory had not provision been made to brand the man as a traitor to his brother's family for allowing personal consideration to outweigh a solemn duty he owed to a deceased brother. As the ceremony was public, and the disgrace which it entailed was to last as long as the person lived, it would, no doubt, have the effect of deterring many from shirking the duty on mere trivial grounds. The mode of conducting the ceremony is laid down with such great precision as altogether to preclude the possibility of any undue harshness being exercised, whilst, on the other hand, the importance of the preservation of family name is in the most impressive manner brought before those witnessing the ceremony. We may remark, that the loosing of the shoe, which formed the chief part of the ceremony on such an occasion, had, no doubt, its inception from the custom of any one taking possession of landed property by going to it, and standing upon it in his shoes, and so asserting his right to it. In this way it became the custom of renouncing any claim to property to take off the shoe, and handing it to him who was to become the owner of it. This custom prevailed also among the ancient Germans. By the taking off of the shoe is therefore symbolized, that the brother, by refusing to marry the widow, has likewise forfeited every claim to his brother's property, which might now go to the next nearest relative, upon whom devolved

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Rh the duty, according to the existing custom, to marry the widow. The widow was also to spit out before him, which, among the Orientals, was an expression of extreme detestation or contempt; and is even now so among the Arabians of the present day, and that not only among the common people, but also among the better classes. It may not be out of place to remark here too, that whilst the rendering in the English version "and spit in his face" is certainly quite admissible, yet it is by no means necessary, as "and spit out before him" would afford just as correct a rendering, as every Hebrew scholar will admit. Indeed the Hebrew word (Bephanav), "in his face," is over and over again rendered in our version by "before him." This arises from the idiom that in Hebrew in his presence, or before him, can only be expressed by "in his face."

But all this merely shews, that under certain circumstances it was regarded in those days of such great importance for a man to marry his childless brother's widow that an exception to the general rule forbidding such a marriage was deemed very desirable, but still leaves the main problem unsolved, why a woman should be allowed to marry her deceased sister's husband, whilst a man is strictly forbidden to marry, his deceased brother's wife.

That this difficult subject should have awakened a good deal of discussion might well be imagined, and that from the nature of the question various theories should have been advanced and different conclusions arrived at is no more than might naturally be expected. It is, therefore, but reasonable if we would avoid forming a one-sided opinion, that all that can be said either for or against should be carefully considered.

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Author:Albert Frank Kendrick

Works

 * (in part)

title: Author:Albert Frank Kendrick


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14 It is highly satisfactory to see, that notwithstanding so much having been said and written on the subject, the discussions have generally been carried on in a very kindly spirit. It would appear as if all writers were duly impressed with the difficulty with which the subject is surrounded, and have accordingly shewn due regard to the conscientious opinions of those holding different views. Keeping, then, this praiseworthy example always before us, we will proceed to examine carefully, and as briefly as circumstances will admit of, the various arguments that have been advanced on both sides of the question.

In the first place, it has been suggested by Dr. Kalisch, in his "Commentary on Leviticus," p. 364, published only a few years ago, that the word " (bechayyeha), in her life time," may not originally have existed in the text, but might be an interpolation of later times. This is altogether a new hypothesis, not having before been hinted at, as far as we are aware, by any previous interpreter. But the leaving out of the word in question would still not materially alter the sense of the verse, and would then read: "Neither shalt thou take a wife to her sister, to cause jealousy or enmity, to uncover her nakedness beside her," for the words " (litzror), to cause enmity, (aleha), beside her," would still imply that the sister was yet living, for, if dead, the marriage of her sister with her husband could not possibly be said "to cause enmity," nor could it be said to be "beside her." There remains therefore no other alternative but to expunge these two words also. To this Dr. Kalisch apparently has no objection, for he says, "so that the command would read thus: Thou shalt not take a wife to her sister, to uncover her nakedness." The omitting of the three words would certainly convert it into a distinct prohibition, and thus remove at once the existing difficulty. But the expunging of three

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Rh words out of ten is, to say the least, applying the pruning knife with a vengeance, and what makes it still worse, the words do not even occur consecutively in the verse. This interpolation hypothesis has, however, so very little in its favour, and so much against it, that we cannot wonder that it has never before been even thought of. The very fact; that all ancient and modern versions agree in their rendering with the original Hebrew clearly proves the genuineness of the words.

