2 50 



NATURE 



[July 14, 1892 



These definitions of the absolute unit of lorce are 

 very elegant and useful so long as we confine our- 

 selves to calculations on paper, but they will not 

 satisfy legal requirements. There is no apparatus in 

 existence which will measure a poundal or dyne from 

 these academic definitions within, say, lo per cent. For 

 accurate definition we must return to the old gravitation 

 measure, and define the poundal or dyne as one-^th 

 part of the force with which the Earth attracts a pound 

 weight or a gramme weight, the value of g (in celoes or 

 spouds) being determined by pendulum observations ; 

 and now the standard weight and the value of g are 

 capable of measurement to within, say, one-iooth per 

 cent., an accuracy sufficient to prevent litigation. 



In the recent report of the Committee on Electrical 

 Standards we find the ohm defined as the equivalent of 

 a velocity of ten million metres (ons quadrant of the 

 Earth) per second, to satisfy theoretical requirements ; 

 but as this definition would be useless for commercial 

 purposes. Dr. Hopkinson insisted that it was essential 

 that an alternate definition should be given, legalizing 

 certain bars of metal as standard ohms. 



In converting absolute and gravitation measure, we 

 must notice that there are, strictly speaking, three 

 different _§''s in existence : (i) the g of pure gravity of a 

 body falling freely ; (2) the g determined by a plumb-line, 

 or by a Foucault pendulum of which the plane of oscilla- 

 tion is free to rotate ; (3) the ,f determined by a pendulum 

 oscillating in a fixed vertical plane, about a fixed axis ; 

 this is the legal g, so to speak, although practically 

 undistinguishable from the g given in (2). 



Sir W. Thomson's Standard Electrical Balance Instru- 

 ments are graduated in gravitation measure, so that, if 

 calibrated at Glasgow, they are one-25th per cent, in 

 error in London, and about one-7th per cent, in error 

 at the equator, and a corresponding correction imust be 

 made. 



An absolute Spring Balance instrument would possess 

 a spurious absoluteness, in consequence of the deteriora- 

 tion of temper of the spring, and of its variation of 

 ■strength with the temperature, as experienced in the 

 Indicator. 



8, There is no advantage or gain of simplicity by the 

 use of absolute units in dynamical questions concerning 

 motion which is due to the gravitational field of force ; the 

 ■only change being the removal of ^^'^ from the denominator 

 on the right hand side of our dynamical equations to the 

 numerator on the left-hand side. 



For this reason engineers and practical men invariably 

 ■employ the gravitation unit of force in the dynamical 

 ■questions which concern them ; measuring, for instance, 

 their forces in pounds, pressures in pounds per square 

 foot or square inch, while at the same time measuring the 

 ■quantity of matter in the moving parts by pound weights. 



The absolute unit of force has only recently made its 

 way into dynamical treatment, principally in consequence 

 of the development of Electricity. Previously the gravi- 

 tation unit was universally employed, with the con- 

 sequence that W in the equations of motion always 

 appeared qualified by a denominator g, in the form 



9. Noticing that W never appeared alone, but always 



W 



as — (for instance, that if a celoes is the acceleration 



g 

 which a force of P pounds causes in a weight of W lbs., 

 then 



T, W P 



P = — a, ox a = -- 



or W 



w 



by a single letter M ; so that the dynamical equations 



<early writers on Dynamics were unfortunately tempted to 

 juake an abbreviation in writing and printing, by replacing 



NO. 1185, VOL. 46] 



could be printed 



P = Ma (pounds), 

 P.f = }^v"- (foot-pounds), 

 P^ = Mz/ (second-pounds), 



each occupying one line of print. 



This quantity M was variously called the mass of the 

 body — a quantity sui generis— the massiveness of the 

 body, the inertia, or the invariable quantity of matter in 

 the body. 



But if M denotes the invariable quantity of matter, we 

 have this awkwardness, that M, the invariable quantity, is 

 measured in terms of a variable unit, g pounds ; while the 

 force P, which varies with g, is always measured by 

 means of a definite lump of metal, the pound weight. 



This awkwardness is rectified if we change the unit of 

 force, and measure P in absolute units, poundals, and M 

 in lbs., but now M becomes the same as W, formerly ; 

 and its introduction only causes confusion, because M is 

 still taken by most writers on Dynamics as defined by 



M = — : 



thus making W = M^, the source of all the confusion 

 in our dynamical equations. 



If weight W is measured in pounds, as the Act of Par- 

 liament directs, and if the unit of mass is one pound, so 

 that M is also measured in pounds, then, if W and M 

 refer to the same body, W = M, and not M^. 



If W = M^, and W is measured in lbs., then M is 

 measured in units of g lbs., a variable unit, unsuitable for 

 a cosmopolitan question. 



But if W = M^, and M is measured in pounds, then 

 weight W is measured in units of one-^th part of a 

 pound, ox poundals, which is illegal according to the Act 

 on Weights and Measures, c. 19, 41 and 42 Victoria: 

 "Any person who sells by any denomination of weight 

 or measure other than one of the imperial weights or 

 measures, or some multiple or part thereof, shall be liable 

 to a fine not exceeding forty shillings for each such sale." 



10. The theoretical writer overrides these difficulties 

 by giving a new definition of Weight, not contemplated 

 or mentioned in the Act of Parliament : 



" The weight of a body is the force with which it is 

 attracted by the Earth." 



Let us examine this definition closely. 



In the first place, it does not appear to contemplate the 

 use of the word weight, except in reference to bodies on 

 or near the surface of the Earth. 



According to this definition, what is the weight of the 

 Moon, or of a body on the Moon*? Must the Moon be 

 brought up to the surface of the Earth in fragments, or 

 must the weight be estimated at the present distance of 

 the Moon ? 



What, again, is the weight of the Sun, or of a body on 

 the Sun } and what is the weight of the Earth itself.^ 



And what does Sir Robert Ball mean when he writes 

 that " the weight of Algol is about double the weight of 

 the Sun " 1 



Considering, however, merely bodies of moderate size on 

 the surface of the Earth, the attraction of pure gravity of 

 the Earth is only to be found in a body falling freely ; the 

 tension of a thread by which a body is supported is 

 influenced by the rotation of the Earth. 



Again, the local value of g is, theoretically speaking, 

 influenced by the position of the Moon and Sun ; it is true 

 that the influence is insensible on the plumb-line, although 

 manifest on such a gigantic scale in its tide-producing 

 effects. 



Suppose, then, we employ the gravitation unit of force 

 in the theorist's definition of the weight of a body. The 



