40 



NATURE 



[Nov. II, 1875 



Cambridge 



Philosophical Society, Oct. 25.— Mr. J. W. L. Glaisher 

 read a paper on Herwart ab Hohenburg's Tabulae arithmetical 

 Trpoa-6a^aipeff(a)s universales, Munich, 1610. The book is a 

 very large and thick folio, and contains a multiplication table up 

 to 1000 X 1000, the thousand multiples of any one number being 

 given on the same page. There is an introduction of seven 

 pages, in which the use of the tables in multiplying numbers con- 

 taining more than three figures, and in the solution of spherical 

 triangles, is explained. Very little information with regard to 

 the work is to be obtained from the mathematical bibliographers 

 and historians, Heilbronner, Kastner, Scheibel, Marhard, Rogg, 

 Montucla, Lalande, &c. Ue Morgan writes : "Herwart passes 

 for the author, but nothing indicates more than that the manu- 

 script was found in his collection. The book is excessively rare ; 

 a copy sold by auction a few years ago was the only one we ever 

 saw." "While preparing the report of the British Association 

 Committee on Mathematical Tables, Mr. Glaisher had en- 

 deavoured without success to obtain some further information 

 about this great multiplication table, which has never been ex- 

 ceeded, and which is only equalled by Crelle's Rechentafeln, 

 which first appeared in 1820, and is now in general use. But 

 recently he had found a correspondence of six letters between 

 Herwart and Kepler, which are printed in vol. iv. (1863) of 

 Frisch's complete edition of Kepler's works, and which throw 

 light upon the table in question. In the first, dated September 

 13, 1608, Herwart mentions that he has been in the habit of 

 using a special praxis for avoiding the labour of multiplication, 

 and which his friends have recommended him to print. He 

 adds that without it he should long ago have had to give up all 

 mathematics which involved calculation, on account of his many 

 occupations and because he was not a good computer. He encloses 

 a page as a specimen. Kepler replies that he thinks the table 

 will be useful, and he urges that its uses in the solution of 

 spherical triangles should be noticed, pointing out its superiority 

 in point of clearness to the " irpoadacpaipiffis Vitichiana," which 

 is too complicated to be retained in the memory. Herwart re- 

 plies that he had already thought of its application in prostha- 

 phceresis ; he suggests a title for the book, and asks for Kepler's 

 opinion ; and in the last letter of the correspondence Kepler pro- 

 poses the title "2€jcrax0fia sive Novse Tabulse, quibus Arithme- 

 tici debitis inextricabilibus multiplicand! et dividend! liberantur, 

 ingenio, tempori, viribusque ratiocinantis consulitur." It is thus 

 proved that the table was printed from a manuscript which Her- 

 wart used himself, and which very likely he had had made. As 

 for the word prosthapha^resis, it is well known that the prostha- 

 ph^resis of the orbit is the angle subtended at the planet by the 

 eccentricity, and De Morgan explained the use of the word on 

 the title-page thus : " Prosthaphreresis is a word compounded of 

 prosthesis and aphasresis, and means addition and subtraction. 

 Astronomical corrections sometimes additive and sometimes sub- 

 tractive were called prosthaphsereses. The constant necessity for 

 multiplication in forming proportional parts for the corrections 

 gave rise to this table, which had the name of its application on 

 its title-page." But the prosthaphseresis referred to seems most 

 likely a method of solving spherical triahgles in which the pro- 

 duct of two sines or of a sine and cosine is avoided by the use of 

 formulae such as sin a sin ^ = i (cos (a-l>}~ cos (« + /;) |, and 

 such a method is associated with the name of Wittich. This 

 explains all Kepler's allusions, and why Herwart employed the 

 word on his title-page, as he proposed to avoid the necessity of 

 the transformation by rendering easy the operation of the simple 

 multiplication. A copy of Herwart's work borrowed, through 

 the kindness of Prof. Ilenrici, from the Graves Library at Uni- 

 versity College, London, was exhibited to the meeting. 



Manchester 



Scientific Students' Association, Oct 20. — Mr. Mark 

 Stirrup gave a short account of a visit to the celebrated Chesil 

 Bank, on the coast of Dorset, and exhibited some specimens of 

 the pebbles therefrom. The source whence these pebbles were 

 derived and their mode of accumulation, as explained by many 

 writers on the subject, were referred to. All these explanations 

 have failed to account satisfactorily for a deposit of such vast 

 magnitude, and there is no doubt that the views recently 

 enunciated by Prof. Prestwich, F.R.S. (see NATURE, vol. xi, 

 P- 299), go far to clear up the difhculty. 

 Paris 



Academy of Sciences, Nov. 2. — M. Fremy in the chair. 

