ISIov. 29, 1877] 



NATURE 



79 



it had flowered profusely, I could not find a single normal fruit, 

 and subterranean ones were extremely scarce. 



Acccording to Delpino the changing colours of certain flowers 

 would serve to show to the visiting insects the proper moment 

 for effecting the fertilisation of these flowers. ; We have here a 

 I.antana the flowers of which last three days, being yellow on 

 the first, orange on the second, purple on the third day. This 

 plant is visited by various butterflies. As far as I have seen the 

 purple flowers are never touched. Some species inserted their 

 proboscis both into yellow and into orange flowers {Danais 

 erippus, PUris arlpa), others, as far as I have hitherto observed, 

 exclusively into the yellow flowers of the first day {Ilelicouius 

 apsiudes, Colanh jii'ia, Eurema leuce. This'is, I think, a rather 

 interesting case. If the flowers fell off at the end of the first day 

 the inflorv'jscence would be much less conspicuous ; if they did 

 not change their colour much time would be lost by the butterflies: 

 inserting their proboscis in already fertilised flowers. 



In another Lantana the flowers have the colour of lilac, the 

 entrance of the tube is yellow surrounded by a white circle ; 

 these yellow and white markings disappear on the second day. 



Mr. Leggett's statements about Pontederia cordata appear to me 

 rather strange, and I fear that there is some mistake. In all the 

 five species of the family which I know the flowers are so short- 

 lived, lasting only one day, that a change in the length of the 

 style is not very probable. In the long-styled form of our high- 

 and Pontederia the style has its full length long before the flowers 

 open. In my garden this Pontedaria is visited by some species 

 of Augochlora collecting the pollen of the longest and mid-length 

 stamens ; they are too large to enter the tube of the corolla, and 

 have too short a proboscis to reach the honey ; they can only fer- 

 tilise the long-styled and mid-styled forms, but not the short- 

 styled. 



Among the secondary sexual characters of insects the meaning 

 of which is not understood, you mention ("Descent of Man," 

 vol. i., p. 345) the different neuration in the wings of the two sexes 

 of some butterflies. In all the cases which I know this difference 

 in neuration is connected with, and probably caused by, the deve- 

 lopment in the males of spots of peculiarly-formed scales, 

 pencils, or other contrivances which exhale odours, agreeable 

 no doubt to their female?. This is the case in the genera 

 Mechanitis, Dircenna, in some species of Thecla, &c. 



Fritz Muller 

 Blumenau, St. Catharina, Brazil, October 19 



The Radiometer and its Lessons 



Prof. Osijorne Reynolds's letter in Nature (vol. xvii. 

 p. 26) has directed attention prominently to the circumstance 

 that two hypotheses have been submitted to the scientific world 

 as explanations of the force and motions which Mr. Crookes had 

 shown to exist— one by Prof. Osborne Reynolds, the other by 

 myself. 



Prof. Osborne Reynolds's explanation is based on the fact that 

 when a disc with vertical sides is heated on one side and exposed 

 to a gas, a convection current sets in, which' draws a continuous 

 supply of cold gas into contact with the hot surface of the disc. 

 As this cold gas reaches the disc it is expanded, and thus its 

 centre of gravity is thrown-further from the disc. Accordingly, 

 the disc, it freely suspended, will move in the opposite direction 

 so as to keep the centre of gravity of the gas and disc in tlie 

 same vertical line as before, and, if not freely suspended, will 

 suffer a pressure tending to make it move in that direction. If I 

 have understood Prof. Reynolds aright, this is both a correct and 

 full description of his explanation as last presented. 



My explanation, on the other hand, is based on tnolecular 

 motions which go on in the gas without causing any molar 

 motion, and is independent of convection currents. Prof, Rey- 

 nolds is therefore, I conceive, fully justified in denying that my 

 theory has supplied any deficiency in his explanation. As he 

 points out, the two explanations are incompatible ; if either is 

 correct, the other is wholly wrong. 



It is easy to apply comparative tests to the lival hypotheses by 



making a selection from Mr. Crookes's incomparable experi- 

 ments, from the experiments by Mr. Moss and myself, and from 

 instances of compressed Crookes's layers in the open atmosphere ; 

 but it is not easy to make the choice so as to bring the abundant 

 evidence within the compass of a letter. 



