78 



NATURE 



[November 



the disease." If this happy result is obtained it will, with- 

 out doubt, be due to thr work done by the Royal Society 

 Commission, who gained their knowledge on the subjert 

 by experimentation on animals. 



Cromer, President. 



•Sydney Holi-ano, Chairman of Committee. 



F. M. Saxdwitii, Hon. Treasurer. 



Stephen Paget, Hon. Secretary. 

 21 Ladbroke Square, London, W., November i. 



The Definition of Mass. 



In Nature for October 26 your reviewer, in criticising 

 "An Elementary Text-book of Physics," writes: — 



"In common with so many other text-books on this 

 subject, this book lacks the fundamental definition of 

 'mass.' 'i'he author introduces the term 'mass' without 

 definition in order to define force, and then uses this defini- 

 tion for the purpose of defining mass. Few writers on 

 mechanics appear to realise that a definition of mass apart 

 from force is the essential first step from the point of view 

 of absolute measurement." 



I am not concerned to defend this particular text-book, 

 of which 1 have no knowledge, but I should be grateful, 

 in common with many of your readers, if your reviewer 

 would give us a satisfactory definition of mass apart from 

 force (the italics are his own). I presume he would not 

 be content with the fatuous statement that " Mass means 

 quantity of matter " ! Apparently Sir Oliver Lodge must 

 be included amongst those censured, for in his " Elementary 

 Mechanics " he writes : — 



" We see, then, that mass is measured, and must be 

 held to be defined, by the property of inertness possessed 

 by matter — that is, by its requiring force to move it if at 

 rest, and to stop it if in motion." 



The same view is expressed by Clerk Maxwell in his 

 invaluable little book " Matter and Motion," article xlvi. 



Let us be frank about this question. The idea of force, 

 like the idea of temperature, is derived from our bodily 

 sensations, and is therefore suspect in some quarters. It is 

 said that our sensations are not trustworthy. Neverthe- 

 less, we can form from them by long experience fairly 

 accurate estimations both of force and temperature. To 

 measure temperature we generally observe the expansion of 

 a material body. To measure force we can use the de- 

 formation produced by it when acting on some portion of 

 matter — the statical method ; or we may measure the 

 acceleration produced in a particular body — the dynamical 

 method. The two methods give concordant results. We 

 observe the elTects of changes of temperature ; we infer the 

 passage of " heat " from one body to another. We observe 

 the effects of force in producing acceleration. We find that 

 the ratio of force to acceleration (or, what is equivalent, 

 the ratio of impulse to change of velocity) is (approxi- 

 mately) constant for a particular body. We infer the 

 existence of " mass," which is simply the value of this 

 ratio. To say that " mass " is indestructible is to affirm 

 that this ratio remains constant through the range of our 

 experiments. If we extend the range we are led to believe 

 that the ratio is no longer constant when the velocity of 

 the bodv approaches the velocity of light. 



H. S. A. 



It gives me much pleasure to comply with " H. S. A.'s " 

 request expressed in his letter, but, at the same time, I 

 should like to refer him to chapter iii. of Porter's " Inter- 

 mediate Mechanics " for a clear and exact statement with 

 regard to this question. 



In the first place, it should be pointed out that definitions 

 are of two kinds, qualitative and quantitative, and it was 

 in the latter sense that the term was used in that portion 

 of my review which " H. S. A." quotes. To the definition 

 due to Lodge, regarded as purely qualitative, no objec- 

 tion is offered ; it is when quantitative definitions are re- 

 quired for the purpose of measurement that the difficulties 

 arise. Surely it is obvious that it is meaningless to define 

 unit force as that which produces unit acceleration in unit 

 mass, and then to define unit mass as that which acquires 

 unit acceleration under the action of unit force. Of 

 course, if we are content to define force in terms of the 

 deformation it produces in a given piece of material, mass 

 may then be measured in terms of force and acceleration ; 



NO. 2194, VOL. 881 



but the system of units arrived at will not be a\»< 

 'I'o obtain absolute units, we must be able to con 

 either two forces or two masses by measurements of 

 and time alone The problem of defining i 

 tively therefore resolves itself into defining il 



masses in terms of space and time. This lu... - 



follows. 



