November 15, 1894] 



NA TURE 



51 



t 



exactitude, accurate clocks and watches not being in 

 existence in his day ; but he overcame this difficulty by 

 a modification of his own invention of the ancient 

 Clepsydra. 



The laws of circular motion were next investigated 

 by Huygens ; and a combination of these laws with 

 Kepler's Third Law, on the assumption" that the planetary 

 orbits round the Sun are circles, leads at once to the 

 Law of Attraction varying inversely as the stjuare of 

 the distance. 



This law, generalised into the Law of Universal 

 Gravitation, became in Newton's powerful hands the 

 foundation of his system of Natural Philosophy, in ex- 

 plaining not only the elliptic orbits of the planets in 

 accordance with Kepler's first two Laws, but also the 

 perturbations of these orbits as exemplified in the Lunar 

 Theory, and the Theory of the Tides. 



Prof. Mach suggests in Fig. 139 a very ingenious ex- 

 perimental illustration of the tides on a body in free 

 space, like the Earth, as distinguished from the tides 

 which would be produced if the Earth was fi.xed, by 

 means of a small iron sphere covered with a solution of 

 magnetic sulphate of iron ; this can either revolve as 

 the bob of a conical pendulum in true planetary style 

 round the pole of a fixed magnet, representing the dis- 

 turbing Sun or Moon ; or it can hang suspended at rest 

 at a small distance from the pole, and thus illustrate 

 high water under the disturbing Sun or Moon, and low 

 water at the antipodes when the Earth is supposed 

 fixed. The discrimination of the two cases must be 

 considered one of the most brilliant parts of the 

 " Principia." 



It is curious that Prof. Mach does not accept Newton's 

 distinction between the relativity of motion of translation 

 and the absoluteness of motion of rotation, illustrated 

 experimentally by Newton by means of a revolving 

 bucket of water suspended by a twisted rope (" Principia," 

 Definition VIII. Scholium) ; and here we think he would 

 have been interested in Maxwell's arguments on Rota- 

 tion in § 104, Matter and Motion. 



Maxwell proceeds to explain that it is possible, by 

 means of observation and experiment on or inside the 

 Earth alone (by Foucault's pendulum, for instance), to 

 disprove Milton's assumption, that it is evidently all the 

 same 



" Whether the sun, predominant in heaven, 

 Rise on the earth, or earth rise on the sun ; 

 He from the east his flaming road begin. 

 Or she from west her silent course advance ; " 



&c., although the geometrical configuration of the earth 

 and the heavenly bodies, so far as is discoverable by 

 astronomical observation, is the same on either assump- 

 tion. 



In the Translator's Preface we are told that " Mr. C. S. 

 Pierce has rewritten § 8 in the chapter on Units and 

 Measures, where the original was inapplicable in this 

 country (America) and slightly out of date." 



As might be anticipated, this means that we are now 

 to change the name of the quantity formerly designated 

 by the word weight, poids, gewicht, pondiis, and to use 

 the word mass instead. 



But if a continental mathematician, Prof. Mach in- 

 cluded, is asked to give a numerical definition of the 



NO. 1307, VOL. 51] 



mass of a body, he replies, if in French, " poids divisd- 

 par g " : so that if a body weighs p kilogrammes, its mass^ 



is -, and the unit of mass is thus _§■ kilogrammes. 



<r 



\Vhen the gravitation unit of force was in universal' 

 use, it was considered an abbreviation to write m for 



S and to replace the gravitation measures of momen- 



tum and energy, 2^ and 2^ , by mv and ^mv". 

 g 2^ 



But when Gauss's abso'ute unit of force is employed, 



the 'absolute measures of momentum and energy are ^z/- 



and hi>v-, and the abbreviation of m for -^ is no longer 



required; or if the letter m is employed, then p = m and 

 not mg, as Mr. Pierce asserts ; if the mass of a body is 

 :o kilogrammes, its weight in kg cannot be anything 

 except 10 kilogrammes. 



But if with absolute measures we retain the equation 

 p = mg, and measure m in kilogrammes, then p, the 

 ■weight or poids, is measured in one-;,nh parts of a kilo- 

 gramme ; this is contrary to all practice, and is absolutely 

 forbidden by the laws on Weights and Measures. 



With gravitation units the weight of a body is at once 

 the numerical measure of the quantity of matter in the 

 body (Newton's quantitas materice) and of its gravita- 

 tion, or the force with which it tends to the Earth ; if a 

 body weighs/ kilogrammes, it is attracted by the Earth 

 with a force of / kilogrammes. The loose definition 

 usually given that " the weight of a body is the force with 

 which it is attracted by the Earth," is really no definition 

 at all, but a mere description ; it should at least be 

 amended to " the weight of a body is the number of 

 units of force with which the body is attracted by the 

 Earth" ; and it will be found that this definition is never 

 employed except with the gravitation unit of force ; so 

 that this definition merely asserts in a roundabout way 

 that the weight of a body is a measure of the quantity of 

 matter, as measured out by weighing against pound or 

 kilogramme weights. 



It is incorrect to say that there are two systems of 

 measurement , the absolute and \k\e. gravitational (p. 2S4). 

 There is no practical method for the measurement of 

 forces in absolute measure with any pretence to accuracy ; 

 the absolute system is merely a system for recording 

 numerically the results of experiment ; the measurements 

 themselves are always made in gravitation measure, and 

 afterwards converted into absolute measure by multiply- 

 ing by the local value of g. There is thus no need for 

 absolute units with our insular British F.P.S. (foot- 

 pound-second) system ; and Prof. James Thomson's 

 poundal, although a convenient name, is of no practical 

 or theoretical use. 



In experiments at Washington, the Paris gravitation 

 unit would not be employed, so that the statements on 

 p. 286 do not tend to clear up the subject. What appears 

 to be meant is that if a perfect spring balance could be 

 constructed such that a kilogramme deflected it at Paris 

 through 981 divisions, then when carried to Washington 

 the deflection would fall to gSo'i divisions, and if carried 

 to the Moon to about 164 divisions, but if carried to the 

 surface of the Sun the deflection would rise to about 

 30,000 divisions, provided Newton's " Law of Universal 