 The following papers were read :— Determination of the class 



of envelope-curves which present themselves in questions of 

 equality of size of two segments made on tangents of geometric 

 curves, by M. Chasles.— On the steam carriage of M. Bollee, of 

 Mans, by M. Tresca.— Fourteenth note on the electric conduc- 

 tivity of mediocre conductors, by M. Du Moncel. These expe- 

 riments were with various metallic filings and the powder of 

 metallic minerals, graphite, and retort charcoal, which were 

 compressed into prisms between mica-plates. When heated, 

 their conductivity at first diminishes somewhat, but it then in- 

 creases very rapidly. When the heating ceases, it diminishe 

 again, and after some time the intensiiy of the current become 

 much less than it was at first. Thcrmo-electrical and chemical 

 effects are also described.— On the useful effect of steam in- 

 jectors (concluded), by M. Ledieu.— On the laws which govern 

 reactions with direct addition (continued), by M. Markoviiikofir. 

 — On the unipolar electric excitation of nerves : comparison of 

 the acti\'ity of the two poles during the passage of battery 

 currents, by M. Chauveau. The subject was placed half in 

 salt water, and a fine electrode applied to a point selected 

 on the skin of the emergent portion ; the other electrode was 

 held in the liquid. Or the two electrodes were placed on two 

 nerves sufficiently apart. M. Chauveau finds that for every 

 healthy subject there is a certain moderate intensity of current, 

 with which the contractions produced by the positive and nega- 

 tive excitation are equal in extent and duration ; Mow this 

 intensity the negative pole has the greater action ; aioz'e it, the 

 positive. — On the general arrangement of the nervous system in 

 stylommatophorous pulmonale gasteropod molluscs, by M. 

 Fischer. — Results obtained by means of sulphocarbonate cf 

 potassium on vines attacked by Phylloxera at Mezel. M. Dumas, 

 summing up the testimony on this point, said the sulphocar- 

 bonates had every where proved effective (where used) in destroy- 

 ing the insect, and they rather improved than injured the qualif. 

 of the vines. — On the method of Cauchy for the integration Ci 

 an equation with partial derivatives of the first order, by M. 

 Mansion. — M. Sainte-Claire Devillegave an extract from a letter 

 by M. Fouque, describing observations of volcanic phenomena 

 in the island of Santorin. — The Perpetual Secretary called atten- 

 tion to a work of " Researches on the Combustion of Coal," by 

 MM. Scheurer, Kestner, and Mennier-Dollfus ; also to a memoir 

 by MM. Marion and Borretzky, on the Annelids of the Bay of 

 Marseilles. He further announced the publication, by M. 

 Dummler, of a risiime of works of the Berlin Academy of 

 Sciences from 1822 to 1872. 



BOOKS AND PAMPHLETS RECEIVED 



British.— Air and its Relations to Life : W. Noel Hartley, F.C.S. (Long- 

 mans).— The Princes of India : Sir E. Sullivan, Bart. (Stanford).— Inaugural 

 Address of the West London Scientific Association and Field Club. Session 

 1875-6: Rev. G. Henslow, M.A., F.L.S.— Notes of Travel in South Africa: 

 Chas. J. Anderson. Edited by J. Lloyd (Hurst and Blackett).— Tne Revised 

 Theory of Light : W. Cave Thomas (Smith, Elder, and Co.) 



CONTENTS pagb 



Seventh Report of the Science Co.mmission 21 



Her.m.vnn's " Elements of Hum.\n Physiologv 23 



White Conquest . - 23 



Our Book Shelf : — 



Vyvyan's " Analytical Geometry " ..•;.. 24 



Besant's " Conic Sections" 24 



Pfeffer's " Periodic Movements of Leaf-organs " 24 



" Meteorology in Baden " 25 



Letters to the Editor : — 



Dr. Richardson's Hygeia. — Dr. F. de Chaumont 25 



Photography in the " Challenger."— Col. H. Stuart Wortley . 25 



Bees and Clover. — Thomas Belt 26 



Cherry Blossoms destroyed by Squirrels. — F. H. Stoker . ... 26 



Plagiarism. — Henry Walker 26 



Curious Australian Implement.— J. P. Gi-OVfLR {IVith lUusiratiou) 27 

 Our Astronomical Column : — 



Variable Stars x-j 



The Minor Planets 27 



Bessel's Works ., • 27 



Among the Cyclometers and so.me other Paradoxers, II. . . . 28 



Science in Germany (IVith Illustration) 30 



Evidences of Ancient Glaciers in Central France. By Dr. 



i. D. HooYian, C.B , Vies. K.S.(lVith /llustrattons) 31 



Association of German Natural Philosophers and Physicians. 



By Dr. A. Oppenheim 3a 



The German Commission on ArcticJExploration 34 



Notes 34 



Observations on Bees, Wasps, and Ants. By Sir John Lubbock. 



FR.S .37 



Our Botanical Column : — 



Irish Hepatica; 38 



Marine Algar of the United States 38 



CofTee in Dominica 38 ' 



Scientific Serials 38 



Societies and Academies 39 



Books and Pamphlets Uecbivko ,...,.,.40 