The ancient versions, we may safely assume, were made from the most carefully executed and authenticated manuscripts that could be procured. We may further also take it for granted that in doubtful passages the translators would consult different manuscripts and adopt the reading which had the greatest preponderance of evidence in its favour. These versions, therefore, have been always justly appealed to when necessary in establishing the authenticity of the sacred text, and we can in the present case do no better than to follow the established practice likewise.

The Greek version, generally called the Septuagint, is no doubt the oldest version. It is now generally supposed that it was begun in the time of the early Ptolomies, about 280 or 285 B. C, and that the translation of the Pentateuch alone was first made, whilst the translation of the other books followed at uncertain intervals afterwards. Aristobulus, who wrote in the second century before the Christian era, says, "that the Pentateuch was translated very early." This version was very highly esteemed both by the Egyptian and Palestine Jews, who seemed to have read it in their Synagogues. Philo Judæus carried his regard for this version so far as to believe it to have been inspired. Now on referring to this version it will be found that it perfectly agrees with the present Hebrew text.

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16 The next, both in point of antiquity as well as in importance, come the Targums. The term Targum is a Chaldee word and signifies simply a translation or version. The name was, however, in course of time restricted in its use so as to apply only to the Chaldee version or Paraphrases of the Old Testament.

The necessity of a Chaldee version soon made itself felt after the Babylonian captivity. The Jews had, during their long intercourse with the Babylonians, to a great extent, if not in many cases altogether, forgotten their own language. It was, however, imperative that the law and other portions of Scripture should be read in their Synagogues in the original Hebrew, as it is even to the present day. It became, therefore, necessary, in order that all might understand what was read, to have it immediately translated into Chaldee. These translations, although at first made orally, were, in course of time, committed to writing, and thus they have come down to us. These translations, according to the best supported opinions, were made either a little before or about the Christian era. The translation of the Pentateuch is ascribed to Onkelos, who is said to have been a pupil of the celebrated Hillel, whilst the translation of the other books of the Old Testament is ascribed to Jonathan ben Uzziel, who, according to some authorities, was a disciple of Gamaliel, the teacher of St. Paul.

From the foregoing remarks the reader may now form some idea of the importance of the Chaldee version in Biblical criticism, and especially in assisting us to set at rest any doubt that may arise as to the correctness or authenticity of the Hebrew text since this version bears the stamp of authority of the ancient Jewish Church. If we now appeal to this version, as evidence of the correctness and authenticity of the sacred text in the passage under consideration, we find that it also agrees, word for word, as it is now found in the Hebrew Bible.

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Rh A few centuries later the Syriac version, which, from its close adherence to the original Hebrew, is called "the Pshito," i. e., the literal, likewise affords its testimony to the authenticity of the Hebrew text, as the rendering in this version also agrees, word for word, withh the original. This version was in common use among the Christians throughout Syria, and hence Ephraim, the celebrated Syrian divine and writer, who flourished in the fourth century of the Christian era, speaks of it as "our version."

Still a few centuries later, about the beginning of the sixth century, we have a most overwhelming testimony furnished, in the revision of the Biblical text undertaken by a celebrated body of Jewish scholars from the principal seats of learning in Palestine. It was found that during the many centuries in which the Hebrew Scriptures had to be multiplied by manuscript, a great many errors had gradually crept into the sacred text. These errors may have originated either from the paleness of the ink in the manuscripts from which the transcriptions were made, or from the carelessness of transcribers. In order to free the text from such errors, the scholars, above referred to, collected the best manuscripts extant, and by a careful collation were thus enabled to detect any faulty reading. Still so great was the veneration in which they held the sacred text that they would not take upon themselves the responsibility of making any alteration; they, therefore, suffered such erroneously written words, no matter how faulty or how evident the error, to remain in the text, and placed the emendation in the margin, merely placing a little circle or asterisk above the word in the text in order to draw the reader's attention to the existing mistake, and to direct him to look at the bottom of the page. These emendations are very numerous, and are now found in the margin of all Hebrew Bibles. Among these