These tests might take various forms, of which perhaps the 

 most direct is to ascertain whether the force is affected by varia- 

 tions in the convection current, as required by Prof. Reynolds's 

 hypothesis, or is independent of convection, but increased when 

 the heater and copier are brought nearer together, as required 

 by mine. 



To test this Mr. Crookes mounted a radiometer in a receiver 

 consisting of two unequal bulbs connected by a large tube. The 

 movable portion could be transferred from one bulb to the other 

 through the tube. In the small bulb the convection current is 

 most impeded, and at the Fame time the heater and cooler are 

 closest together. Mr. Crookes found that the motion of the 

 radiometer was more rapid in the small bulb than in the large 

 one, ia conformity with my theory, and in opposition to Prof. 

 Reynolds's. The same is the uniform drift of a vast number of 

 other experiments by Mr. Crookes, and of those by Mr, Moss 

 and myself, from which it appears that whenever the heater and 

 cooler are ma Je to approach there is an increase in the force, 

 and that the force is not appreciably affected by variations of tl:e 

 convection current, or by its suppression. 



This may also be proved, and quite conclusively, by observa- 

 tions not requiring apparatus. Drops in the spheroidal state 

 and the drops which are often seen floating on the surface of 

 volatile liquids, as, for example, the drops which run about on 

 the surface of the sea in certain states of the weather when water 

 drips from an oar, are supported by Crookes's layers of air inter- 

 vening between them and the liquid beneath. Similarly a red- 

 hot copper plate will float on water, supported on a Crookes's 

 layer, and many other instances of a like kind might be adduced. 

 In such cases, where the film of air is thin and for the most part 

 horizontal, it is manifest that there is no opportunity for those 

 convection currents to arise which are required by Prof. 

 Reynolds's hypothesis, while in all of them there are the peculiar 

 molecular motions of my theory. 



The absence of convection currents which could produce an 

 appreciable effect may also be proved in those radiometers of 

 which the arms whisk round at a very rapid speed, and in many 

 other cases that would take too much space to describe here. 



Again, a tangen'ial force which may be rendered considerable 

 is an immediate consequence of my theory, but has no place as 

 a consequence of Prof. Reynolds's. Now its presence has been 

 verified by Mr. Moss and myself, and by Mr, Crookes in an 

 exquisitely beautiful apparatus suggested for this purpose by 

 Prof, Stokes, as well as, in a less degree, in all Mr. Crookes's 

 apparatus with curved or crumpled discs. 



Hence Prof, Osborne Reynolds's hypothesis is not the ex- 

 planation of Crookes's stress. It alleges a cause which is in 

 certain cases a vera causa, but not the cause of what is to be 

 explained. So far as I can form a judgment, its merit was col- 

 lateral, and not intrinsic. It was the first attempt at a reduction 

 of the observed phenomena to known physical laws. Though 

 not accounting for them, it was sufficiently plausible to attract 

 the attention of Prof, Reynolds and other physicists. It thereby 

 had the important effect of suggesting Dr, Schuster's most valu- 

 able experiment, which was the first that established the cardinal 

 fact that the forces within a radiometer case are balanced. 



The conclusion to which we are thus led by a purely experi- 

 mental inquiry is supported by an examination of the chief 

 theoretie assertions of Prof. Osborne Reynolds's letter, viz., 

 I. That an essential part of my explanation "is contrary to the 

 law of the diffusion of heat in gases ; " and 2, " That the force 

 arising from the communication of heat from a surface to adjacent 

 gas of any particular kind depends only on one thing, ^q rate at 

 which heat is communicated, and lo this it is propo:tional." 



Both of these statements have been set down by Pro^ Osborne 

 Reynolds in error ; the first from not observing that the ordinary 

 laws for the propagation of heat through a gas do not apply to 

 compressed Crookes's layers; and the second from a misap- 

 prehension of the actual agency at work in radiometers and 

 other similar apparatus. I will proceed to establish these two 

 positions. 



I. So long as a gas is in its ordinary state the distribution of 

 the velocities of the molecules is the same in all directions, and 

 when heat is imparted to the gas it does not disturb this uni- 

 formity of structure. The heat simply increases ilie mem 

 velocity, and the actual velocities continue lo be distributed about 



