March 17, 1892] 



NATURE 



463 



1844," published at Leipzig in 1878, speaks of " Phorometrie " as 

 representing "die reine Bewegungslehre " ; and I see that 

 Mobiususes the adjective in an article on the " Phoronomische 

 Deutung des Taylor'schen Theorems." 



A change in scientific nomenclature is by no means an 

 unprecedented occurrence. 



For instance, notwithstanding the great authority of 

 Lagrange, the phrase "virtual velocity" has been practically 

 superseded by the phrase "virtual work," and in the year 1876 the 

 word "work" was substituted for "virtual velocities" in the 

 regulations, published in the Cambridge University Calendar, 

 for the Mathematical Tripos. 



Another instance is the fact that the phrase vis viva has been 

 superseded by kinetic energy, as a more convenient term in the 

 expression of the principle of energy. 



Further, I notice that Prof. Tait, in lectures on "Recent 

 Advances in Physical Science," gives the suggestion that the time- 

 honoured word force is in all probability destined, as science 

 advances, to be relegated to the limbo of departed 

 nomenclature. 



For these various reasons, then, I trust that I shall not be 

 regarded as an iconoclast, if I venture to substitute, for the 

 VI ord kinematics, the ■word phoronomy. 



W. H. Besant. 



St. John's College, Cambridge, February. 



On the Terms " Centrifugal Force " and " Force of 

 Inertia." 



The retention, in ihe last edition of Mr. Loney's " Elements 

 of Dynamics," 1891, of a paragraph (p. 141) which resuscitates 

 the objections formerly urged by some writers against the use of 

 the term " centrifugal force " seems to call for a protest. It is 

 to be regretted that students of dynamics should find absolutely 

 contradictory statements presented to them respecting the validity 

 of this term. While, however, in one set of text- books we find 

 a perfectly clear definition and consistent use of the phrase 

 "centrifugal force," there does not, on the other hand, appear 

 to be unanimity of ideas amongst the objectors, nor always 

 sufficient clearness in expressing the same. 



In the uniform circular motion of a ball rolling on a table 

 against the inner surface of a vertical cylinder, the pressure of 

 the cylinder upon the ball is a centripetal force directed towards 

 the centre of the circle. Tbe contrary pressure of the ball upon 

 the cylinder is the "centrifugal force," which is defined as the 

 reaction to the centripetal in this case, and in every case as the 

 reaction to the normal component of the centrifugal force. 



The foregoing definition or usage of the term is adopted 

 without hesitation or apology in the following works, named in 

 order of date : — 



Poisson's " Traite de Mecanique," 1833, vol. i. p. 332, or 

 Harte's translation, 1842, p. 256. 



Walton's "Mechanical Problems," 1842, pp. 240, 260, 269. 



Prof, Niven in " Cambridge Senate-house Problems," 1877, 

 p. 78. 



Thomson and Tait's "Natural Philosophy," 1879, p. 221, 



Garnett's "Elementary Dynamics," 1875, p. 205, and 1882, 

 P- 255 



Routh's "Rigid Dynamics," Part I., 1882, p. 217, and Part 

 II., 1884, p. 15. 



Williamson and Tarleton's "Dynamics," 1889, p. 88. 



Objections to the term appear in — 



Goodwin's "Course of Mathematics," 1849, p. 275. 



Parkinson's " Mechanics," 1863, p. 249. 



Biaikie's "Dynamics," 1887, p. 32. 



Rankint, "Encyclopaedia Britannica," "Mechanics," 9th 

 edition. 



Loney's " Statics and Dynamics," 1891, p. 141. 



Other authors might have been cited, but I have referred to 

 such as I happen to possess. 



Nearly all these objectors evince the same reluctance to giving 

 the name of " force" to the reactionary effect of the body's in- 

 ertia in the direction of the normal outwards. Yet, if we admit 

 that " to every force there is an equal and opposite reaction," 

 it is not easy to escape from the conclusion that such a reactionary 

 force exists. 



Mr. Loney, however, postulates both forces, but adds : — 

 "Centrifugal force is a very misleading term. It seems to 

 imply that the force belongs to the mass instead of being an 

 external force acting on the mass. A somewhat less misleading 



NO. II 68, VOL. 45] 



term is centripetal force. We shall avoid the use of either ex- 

 pression ; the student who meets with them will understand 

 that either (sic) means the force which must act on a mass to 

 give it the acceleration normal to the curve in which it moves." 



