78 



KNOWLEDGE 



[April 1, 1898. 



from train to train, leaping from one and alighting in the 

 next, and going backwards and forwards. A passenger 

 passing from train '( to e has his momeutum increased. 

 On returning from c to a he is going from faster to slower 

 moving trains, and he takes away momeutum from the 

 trains with the greater speed and gives it up to those 

 possessing less velocity. The increased momeutum which 

 a passenger gains by passing from the slower to the quicker- 

 moving train is yielded up again to the slow one when he 

 jumps into it. In this way the tendency of the to and fro 

 motion of the passengers is to bring all the trains to one 

 uniform speed, i.e., to make the momentum of all the trains 

 equal. 



Suppose the trains replaced by layers of gas particles, 

 and instead of the leaping passengers consider the back 

 and forward translational movements of the molecules 

 themselves, and we have a correct picture of what is 

 happening in a mass of gas which is extended between a 

 stationary plate and a mo\-ing plate (or a layer of the gas 

 itself) at some distance above it. The eftect produced is a 

 tendency to stop the motion of the mo\-ing plate, or, if the 

 motion of the plate is kept up by an external force, a 

 tendency to drag along the neighbouring stationary plate. 

 Thus, by the observations of Maxwell on his mo\ing disc 

 rotating backwards and forwards in its own plane, he 

 obtained a measurement of the value of the viscosity of 

 air and other gases. 



Let 1/ represent the viscosity of the gas, then the length, 

 /, of the mean path of the molecules follows thus : — 

 I = -— -. Where the product //' n is simply the mass of a 

 unit of volume (the mass, m, of a single molecule multi- 

 plied by the number of molecules in unit volume), and the 

 quantity, ;/, is the mean velocity of the molecules whose 

 value for hydrogen and oxygen we saw above. 



The values obtained by 0. E. Meyer for the coefficient 

 of viscosity expressed in centimetre — gramme — second 

 units are : — 



Centimetres. 



Oxygen 000022:5 



Air 0-000-'2ll 



Xitrogen 0-OOU19(J 



Carbon monoxide ... 0-000194 



Carbonic add ... 0-000068 



Hydrogen 0-000098 



From these numbers, by means of the formula given 

 above, the following values for the mean free path are 

 obtained ; — 



Centimetres. 



Oxygen .. 00000096 



Air 00000090 



Nitrogen ... 00000089 



Carbon monoxide OOUWXKSi) 



Carbonic acid 0-0000062 



Hydrogen 0-0000109 



These values of the free path are expressed in centimetres. 

 Reducing the number for that of oxygen to inches, we get 

 four mUlionths of an inch for its mean free path at ordinary 

 pressures. This number is of the same range of value 

 as that given above from Clausius' formula, and consider- 

 ing the difficulty and the uncertainty necessarily attending 

 the experiments till the methods ai'e further perfected, the 

 correspondence is as good as can be expected. Perhaps 

 all we can at present say is that for air or oxygen the 

 length of the free path is very small, about -00001 centi- 

 metre, or ..-joVijij inch— that is, a length outside tbe limits 

 of the microscopically visible. A cube, with an edge 

 40000 centimetre in length, is the smallest possible area 

 which can be seen with modern microscopes, but the length 

 of the patli of a particle of air between its collisions is 

 on the average five times shorter than the edge of this 

 cube. 



When the pressure is reduced, as in the vacuum pro- 

 duced by a good mercury-dropping Sprengel pump, in 

 which a pressure of only a millionth of an atmosphere 

 may be readily obtained, the length of the free path is 

 enormously increased. The free path, therefore, in an 

 ordinary electric glow lamp is large. The phenomena of 

 phosphorescence in electric discharges in high vacua has 

 been explained by Crookes as due to the bombardment 

 of the glass or ythium used by gas molecules moving on an 

 uninterrupted free path of a foot or so in length, and 

 striking at their high speed on the siu-face exposed to 

 them. 



The shortness of the free path at ordinary pressures 

 explains how it is that the odour of a strongly smelling 

 gas, as ammonia, does not penetrate almost instan- 

 taneously to the end of a room in which a bottle of it is 

 uncorked, as wo would expect it to do if its particles are 

 moving at about 1000 feet per second. The rapidly moving 

 molecules are so continually knocked about amongst each 

 other, and by the surrounding air, that their direction is 

 constantly changing, and they are so thickly crowded . 

 together that their uninterrupted course is only the smaU 

 fraction of an inch referred to above, and it is now not 

 surprising that a prolonged period is necessary for the 

 strongly smelling particles to reach an observer across a 

 room. 



THE FACE OF THE SKY FOR APRIL. 



By Herbert Sadler, F.R.A.S. 



SOLAR spots continue to increase in number and 

 magnitude. A total eclipse of the Sun occurs on 

 the 16th, no portion of which wiU be visible in 

 these islands, though a partial eclipse is visible in 

 southern Europe. The line of central eclipse 

 touches the coast of South America at Chanaral, in Chili, 

 crosses South America, and leaves the continent at about 

 forty miles to the north-west of Ceara, in Brazil. It touches 

 Africa, after crossing the Atlantic, at Joal, in Senegambia, 

 and leaves the earth in the Sahara. The longest duration 

 of the total phase is 4m. 49s. Conveniently observable 

 minima of Algol occur at llh. Im. p.m. on the 4th, 

 at 7h. 50m. p.m. on the 7th, and at 9h. 32m. p.m. on the 

 27th. 



Mercury is in inferior conjunction with the Sun on the 

 1st, and at his greatest western elongation (26|°) on the 

 28th, but as he never rises more than forty minutes before 

 the Sun during the whole month, and is therefore quite 

 invisible to the naked eye, an ephemeris of him would 

 be useless. Both ^'enus and Jupiter are also invisible, 

 the latter being in conjunction with the Sun on the 

 27th. 



Mars is still visible, but is becoming more uninteresting 

 than ever. He sets on the 1st at llh. 24m. p.m., with a 

 northern declination of 21° 38', and an apparent diameter 

 of 5|". On the 30th he sets at llh. 10m. p.m., with a 

 northern declination of 24° 17', and an apparent diameter 

 of 5". He is in conjunction with Neptune on the 12th, 

 Mars being 2 ' 35' north. He describes a direct path in 

 Taurus during the month. 



Saturn is an evening star, and is excellently placed for 

 observation. On the 1st he rises at 5h. 58m. p.m., or 

 twenty minutes after sunset, with a southern declination of 

 1° 11', and an apparent equatorial diameter of 19" (the 

 major axis of the ring system being 43^" in diameter, and 

 the minor 5i"). On the 30th he rises at 3h. 52m. p.m., 

 with a southern declination of 0° 24^', and an apparent 

 equatorial diameter of 18-6" (the major axis of the ring 



