June 3, 1892.] 



SCIENCE. 



319 



"Silver Top" in grass is caused by the working of leaf- 

 hoppers, and that the Jassidce furnish many of the insects 

 as well as those in the families named in this paper. In our 

 Park meadows, some of which are left to develop hay, 

 "silver top" is very common, especially on the earlier 

 grasses, and throughout the season a weakening and deform- 

 ing of grass stalks are everywhere noticeable, which in most 

 cases, no doubt, is due to the extraction of the juices by these 

 insects. The node of the grass, especially on the upper side 

 and for an inch or more, is very tender and succulent; but 

 as we traverse the internode, we find it becomes more Arm 

 and woody, as it were. Every boy knows where to find the 

 succulent portion of a grass-stem, and proceeds to pull it out, 

 when it breaks just above the node at the tenderest place. 

 This succulent feeding ground is soon discovered by the 

 "hoppers" in their tours of prospecting up and down the 

 stem; veritable " sappers, if not miners," they are often seen 

 in numbers in such situations, and the punctures can also be 

 noticed. The exhausted stems of the dead part of the grass 

 culm show every sign of having been pumped dry by these 

 creatures, as at that point nothing seems to be left but a 

 bundle of woody fibres, and the internode for some distance 

 diminishing in size from the loss of sap, and that loss occur- 

 riog befoi'e the cells had been sufficiently developed to stand 

 without collapsing. My success in finding Thrips, or Mero- 

 niyza, in the stems or under the leaf-sheaths has been no 

 better than Professor Osborn's. 



As I am working on a list with food-plants and habits of 

 Hemiptera for New York State, I should be glad to receive 

 from collectors information in regard to those found here 

 and their distribution elsewhere, so that the list can be made 

 a? complete as possible; for all "local lists" are of the great- 

 est value, not only to local students but to students of North 

 American entomology also. Edmund B. Southwick. 



LETTERS TO THE EDITOR. 



,** Correspondents are requested to he as brief as possible. Tlie writer's name 

 is in all cases required as proof of good faith. 



On request in advance, one hundred copies of the number containing his 

 communicatio^i tvill be furnished free to any correspondent. 



TJie editor will be glad to publish any queries consonant with the character 

 of the journal. 



Four-Fold Space and Two-Fold Time. 



Any attempt at expounding popularly the recent developments 

 of the old idea of space should be prefaced by the explanation 

 that their tremendous value to mathematics is utterly indepen- 

 dent both of their external reality and of the possibility of their 

 realization. For example, had either M'Clelland or Preston ever 

 glanced through Bolyai's " Science Absolute of Space," we 

 would not to-day read in their excellent " Treatise on Spherical 

 Trigonometry," p. 10, '• The student must be careful, however, 

 not to regard a solid angle as an area, but as a mere number, like 

 the circular measure of a plane angle. . . . and the solid angle 



subtended at O bv the — part of the surface of the sphere is 

 , which is thus a mere number." A solid angle is a magni- 



tude as different from a mere number as is the current of elec- 

 tricity which kills a man. Though its scientific unit, the 

 steradian, is American, yet they could have found it in the 

 " Encyclopaedia Britannica, in William Thomson's article " Men- 

 suration." 



Because these magnitudes, solid angles, have a natural unit, 

 the steregon, and a scientific subsidiary unit, the steradian, 

 therefore mathematicians, unused to the idea of a natural 

 unit, blunder about them. To Bolyai belongs the honor of show- 

 ing that each geometric magnitude has its natural unit, which 

 never could have been discovered in Euclidean space, since 



homaloidal, parabolic space appears as a limit in which the na- 

 tural unit for length becomes indefinitely great, so calling, in 

 practice, for an artificial unit for length, a finite sect, as the 

 centimeter. The fundamental importance of the pseudospheric 

 hyperbolic space of Bolyai and Lobatschewsky in no wise 

 depends on whether C. S. Peirce is right in maintaining that 

 such is the real space in which we live. It has already enriched 

 us eternally by the gift of the Science of Comparative Geometry, 

 and so of pure spherics. 



Now, in his beautiful paper in Crelle, on " Single Elliptic 

 Geometry," Professor Newcomb has used, unnecessarily we think, 

 space of four dimensions. Elliptic space, though finite, is un- 

 bounded. But there is a sense in which hyperbolic space, though 

 infinite, is bounded, and so its realization is naturally connected 

 with that of four-fold space. For this the most fruitful idea has 

 ever been Professor Sylvester's, of working up from two-dimen- 

 sional beings. And here let me say that thinkers must not confine 

 themselves as in the past to "an imaginary plane being," but 

 must likewise draw from two dimensional spherics and pseudo- 

 spherics. Not only must we think of a flexible closed shell 

 turned inside out, as we turn a glove; we must try if we can 

 realize that as the flexibility of the "thin hoop" mentioned by 

 Dr. Hall is only needed because the hoop has as many dimensions 

 as the space in which we wish to turn it, therefore can we not 

 turn an inflexible closed shell, an unbroken eggshell, inside out, 

 without flexure "i 



The corresponding generalizations for time are harder, because 

 in time's domain we are one-dimensional beings; therefore our 

 best space-method fails us. Cannot genius give us a next-best 

 almost as good ? Geokge Beuce Halsted. 



Univeralty of Texas, Austin, Tex., May 22. 



Family Traits. 



In your issue of May 20, " Veritas" again combats the proposi- 

 tion that family traits are a reality. The statement was made in 

 my original communication that questions of descent were ques- 

 tions of heredity and environment, and that heredity, consisting 

 as it does of questions relating to the reproduction of the race as 

 an animal, must be referred to biology. The results of all de- 

 partments of research for the last fifty years refer man to his 

 place in nature as an animal, and as an animal a fit subject for 

 biological investigation. 



Will Veritas please explain how, if it be admitted that a man 

 may resemble his father and grandfather, that with the great- 

 grandfather the resemblance must cease? Is not every man the 

 son of his father, and is his father not also the son of his grand- 

 father, an J so on from generation to generation back in an infinite 

 series ? If a man may or does resemble his father, that is the 

 Umit of the question, and further argument is unnecessary. 



I freely admit that the Does of the present know, of their own 

 knowledge, nothing of 100 per cent of the traits of John Doe the 

 first. I was not referring to any positive knowledge held in this 

 generation of the ninth generation from the present. Neverthe- 

 less John Doe of the seventeenth century had personal traits, and 

 if the oldest Doe now living has seen and known 100 Does in per- 

 haps five generations, and afiirms that, out of the almost infinite 

 diversity of traits that constitute human character, a few have 

 been observed in all these generations common to a large majority 

 of the 100 Does, I assert that there are " Doe " traits or " family 

 traits," and in my former article I gave a scientific explanation of 

 the occurrence of such traits, with a number of illustrations that 

 were neither a figment of the imagination nor a delusion. If 

 these are not facts, what are facts ? 



Moreover, in your issue of April 15, Ed. H. Williams Jr. gave a 

 number of other reasons why family traits should descend on the 

 male side strongest, that are either "facts" or delusions. Facts 

 are estabhshed by observation of the repeated recurrence of 

 identical phenomena under like conditions. 



What fact is developed by speculation concerning a man's 

 ancestor of the seventeenth century relative to the occurrence of 

 traits common to forty people now living, who all bear his sur- 

 name, and who are likewise his descendants? Suppose these 



