LITERARY NOTICES. 



753 



raent is more or less beneficial according as 

 one or other effect predominates in it. 



Mathematics may be loved by a syba- 

 rite, but it will never be his occupation. 

 Yet it is a most gentlemanly amusement, 

 pursued far from vulgar passions and ap- 

 plause, in the calm of a library, nothing 

 sordid mingling with it. Those harsh and 

 crabbed formulas which fill us outsiders 

 with such dismay, and from which we flee in 

 terror, doubtless become, after a while, to 

 the devotee as musical as is Apollo's lute, and 

 are regarded by him as affectionately as a 

 chess-player regards his finely-carved queens 

 and castles. 



Everybody, of course, knows that the 

 practical utility, not to say necessity, even 

 of the highest mathematics, is immense. 

 But we have preferred to consider it in re- 

 lation to the purely theoretical or very re- 

 motely practical departments which will no 

 doubt occupy a large portion of the Ameri- 

 can Journal of Mathematics. Even so con- 

 sidered, the present mathematical revival 

 which the coming of Mr. Sylvester has occa- 

 sioned, and the establishment of this journal, 

 may be characterized as important events for 

 the highest welfare of the country impor- 

 tant even for its material welfare. It is not 

 to be expected that the actual readers of such 

 a journal should be very numerous, and, 

 though subscriptions will be drawn from Eu- 

 rope, yet the success of it must depend upon 

 its finding subscribers who do not read it, but 

 who appreciate its value. Whether a suffi- 

 cient class exists in America which under- 

 stands the importance of intellectual activity 

 of the profoundest kind to enable such ac- 

 tivity to exist here, is a vital question for 

 our destiny. 



Not to close this notice without a bit of 

 criticism, we may mention that one of the 

 editors of the Journal has by means of a 

 " Crelle's Table " found in a few minutes 

 that the number 191,071 is either a prime 

 or else divisible by a factor less than 137. 

 This is pronounced by another of the editors 

 to be " a real stroke of genius." We should 

 like to have the glory of it a little further 

 elucidated. We have put Crelle's Table in- 

 to the hands of a computer, and requested 

 him to find the divisors of the number in 

 question. Having no pretensions to genius, 

 he did not stop at 137, but, proceeding in the 

 ordinary humdrum way, announced abso- 

 vol. xni. 48 



lutely, in a quarter of an hour, that the num- 

 ber was prime. We confidently look for an 

 article in the coming number setting out 

 and explaining the wonderful stroke of gen- 

 ius in question, the marvel of which does 

 not seem to have lain in its reaching a very 

 speedy or complete solution of the problem 

 undertaken. 



Democracy in Europe : A History. By Sir 

 Thomas Erskine May. New York: 

 W. J. Widdleton. 1878. 2 vols. 



In an appropriate introductory essay 

 to this work the author sets forth the 

 principles that constitute its foundation. It 

 can scarcely be said that he offers anything 

 new here; he, however, points out truths 

 that can never be too sedulously insisted 

 upon. After stating that by democracy he 

 understands " the political power or influ- 

 ence of the people under all forms of gov- 

 ernment," that " it denotes a principle or 

 force and not simply an institution," he 

 discusses the moral, social, and physical 

 causes of freedom, supporting his asser- 

 tions, the while, with historical instances. 

 He next shows that, as the constant de- 

 velopment of popular power is the result 

 of the intellectual and material progress 

 of a nation, it must be accepted as a nat- 

 ural law ; and that, instead of striving to 

 breast the current, statesmen should en- 

 deavor to urge it forward in the most ad- 

 visable channels. As a matter of course, 

 the author has not avoided the opportunity 

 of commenting upon the excesses of demo- 

 cratic ideas, and of breaking lances with 

 devotees of eommunism and socialism. 



Sir Erskine May enters the historical 

 field with a gloomy portraiture of the con- 

 stitutions of the old Eastern nations, and, 

 in order to show that freedom is a growth 

 wholly peculiar to European soil, he en- 

 deavors to prove that in all times even the 

 present the main characteristics of Eastern 

 society have been immutability and immo- 

 bility. He begins with an examination of 

 the constitution of India, and claims that 

 the Hindoos have never known freedom ; 

 that their ignorance has been opposed to 

 it ; that their enslavement has fostered their 

 ignorance ; and concludes that" England has 

 already given more ' liberty ' to India than 

 ever she aspired to under her former rulers." 

 In the histories of Persia, China, Japan, 