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Author:Frida Kahlo

Works

 * Frida Kahlo, letter to Nickolas Muray (1939)

title: Author:Frida Kahlo


text: Index:Red Riding Hood.ogv

title: Index:Red Riding Hood.ogv


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 From his earliest days he had flung himself upon that study with an unprecedented ardour of delight and curiosity. In drawing from life he had early found the way to unite precision with freedom and fire—the subtlest accuracy of expressive definition with vital movement and rhythm of line—as no draughtsman had been able to unite them before. He was the first painter to recognize the play of light and shade as among the most significant and attractive of the world’s appearances, the earlier schools having with one consent subordinated light and shade to colour and outline. Nor was he a student of the broad, usual, patent appearances only of the world; its fugitive, fantastic, unaccustomed appearances attracted him most of all. Strange shapes of hills and rocks, rare plants and animals, unusual faces and figures of men, questionable smiles and expressions, whether beautiful or grotesque, far-fetched objects and curiosities, were things he loved to pore upon and keep in memory. Neither did he stop at mere appearances of any kind, but, having stamped the image of things upon his brain, went on indefatigably to probe their hidden laws and causes. He soon satisfied himself that the artist who was content to reproduce the external aspects of things without searching into the hidden workings of nature behind them, was one but half equipped for his calling. Every fresh artistic problem immediately became for him a far-reaching scientific problem as well. The laws of light and shade, the laws of “perspective,” including optics and the physiology of the eye, the laws of human and animal anatomy and muscular movement, those of the growth and structure of plants and of the powers and properties of water, all these and much more furnished food almost from the beginning to his insatiable spirit of inquiry.

The evidence of the young man’s predilections and curiosities is contained in the legends which tell of lost works produced by him in youth. One of these was a cartoon or monochrome painting of Adam and Eve in tempera, and in this, besides the beauty of the figures, the infinite truth and elaboration of the foliage and animals in the background are celebrated in terms which bring to mind the treatment of the subject by Albrecht Dürer in his famous engraving done thirty years later. Again, a peasant of Vinci having in his simplicity asked Ser Piero to get a picture painted for him on a wooden shield, the father is said to have laughingly handed on the commission to his son, who thereupon shut himself up with all the noxious insects and grotesque reptiles he could find, observed and drew and dissected them assiduously, and produced at last a picture of a dragon compounded of their various shapes and aspects, which was so fierce and so life-like as to terrify all who saw it. With equal research and no less effect he painted on another occasion the head of a snaky-haired Medusa. (A picture of this subject which long did duty at the Uffizi for Leonardo’s work is in all likelihood merely the production of some later artist to whom the descriptions of that work have given the cue.) Lastly, Leonardo is related to have begun work in sculpture about this time by modelling several heads of smiling women and children.

