Jan. 24, 1878] 



NATURE 



239 



Then the vibrations of a unifonnly-stretched membrane 

 are investigated. This investigation is of more theoretical 

 than physical importance, since it shows in a case which 

 may be treated in an easier way, the pecuHarities of vibra- 

 tions which are capable of spreading in two dimensions. 

 Unfortunately we have not yet succeeded up to the pre- 

 sent in obtaining good membranes which would be fit for 

 experiments of measuring in order to investigate, with 

 some degree of exactness, how far theory corresponds 

 with the experiment. 



On the contrary, in the case of elastic plates, the vibra- 

 tions of which the author treats in the last chapter of the 

 present volume, the experiments can be made with more 

 accuracy, while the analytical difficulties are so great that, 

 on the whole, only few cases permit of a solution of the 

 problem. Indeed, even the formulae expressing the con- 

 ditions which must be fulfilled at the edge of the plate 

 have given rise to discussions. Poisson had thought that 

 three conditional equations were necessary for the edge ; 

 Kirchhoff has shown that in reality only two are required. 

 Lately M. Mathieu opposed this view. Lord Rayleigh has 

 adopted Kirchhoff's views, and no doubt with perfect 

 right. He gives the analysis of the latter of the vibra- 

 tions of a circular plate, and has made an important 

 addition of his own to the solvable cases, by teaching us 

 how to deduce theoretically a series of vibration forms of 

 square plates, at least for that case where they consist of 

 an elastic substance the resistance of which to change of 

 volume may be neglected ; and these theoretical deduc- 

 tions sufficiently correspond with the forms observed. 

 Also for elastic rings and for cylinders vibrating in the 

 manner of bells, he has improved the theory in an 

 essential point, by proving theoretically and experi- 

 mentally, that the node lines of such plates execute 

 vibrations in a tangential direction. These tangential 

 vibrations are the ones which are first produced if the 

 edge of a drinking-glass is rubbed with the wet finger. 



The above [survey will give an idea of the numerous 

 contents of the book. As in the treatment of the separate 

 problems it touches everywhere the limits of our present 

 knowledge, it cannot but demand sound mathematical 

 knowledge on the part of the reader. Yet the author has 

 rendered it possible, by the very convenient systematic 

 arrangement of the whole, for the most difficult pro- 

 blems of acoustics to be now studied with far greater 

 ease than hitherto. He thus proves himself to be a 

 philosopher who does not lose the liberty of intellectual 

 supervision, even when he is occupied with the most 

 abstruse calculations. H. Helmholtz 



HINDUISM, BUDDHISM, AND ISLAM 

 I. Hinduism. By Monier Williams, D.C.L. 2. Buddhism, 

 By T. W. Rhys Davids. 3. Isldm and iis Founder. 

 By J. W. H. Stobart, B.A. (London : Society for 

 Promoting Christian Knowledge, 1877.) 



IT is a sign of the times that a " Society for Promoting 

 Christian Knowledge " should undertake a series of 

 works on " non- Christian religious systems." Nor is it a 

 less striking characteristic of our day that it should 

 entrust the work to scholars of so liberal a faith as Prof. 

 Monier Williams and Mr. Rhys Davids. Dr. Monier 

 Williams's volume on Hinduism forms a model of a 



popular exposition of a religious system. He explains 

 with great clearness the historical catena of the sacred 

 writings on which the Sanskrit religion was based. He 

 delineates the various movements, from the Buddhistic 

 reformation 2,500 years ago, down to the modern revivals 

 among the Sivaite and Vishnuvite sects, which have 

 developed the Vedic worship into that complex structure 

 of ritual, dogma, and social institutions, which we call 

 Hinduism. To the ordinary English reader, this little 

 volume will reveal a different aspect of Hindu faith and 

 morals from that which he has been accustomed to hear 

 from the pulpit or missionary platform. He will find that 

 the great questions of how a nian should rule his life, and 

 what prospect lies before him after he has done with this 

 world, have formed the subjects of religious thought and 

 practical experience, not less anxious nor less deep among 

 the people of India than among the western races. The 

 ethical replies which they have given to those questions 

 differ more in form than in spirit from the higher beliefs 

 of Christendom. The hard and narrow judgments of the 

 elder Mill and the zealous statements of missionaries, 

 have too long possessed the popular mind. Prof. Williams 

 does not appear as the advocate or admirer of Hinduism.. 

 In fact he tacks on to the end of his book a proselytising 

 page or two, which, however in accord with the object of 

 the Society for which he writes, form a strange contrast 

 to the scholarly tone of his volume. 



Dr. Monier Williams's tours in India have enabled him 

 to deal with the modern phases of Hinduism from a prac- 

 tical, as well as from the professorial point of view. Three 

 features of Hinduism must be distinctly realised in order 

 I0 understand its vitality and influence on the people. 

 Hinduism represents, in the first place, a very ancient 

 growth of worship and belief; and is invested with all 

 the authority of age and unquestioned prescription. In 

 the second place, it is a very modern religion, whose later 

 developments have neither been reduced , to, nor are 

 restrained by, any systematic theology ; which is, there- 

 fore, plastic, sensitive to every change in the popular 

 beliefs or modes of thought ; and which, in each province 

 of India, takes on a local colouring adapted to the neces- 

 sities or customs of the local population. In the third 

 place, Hinduism is not only a religious system, but an 

 all-powerful social institution. It forms the outcome of 

 religious and philosophical thought in India during several 

 thousands of years ; it also represents the 'organised 

 modes of life at which a great variety of tribes and races 

 have slowly arrived. This threefold source of strength 

 makes itself felt in every detail. To take one instance : 

 Caste is enforced alike by the sanctions of ancient pre- 

 scription, modern religion, and social utility. It articulates 

 the population into communities, each bound together by 

 ties of a useful, not less than of a doctrinal sort. Caste, 

 with the feelings of kindred and family on which it rests, 

 forms the substitute for a Poor-Law in India ; it supplies 

 a bond something like that which in America is felt by 

 people who attend the same meeting-house or chapel ; 

 and it discharges many of the functions of the mediaeval 

 guilds of Europe, together with others which are effected 

 less smoothly by modern Trades' unions. It has its 

 disadvantages —some of them very serious ones ; but it 

 curiously resembles, in several of its judicial, social, and 

 charitable aspects, the ekklesia of the early Christians. 



