July 1, 1892.] 



KNOWLEDGE 



139 



provided the same nimiber of molecules per second struck 

 the warm and the cold face of the vane, it is certain that 

 the additional work of repulsion done upon them at the 

 former surface would react upon the vane itself, and 

 drive it in the opposite direction from the shower of 

 heated molecules. As a matter of fact, however, this does 

 not take place ; for the density of the gas in that thin 

 heated layer, contiguous to the lampblacked surface, is 

 less in proportion as its temperature is higher than in any 

 other part of the bulb. The quickened molecules, shooting 

 away from the lampblack, beat back a proportion of those 

 that move more slowly ; and thus the number of impacts 

 on the heated surface is reduced, and the equilibrium of 

 the two sides of the vane is almost perfectly maintained. 



Nest consider the effect of exhausting the glass bulb of 

 the radiometer. The mean free path of the gas molecules 

 will increase directly with the exhaustion, while the 

 average distance from centre to centre of the molecules 

 will only increase with its cube root. Hence, by a sufficient 

 degree of rarefaction, the free path can be made quite 

 considerable, though the molecules are still crowded 

 together in enormous number. At an exhaustion of one- 

 millionth of an atmosphere, the free path will be a million 

 times augmented— that is, to a length of about ten centi- 

 metres — and it is under pressures ranging fi-om this point 

 up to about fifty-milliouths of that of the atmosphere 

 that light mills exhibit the highest eflScieucy. As 

 exhaustion of the bulb is carried out, new conditions of 

 cooling begin to manifest themselves before the heated 

 lampblack. As the free path increases, the " molecular 

 wind " that has been spoken of blows further, and cooler 

 particles of gas crowd in upon the blackened surface from 

 the sides. By-and-by the shower of molecules (moving 

 at a velocity corresponding to 1-5-i', and in a du-ection 

 normal to the surface of the vane) will extend to the glass 

 envelope, and will communicate their heat to it directly. 

 Comparatively few wiU now collide with the colder mole- 

 cules travelling in the opposite direction ; and these colder 

 molecules, no longer unduly checked in their journeys to 

 the blackened surface, encounter it as often as they do the 

 other side. The reaction, or Crookes' pressure, at the 

 warmed surface will therefore assert itself, and occasion 

 the rotation of the fly. 



When first the radiometer was exhibited, it was suggested 

 that the sunny side of the earth would suffer a force of 

 repulsion comparable with that upon the vane of such an 

 instrument. It is almost unnecessary to say, however, 

 that there is no foundation for this idea in the now accepted 

 explanation of Prof. Crookes' discovery. Crookes' pressure 

 is only indirectly due to radiation, and it is quite distinct 

 from that estimated by Maxwell (see his Electricitii tind 

 MaijHttisin, vol. ii., p. 402) at about 2i lbs. per square mile 

 of the sunlit surface of the earth. 



>^ Prof. Crookes' mechanism is applicable 



to the conversion of radiant energy, of 

 probably almost any wave length, into a 

 form convenient for approximate measiu-e- 

 ment. But, from the definition that has 

 been given of absorption, it follows that 

 the layers of lampblack on the vanes may 

 have to be replaced by various other 

 materials, according to the quality of the 

 radiation that it is desired to measure. 

 Eadiometers sensitive to actinism and to 

 radiant heat have been constructed, and it 

 may be presumed that such instruments 

 can also be made to respond to the 

 electrical radiations that have been studied 

 by Prof. Lodge and others. 



The constructive details of the apparatus can be modified 

 in very many ways. For instance, a fly having several 

 plain mica vanes, skewed like the blades of a screw propellor, 

 may be placed in the path of the shower of molecules 

 proceeding from a fixed disc of lampblacked material. In 

 consequence of the favourable situation of the reacting 

 surfaces, very rapid rotation takes place in this modification 

 of the radiometer. It has been named by Prof. Crookes 

 the otheoscope, and is shown in Fig. 2. If the skewed 

 vanes of the otheoscope could be rotated sufiieiently rapidly 

 by mechanical means, a stream of molecules would be 

 generated, not unlike that which is set up by the heating 

 of the lampblacked disc. The study of molecular motion 

 under such conditions is not without practical interest. 

 Indeed, with every difl'erent point of view from which the 

 radiometer can be regarded, some attractive suggestion 

 presents itself. 



Ctjcss Column. 



By C. D. LococK, B.A.Oson. 



All coiiiiTJNicATioNs for this column should be addressed 

 to the " Chess Editor, Knowledge Office," smi posted before 

 the 10th of each month. 



Solution of June Prohlem (by C. D. Locock). — 1. Q 

 to R5, and mates next move. 



Correct Solutioss received from Alpha and C. T. 

 Blanshard. 



H. S. Brandivth.—U 1. Q to Bo, Black replies P x R, 

 or Kt to K6, and no mate results. 



./. ( '. A'n,ot/.cr. — There is a flaw in your conclusion. 

 After 1. Q xP, Black provides an escape for his King by 

 Kt to K6. 



C. Leeson I'rincf. — After 1. Q x Ktch there is no mate. 



Alpha. — '• Dummy Pawns,' as they are called, are no 

 longer allowed. There is also a prejudice against any 

 promotion on the first move, just as there is against checks 

 and captures. 



C. T. Blanshard. — Thanks for the Problems. The pro- 

 motion problem is a little too simple, apart from the fact 

 that HP becomes a Queen is equally effective. The other 

 seems all right. The three-maver is neatly solved in one 

 move. In the variation you give the Rook and not the 

 Bishop mates. Perhaps the diagram was wrong. 



PROBLEM. 



By .J. JucHLY, Munich. 



(From the Field.) 



Black. 



'^m" ^p ^^p ^^p 



11 ^ 







«i¥. 



'^M 9 



m^ 



White. 



■White mates in thi-ee moves. 



Fis. 2. 



We fully endorse a statement in the Harhie;/ Mercury 

 as to the difficulty of the above. The chief difficulty lies 



