August i, 1895] 



NA rURE 



117 



ihree conditions reducing the five coefficients to two independent 

 ■ >nes. It will be found that mii^ = m'li'^, as in the ordinary' 

 theorj'. 



I doubt not that Boltzmann's minimum theorem can with 

 some modification be applied to this system, at all events if he 

 will take up the theory of dense gases himself. 



S. H. BuRRURY. 



On Skew Probability Curves. 



In a memoir, entitled "Contributions to the Mathematical 

 Theory of Evoluti(jn. II. Skew \'ariation in Homogeneous 

 Material " (Phil. Trans. iS6, A, pp. 343-414), and noticed in 

 your columns by Mr. Francis Galton (Januar)- 31, 1S95), I ''^^'^ 

 dealt with four types of skew frequency curves. 



Last Tuesday, I'rof. Edgworth drew my attention to the fact 

 that a portion of my results has been anticipated by Mr. E. L. 

 De Forest in vols. vi. , ix. , and x. of The .-Inalyst, an excellent 

 American mathematical journal, the acquaintance of which, I 

 am sshamed to say, I have only to-day made for the first time. 



So far as Mr. De Forest's priority is concerned, it covers the 

 special class of curve I have in my memoir termed Type III. He 

 has fully worked out the geometry of this type, and I consider his 

 deduction of it, if somewhat more lengthy than mine, to have 

 the advantage of greater generality. .So far as my own memoir 

 is concerned, a knowledge of Mr. De Forest's memoir -vould not 

 have led me to rewrite pp. 373-6 of mine, which deal with this 

 type, because my discussion there is only a branch of my general 

 treatment of a series of skew frequency curves. I should, how- 

 ever, have referred to Mr. De Forest's priority and the excellency 

 of his work. In particular I should have cited the whole of his 

 numerical table iii. x. p. 69, w hich gives the values of the fre- 

 quency in excess and defect of the mode, and the probable 

 errors in excess and defect, for a considerable range of values. 

 These results are only given Ijy algebraic or empirical formulje 

 in niy i")aper. The statisticians among your readers, who may 

 be proposing to deal with skew frequency, would find a copy of 

 Mr. De Forest's Table III. of considerable service should they 

 come across a curve of Type III. Karl Pearson. 



University College, London, July 24. 



Evolution, or Epigenesis? 



In the English translation of I'rof. Ilertwig's book "The 

 Cell," it is stated (p. 295), " When the female gamete of the 

 Alga Ectocarptts comes to rest, for a few minutes it becomes 

 receptive. If the egg is not fertilised at this time . . . parthe- 

 nogenetic germination begins to make its appearance ... It 

 may be accepted as a law of nature (italics mine) for mammals, 

 and for the majority of other organisms, that their male and 

 female sexual cells are absolutely incapable of development by 

 themselves." Thus, what occurs in the lower organisms is no 

 criterion of what occurs in the higher, and vice versA. Then 

 why does I lertwig remark (ji. 348), " It is quite sufficient for our 

 purpose to acknowledge, that in the plants and lower animals, 

 all the cells which are derived from the ovum contain equal 

 i/uaiilities 0/ the hereditary ma-is. . . . All idioblasts must divide 

 and must l)e transmitted to the daughter-cells, in ei/iial propor- 

 tions hoth as regards equality and <juantity^^ (italics mine). 

 According to the above, it is "quite sufficient" for Hertwig's 

 purpose of discrediting Weismann's contention for differentiated 

 distribution of hereditary elements among somatic cells, to show 

 that there is imdifferentiated distribution in the case of plants 

 and lower animals. Hut, reverting to the earlier quotation, if it is 

 not sufficient to prove sexual reproduction in the case of the 

 higher organisms, in order to disprove parthenogenesis in the 

 case of the lower organisms, why should it be "quite sufficient," 

 in order to disprove distribution through germ-cells, in the case 

 of the higher organisms, to show that, in plants and the lower 

 animals one cell contains the same hereditary constituents as 

 another? It is permissible to infer that differentiation in regard 

 to germ-cells, in the higher animals, is no more disproved by the 

 assumed demonstration that, in plants and the lower animals, 

 there is no such differentiation, than that a.sexuality in lower is 

 disproved by sexuality in higher organisms. Weismann, in my 

 opinion, has proved to rational satisfaction that difTcrenliation 

 of germ from other cells must occur in the higher org.anisms, and 

 he has offere<l a rational explanation, confi)rmable with the theory 

 of germ-plasm, of the apparently summational distribution of 

 hereditary elements through somatic cells. Until Weismann's 



NO. 1344, VOL. 52] 



position is seriously undermined, which, so far, is not even a 

 likely contingency, we must decline to accept Hertwig's assunie<l 

 dentonstrations in regard to plants and lower animals as invalidat - 

 ing the theory of germ-jjlasm. Similarly, that environment ma)' 

 affect the hereditar)- character of a primitive organism is no more 

 evidence that it may so aft'ect a mammal, than sexuality in 

 the latter is evidence against parthenogenesis in the former. 

