Bolt Wood 260 Boltzmann

BOLT WOOD BOLTZMANN rocks. If the rate of formation of an inactive decay prospectors, mine owners, speculators, chemical re- product could be determined, the total amount found finers, and wholesalers to analyze samples, devise in a mineral would immediately yield its age . Both separation processes, and find financial backing (from lead and helium (believed by most to be the alpha wealthy Yale alumni) for various projects . These particle) were seen as suitable elements and, indeed, efforts probably helped stimulate the production of served in radioactive dating techniques . The helium radium, in which the United States led the world by method, pioneered in England by R . J. Strutt (later about 1915, although they did not appreciably aid the fourth Baron Rayleigh), could not, however, give the progress of science. more than a minimum age because a variable portion In 1918 Boltwood was appointed director of the of the gas would have escaped from the rock. But Yale College chemical laboratory and presided over the lead method, developed by Boltwood in 1907, the consolidation of the Yale and Sheffield chemistry proved satisfactory and is still in use today . In effect, departments. To cement this union, the new Sterling Boltwood reversed his procedure of confirming the Chemistry Laboratory was proposed, and Boltwood accuracy of lead :uranium ratios by the accepted was placed in charge of its design . He completed it geological ages of the source rocks, and used these successfully, but the strain of this effort caused a ratios to date the rocks. Because most geologists, breakdown in his health from which he never fully under the influence of Lord Kelvin's nineteenth- recovered . Periods of severe depression alternated century pronouncements, inclined toward an age of with his more customary cheerful spirits, and resulted the earth measured in tens of millions of years, in his suicide during the summer of 1927 . Boltwood's claim for a billion-year span was met with Boltwood's influence in radioactivity was wide- some skepticism . However, the subsequent work of spread-through his published papers, correspon- Arthur Holmes, an understanding of isotopes, and the dence, and personal contacts, for he trained surpris- increasing accuracy of decay constants and analyses ingly few research students. Part of his success finally brought widespread acceptance of this method stemmed from his close association with Rutherford, in the 1930's . but like Rutherford's other chemical collaborators, Boltwood's major contributions lay in the under- Soddy and Hahn, he was eminently capable of major standing of the uranium decay series . Still, he was contributions in his own right . able to suggest, with Rutherford in 1905, that actin- ium is genetically related to uranium, though not in the same chain as radium, while in the thorium series BIB1_IOGRAPIIY he almost beat Hahn to the discovery of mesothorium in 1907 . His other significant service to the study of I. ORIGINAL WORKS . A reasonably complete list of radioactivity was to bring greater precision and ad- Boltwood's publications is in Alois F . Kovarik's sketch of him in Biographical Memoirs of the National Academy of vanced techniques into the laboratory, as in his insis- Sciences, 14( 1930), 69-96 . His unpublished correspondence . tence that only by complete dissolution and boiling papers, and laboratory notebooks are preserved in the of the mineral could all the emanation be extracted Manuscript Room, Yale University Library . His extensive from radioactive bodies . correspondence with Rutherford is in the Rutherford Col- Boltwood remained at Yale the rest of his life, lection, Manuscript Room, Cambridge University Library . except for the academic year 1909-1910, when he 11 . SECONDARY LITERATURE . In addition to Kovarik's accepted an invitation to Rutherford's laboratory at the memoir (see above), the following obituary notices offer University of Manchester . Yale, fearing that he would information about Boltwood : Yale Alumni Weekly, 37 (7 remain in England indefinitely, offered Boltwood a Oct. 1927) . 65; Kovarik, in Yale Scientific Magazine, 2 full professorship in radiochemistry . This appoint- (Nov . 1927), 25, 44, 46 : Rutherford, in Nature, 121 (14 Jan . ment brought him back to New Haven, but it also 1928), 64-65 ; Kovarik, in American Journal of Science, 15 1928) . 