Of certified and accepted paintings produced by the young genius, whether during his apprentice or his independent years at Florence (about 1470–1482), very few are extant, and the two most important are incomplete. A small and charming strip of an oblong “Annunciation” at the Louvre is generally accepted as his work, done soon after 1470; a very highly wrought drawing at the Uffizi, corresponding on a larger scale to the head of the Virgin in the same picture, seems rather to be a copy by a later hand. This little Louvre “Annunciation” is not very compatible in style with another and larger, much-debated “Annunciation” at the Uffizi, which manifestly came from the workshop of Verrocchio about 1473–1474, and which many critics claim confidently for the young Leonardo. It may have been joint studio-work of Verrocchio and his pupils including Leonardo, who certainly was concerned in it, since a study for the sleeve of the angel, preserved at Christ Church, Oxford, is unquestionably by his hand. The landscape, with its mysterious spiry mountains and winding waters, is very Leonardesque both in this picture and in another contemporary product of the workshop, or as some think of Leonardo’s hand, namely a very highly and coldly finished small “Madonna with a Pink” at Munich. The likeness he is recorded to have painted of Ginevra de’ Benci used to be traditionally identified with the fine portrait of a matron at the Pitti absurdly known as La Monaca: more lately it has been recognized in a rather dull, expressionless Verrocchiesque portrait of a young woman with a fanciful background of pine-sprays in the Liechtenstein gallery at Vienna. Neither attribution can be counted convincing. Several works of sculpture, including a bas-relief at Pistoia and a small terra-cotta model of a St John at the Victoria and Albert Museum, have also been claimed, but without general consent, as the young master’s handiwork. Of many brilliant early drawings by him, the first that can be dated is a study of landscape done in 1473. A magnificent silver-point head of a Roman warrior at the British Museum was clearly done, from or for a bas-relief, under the immediate influence of Verrocchio. A number of studies of heads in pen or silver point, with some sketches for Madonnas, including a charming series in the British Museum for a “Madonna with the Cat,” may belong to the same years or the first years of his independence. A sheet with two studies of heads bears a MS. note of 1478, saying that in one of the last months of that year he began painting the “Two Maries.” One of the two may have been a picture of the Virgin appearing to St Bernard, which we know he was commissioned to paint in that year for a chapel in the Palace of the Signory, but never finished: the commission was afterwards transferred to Filippino Lippi, whose performance is now in the Badia. One of the two heads on this dated sheet may probably have been a study for the same St Bernard; it was used afterwards by some follower for a St Leonard in a stiff and vapid “Ascension of Christ,” wrongly attributed to the master himself in the Berlin Museum. A pen-drawing representing a ringleader of the Pazzi conspiracy, Bernardo Baroncelli, hung out of a window of the Bargello after his surrender by the sultan at Constantinople to the emissaries of Florence, can be dated from its subject as done in December 1479. A number of his best drawings of the next following years are preparatory pen-studies for an altar-piece of the “Adoration of the Magi,” undertaken early in 1481 on the commission of the monks of S. Donato at Scopeto. The preparation in monochrome for this picture, a work of extraordinary power both of design and physiognomical expression, is preserved at the Uffizi, but the painting itself was never carried out, and after Leonardo’s failure to fulfil his contract Filippino Lippi had once more to be employed in his place. Of equal or even more intense power, though of narrower scope, is an unfinished monochrome preparation for a St Jerome, found accidentally at Rome by Cardinal Fesch and now in the Vatican gallery; this also seems to belong to the first Florentine period, but is not mentioned in documents.

The tale of completed work for these twelve or fourteen years (1470–1483 or thereabouts) is thus very scanty. But it must be remembered that Leonardo was already full of projects in mechanics, hydraulics, architecture, and military and civil engineering, ardently feeling his way in the work of experimental study and observation in every branch of theoretical or applied science in which any beginning had been made in his age, as well as in some in which he was himself the first pioneer. He was full of new ideas concerning both the laws and the applications of mechanical forces. His architectural and engineering projects were of a daring which amazed even the fellow-citizens of Alberti and Brunelleschi. History presents few figures more attractive to the mind’s eye than that of Leonardo during this period of his all-capable and dazzling youth. He did not indeed escape calumny, and was even denounced on a charge of immoral practices, but fully and honourably acquitted. There was nothing about him, as there was afterwards about Michelangelo, dark-tempered, secret or morose; he was open and genial with all men. He has indeed praised “the self-sufficing power of solitude” in almost the same phrase as Wordsworth, and from time to time would even in youth seclude himself for a season in complete intellectual absorption, as when he toiled among his

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 bats and wasps and lizards, forgetful of rest and food, and insensible to the noisomeness of their corruption. But we have to picture him as anon coming out and gathering about him a tatterdemalion company, and jesting with them until they were in fits of laughter, for the sake of observing their burlesque physiognomies; anon as eagerly frequenting the society of men of science and learning of an older generation like the mathematician Benedetto Aritmetico, the physician, geographer and astronomer Paolo Toscanelli, the famous Greek Aristotelian Giovanni Argiropoulo; or as out-rivalling all the youth of the city now by charm of recitation, now by skill in music and now by feats of strength and horsemanship; or as stopping to buy caged birds in the market that he might set them free and watch them rejoicing in their flight; or again as standing radiant in his rose-coloured cloak and his rich gold hair among the throng of young and old on the piazza, and holding them spellbound while he expatiated on the great projects in art and mechanics that were teeming in his mind. Unluckily it is to written records and to imagination that we have to trust exclusively for our picture. No portrait of Leonardo as he appeared during this period of his life has come down to us.

