304 SCIENCE PROGRESS 



with an essentially mathematical topic. But freedom from sheer dynamical 

 fallacies should still be retained as a minimal standard. I submit, therefore, a 

 short selection of errors, from my own marginal notes, solely with the hope 

 of saving non-specialist readers from attempting an impossibly thorough 

 comprehensio-n of the text. 



The author contemplates early (p. 5) the common horizontal precessional 

 movement of a gyroscope with its axis level and loaded at one end. He 

 says (truly enough) that " there is here no question of perpetual motion " ; 

 and goes on to say that " the work expended in overcoming the friction at 

 the vertical journals is derived from the energy of the spinning-wheel." This 

 is entirely wrong. The friction spoken of would inevitably cause the axis 

 to tilt and the weight to drop, regardless of maintenance of the spin. The 

 rate of precession is then stated to be proportional to the speed of rotation 

 of the wheel. The word " inversely " needs inserting to make the statement 

 true. 



In the description of the mounting of a gyroscope with three degrees of 

 freedom it appears (pp. 12-14) that the author definitely supposes that the 

 three axes of rotation must be mutually perpendicular. When one of the 

 angles is changed it " tends to destroy one of the three degrees of freedom." 

 This is a kinematic fallacy. The three degrees of freedom exist in all com- 

 pleteness so long as the axes are not coplanar. The lapse to two degrees of 

 freedom is no gradual matter. 



The eighty-five-minute period prescribed for dead-beat compasses is 

 described (p. 37) as "the period which a simple pendulum would have if its 

 length were equal to the radius of the earth." This error is a common one. 

 It results probably from assuming the usual formula to hold for the period 

 of a pendulum even when its length is comparable with the earth's radius. 

 The length of the eighty-five-minute pendulum is infinite. The bob moves in 

 a straight line, and the curvature of the earth alone accounts for the period. 

 As illustrating one type of disturbance of the compass, " the ballistic 

 deflection of a pendulum hung from the roof of a railway carriage is dependent 

 upon the length of the pendulum " (p. 87). The deflection depends, of course, 

 only on the ratio of the acceleration of the train to that of gravity, and not 

 on the length of the pendulum. The ballistic deflection of the compass is 

 wrongly made out (pp. 88-89) to depend on the time occupied by the change 

 of the ship's speed. The point is altogether confused. The simple fact is 

 that the rate of westerly deflection of the compass is proportional to the 

 ship's northerly acceleration ; and so the deflection produced is proportional 

 to the change of northerly speed. 



The explanation (pp. 122-128) of the action of the three gyroscopes 

 mounted on the float of the Anschiitz compass is entirely wrong. The East 

 and West gyroscopes are credited with but one degree of freedom relatively 

 to the float, and yet are made out as stiffening the float against tilting about 

 its north-and-south diameter. The fallacy is in defiance of the simple fact 

 that for a stiff configuration of their axes any number of gyroscopes are 

 merely equivalent to a single one possessing their resultant angular momentum. 

 Each of the two gyroscopes has two degrees of freedom relatively to the float, 

 and the stiffening depends fundamentally on the extra degree of freedom. 



The compass is said (p. 92) to be placed usually " above the vessel's 

 metacentres — transverse and longitudinal — about which rolling and pitching 

 take place." The metacentre for pitching being usually located somewhere 

 high up the mast, it ought to be clear that the last statement is certainly 

 wrong ; and if so then equally the notion (though a common one) that the 

 metacentre for rolling remains stationary is (qualitatively) baseless. 



I suppress reference to many other like instances of error. But, as regards 

 general method, the author claims to have appealed only to " the most familiar 

 physical principles " ; yet the gyroscope on. various occasions " does its best " 



