January 30, 1908 J 



NA TURE 



295 



century, say from fifty to seventy-five generations — pre- 

 sumably a quite inadequate period for the evolution and 

 fixing of tfie form by the selection of small chance varia- 

 tions. Certainly, if the analogy of language in the human 

 race is permissible, the number of generations is far short 

 of what would be required to impress any character on 

 the heredity of a species by the inheritance of acquired 

 characters, even if we could find any reasonable connec- 

 tion between soot-stained bark and darkened wings for 

 the purposes of the theory. 



But gradual adaptation during the present epoch does 

 not fit the facts for another reason. The darkening, if 

 gradual, would have been noticed by entomologists, as is 

 the case with Aplecta nebulosa in Delamere Forest and 

 Hybernia leucophaearia in Epping Forest. The species 

 would be a beautiful example of a mutation if it were not 

 for the fact that intermediates, though rare, have a 

 puzzling habit of turning up ; and, what is more serious, 

 a careful examination of the melanic forms reveals the 

 fact that on the upper margin of the hind wings, where 

 they are covered by the fore wings when the moth assumes 

 its normal resting position, there is an area of the original 

 pale coloration. As in the reverse case of the exposed tip 

 of the underside of the fore wings of many butterflies being 

 coloured quite differently from the rest of the wing area, in 

 order that it may match the cryptic pattern on the under- 

 side of the hind wings, the retention of the pale area in 

 var. Doubledayaria can only be accounted for by the sup- 

 position that the variability is the work of natural 

 selection. 



If the above reasoning be correct, the black variety 

 must either be regarded as the recurrence of a pattern 

 slowly evolved in some previous epoch, or we must consider 

 it as an example of the working of Weismann's germinal 

 selection. The needs of cryptic adjustment to environ- 

 ment having put a premium upon darker, but not neces- 

 sarily black forms, the determinants of the darkened 

 characters tend by the operation of selection within the 

 germ to increase progressively to a point where they are 

 cut off by the operation of natural selection upon the 

 individual. As a consequence, a few rare examples will 

 always be thrown having such a progressive character in 

 excess, and should any rare and sudden chance such as is 

 afforded to melanism by our smoky civilisation occur, an 

 enormous premium is placed upon the survival of their 

 offspring. A. Bacot. 



154 Lower Clapton Road, London, N.E. 



Inductance in Parallel Wires. 

 A PROBLEM of some considerable importance to the prac- 

 tical engineer or physicist is that of calculating the effective 

 self-induction of a circuit consisting of two parallel wires, 

 the one being the return of the other. When the wires 

 are not very close together, and their current is either 

 steady or only very slowly alternating, satisfactory results 

 are known to be given by the formula 



/ 



a/, 



where L is the self-induction of a length /, c the distance 

 between the wires, which have radii a, b, and ^l■^, ;u, the 

 permeabilities of their materials. But if the current 

 oscillates rapidly, this formula fails to give even approxi- 

 mately correct results. Now in many practical problems, 

 such, for example, as the measurement of small induct- 

 ances not greater than looo microhenries, it is necessary 

 to employ long leads to keep them at some considerable 

 distance from bridge and other circuits. A knowledge of 

 the self-induction of such leads is very desirable. Some 

 results which I have recently obtained are capable of find- 

 ing this quantity in most useful cases, and it may prove 

 of use to give a short statement of them, pending more 

 detailed publication. 



The self-induction has a simple expression only if the 

 two w-ires be equal in radius. In this case it takes the 

 form 



/ ''"^a A ' {het' x)- + {heV jc]- 



No. 1996, VOL. yyl 



where ber x, bei x are the functions introduced by Lord 

 Kelvin, and subsequently tabulated (vide Presidential 

 Address to the Institution of Electrical Engineers, 1889). 



If — be the frequency of alternation per second, o- the 



specific resistance of a w'ire, fi. its permeability, then 



This formula, passing naturally into the former when 

 the frequency is small, becomes less accurate as c 

 decreases and as the frequency or radius of a wire 

 increases. So far as the first cause is concerned, it is 

 subject to an error of not more than i per cent, when 

 c=ioa, and 4 per cent, if c = ^a. If c = 3a, which is the 

 limiting closeness for most practical purposes, the error 

 is about 10 per cent., which is not usually too great. 

 The other causes of error may be considered together. 



The per cent, error they produce is of order 100. -~^, where 



V = 3'io". Practically, a is never more than about 

 2 millimetres, and thus, with a frequency of a hundred 

 million per second, the error is not more than one-tenth 

 per cent. The range of application of the formula is 

 therefore extremely wide. A formula equally accurate may 

 be given when the wires are unequal, but it is somewhat 

 cumbrous. J. W. Nicholson. 



Trinity College, Cambridge, January 21. 



Stock Frost or Ground Ice. 



During the recent frosty weather the subject of what 

 is locally called " stock frost " has been much to the front 

 in this neighbourhood. This phenomenon is known to the 

 scientific w^orld, I believe, as " ground ice," and the 

 circumstances in which it appears and disappears present 

 to the ordinary observer a very great many puzzling 

 features. 



I should be exceedingly glad if some of your readers 

 would kindly give me, through the columns of Nature, 

 their opinion on several points which puzzle and interest 

 me and others in connection with " stock " or ground ice. 



(i) I wish to know, first of all, what are the essential 

 conditions for the formation of ground ice on the bed of 

 a river? 



(2) Is it essential, or does it favour the formation of 

 " ground " ice, that there should be no surface ice? We 

 notice that when a very cold and very strong north-east 

 wind is blowing, violently agitating the surface water, 

 there is no surface ice, but a formation of ground ice at 

 the bottom of the river. 



(3) What are the circumstances to which is due the 

 presence of ice-cold water at the bottom of a river, cold 

 enough to be precipitated into ice? 



This ice-cold water cannot reach the bottom of the 

 river by gravitation, because its density is inferior to that 

 of water at a higher level. To what, then, is due this cold 

 temperature on the river bed? 



(4) Can the bulk of water in the river bed be a conductor 

 of cold from the surface to the bottom of the river in 

 any other way than that of the mechanical action of 

 running water? I assume that when ground ice appears 

 in a river the whole of the water above it is of an ice- 

 cold temperature, but it has not formed into ice because 

 of the lack of the ice-precipitating conditions which exist 

 on the bed of the river. 



(5) Do the conditions necessary for the formation of 

 ground ice operate more favourably in ice-cold still 

 water or in that which is agitated, say, by passing 

 through a mill? My own observation is that ground ice 

 appears nearer to a' mill on its upper side than on its 

 lower side, and I want to know the reason of this. 



There is quite a long list of questions which might be 

 asked in connection with the formation of ground ice, but 

 I fear that I have already trespassed too much upon your 

 space. John J. Hampson. 



Costessey Vicarage, near Norwich, January 20. 