But his far-reaching schemes and studies brought him no immediate gain, and diverted him from the tasks by which he should have supported himself. For all his shining power and promise he remained poor. Probably also his exclusive belief in experimental methods, and slight regard for mere authority whether in science or art made the intellectual atmosphere of the Medicean circle, with its passionate mixed cult of the classic past and of a Christianity mystically blended and reconciled with Platonism, uncongenial to him. At any rate he was ready to leave Florence when the chance was offered him of fixed service at the court of Ludovico Sforza (il Moro) at Milan. Soon after that prince had firmly established his power as nominal guardian and protector of his nephew Gian Galeazzo but really as usurping ruler of the state, he revived a project previously mooted for the erection of an equestrian monument in honour of the founder of his house’s greatness, Francesco Sforza, and consulted Lorenzo dei Medici on the choice of an artist. Lorenzo recommended the young Leonardo, who went to Milan accordingly (at some uncertain date in or about 1483), taking as a gift from Lorenzo and a token of his own skill a silver lute of wondrous sweetness fashioned in the likeness of a horse’s head. Hostilities were at the moment imminent between Milan and Venice; it was doubtless on that account that in the letter commending himself to the duke, and setting forth his own capacities, Leonardo rests his title to patronage chiefly on his attainments and inventions in military engineering. After asserting these in detail under nine different heads, he speaks under a tenth of his proficiency as a civil engineer and architect, and adds lastly a brief paragraph with reference to what he can do in painting and sculpture, undertaking in particular to carry out in a fitting manner the monument to Francesco Sforza.

The first definite documentary evidence of Leonardo’s employments at Milan dates from 1487. Some biographers have supposed that the interval, or part of it, between 1483 and that date was occupied by travels in the East. The grounds of the supposition are some drafts occurring among his MSS. of a letter addressed to the diodario or diwâdar of Syria, lieutenant of the sultan of Babylon (Babylon meaning according to a usage of that time Cairo). In these drafts Leonardo describes in the first person, with sketches, a traveller’s strange experiences in Egypt, Cyprus, Constantinople, the Cilician coasts about Mount Taurus and Armenia. He relates the rise and persecution of a prophet and preacher, the catastrophe of a falling mountain and submergence of a great city, followed by a general inundation, and the claim of the prophet to have foretold these disasters; adding physical descriptions of the Euphrates river and the marvellous effects of sunset light on the Taurus range. No contemporary gives the least hint of Leonardo’s having travelled in the East; to the places he mentions he gives their classical and not their current Oriental names; the catastrophes he describes are unattested from any other source; he confuses the Taurus and the Caucasus; some of the phenomena he mentions are repeated from Aristotle and Ptolemy; and there seems little reason to doubt that these passages in his MSS. are merely his drafts of a projected geographical treatise or perhaps romance. He had a passion for geography and travellers’ tales, for descriptions of natural wonders and ruined cities, and was himself a practised fictitious narrator and fabulist, as other passages in his MSS. prove. Neither is the gap in the account of his doings after he first went to the court of Milan really so complete as has been represented. Ludovico was vehemently denounced and attacked during the earlier years of his usurpation, especially by the partisans of his sister-in-law Bona of Savoy, the mother of the rightful duke, young Gian Galeazzo. To repel these attacks he employed the talents of a number of court poets and artists, who in public recitation and pageant, in emblematic picture and banner and device, proclaimed the wisdom and kindness of his guardianship and the wickedness of his assailants. That Leonardo was among the artists thus employed is proved both by notes and projects among his MSS. and by allegoric sketches still extant. Several such sketches are at Christ Church, Oxford: one shows a horned hag or she-fiend urging her hounds to an attack on the state of Milan, and baffled by the Prudence and Justice of Il Moro (all this made clear by easily recognizable emblems). The allusion must almost certainly be to the attempted assassination of Ludovico by agents of the duchess Bona in 1484. Again, it must have been the pestilence decimating Milan in 1484–1485 which gave occasion to the projects submitted by Leonardo to Ludovico for breaking up the city and reconstructing it on improved sanitary principles. To 1485–1486 also appears to belong the inception of his elaborate though unfulfilled architectural plans for beautifying and strengthening the Castello, the great stronghold of the ruling power in the state. Very soon afterwards he must have begun work upon his plans and models, undertaken during an acute phase of the competition which the task had called forth between German and Italian architects, for another momentous enterprise, the completion of Milan cathedral. Extant records of payments made to him in connexion with these architectural plans extend from August 1487 to May 1490: in the upshot none of them was carried out. From the beginning of his residence with Ludovico his combination of unprecedented mechanical ingenuity with apt allegoric invention and courtly charm and eloquence had made him the directing spirit in all court ceremonies and festivities. On the occasion of the marriage of the young duke Gian Galeazzo with Isabella of Aragon in 1487, we find Leonardo devising all the mechanical and spectacular part of a masque of Paradise; and presently afterwards designing a bathing pavilion of unheard-of beauty and ingenuity for the young duchess. Meanwhile he was filling his note-books as busily as ever with the results of his studies in statics and dynamics, in human anatomy, geometry and the phenomena of light and shade. It is probable that from the first he had not forgotten his great task of the Sforza monument, with its attendant researches in equine movement and anatomy, and in the science and art of bronze casting on a great scale. The many existing sketches for the work (of which the chief collection is at Windsor) cannot be distinctly dated. In 1490, the seventh year of his residence at Milan, after some expressions of impatience on the part of his patron, he had all but got his model ready for display on the occasion of the marriage of Ludovico with Beatrice d’Este, but at the last moment was dissatisfied with what he had done and determined to begin all over again.

