238 



SCIENCE 



[N. S. Vol. LIII. No. 1367 



Alpine, Prospero (1553-1616) botanist, by 



A. BegTiinot. 

 Amici, Giovanni Battista (1786-1863) physi- 

 cist, naturalist, by G. B. De Toni. 

 Anguillara, Luigi (c. 1512-1570) botanist, by 



G. B. De Toni. 

 Baranzano, Eedento (1590-1622) pHlosopber, 



astronomer, by G. BoiEto. 

 Bertini, Anton Francesco (1658-1726), pbys- 



ician, by A. Oorsini. 

 Bertini, Giuseppe (1772-1845) physician, by 



A. Corsini. 

 Bertini, Giuseppe Maria Saverio (1694^1756), 



physician, by A. Corsini. 

 Biringuccio, Vannoccio (1480-1530?), tech- 

 nician, chemist, by A. Mieli. 

 Cestoni, Diacinto (1637-1718), naturalist, by 



G. Stefanini. 

 Chiarugi, Vincenzo (1759-1820) psychiatrist, 



physician, by A. Vedrani. 

 Coechi, Antonio (1695-1758), physician, by 



A. Corsini. 

 Corti, Bonaventura (1729-1813), botanist, by 



G. B. De Toni. 

 Cotug-no, Domenico (1736-1822), physician, 



by G. BOancioni. 

 De Visiani, Eoberto (1800-1878), botanist, by 



A. Beguinot. 



Dini, Ulisse (1845-1918), mathematician, by 

 G. Loria. 



Fibonacci, Leonardo (sec. xii-xiii), mathe- 

 matician, by G. Loria. 



Figari, Antonio (1804-1870) traveler, nat- 

 uralist, by G. Stefanini. 



Folli, Francesco (1624-1685), physician, nat- 

 uralist, by G. Goretti-Miniati. 



Ghini, Luca (c. 1490-1556), botanist, by G. 



B. De Toni. 



Guilandino, Melchiorre (c. 1520-1589), botan- 

 ist, by G. B. De Toni. 



Inghirami, Giovanni (1779-1851), astronomer, 

 by G. Giovannozzi. 



Magini, Giovanni Antonio (1555-1617), as- 

 tronomer, geographer, by A. Favaro. 



Maranta, Bartolomeo (c. 1500-1511), phys- 

 ician, botanist, by G. B. De Toni. 



Moletti, Giuseppe (1531-1588) astronomer, 

 cosmographer, by A. Favaro. 



Passerini, Giovanni (1816-1893), botanist, by 



G. B. De Toni. 

 Piccone, Antonio (1844^1901), botanist, by 



G. B. De Toni. 

 Pontedera, Giulio (1688-1737), botanist, by 



A. Beguinot. 

 Eiva, Giovanni Gugliehno, (1627-1677), phys- 

 ician, by C. Artom. 

 Schiaparelli, Giovanni Yirginio (1835-1910) 



astronomer, historian of science, by E. 



Millosevich. 

 Silvestri, Francesco (1474^1528), philosopher, 



by G. Sestili. 

 Sterzi, Giuseppe (1876-1919), anatomist, by 



G. Favaro. 

 Valli, Eusebio (1755-1816), physician, by 



A. Vedrani. 

 Zanardini, Giovanni (1804^1878), physician, 



botanist, by G. B. De Toni. 



Louis C. Kaepinski 



TjNrVBRSITY OF MICHIGAN 



SPECIAL ARTICLES 



THE EINSTEIN SOLAR FIELD AND SPACE OF 

 SIX DIMENSIONS 



The Einstein theory is four-dimensional in 

 the sense that four (general or world) coordi- 

 nates xi, xi, x%, Xi are employed. The funda- 

 mental quadratic form 



ds^ = 'Sgncdxidxjc, 



where the ten potentials g^ are functions of 

 the four coordinates, in general has a curva- 

 ture tensor which does not vanish, and there- 

 fore defines a curved manifold M of four di- 

 mensions. In fact M is flat or euclidean or 

 homodoidal only when there is no actual 

 gravitation. Excluding this trivial case, the 

 question arises what is the flat space of fewest 

 dimensions n, which can be regarded as con- 

 taining the curved manifold M? 



Abstractly considered the possible values of 

 n are 5, 6, 7, 8, 9, 10 ; that is, any M can surely 

 be immersed in a flat space of not more than 

 10 dimensions. But if we take into account 

 Einstein's differential equations of gravita- 

 tion, Rij^^'O, or Gifc = 0, we find that the 

 simplest case, n = 5, is actually impossible. 

 That is to say: 



