222 



NATURE 



[July 4, 1895 



side in |>assing through the distance s is f/z, and the time is 

 s -=- z'/2 = 2 siv, the same as in the first case. Which proves 

 the proposition. 



Since from (I) we have 3 I'V = * m7* or 3 PV = \ y\T~, 

 we may substitute this value in the virial equation, and remem- 

 bering that 1.\iii-- = \'S\-y-, we get - ^2Rr = - ^Mt". 

 Hence also 



1' = J pr^ (2) 



The above equation is easily ob- 



where f — '-- the density. 



tainable without the use of the virial equation U'lien the time of 

 impact is taken into consideration. \ phenomenon which can- 

 not be assumed to be instantaneous without upsetting the 

 dynamical definition of the measurement of a force ; which 

 expressed algebraically is Vt = Mj'. From which it is evident 

 that when / the time is o, £• the velocit)', is also o. 



When the virial equation is made applicable to the case of a 

 gas composed of molecules capable of vibrating, it seems 

 obrious that the term 'S,\niv'- should be written ShBmv- ; be- 

 cause, as shown by Clausius, the internal energ)' of the mole- 

 cules bears a constant ratio to the energy of agitation. We 

 must look to the tnec/iaiiical stnuture of the tiiolaule for the 

 reason of this. Here the fact is simply accepted, not explained ; 

 but it is obvious that the same forces which impart translator)' 

 energy to a molecule will imi>arl vibratory energ)' also. The 

 same reasoning applies to the term - j2Rr, which now be- 

 comes — 2fl(Rr). The volume of the gas is unaltered by the 

 nbrations, and the pressure is dependent on the two other 

 terms. Hence the equation may be written 



3PV = 2iSwE'- - 

 And from this we get 



P = \&fv 

 The above equation may be written 



i2«K') (3) 



(4) 



(5) 



P„ = \fm.'i ; 



Where Vi — $v. .»\gain equation (2) may be w rillen 



Vi = Iv.ii' ; (6) 



the suffix i denoting that the pressure, density, and mean square 

 velocity are those of an ideal gas composed of smooth elastic 

 spheres. 



If P„ pi, and Vi in (6) are taken respectively equal to P, p, 

 and Vt in (5) ; then it is evident that J', in (5) is the velocity of 

 mean square of an ideal gas which, having the same density, 

 would give the same pressure as a natural gas. Hence f, can 

 l)e found from (6). Now the total energy in unit mass of a gas 

 is given by the equation 



K.T = Jflz?; (7) 



where K- is the specific heat at constant volume, and T is the 

 al)5olute tem)>erature. Krom which equation vs,'0 can be found. 

 Wc have also from above 



(8) 



from which ctjuation the value of s/ff and conse<|Ucnlly B can he 

 found. 



The equation — ^iiy - I) can now be proved as follows. 

 Multiplying both siilcs of (4) by V, the volume of unit mass, and 

 combming with (7), we get 



K,.T = 3PV (9) 



Now from (5) and (6), taking p = pt we get 1' = P,/fl, and 

 sulKtituting in (9) K„ = 3P,\7i8T. Hut PA/T = K<^ - K„. ; or 

 the difference between the specific heats at con.stant pressure 

 and constant volume ; the suffix i indicating, a-s before, that the 

 symlKils refer to an ideal gas. Hence 



^ = 3(K,^ -Jw)^3*(K, - K.)^3^.y_ , ) , ,0, 



Here/' is wmc factor which for so-called permanent gases is 

 very nearly unity. Kor such gases we may w rile ( 10) 



fi = ih- >); or7=l(fl-f-3) . . . .(II) 

 In the following table the values of $, except in the case of 

 argon, arc calculated from equation (8) ; and P, the velocity of 

 ideal gases having the same pressure and density as their cor- 



NO. 1340, VOL. 52] 



responding natural gases, at standard temperature and pressure, 

 from (6). The velocities are given in feet per second, .and the 

 value of gravity is t.iken at 32-2. Column (4) gives the values of 

 y for the diflerent gases calculated from equation (11); and 

 column (5) gives the experimental values of 7. The close 

 agreement between these values is a significant fact. 



(■) 



(2) 



Hydrogen ... 

 Oxygen ... 

 Nitrogen ... 

 Drj- air 

 Argon 



8551 

 2140 

 3282 

 2250 

 1940 



8, Norfolk Square, W. , 



1-234 - 

 1197 .-. 



1-227 — 



1-222 ... 

 a (about).. 



(.3) 



... 6925 



... 1787 



... i8«o 



... 1841 



... 970 



lune 13. 



(4) 



(5) 

 K.X- 



7 JWTj/ penment 



(6) 



1-4115 



'■399 

 1-409 

 1-407 



... 1*412 



... 1 -402 



... 1-411 



... 1-409 



... 1-7 



C. E. B.^SEVi. 



1-00035 



I-0021 

 1-0014 

 I -001 4 



Romano-British Land Surface.— Flint Flakes 

 Replaced. 



In the early spring of the present year, whilst passing a newly- 

 opened excavation near Caddinglon Church, three miles south- 

 east of Dunstable, I noticeil a very thin horizontal line of sharp 

 flint flakes, embedded a foot deep from the surface-line of .in old 

 pa.sture. I could see at once that the line represented an old 

 living surface, so I took a few of the flints away. In removing 

 the stones from the soil, one or two little fragments of Romano- 

 British pottery came away with them. The flakes were lustrous. 



Fk;. I. — Fragment of perforated Roniano-liriti>li pottery (half .actual si/c). 



chiefly black and brown-grey, and as sharp as when first struck. 

 On looking over the flints in the evening, I was able to repl.tce 

 five on to each other. This fad, and the occurrence of the pottery 

 fragments, proved the old surface to have remaineil intact from 

 Romano-British times. 



A little later in the spring, about six square yards of the super- 

 incumbent soil were carefully removed for me, \\hen other flakes 

 were found i/i situ to the exact number of fmir hiiinlrcil : with 

 these were eighteen fragments of Romano-British pottery, one 

 piece — somewhat like the bottom of a pot — perforated, as here 



I'lG. a. — Four conjoined flint-tl.akcs (lialf.ictual si/e). 



illustrated. Amongst the flints were two cores, two hammer- 

 stones, three scrapers, part of one edge of a chipped celt, and 

 several neatly chipped but ap]iarcnlly unfinished lillle im)ile- 

 mcnts. A middle-br.iss Roman <-r)in, too corroiled for idcniili- 

 cation, was found on the same surface in a second excavation 

 close by j with this was a small piece of wood carved to repre- 

 sent a horse's fore-leg, and a well-finished ami perfect unpolished 

 flint celt. 



In .sorting the flints I was able to replace thirty-eight on to 

 each other in groups f>f from two to five. Two of these groups 



