10)0 



NA TORE 



\Jan. i, 1885 



cubic curves by a novel method, but not many new- 

 theorems are the result ; and Mr. E. W. Davis gives an 

 expression for the co-ordinates of a point on a binodal 

 quartic curve as rational functions of the elliptic functions 

 of a variable parameter. 



The only purely geometrical article is one by Mr. li. 

 Alvord, entitled " The Intersection of Circles and the 

 Intersection of Spheres." The problems discussed are 

 to draw a circle which shall make a given angle with 

 three given circles ; to draw a sphere which shall cut 

 each of four given spheres at a given angle ; and then two 

 Steinerian problems, viz. to draw a circle which shall cut 

 four given circles at the same angle (angle unknown), and 

 the analogous problem for five spheres. The number of 

 solutions in each case is given, and there are four plates 

 containing thirteen figures. Prof. C. H. Smith supplies a 

 graphic method of solving spherical triangles. 



There is a single astronomical article on certain pos- 

 sible abbreviations in the computation of the long-period 

 inequalities of the moon's motion due to the direct action 

 of the planets, by Mr. G. W. Hill, who states that Hansen 

 has characterised the calculation of the coefficients of 

 these inequalities as extremely difficult, but he himself 

 thinks that, if the shortest methods are followed, there is 

 no ground for such an assertion. 



Prof. Turazza gives a note (which the editor had mis- 

 laid for three years), " Di un nuovo teorema relativo alia 

 rotazione di un corpo ad un asse." 



The only physical paper is Prof. Rowland's, " On the 

 Propagation of an Arbitrary Electro-magnetic Disturb- 

 ance on Spherical Waves of Light and the Dynamical 

 Theory of Diffraction." The classical paper by Stokes 

 " On the Dynamical Theory of Diffraction" is discussed ; 

 in addition the author treats of the general problem of 

 spherical waves of light, which he has not seen considered 

 anywhere else. 



We think the titles of the papers and a perusal of their 

 contents quite bear out Mr. Glaisher's opinion, pro- 

 nounced in his notice of the previous volumes (vol. xxvii. 

 ubi supra), viz. that " the volumes represent a consider- 

 able amount of mathematical work, a fair proportion of 

 which may have real influence on the advancement of 

 the science." Some readers might like to have a more 

 diversified bill of fare set before them, but no one can 

 say that what is offered is not generally first class. The 

 form of the Journal lends itself admirably to the im- 

 portant tables with which it has been enriched from its 

 earliest days. We are glad to find this young work 

 maintaining its early promise, and we wish for it even a 

 higher success in the days to come. 



A SYSTEM OF PSYCHOLOGY 

 A System of Psychology. By Daniel Greenleaf Thomp- 

 son. 2 vols. (London: Longmans, 1 884.) 

 PSYCHOLOGY, like other sciences, may be regarded 

 * as a pure science, or as a set of generalisa- 

 tions capable of application to practice, or as material 

 for a philosophical construction. Mr. Thompson has 

 treated it, for the most part, in the spirit of a scientific 

 inquirer. He does not stop to make applications to 

 practical questions, and although he is not without meta- 

 physical views of his own, it is evident that he is inter- 



ested in psychology more for its own sake than for the 

 sake of its bearing on his theory of the universe. There 

 is, therefore, no need to discuss here the questions in 

 dispute between the empirical school to which Mr. 

 Thompson belongs and its various critics. As he has 

 treated psychology so much in the scientific spirit, we 

 may confine ourselves to indicating the kind of work he 

 has done in his own special line. 



Some have denied that psychology is a science, on the 

 ground that it does not make progress ; but it is 

 only necessary to compare Locke's " Essay " with any 

 modern work in which the treatment is not altogether 

 inadequate, in order to see that progress has been made 

 both in accuracy of description and in refinement of 

 analysis of psychological facts. The admiration that 

 must be felt for what Locke was able to do only makes 

 the comparison more conclusive so. far as the establish- 

 ment of the scientific character of psychology is con- 

 cerned. In criticising any new book, then, we ought to 

 ask whether the author has made any advance on his 

 immediate predecessors. We ought, in fact, to apply to 

 the -particular author we are criticising the test of pro- 

 gress to which psychology as a whole may be submitted. 

 Mr. Thompson's book will emerge successfully from an 

 examination such as that which is here suggested. In 

 dealing with many special questions he goes beyond the 

 later English psychologists just as they themselves have 

 gone beyond Locke. 



A student might very well begin with the sixth part ot 

 Mr. Thompson's book, entitled "The General Develop- 

 ment of States of Consciousness," in order to get at the 

 author's more important results, and then read the parts 

 that come before it to understand more fully his general 

 view of his subject, and the parts that come after it for new 

 details. In this division of his work, the author brings 

 out very clearly the difference between " presentative " 

 and "representative" states of consciousness, and shows 

 the influence of this difference in the spheres of feeling 

 and of will, as [well as of cognition. Emotional states 

 are classified according to their relation to the environ- 

 ment, which may take the form of " pleasurable interest 

 in external objects " or of " aversion to external objects." 

 The chapter on "volitional development" (the first of 

 the second volume) deserves the special attention of the 

 psychological student. Mr. Thompson's introduction into 

 the view he gives of the external world in its relation to 

 mind (in Part III.), of a sort of Cartesian conception of 

 "matter" as including "space," must be at least alluded 

 to as likely to be found interesting both by physicists and 

 metaphysicians. Although philosophy and science are 

 now too much specialised for an idea of this kind to have 

 any direct influence on research, yet all discussion 

 between philosophers and men of science of the more 

 general terminology of the sciences, and especially of 

 physics, must have some effect in compelling clear defini- 

 tion of terms on the part of physicists and at the same time 

 in keeping philosophic thought in contact with its basis of 

 scientific law. 



Mr. Thompson might perhaps have given a better 

 account of the introspective method in psychology if he 

 had had fuller possession of the idea of mind as some- 

 thing common to all individuals ; if he had been able to 

 show more clearly that it is not simply the individual 