In the same year, 1490, Leonardo enjoyed some months of uninterrupted mathematical and physical research in the libraries and among the learned men of Pavia, whither he had been called to advise on some architectural difficulties concerning the cathedral. Here also the study of an ancient equestrian monument (the so-called Regisole, destroyed in 1796) gave him fresh ideas for his Francesco Sforza. In January 1491 a double Sforza-Este marriage (Ludovico Sforza himself with Beatrice d’Este, Alfonso d’Este with Anna Sforza the sister of Gian

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 Galeazzo) again called forth his powers as a masque and pageant-master. For the next following years the ever-increasing gaiety and splendour of the Milanese court gave him continual employment in similar kinds, including the composition and recitation of jests, tales, fables and “prophecies” (i.e. moral and social satires and allegories cast in the future tense); among his MSS. occur the drafts of many such, some of them both profound and pungent. Meanwhile he was again at work upon the monument to Francesco Sforza, and this time to practical purpose. When ambassadors from Austria came to Milan towards the close of 1493 to escort the betrothed bride of their emperor Maximilian, Bianca Maria Sforza, away on her nuptial journey, the finished colossal model, 26 ft. high, was at last in its place for all to see in the courtyard of the Castello. Contemporary accounts attest the magnificence of the work and the enthusiasm it excited, but are not precise enough to enable us to judge to which of the two main groups of extant sketches its design corresponded. One of these groups shows the horse and rider in relatively tranquil march, in the manner of the Gattemalata monument put up fifty years before by Donatello at Padua and the Colleoni monument on which Verocchio was now engaged at Venice. Another group of sketches shows the horse galloping or rearing in violent action, in some instances in the act of trampling a fallen enemy. Neither is it possible to discriminate with certainty the sketches intended for the Sforza monument from others which Leonardo may have done in view of another and later commission for an equestrian statue, namely, that in honour of Ludovico’s great enemy, Gian Giacomo Trivulzio.

The year 1494 is a momentous one in the history of Italian politics. In that year the long ousted and secluded prince, Gian Galeazzo, died under circumstances more than suspicious. In that year Ludovico, now duke of Milan in his own right, for the strengthening of his power against Naples, first entered into those intrigues with Charles VIII. of France which later brought upon Italy successive floods of invasion, revolution and calamity. The same year was one of special importance in the prodigiously versatile activities of Leonardo da Vinci. Documents show him, among other things, planning during an absence of several months from the city vast new engineering works for improving the irrigation and water-ways of the Lomellina and adjacent regions of the Lombard plain; ardently studying phenomena of storm and lightning, of river action and of mountain structure; co-operating with his friend, Donato Bramante, the great architect, in fresh designs for the improvement and embellishment of the Castello at Milan; and petitioning the duke to secure him proper payment for a Madonna lately executed with the help of his pupil, Ambrogio de Predis, for the brotherhood of the Conception of St Francis at Milan. (This is almost certainly the fine, slightly altered second version of the “Virgin of the Rocks,” now in the National Gallery, London. The original and earlier version is one of the glories of the Louvre, and shows far more of a Florentine and less of a Milanese character than the London picture.) In the same year, 1494, or early in the next, Leonardo, if Vasari is to be trusted, paid a visit to Florence to take part in deliberations concerning the projected new council-hall to be constructed in the palace of the Signory. Lastly, recent research has proved that it was in 1494 that Leonardo got to work in earnest on what was to prove not only by far his greatest but by far his most expeditiously and steadily executed work in painting. This was the “Last Supper” undertaken for the refectory of the convent church of Sta Maria delle Grazie at Milan on the joint commission (as it would appear) of Ludovico and of the monks themselves.

