78 



SCIENCE. 



Vol. XXII. No. H9 



each other over the whole surface of the entire field. It 

 was a glory not to be forgotten. This year not a plant of 

 the species is visible riding past. Scattered daisies, 

 o-olden rod (not S. nemoralis), a few OS. biennis, and an 

 occasional lespedeza (L. capitata) are all that show. The 

 ground is very sparsely covered, whereas last year it was 

 completely occupied, as indeed also by the daisies, the 

 ceuothera, and the golden rod in their respective years. 



I am satisfied the same thing takes place on other un- 

 occupied sandy fields about here, but I have not watched 

 them as closely nor as regularly as this one. M. Vf. V. 



Fort Edwiird, N. Y., July 29. 



Worms on the Brain of a Bird. 



To judge from Professor French's communication under 

 this title in the current volume of Science, p. 20, he is un- 

 acquainted with the description and figures of the thread- 

 worm of the snake bird given by Prof. Jeffries Wymau, in 

 1868, in the Proceedings of the Boston Society of Natural 

 History, Vol. 12, p. 100. Samuel H. Scuddek. 



A Space-relation of Numbers. 



The recent notes and discussions as to certain curious 

 relations observed by some persons between sensations of 

 color and of sound,— relations hardly conceivable by 

 others who, like myself, have never experienced them, — 

 have led me to reflect upon a peculiar conception of my 

 own, which may be called a space-relation of numbers. I 

 have never heard it alluded to by any one; but it has been 

 constant with me since childhood, and seems so jjeouliar 

 and inexplicable that it may be worthy of mention and 

 inquiry. It is presented, therefore, in the hojje that the 

 exj)erience of others may throw some light upon it as a 

 mental phenomenon, and help to show whether it be a 

 mere idiosj-ncrasy or an experience at all known, and, if 

 the latter, how far familiar, and with what, if any, modifi- 

 cations. 



My first distinct recollection of this idea goes back to 

 the age of nine or ten years, in connection with learning 

 the multiplication table. This I was taught, not at 

 school, but by home instruction, and without any use of 

 cards, tables, slates, abaci, or any visible signs or aids 

 whatever. It was purely abstract and memoriter. Some- 

 how, then, and ever since, the numbers from 1 to 100 

 have been conceived of by me as holding, relatively, defi- 

 nite 230sitions in space, from which they never vary, — the 

 mention or use of the number being at once associated 

 Avith its position relative to other numbers, in the same 

 way that the mention of a well-known coxmtry or river 

 brings up a mental picture of its geographical location. 



This numerical position has no relation with that of any 

 other object or thing, nor with the j)osition of the body 

 or the points of the comjoass. In describing it, however, 

 I must employ the latter, but simply as aids, in place of a 

 diagram. The niimbers, which are conceived of merely 

 as j)oints or stations in sjsace, appear to be arranged in a 

 peculiar line or lines in a horizontal plane. Beginning 

 with unity, the series runs in a straight line to 20, where 

 it turns ninety degrees to the right, and so goes to 30. 

 Using the points of the comj^ass merely for the present 

 description, as above stated, and not from any connection 

 with the number-scheme itself, — if the series 1-20 runs 

 (say) northward, 20-30 runs always east, 20 being the 

 apex of the right angle. From 30 to 40 the course is 

 reversed and runs back westward ; at 40 it again turns at a 

 right angle and proceeds south, without interruption, to 

 90, where the line again turns east from 90 to 100. Above 

 this point, the numbers have the same jDOsitions again, and 

 so in each succeeding hundred; so that the same descrij)- 

 tion appHes to all. 



It will be seen by any one who attempts to put this 

 scheme on jsaper, that, according , to the arrangement, 

 the niimbers 30 to 40 would coincide, in reverse order, 

 with 20-30, 40 falling upon the same spot as 20; while 

 40-60 would coincide with 1-20, in reverse order. But in 

 the mental conception this is not the case. The line 

 30-40 seems jjarallel to 20-30, but at some little distance; 

 and a vague sense of space, gradually increasing until no 

 distinct relation is consciously noted, pirevents any ap- 

 proach or interference between the numbers above 40 and 

 those below 20. This fact confirms the impression that 

 the idea is not due to any artificial aid in the way of dia- 

 gram, table, or the like, in childhood. 



The only suggestion that occurs is found in the fact 

 that about that period the family had lived for some time 

 in a large hotel (the Delavan, at Albany), whose corri- 

 dors and numbered rooms may have impressed themselves 

 on the child-mind in some such Avay. But I distinctly re- 

 call that certain of those rooms, occuijied at different 

 times by the family, did not at all have the positions that 

 their numbers hold in this mental scheme. 



Be this as it may, however, the clearness and the per- 

 sistence of this association are remarkable, and I should 

 be greatly interested to know if others can report any 

 similar experience. If certain chords in music can sug- 

 gest the sensation of j)urple, or the sound of a word a 

 corresponding imjjression of blue, etc., as ajjparently is 

 the case with some persons, why may not certain abstract 

 numbers have similar associations of space-position ? 



D. S. Maktin. 



New York, Aug. ^. 



Preliminary Note on the Cottony Scale of the Osage Orange. 



In June I found a Cottony Scale {Fulvinaria) in some 

 abundance on an osage-orange tree {macliira) in Las 

 Cruces, N. Mex. The young were hatching on and about 

 June 14th. This scale would be referred by modern ento- 

 mologists to Fulvinaria innumerabilis (Eathvon) Putnam, 

 but finding that it did not agree very well with ^SLiblished 

 accounts of that species, I sent to Professor Bruner for 

 specimens of the true insect, which abounds at Lincoln, 

 Neb. Professor Brimer very kindly forwarded without 

 delay a number of examples from box-elder, which were 

 evidently not quite the same as my osage-orange scale. 



The box-elder scale, however, agrees with innumerabilis, 

 while the maclura scale is what was formerly named 

 maclurcB, and afterwards sunk as a synonym of innumera- 

 bilis. 



The most consfiicLious and constant difference is in the 

 size. In order to show this, I boiled the adult females 

 (which had formed ovisacs) in caustic soda, and spread 

 their skins flat on a glass slide. Thus treated, the meas- 

 lu'ements were as follows: 



P. maclurae (Las Cruces) . . length 10, breadth 10 mm. 



P. innumerabilis (lAjxcohi) . . " 7^, " 5 " 



It is thus seen that maclurae is both larger and broader 

 in proportion; and no intermediate specimens were found. 

 Another diiierence is in the length of the fourth joint of 

 the antenna: in the Las Cruces marfwrae it is about as long 

 as the third joint, whereas in the Lincoln innumerabilis it 

 is decidedly shorter than the third. I have not yet ex- 

 amined enough specimens to make sure if this character 

 is invariable. I do not wish to assert j'ositively that L. 

 maclurae is a valid sjiecies, but its characters are such as 

 have been held to distinguish species of Pulvinaria in 

 Europe. I hope to set the matter at rest hereafter by 

 the examination of more extensive material, but it must 

 be admitted at least that it is a very distinct race or vari- 

 ety'. In this we revert to the original opinion of Fitch, 

 Walsh and Eiley (1855, 1860, 1868), which ha.?_ been set 

 aside for so many years. 



