392 



SCIENCE. 



[Vol. I., No. 14. 



58 = jp + 47r3, .ip == R - IttS, and 3 ■■ 

 whence 



§ = 4.19 3 -f t3 = 0, 

 and 



SB = 4Tr5 = 47r X 



JL 

 4.19 



3S, 



which is the result reached by Stefan and Thomson. 



A' precisely similar line of reasoning api^lles in 

 case of the disk ; the fact that .'p in both the sphere 

 and the disk_ becomes explaining how it happens 

 that 3 [= K S^\ remains finite, though k is supposed 

 infinite. 



The fact seems to be, that Mr. Bosanquet does not 

 understand the full meaning of Maxwell's §. He 

 apparently supposes that it is the magnetizing force 

 arising from external sources,^ just what has been 

 denoted above by Jv- Having, therefore, found that 

 his own formula, iB = 4 5t3, gives, in the case of 

 the sphere of infinite conductivity, S3 = 3 (V, he 

 naturally concludes that Maxwell would obtain 



The two above-mentioned cases, then, are of inter- 

 est, not as showing the inaccuracy of the ordinary 

 formulas, but as instances in which Mr. Bosanquet's 

 formulas hold good. In any medium possessing finite 

 magnetic conductivity only, i.e., in any known me- 

 dium, Mr. Bosanquet's formulas will evidently lead 

 to results different from those given by Maxwell's; 

 and it remains to be shown, I tliink, that Maxwell is 

 in error. 



Indeed, it is by no means evident that Maxwell's 

 formulas need be essentially changed in order to be 

 in accordance with the requirements of the theory 

 Mr. Bosanquet is advocating; for, though Maxwell 

 preferred to speak of magnetization as an induction 

 phenomenon, he was, of course, perfectly well aware 

 of its analogy to conduction, as might be shown by 

 numerous quotations from his treatise, of which only 

 one need be given. 



"In many parts of physical science, equations of 

 the same form are found applicable to phenomena 

 whicli are certainly of quite different natures, as, for 

 instance, electric induction through dielectrics, con- 

 duction through conductors, and magnetic induction. 

 In all tliese cases the relation between the force and 

 the effect produced is expressed by a set of equations 

 of the same kind, so that when a problem in one of 

 these subjects is solved, the jaroblem and its solution 

 may be translated into the language of the other 

 subjects and the results in tlieir new form will still 

 be true." ^ E. H. Hall. 



Cambridge, Mass., April 19, 1S83. 



THE SMALL PLANETS. 



The following statement of the condition of the 

 prize question of tlie Koyal Danisli society of sciences 

 appears in Copernicvs for March, 1883: — 



The number of small planets between the orbits of 

 Mars and Jupiter has by degrees become so large, 

 that it is not to be expected that it will in futurebe 

 possible to compute, in advance, the motion of every 

 single one. And it will even be less possible to com- 

 pute their influence singly on the motions of the 

 large planets or of comets. Fortunately, however, 

 the masses of the small planets are so trifling that 

 the perturbation caused by any one separately may 

 be left out of consideration ; but it is very doubtful 



1 Maxwell does, in art. 437, use § in this sense; hut he does 

 not use it thus in his formulas. 



2 Art. 62, new edition. 



whether their collective influence might not be traced 

 in the motion of the nearer planets or comets. In 

 order that researches on this point should give a 

 reliable result, it is necessary first to know the form 

 and position of the ring formed by all the small 

 planets, and the distribution of the masses in this 

 ring. 



_ No degree of accuracy can be attempted in the sta- 

 tistical description of the ring; and, witli very few 

 exceptions, the systems of elements already deduced 

 for each planet may be adopted; tlie more so, as it 

 ,will be of no importance whereabouts in its orbit a 

 planet is at any time. As to the single masses, it is, of 

 course, necessary to draw conclusions from tlie appar- 

 ent' brightness; but the number is so considerable 

 that a fairly reliable result may be hoped for. In the 

 statistical researclies hitherto made, the separate ele- 

 ments only have been discussed, apart from their 

 connection witli the other elements; but this cannot 

 be considered satisfactory. Thus the fact that the 

 planets, arranged according to their mean distances, 

 are divided into a number of distinct groups, does 

 not, by any means, prove that tlie ring formed by 

 them around the sun is dissolved into a number of 

 fairly concentric rings. 



The Eoyal Danish society of sciences, therefore, 

 offers its gold medal (value 320 crowns, equal to 

 nearly ninety dollars) for a statistical investigation of 

 the orbits of the small planets considered as parts 

 of a ring around the sun. The form, position, and 

 relative distribution of mass, should, if possible, be 

 stated with at least so much accuracy as is judged 

 necessary for computing its perturbing influence on 

 planets and comets. 



The memoirs sliould be written either in Latin, 

 French, English, German, Swedish, or Danisli, and 

 must be sent before the end of October, 1884, to the 

 secretary of the society, Dr. H. G. Zeuthen, Copen- 

 hagen. Tliey should not bear the author's name, but 

 only a motto, while the name should be enclosed in 

 a sealed envelope. 



RESEARCHES ON THE DICYEMIDAE. 



Dr. C. O. Whitman has published an article i on 

 these puzzling and imperfectly known parasites of 

 the cephalopods. The number of genera is reduced 

 to two, — Dicyema, with eight cells around the ante- 

 rior end of the body; and Dicyemennea, with nine. 

 The number of species is increased to ten, all of 

 wliich are carefully described. Three are new. 



As tliese animals have been taken by Ed. van 

 Beneden as tlie type of a new division of the animal 

 kingdom, and as they liave been the subject of much 

 discussion, we reproduce Wliitman's summary. The 

 dicyemids may be divided, according to the share 

 they take in the work of reproduction, into mono- 

 genic and diphygenic individuals. The first produce 

 only vermiform, the latter, first infusoriforni, and 

 then vermiform embryos. It is doubtful whether the 

 two kinds of individuals are heterogeneous forms; 

 for they are alike in origin, development, and adult 

 form and structure; but their germ-cells, for un- 

 known reasons, pursue different courses of develop- 

 ment. There is a relation, the meaning of which 

 is unknown, between the age of the host and the 

 condition of the parasites; the nematogens predomi- 

 nating in the young, tlie rhombogens in the adult 

 cephalopods. The rhombogens alone have a pluri- 

 nucleate axial cell, which then contains, first, its own 

 large nucleus; second, bodies, probably correspond- 

 1 Mittheil. zool. stat. Neapel, iv. 1. 