188-198 . marked the end of his research career. Heavy aca- (Mar. demic duties, including supervision of construction of LAWRENCE BADASH the new Sloane Physics Laboratory and unsuccessful efforts to obtain large quantities of radioactive min- BOLTZMANN, LUDWIG (b. Vienna, Austria, 20 erals for research, seem to have taken all his time February 1844 ; d. Duino, near Trieste, 5 September and energy. His stature as the foremost authority on 1906), physics. radioactivity in the United States brought him mem- Boltzmann's father, Ludwig, was a civil servant bership in the National Academy of Sciences, the (Kaiserlich-Koniglich Cameral-Concipist) ; his mother American Philosophical Society, and other organiza- was Katherina Pauernfeind . He was educated at Linz tions, but it also brought him numerous requests from and Vienna, receiving his doctorate in 1867 from the 260 BOLTZMANN BOLTZMANN University of Vienna, where he had studied with Josef given time, only the average number of molecules Stefan. Boltzmann held professorships at the uni- having various positions and velocities . In many cases versities of Graz, Vienna, Munich, and Leipzig. In it seems reasonable to assume that the gas is spatially 1876 he married Henrietta von Aigentler, who bore uniform, that is, the average number of molecules is him four children . the same at different places in the gas. The problem Distribution Law. The first stimulus for Boltzmann's is then to determine the velocity distribution function researches came from teachers and colleagues at the f (v), defined so that f (v) dv is the average number of University of Vienna, especially Stefan and Josef molecules having speeds between v and v + dv. Loschmidt. In a lecture Stefan suggested the problem Maxwell argued that f(v) should be a function that in electrical theory whose solution constituted depends only on the magnitude of v, and that the Boltzmann's first published paper (1865) ;' he also velocity components resolved along the three coor- published a few papers on kinetic theory and did dinate axes should be statistically independent . important experimental work on gases and radiation Hence, he inferred that that provided the basis for some of Boltzmann's f(v) = ( a3i3/2)e-(v2/•z) (1) theories . Loschmidt (also in 1865) accomplished the N/ first reliable estimate of molecular sizes with the help where N is the total number of molecules, and a 2 of the Clausius-Maxwell kinetic theory . Although is inversely proportional to the absolute temperature . Loschmidt was later to dispute Boltzmann's interpre- In his long memoir of 1866, Maxwell admitted that tation of the second law of thermodynamics, the the assumptions used in his previous derivation of problem of finding quantitative relations between the distribution law "may appear precarious" ; he atomic magnitudes and observable physical quantities offered another derivation in which the velocities of was a common interest of both men . two colliding molecules, rather than the velocity Boltzmann began his lifelong study of the atomic components of a single molecule, were assumed to theory of matter by seeking to establish a direct be statistically independent. This means that one can connection between the second law of thermo- express the joint distribution function for the prob- dynamics and the mechanical principle of least action ability that molecule 1 has velocity v 1, while at the (1866). Although Clausius, Szily, and others later same time molecule 2 has velocity v 2, as the product worked along similar lines, and Boltzmann himself of the probabilities of these two separate events : returned to the subject in his elaboration of 1 Helmholtz' theory of monocyclic systems (1884), the F(v ,v2) =f(v1)f(v2) . (2) analogy with purely mechanical principles seemed To derive the distribution function itself, Maxwell insufficient for a complete interpretation of the second argued that the equilibrium state would be reached law. The missing element was the statistical approach when the number of collisions in which two molecules to atomic motion that had already been introduced with initial velocities (v 1 ,v2) rebound with final veloci- by the British physicist James Clerk Maxwell .2 ties (v 1 ',v2') is equal to the number of collisions in Boltzmann's first acquaintance with Maxwell's writ- which two molecules with initial velocities (v 1',v2') ings on kinetic theory is indicated by his paper on rebound with final velocities (v 1,v 2) ; from this condi- thermal equilibrium (1868) . In this paper, he ex- tion it follows that tended Maxwell's theory of the distribution of energy F(v 1,v 2) = F(v1',v2') (3) among colliding gas molecules, treating the case when . external forces are present . The result was a new By combining this equation with that for the conserva- exponential formula for molecular distribution, now tion of energy (in the case when no forces act), known as the "Boltzmann factor" and basic to all . To un- 2 M JV1 2 + 2 m2v22 m lv l 2 + m2V2 2, (4) modern calculations in statistical mechanics 2 2 derstand how Boltzmann arrived at this result, we must first review the work of Maxwell on which it Maxwell deduced (as before) that is based . ( a313/2) e-(" /•z). (5) Maxwell, in his first paper on kinetic theory (1859), f(vl) = N/ had pointed out that the collisions of gas molecules This type of reasoning about velocity distribution would not simply tend to equalize all their speeds functions was repeatedly used and generalized by but, on the contrary, would produce a range of differ- Boltzmann in his own works on kinetic theory .

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