September to, 1891] 



NATURE 



443 



occasionally tell in the right direction. Had Father 

 Gerard not sacrificed his position by aiming so much 

 at smart writing— had he favoured us with more solid 

 thought instead of endeavouring "to split the ears of 

 the groundlings" — his lucubrations would have received 

 more respectful attention. But satire and cynicism, 

 interspersed with ridicule, are not the best methods for 

 securing consideration from men of science, and it is sur- 

 prising that the author should have resorted so largely to 

 their use. R, Meldola. 



THE LA WS OF FORCE AND MOTION. 

 The Laws of Force and Motion. By John Harris 



(Kuklos). (London : Wertheimer, Lea, and Co., 



1890.) 

 T N his preface the author, very rightly, sounds a warning 

 *- note against the arrogance of Conventional Science, 

 in its tendency to become ultra-conservative, intolerant, 

 and extremely dogmatic. 



But Real Science will always welcome and encourage 

 attack and contradiction, feeling sure that Truth will 

 ultimately prevail in the consensus of the majority who 

 have devoted themselves dispassionately to the con- 

 sideration of the facts in dispute. '• Transibunt multi et 

 augebit Scientia." 



We presume the author would not ask to be judged 

 with more leniency than he has displayed for the oppo- 

 nents he has singled out ; so we may say at once that^ 

 after careful winnowing, we have not secured those grains 

 of fact and truth which we were led to expect. 



The experimental apparatus described seems carefully 

 constructed and suitable for exact measurements ; but 

 does not differ essentially from that employed by Smeaton 

 more than loo years ago. However, the author assumes 

 the true scientific sceptical spirit, in refusing to accept im- 

 plicitly the statement of theoretical laws without putting 

 them to the test of practical experimental verification. 



Mathematicians will understand the nature of the 

 author's attacks on Conventional Science from the speci- 

 men on p. 31 : — 



" It would seem that, some time ago, a highly influen- 

 tial party of natural philosophers (Leibnitz, the two Ber- 

 noullis, &c.) entertained and supported the idea that the 

 momentum of a moving body varies as the square of the 

 velocity. This idea or conclusion was probably based on 

 an inference, that, since a double velocity of the resistance 

 required four times the force to produce it, four times the 

 momentum must have been imparted to the resistance." 



After this wavering as to the meaning of momentum, 

 we are quite prepared to find (p. 60) that the author is of 

 the school who declare that the moon does not rotate. 



The author cannot decide between i6'i or 32"2 for the 

 value of g (p. 24) ; and cannot settle in consequence 

 whether the normal acceleration in a circle is the squared 

 velocity divided by the radius or by the diameter (p. 19). 



" Tangential force " is, in the author's opinion, a more 

 correct scientific term to use than "centrifugal force," 

 although he allows that the latter is hallowed by long 

 usage ; but in his treatment he enunciates a theorem on 

 p. 21, " The actual lineal ratio of the sine to the arc, when 

 the arc is an octant, is 9 to 10," quoted from his own 

 ^'Treatise on the Circle and Straight Line"; this makes 

 NO. I I 4 1 , VOL. 44] 



TT = 2 ^2 -T- o'9, a result worth recording by collectors of 

 mathematical curiosities. 



We hoped to find something combative in the articles 

 on the Tidal Effect of Lunar Gravitation (p. 57), and on 

 the Moon's Gravitative Influence at the Equatorial 

 Surface of the Earth measured by Pendulum Oscillations 

 (p. 76), considering that even the great Abel went astray 

 in his theory at this point ; but our author confines him- 

 self to vague generalities. 



He would perform a valuable service to Science if he 

 employed his experimental skill in observing the effect of 

 Lunar Gravity on the Seconds Pendulum, as Conventional 

 Science asserts that this effect does not amount to more 

 than a rate of one 200th of a second in the day, although 

 so noticeable in the Tides. 



" Some Propositions in Geometry," by the same author, 

 is advertised at the end of the book, whereof the Tri- 

 section of the Angle, the Duplication of the Cube, and 

 the Quadrature and Rectification of the Circle, occupy 

 the chief part ; but we wonder whether the author has 

 quite settled in his Geometry that the versed sine (or 

 vertical height) is proportional to the chord, in a circle 

 (p. 71). This might have been a misprint, but that the 

 author adds immediately a numerical illustration, by 

 saying that, if the chord is duplicated, the versed sine is 

 also duplicated. 



And this homely mode of verifying a law of com- 

 parison, by halving or doubling some quantity, and then 

 observing the consequent change in the phenomena, is 

 the single idea we consider worth lifting from the book, 

 for general purposes of convincing argument and illustra- 

 tion of a mathematical law. A. G. G. 



OUR BOOK SHELF. 



An Introduction to the Mathematical Theory of Electri- 

 city and Magnetism. By W. T. A. Emtage, M.A. 

 (Oxford: Clarendon Press, 1891.) 

 The want of a text-book especially designed for the 

 use of candidates for examinations in which a know- 

 ledge of the more elementary portions of the mathema- 

 tical theory of electricity and magnetism is demanded 

 has been felt for some time. Though the absence of 

 such a book has caused some inconvenience, we are 

 not at all sure that it has been detrimental to the 

 study of electricity, for hitherto the candidate for a 

 mathematical examination in electricity has been com- 

 pelled to learn the subject from books such as those 

 of Maxwell, or of Mascart and Joubert, in which elec- 

 tricity is treated as what it really is outside the ex- 

 amination-room — a subject in which mathematics and 

 experiment are closely mixed and mutually helpful : it is 

 to this that, we think, is to be ascribed a good deal of 

 that interest which electricity, above all other subjects, 

 seems to excite in its students. When, however, the 

 analytical parts of the subject are divorced from the 

 experimental, we do not believe they will be found to 

 excite any special enthusiasm, or that the result will be 

 much more interesting than an ordinary text-book for the 

 Mathematical Tripos on, say, hydrostatics. 



There is no doubt, however, that there is a demand for 

 a text-book suitable for examination purposes, and this 

 demand will, we think, be well met by the book before 

 us. The scope of the work may be described by saying 

 that it includes nearly all the analytical parts of Maxwell's 

 larger treatise which do not involve analysis higher than 

 the simpler parts of the differential and integral calculus; 



