December 11, 1914] 



SCIENCE 



857 



mously in 1596, contained tables to ten decimal 

 places of tlie natural trigonometric functions 

 at intervals of ten seconds. This was sur- 

 passed in 1613 by the tables in the " Thesaurus 

 Mathematicus," which were based by Pitiscus 

 upon unpublished tables computed by Eheticus, 

 and gave the values of the natural functions 

 to fifteen decimal places. 



Soon after the appearance of these exten- 

 sive tables the public began to realize the great 

 advantages of logarithmic computation. The 

 " Trigonometria Britannica " by Briggs and 

 the " Trigonometria artificialis " by Vlacq 

 appeared in 1633, and served as sources for 

 numerous briefer logarithmic tables of trigo- 

 nometric functions. Por about three hundred 

 years it appeared as if the greater part of the 

 labor put on the natural function tables had 

 been wasted. In recent years calculating 

 machines have to a considerable extent re- 

 placed logarithmic tables, and have brought 

 the natural function tables into more promi- 

 nent use; thus furnishing another instance of 

 unforeseen usefulness of mathematical lore. 



In 189Y W. Jordan published a table of the 

 natural trigonometric functions to seven 

 decimal places, basing his work upon the 

 " Opus Palatinum." To-day we have before 

 us this work by E. Gifford based on the tables 

 of Rheticus and aiming to facilitate the use 

 of these tables by computing the values of 

 the natural functions from second to second 

 by interpolation. In view of the recent refine- 

 ment in observation seven place tables do not 

 always secure sufiicient accuracy. Hence the 

 present tables are computed to eight decimals. 



One of the most important elements in such 

 tables is accuracy. As the main tables of 

 Eheticus have been improved by successive 

 computers it would appear that serious in- 

 accuracies in such tables as the present 

 could easily be avoided. The author of 

 the present table does not inform us as re- 

 gards his precautionary measures except that 

 " the sines to 1" were interpolated by the 

 Thomas calculating machine from Eheticus's 

 figures for 10", each being copied to 10 

 places and obvious mistakes corrected so that 

 the differences run in descending series." It 



is a somewhat curious fact that at the top of 

 the first page of the table we find cosine 1 in 

 place of cosine 90°. G. A. Miller 



University of Illinois 



Zur Frage der Entstehung maligner Tumoren. 



By Th. Boveri. Jena, Gustav Fischer. 



1914. 64 pages. 



The eminent position held by Professor 

 Boveri in the field of cytology, if for no other 

 reason, entitles him to a careful hearing in 

 any allied field of research, and the present 

 highly suggestive hypothesis as to the origin 

 of malignant tumors is by no means inappro- 

 priate from him since the tumor problems in 

 their last analysis are cell problems. The 

 medical man will probably pay little attention 

 to this theory because it oflrers no practical 

 solution of the cancer problems. Medical 

 men interested in the theories as to the cau- 

 sation of cancer, and especially those who fol- 

 low von Hansemann, however, will find in 

 Boveri's hypothesis a most interesting and 

 suggestive modus operandi for their favorite 

 theory. 



In, any hypothesis of cancer origin the difii- 

 culty to be overcome is the phenomenon of 

 unrestricted cell division of the malignant 

 cancer cells. This is the crux of the whole 

 matter and it is here that every current hy- 

 pothesis of cancer origin falls down, but in 

 Boveri's hypothesis this point is met. 



The theory rests upon a number of as- 

 sumptions, some of which are supported by ex- 

 perimental evidence, some are purely conjec- 

 tural. We may briefly summarize these as- 

 sumptions as follows: First, the chromosomes 

 are qualitatively different and a certain num- 

 ber and assortment of them are necessary for 

 normal balanced activities of the cell; sec- 

 ond, abnormal mitosis in the form of multi- 

 polar spindle formation, leads to unequal dis- 

 tribution of the chromosomes in the resulting 

 cells; third, lost chromosomes are never re- 

 placed and the abnormal cell, if it divides 

 further, must give rise to similar abnormal 

 cells; fourth, such an abnormal cell with 

 its chromosome complex has a different set 

 of interactions with the surrounding tissues 