 On page 348 we are told : "Johannes Miiller has raised the 

 question, ' How does it happen that certain of the cells of the 

 organised body, although they resemble both other cells and 

 the original germ-cell, can produce nothing but their like, i.e. cells 

 which are (in- ?) capable of developing intothecompleteorganism? 

 Thus epidermal cells can only, by absorbing material, develop 

 new epidermal cells, and cartilage cells only other cartilage cells, 

 but never embryos or buds. ' To which he has made answer : 

 ' This may be due to the fact that these cells, even if they possess 

 the power of forming the whole, have, by means of a particular 

 metamorphosis of their substance, become so specialised, that 

 they have entirely lost their germinal properties, as regards the 

 whole organism, and when they become sejiarated from the 

 whole, are unable to lead an independent existence."' The above 

 is simply a restatement of Weismann's doctrine regarding the 

 origin of germ-cells. All cells which have not, as Miiller states, 

 " lost their germinal properties, as regards the whole organism," 

 are W^eismann's germ-cells. 



So far as regards the essential question of heredity, Hertwig 

 agrees with W'eismann. Special units (idioblasts) are the 

 bearers of hereditary qualities. This is "evolution," and no 

 superstructural epigenetic thesis attributing modifying effects by 

 environment, as the cause of a somatic cellular development, can 

 aftect the point that differentiation, through hereditary units, is 

 the fundamental condition of morphological development. To 

 accept "hereditary units," in my opinion, excludes "hereditary 

 effect through environment,"' never mind to what matter-system 

 the latter assumption be applied, whether the systems be, for 

 instance, unicellular organisms or somatic cells. On the other 

 hand, if we accept " hereditary extraneous influence," we need 

 not trouble ourselves with " hereditary units." If " extraneous 

 influences " have hereditary effect, " hereditary units " have no 

 logical existence. All we then need for a theory of heredity are 

 primordial homogeneous matter and environment. Mr. Herbert 

 Spencer's earlier hypothesis, in which he attributed all variation 

 to extraneous influence, would have been logical had he ex- 

 cluded " physiological units.'' With these, it became illogical. 

 For this reason : if all organic variability depended on the effect 

 of extraneous influences, why should such influences not have 

 produced the diflerentiations called physiological units ? W'hy 

 should the only logical ' ' unit '' not be homogeneous priniordium .' 

 That the conception "hereditary unit" shall be logical, involves 

 that the " unit'' shall be as unchangeable as an "atom.'' If, on 

 the contrary, we have a variable "unit," it is not a genuine 

 " hereditary unit,'' but merely the equivalent of any later variable 

 " unit." Hertwig's " hereditary units,'' or " idioblasts" (p. 340), 

 "are the smallest particles of material into which the hereditary 

 mass or idioplasm can be divided, and of which great numbers 

 and various kinds are present in this idioplasm. They are, 

 according to their diflerent composition, the bearers of different 

 properties." They are not indivisible, like atoms, but assimilate 

 food, grow and divide, as do Weismann's " bio])hors," from 

 which they appear to differ only to the extent that they are com- 

 plex organisms. The hereditary factor in Weismann's theory 

 which corresponds with these " idioblasts" of Hertwig appears 

 to be the "determinant." All the functions of the latter seem 

 to be performed by the former. These "idioblasts" (p. 343) 

 " must evolve in regular sequence during the process of develop- 

 ment." As sentences are formed from words, so are organisms 

 formed from these " idioblasts.'' We can attain a clear conception 

 of the formation of sentences from words, but Hertwig does not 

 enable us to apjjrehend how organisms can arise from " idio- 

 blasts." As he very truly observes (p. 344), " this portion of the 

 theory is the most difficult to understand." 



Hertwig, like Spencer, takes his stand on cpigene.sis. It iiiay 

 be asked, wherein is the epigenetic character of his (Hertwig's) 

 theory? Unlike Sjiencer's "physiological units," Hertwig's 

 "idiobla.sts" are intrinsically differentiated organisms with 

 specific tendencies. Now, for a genuine epigenetic theory, 

 hereditary units must merely compose a plastic mould to take the 

 impress of environment, whereas these " idioblastic " cells arc 

 composed of elements with predetermined peculiarities. Ac- 

 cordingly they must function in a predetermined manner, and 