This picture, the world-famous “Cenacolo” of Leonardo, has been the subject of much erroneous legend and much misdirected experiment. Having through centuries undergone cruel injury, from technical imperfections at the outset, from disastrous atmospheric conditions, from vandalism and neglect, and most of all from unskilled repair, its remains have at last (1904–1908) been treated with a mastery of scientific resource and a tenderness of conscientious skill that have revived for ourselves and for posterity a great part of its power. At the same time its true history has been investigated and re-established. The intensity of intellectual and manual application which Leonardo threw into the work is proved by the fact that he finished it within four years, in spite of all his other avocations and of those prolonged pauses of concentrated imaginative effort and intense self-critical brooding to which we have direct contemporary witness. He painted the picture on the wall in tempera, not, according to the legend which sprung up within twenty years of its completion, in oil. The tempera vehicle, perhaps including new experimental ingredients, did not long hold firmly to its plaster ground, nor that to the wall. Flaking and scaling set in; hard crusts of mildew formed, dissolved and re-formed with changes of weather over both the loosened parts and those that remained firm. Decade after decade these processes went on, a rain of minute scales and grains falling, according to one witness, continually from the surface, till the picture seemed to be perishing altogether. In the 18th century attempts were first made at restoration. They all proceeded on the false assumption, dating from the early years of the 16th century, that the work had been executed in oil. With oil it was accordingly at one time saturated in hopes of reviving the colours. Other experimenters tried various “secrets,” which for the most part meant deleterious glues and varnishes. Fortunately not very much of actual repainting was accomplished except on some parts of the garments. The chief operations were carried on by Bellotti in 1726, by Mazza in 1770, and by Barezzi in 1819 and the following years. None of them arrested, some actually accelerated, the natural agencies of damp and disintegration, decay and mildew. Yet this mere ghost of a picture, this evocation, half vanished as it was, by a great world-genius of a mighty spiritual world-event, remained a thing indescribably impressive. The ghost has now been brought back to much of true life again by the skill of the most scrupulous of all restorers, Cavaliere Cavenaghi, who, acting under the authority of a competent commission, and after long and patient experiment, found it possible to secure to the wall the innumerable blistered, mildewed and half-detached flakes and scales of the original work that yet remained, to clear the surface thus obtained of much of the obliterating accretions due to decay and mishandling, and to bring the whole to unity by touching tenderly in with tempera the spots and spaces actually left bare. A further gain obtained through these operations has been the uncovering, immediately above the main subject, of a beautiful scheme of painted lunettes and vaultings, the lunettes filled by Leonardo’s hand with inscribed scutcheons and interlaced plait or knot ornaments (intrecciamenti), the vaultings with stars on a blue ground. The total result, if adequate steps can be taken to counteract the effects of atmospheric change in future, will remain a splendid gain for posterity and a happy refutation of D’Annunzio’s despairing poem, the Death of a Masterpiece.

Leonardo’s “Last Supper,” for all its injuries, became from the first, and has ever since remained, for all Christendom the typical representation of the scene. Goethe in his famous criticism has said all that needs to be said of it. The painter has departed from precedent in grouping the disciples, with their Master in the midst, along the far side and the two ends of a long, narrow table, and in leaving the near or service side of the table towards the spectator free. The chamber is seen in a perfectly symmetrical perspective, its rear wall pierced by three plain openings which admit the sense of quiet distance and mystery from the open landscape beyond; by the central of these openings, which is the widest of the three, the head and shoulders of the Saviour are framed in. On His right and left are ranged the disciples in equal numbers. The furniture and accessories of the chamber, very simply conceived, have been rendered with scrupulous exactness and distinctness; yet they leave to the human and dramatic elements the absolute mastery of the scene. The serenity of the holy company has within a moment been broken by the words of their Master, “One of you shall betray Me.” In the agitation of their consciences and affections, the disciples have started into groups

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