Let two masses m, and m, be isolated (a state of a: 

 approximately realised in Hicks 's balance), and Irt 

 interact in any way. Let their accelerations at any in 

 bo a, and a, respectively. These will be ■ 

 directed. Then the ratio of the masses is defined 

 numerically equal to the inverse ratio of •'^' 

 tions, or 



m,/m,= -aj/a,, 



the negative sign expressing the fact that the acceler 

 are opposed in direction. We may prove that the >l 

 tion is valid by extending the experiments to a numl- 

 masses taken in pairs, and finding that tne result - 

 consistent. The unit of mass may now be fixed, an(! 

 of force defined in terms of it. Further, it may be 'p< 

 out that as consequences of the experimental verifii 

 of the validity of the above mode of definition, the 

 ciples of the equality of action and reaction, and tl 

 the conservation of momentum, immediately follow. 



From this point of view, therefore, we regard for^ 

 being a mass-acceleration rather than mass as the ra 

 force to acceleration. The thermal analogy of Dr. .\ 

 if extended, suits the argument excellently. We d< 

 obtain an absolute scale of temperature until we mu 

 independent of any particular substance ; neither at 

 able to measure force absolutely until its scale cea- 

 depend upon the behaviour of any special body und' 

 action. The Review ! 



Altitude and Animal Development. 



S0.ME time ago I found in the alluvium of a little I> 

 shire stream a tubificid of a sjjecies and genus n* 

 Britain. It was characterised by its large lymph corpi 

 and its Pachydrilus-like form, on which account it 

 named Meganympha pachydriloides, P'riend. The d> - 

 tion showed that the animal possessed an average of '. 

 five segments, three or four forked setae like Limnod 

 a brain deeply lobed behind, spermathecae pear-shap 

 globular, and a penis-sheath, or large penial seta. \ 

 working out some species of Fridericia a few days 

 and turning to Bretscher {Revue Suisse de Zoologie, 

 for some details, my attention was directed to his de- 

 tion of Rhyacodrilus falciformis, and it appeared ev 

 that the Derbyshire worm was one with the Swiss.' 

 Bretscher states that the alpine forms have only i 

 segments. Issel, de Ribaucourt, and Bretscher 

 recently given us many facts to show that annelids cv 

 same species are very much smaller when found hii, 

 in the Alps than when found in the valleys. The for* _ 

 seems to be an interesting confirmation of these stateiv 



But I find that other factors are at work. It is ; 

 years since Vejdovsky first described the little ar 

 known as Achaeta, on account of the absence of seta, 

 it is only within the last few months that specimens 

 been found in England. Southern found three difij 

 species in Ireland two years ago, and I have four 

 same number, though differing in kind, in England. 

 \'ejdovskv gives 15 mm. as the length of .4( 

 bohemica ; but Southern says that though the Irish 

 mens agree with the Bohemian in other respects, the 

 but 5-6 mm. in length. In .August I found .4. boht 

 Vej., in Kew Gardens, and the length agreed with the| 

 forms. On November 7 I took the same species fr 

 little grass plot in the heart of the city of Nottinghar 

 the specimens again measure 5-6 mm. 



It seems easy to account for the difference in 

 the case of Rhyacodrilus ; but can any zoologist or b^ 

 suggest an explanation of the difference betwe 

 Bohemian and British forms of Achaeta? 



HiLDEKic Frii 



no Wilmot Road, Swadlincote, Burton-on-Trent. 



1 Since writing the above I have diecovered that Rhyacodrilfl 

 described in 1Q04 by Ditlevsen as Jlyodrilus filiformis. He was <»« 

 with Bretscher's work, but did rot observe that the Danish tubific 

 already been diagnosed. 