These are confusing directions to the student, who must be left 

 in complete bewilderment as to any distinction in meaning between 

 " centripetal " and " centrifugal." " Centrifugal," from its deri- 

 vation, signifies that the force has a tendency to make the body 

 fly away radially from the centre. And such a tendency there is, 

 and such a motion would result if we could make the centrifugal 

 force last ^ter the centripetal has ceased. But in the objections 

 taken the word "tendency" is regarded as though it implied 

 an actual subsequent motion in the direction of the tendency. 

 A beginner is almost certain to fall into the error of imagining 

 that, when the cord is slipped, the stone from a sling will dart 

 away in a direction intermediate between that of the string and 

 its own previous motion in the circle. But the name "centri- 

 fugal " is not answerable for this. The idea is due to the un- 

 mistakable pull upon his hand of an outward tending force, to 

 which "centrifugal" merely gives th2 right name. Clearer 

 conceptions show him that the two forces, the action and the 

 reaction, cease at the same instant when the string is cut, and 

 that there is no initial velocity in either direction. 



Uniform circular motion is perfectly unique. In the direction 

 of the force there is no motion, in the direction of the motion 

 there is no force. The real cj-tix lies in this conception of a 

 constant acceleration with a perpetual zero velocity in the direc- 

 tion of the acceleration. How, says one, can there be a rale of 

 change when the change itself is zero ? But the objection is a 

 metaphysical one, and it may be urged with equal force against 

 the whole doctrine of limiting ratios. 



Mr. Loney's statement that the centrifugal reaction is not a 

 force belonging to the mass, but "an external force acting on 

 the mass," requires some elucidation. Dr. Parkinson, in the 

 paragraph referred to, has something similar. He says that the 

 term " centrifugal force" "vaguely conveys an impression, as it 

 were, that the j. article of itself resisted curvilinear motion and 

 exerted a force per se to move in a rectilinear path, which innate 

 tendency was only overcome by the action of some external 

 force." He also grudgingly recommends the student to use the 

 obnoxious phrase "simply as an equivalent for the moving 

 force in the direction of the normal." Here again " centrifugal " 

 is made to signify a tendency towards the centre ! Is not the 

 vagueness complained of imported into the subject in some 

 measure by the writers themselves ? 



Whatever names are employed, the facts are these. The force 

 towards the centre communicates to the body an acceleration in 

 that direction, which acceleration gives rise (we know not how, 

 but we say by the law of inertia) to a force equal and opposite 

 to the force which produced the acceleration. This reaction 

 always appears to emanate from the mass of the moving body, 

 and it has therefore been called "the force of inertia" of the 

 body. Although this view has been combated by Poisson and 

 others, some of the latest authorities are reasserting it. Thus in 

 Thomson and Tait, 1867 and 1879, we find in Article 216 : 

 "Matter has an innate power of resisting external influences. 

 . . . This the inertia of matter, &c." Again, in Sir Robert 

 Ball's "Experimental Mechanics," 1888, p. 252: "When any 

 agent acts to set a body in motion or to modify its motion in 

 any way, the body reacts on the agent, and this force has been 

 called the kinetic reaction." 



I cannot see any objection to designating this reaction " the 

 force of inertia. " It is a provisional term, which will serve our 

 purpose until the nature of force is better understood. Poisson's 

 argument against it, derived from our experience of friction, 

 appears to me invalid, and his illustration irrelevant, because 

 the law of resistance is not the same as in the case of inertia. 

 If it had happened that the law governing friction was that the 

 resistance to motion was directly proportional to the accelera- 

 tion, then if a body were moving with constant velocity upon 

 a rough plane there would be no resistance from friction. "The 

 smallest acceleration of velocity would give rise to a correspond- 

 ingly small amount of friction, a double acceleration would 

 double the resistance from friction, and so on, precisely as with 

 the resistance from inertia. George S. Carr. 



A Lecture Experiment in Surface Tension. 



Hoping it may be of interest to some of your readers, I 

 venture to send you the following description of a simple ex- 



