ISO 



NA TURE 



[Dec. 1 6, 1886 



same or different molecules, is the algebraical sum of the powers 

 of the incliviilual forces. 



From the jiarallelogram of motions it follows that — 



Prop. I. 'Ihe power of the re-ultant of a system of forces 

 imparted to a single molecule is equal to the power of the forces. 

 Whence — 



Cor. I. If the forces imparted to a molecule are in equi- 

 librium, their power for any actual or hypothetical motion of 

 the molecule is zero. 



Cor. 2. If the forces imparted to a molecule are not in equi- 

 librium, their piower for any motion in the direction of the 

 resultant is positive. 



Definition. — A system of molecules is said to be passive for a 

 given motion when for that motion the power of its internal 

 forces is zero. 



Prop. II. The power of the external forces of a system for 

 actual or hypothetical motions-for which the system is passive 

 is equal to the power of the resultant motions of the several 

 molecules of the system. 



For (by Prop. I. ) the power of the resultant forces for each 

 (and therefore for all) of the molecules is equal to the power of 

 the external together with that of the internal forces, but the 

 latter, in the case of the entire system, is zero by hypothesis. 



Cor. I. If external forces be imparted to a passive system at 

 rest in a given position such that for any hypothetical motion 

 through that position the power of such forces is zero, the system 

 will remain at rest. 



For if motion ensued, the resultant and therefore (Prop. I.) 

 the external forces would have positive power for such motion, 

 which is contrary to hypothesis. 



Cor. 2. If external forces be imparted to a passive system at 

 rest, and be in equilibrium, the power of these forces for any 

 hypothetical motion of the system through this position of rest 

 is zero. 



For as the whole system is at rest each molecule is at rest, 

 and the resultant forces of the molecules are all of them zero, 

 whence their power and therefore that of the external forces 

 (Prop. I.) is zero. 



It will be seen that Prop. II. is (or is equivalent to) D'AIcm- 

 bert's Principle, and its two corollaries con-titute what is called 

 the Principle of Virtual Velocities. 



It may be urged that this merely relegales the difficulty to 

 determining for what motions systems are jiassive. This really, 

 however, presents no difficulty, for it is obvious that a systejn 

 is passive generally when its internal forces neither tend to pro- 

 duce or destroy kinetic energy in the system ; so that (l) rigid 

 systems are passive for all m .tions consistent with their rigidity ; 

 (2) all systems are pa-sive for rigid motion ; (3) inelastic and 

 theoretically perfect funicular systems are pasdve ; and (4) in- 

 elastic and theoretically perfect fluid systems are passive, etc. 



D'Alembert's principle and the principle of virtual velocities 

 ought to form the basis of that part of kinetics which involves 

 the idea of the transmission offeree, whether the result ismoli n 

 or equilibrium. D'Alembert's principle is the most general. 

 The principle of virtual velocities is to it what Maclaurin's 

 theorem is to Taylor's. The form in which it is given in Prop. 

 II. above is more convenient for use than that in which it is 

 generally stated, viz. that the resultant forces reversed balance 

 the impressed forces. 



L-agrange's proof of the principle of virtual velocities and its 

 modifications are altogether too artificial and unsatisfactory. 



Cape of Good Hope F. GuTHiiiE 



Recent Gales 



The gales of October 16 and December S varied considerably. 

 In the former gale there were constant oscillaiions, from '004 to 

 ■010 of an inch, eveiy 30 seconds between i a.m. and 2 a.m. ; 

 whilst in the December gale there were no oscillati ms, but a 

 constant fall that was most rapid during squalls. The difference 

 between the dry and wet bulb thermometers in the October gale 

 was only a quarter of a degree, whilst in that of December it 

 exceeded from 2j° to 3i° (or a difference of from tiiirteen to 

 eighteen times as great). During the gale in October, i-i6o 

 inches of rain fell, and in that of December 0758 of an inch. 



The lowest reading (corrected for temperature) of the baro- 

 meter at 530 feet above the sea was on October 16, 28-019, and 

 on December 8, 27-693 inches (this occurred at S p.m.). 



The barometer reduced to sea-level was less than 28-5 inches 

 from 11.30 a.m. of the 8th till 8.15 a.m. of the 9th (or neariy 



21 hours). The October gale was W.S.W., and the December 

 gale W. 



The last gale commenced at I a.m. on the 8th (with constant 

 squalls of hail and rain), and was most violent from 4.45 p.m. 

 till 8.30 p.m. 



Thtmder and lightning occurred from 11 a.m. till 11.30 a.m. ; 

 and from 4 p.m. till 4,40 p.m. on the 8th, and from 1.35 a.m. 

 till 2.45 a.m. on the 9th. 



Much damage was done to house-roofs. Very few trees were 

 blown down here, for in this exposed situation trees are better 

 prepared to resist gales. About 1 1 feet of the top of a large 

 specimen of Picea Wcbbiana was destroyed. E. J. Lowe 



.Shirenewton Hall, Chepstow, December II 



Note on the Manipulation of Glass containing Lead 



In reading Mr. Shenstone's very useful little treatise on glass- 

 blowing (reviewed in Nature of the 9th inst. , p. 123), I have 

 failed to notice any mention of an expedient which I have found 

 very useful for dealing with English flint-glass containing much 

 lead silicate ; although I greatly prefer for most purposes the 

 readily fusible "soda-glass" used probably every where except in 

 England.' 



Of course, all ordinary flames, such as those of the Bunsen 

 burner and the blow-pipe, consist, in part, of reducing gases 

 which cause the separation cH" lead from glass introduced into 

 them. This reduction can be prevented or remedied, as Mr. 

 Shenstone says, by holding the glass a little in front of the 

 visible flame ; but there is in this region hardly enough heat to 

 do all that is required in the manipulation of the glass. 



If, however, oxygen instea 1 of air is used in a Herapath blow- 

 pipe, the resulting flame has so little reducing power, that lead- 

 glass can be safely held well within it ; and this is the flame that 

 I always use in dealing with such glass. 



It is true that oxygen is, at present, rather more expensive 

 than air ; but most, if not all, laboratories have a supply of the 

 gas, either in a gas-holder or a bag, for the optical lantern and 

 other purposes ; and with it the manipulation of lead-glass 

 becomes vvha'- shavi ig is, in certain advertisements, said to be — 

 "a luxury." H. G. Madan 



Eton College 



P. S. — The oxy-coal-gas blow-pipe is also extremely useful for 

 difficultly-fusible "combustion-tubing." Bulbs of fair size can 

 be blown, and side-junctions, &c., made in this glass, with 

 almost the same facility as in ordinary " soda-glass." 



1 The best glass of this kind is that used by Geissler, Alvergniat, and 

 others, for making thqir marvellous specimens of glass-work ; but I doubt if 

 glass of the sarne excellence, in regard to fusibility and freedom from any 

 tendency to devitrify, is generally procurable. 



