io8 



SCIENCE. 



[Vol. XXII. No. 551 



now record the discovery of three species of the 

 larva of the fresh-water chironomus new to science, 

 and drawings of which accompany these notes, to- 

 gether with that of another new form found only 

 last week by my friend Mr. A. K. Hammond, F. L. S., 

 on the leaves of potamogeton, forming small tunnels 

 therein I have made a few mounts of all these species, 

 which will very likely prove to be larvae of well-known 

 species of flies described by Walker and hsted by 

 Verrall there being over 250 different species of chirono- 

 midre in Britain, while the larvte of only some dozen are 

 known Up to the present time the best work on these 

 and similar "eucaphalous" larvfe is that of Prof. F. Mem- 

 ert published by the Eoyal Society of Copenhagen m 

 1886 full of splendid plates of the larvse only of fresh- 

 water species, but it is in Danish, and I do not know that 

 it has been translated. None of these new specimens are 

 included therein, and Mi-. Hammond, who is well up m 

 the bibliography (he is now bringing out a paper m the 

 transactions in the Linnean Society and shortly to be pub- 

 lished on the structure and life history of Chironomus 

 dorsalif., in collaboration with Professor Miall), informs me 

 that he has not met with any drawings or description of 

 these larva? of mine. I may add that Dr. Johnston's 

 di-awing of campontia does not show the two pairs of long 

 respiratory tubules which the larva can protrude from 

 the eleventh segment and retract again. These are, how- 

 ever, shown very clearly in the micro-photographs of my 

 mounts of campontia and Chironomus dorsalis. Mr. Slater 

 describes these as being also seen in C. phimosis (Ent. 

 Xn., p. 87). They are clearly shown in Meinert's di-aw- 

 ings'as possessed by C. phimosis and also by C. venustus, 

 but this latter is believed to be the same species as C. 

 dorsalis. 



In conclusion, I must not omit to make a note of what 

 I feel sure is an instance of the very interesting develop- 

 ment known as iMrthenogenesis in connection with C. dor- 

 salis. One of the larvEe, fully grown, was put in a bottle 

 late in October, 1891. It sickened and died, but before 

 its death there came forth from the body a large number 

 of young C. dorsaUs, which ultimately became fully devel- 

 oped, though not so large as the other imagenes. The bottle 

 containing them was in a cold room, and they all appeared 

 in the winter before the end of February, and so could 

 not possibly be hatched from eggs laid prior to October. 

 I watched these most sedulously through the pupa state, 

 for they spun their pupa cells on the under side of leaves, 

 and not in the mud at the bottom of the glass, like the 

 ordinary Chironomus dorsalis, waving theii- heads about 

 in the curious way described by Meinert. They did not 

 assume the strong,, deep, blood-red color either, being 

 nearer the surface of the water. There is no question 

 about the flies being C. dmsalis, as I have now one or two 

 in spirits of wine. Finding that Mr. Oscar von Grimm had 

 recorded the fact that the pupa of chironomus laid eggs 

 prepared in the body of the larva, these ova being depos- 

 ited in rows of long threads, just as the female C. dorsalis 

 does, only that they are protruded through two small 

 holes above the anus of the pupa. I therefore watched 

 the older uon-parthenogenetic blood worms most care- 

 fully, when they emerged from the larval into the pupal 

 state, and I must say, that never did the proceeding take 

 place, as far as I could see, and during the following- 

 month there were no young larva of Chironomus dorsalis 

 produced. It is quite evident that further investigation 

 and the closer watching of the life history of these midges 

 will fully repay entomologists, for it is hardly possible to 

 think, after Mr. Grimm's careful and detailed investiga- 

 tions, that his young larvse were parthenogenetically pro- 

 duced. 



LETTERS TO THE EDITOR 



^^Correspondents are requested to be as "brief as possible. The 

 writer's name is in all cases required as a proof of good faith. 



On request in advance, one hundred copies of the number con- 

 taining his communication will be furnished free to any corres- 

 pondent. 



The editor will be glad to publish any queries consonant with 

 the character of the journal. 



A Space-relation of Numbers. 



Me. D. S. Martin's article under this head, in Science for 

 August 11, is of peculiar interest to me in touching upon 

 a mind exj)erience which I had supposed an idiosyncrasy 

 of my own, since I have been unable to find another per- 

 son who had any similar experience, except my own 

 mother. I am glad to find another person of a like mind, 

 since it is an indication that it may not be an exceedingly 

 rare exfierience. 



I date the origin of my idea at the time when I began 

 to learn to count, which was at home, by the "purely ab- 

 stract and memoriter" system. Not only are the numbers 

 from 1 to 100, but from 1 to infinity, and all the fractions 

 in a less degree, conceived of by me "as holding, relatively, 

 definite jDositions in space, from which they never vary." 

 It is simply impossible for me to think of a number except 

 in its relation to the other numbers and in its position in 

 the scheme. 



In my mind the numerical position bears no relation to 

 that of any other object or thing, nor to the position of 

 my body; but it does bear a definite relation to the points 

 of the compass. Beginning at my feet the numbers 1 to 

 10 run due west in a slightly ascending line, 10 being a 

 little beyond and above 9, with 5 above and beyond 

 4 so that it is given greater prominence. 10, 11 and 12 

 are arranged in an ascending spiral. 12 is above the 

 j)lane of 1 say six inches. 12 to 15 are in a horizontal 

 plane in a straight line running W. N. W. 15 to 19 

 changes to W. by S., slightly ascending, with 20 directly 

 above 19, and about 8 inches above 1. 20 to 30 runs due 

 S. 30 to 60 is a zizzag, 30 to 40 running due E., 40 to 50 

 S. B., 50 to 60 E. by S. The whole line ascends so that 

 60 is eighteen inches above 1; but from 20 to 55 the in- 

 cline is uniform, while from 55 to 60 it is enough more 

 abrupt so that the perpendicular distance from 20 to 55 is 

 just equal to that from 55 to 60, 60 being dii-ectly above 

 59. 60 to 70 runs due S., 70 to 100 S. S. E. 100 is twenty 

 inches above 1. In the whole scheme from 20 onward 

 the multiples of ten are elevated a little above the numbers 

 immediately following and preceding, so that they are 

 more jjrominent. From 1 to 100 the numbers get more 

 and more distant and indistinct, and consequently appear 

 smaller as they increase in value; but the twenties and 

 fifties seem plainer, but not larger, than the others, as 

 though they were in the direct sunlight, and the others 

 partly shaded. From 100 I drop back to 1 and repeat the 

 course for every succeeding hundred. 



The hundreds from 100 to 900 (but not with their units 

 and tens) are arranged in a straight line tending W. by S., 

 scarcely if at all ascending. 1,000 is directly above 999. 

 1,000 to 1,000,000 is an indistinct line curving upwards 

 towards S. E. by E. From 1,000,000 onward the tendency 

 is upward and in a S. W. direction; but here a haze 

 envelops the numbers so that they are ill defined and hard 

 to follow. 



I conceive of the numbers as being of the same size, but 

 appearing to vary in size as their value in reverse order on 

 account of their distance from the starting point. There- 

 fore in giving iJerpendicular distances I have given them 

 as they would appear on a chart and not as actual dis- 

 tances. The sense of the true perspective is perfect. 



In the application of this schemf* t? every day use it is 



