February, 1913. 



KNOWLEDGE. 



67 



photographs, it is advisable to draw up a table of the 

 exposures required with plain apertures compared with those 

 of a lens, when used under various conditions ; such as speed 

 of plate, condition of light, time of day, time of year, distance 

 of object, and so on. With regard to the photographs them- 

 selves, they may be said to possess a charm peculiarly their 

 own, while at the same time the method of production is of 

 the most simple and inexpensive kind. 



In making these apertures for use, the writer employs both 

 brass and aluminium foil (preferably the former) as the 

 materia], piercing the holes by means of fine needles, care 

 being taken that any slight burr round the edge is carefully 

 removed by rubbing on an oil-stone, so that there is no appreci- 

 able edge to interfere with the passage of light through them. 

 By examination from time to time under a microscope of 

 moderate power their condition is observed, and when satis- 

 factory the aperture is measured, and the foil containing it 

 mounted up in a frame of blackened card for use. 



ZOOLOGY. 



By Professor J. Arthur Thomson, M.A. 



PROPORTIONS OF SEXES IN EARWIG.— H. H. 



Brindley finds that the proportions of the sexes differ con- 

 siderably in different localities in the same year and sometimes 

 differ considerably in localities quite near each other. The 

 proportions may differ appreciably in the same locality in 

 different years. This may be due to variation in the extent to 

 which the males survive the winter. There is a slight sugges- 

 tion that the percentage of males is higher on small islands. 

 The evidence that the characters of the soil or vegetation or 

 altitude affect the proportions of the sexes is exceedingly 

 slight. The normal length of life of earwigs is unknown. 

 Adult males are found somewhat rarely in the early months of 

 the year. 



COLOUR OF FISHES. — The epidermis of fishes is delicate 

 and transparent. All the colour is in the dermis, and it 

 usually occurs in separate pigment-cells. These usually show 

 numerous radiating processes, and the pigment can be spread 

 out over a large surface or concentrated in the centre. This 



depends on the expansion or contraction of the mobile 

 protoplasm of the pigment-cells. According to the pigment 

 they contain, — black, or yellow, red, and so on — the piginent- 

 cells are called melanophores, zanthophores, erythrophores, 

 and soon. Then there are other cells containing spangles of 

 the waste-product guanin, which are called iridocytes or 

 guanophores. They cause the silvery, metallic, or iridescent 

 appearance familiar on many fishes. But Professor Ballowitz 

 has recently discovered in the weaver and some other bony 

 fish, a new kind of chromatophore, not a single cell, but a 

 group of cells. Each melaniridosome, as he calls them, is a 

 cluster of iridocytes with an encapsuled central melanophore, 

 which sends its ramifying processes through the capsule in 

 complicated courses. 



PARENTAL CARE AMONG ANTARCTIC ECHINO- 

 DERMS. — It is well-known to zoologists that many of the 

 Antarctic sea-urchins, sea-cucumbers, and other Echinoderms 

 show parental care, keeping their young ones sheltered about 

 their bodies and that in a striking variety of different ways. 

 Professor Ludwig has recorded ten cases of parental care in 

 Echinoderms from warm waters, and twenty-nine from the 

 Antarctic. Out of twenty-four different species of coastal 

 sea-urchins from the Antarctic, Mortensen reports that no 

 fewer than fourteen show parental care, and eleven of these 

 are littoral. The puzzle is why this habit, which is rare among 

 Echinoderms as a class, should be so common in the Antarctic. 

 An answer has been suggested by Hjalmar Ostergren (Zeit- 

 schrift wiss. Zool. C. 1912). He points out, first of all, that 

 the numerous sea-cucumbers which exhibit parental care in 

 the Antarctic, belong to families which are known elsewhere 

 to exhibit the same peculiarity. He points out, in the second 

 place, that the distribution of land and water in the south is 

 quite different from that in the north, and that for coastal 

 Echinoderms everything is against the success of free- 

 swimming larvae. The low temperature of the water and its 

 low salinity tend to bring about a shortening of the life-history 

 or at least a suppression of free-swimming larval stages. In 

 point of fact, only three or four cases of free-swimming 

 Echinoderm larvae are known from Antarctic seas. 



CORRESPONDENCE. 



SQUARING THE CIRCLE. 



To the Editors of " Knowledge." 



Sirs, — In a letter in the November issue of "Know- 

 ledge," " Geoma " gives a method of " squaring the circle," 

 stating that the perimeter of a circle of unit diameter is equal 

 to that of a certain triangle. This amounts to no more than 

 the statement that t = \/5 + 1 approximately. This is not in 

 itself a good approximation to the value of w and it would be 

 quite easy to draw a triangle whose perimeter gave a much 

 closer approximation. But, however close the approximation, 

 we should be no nearer " squaring the circle " by geometrical 

 methods. 



3, St. John's Road, R. J. POCOCK. 



Oxford. 



THE FOURTH DIMENSION. 



To the Editors of " Knowledge." 



Sirs, — Referring to recent letters on this subject which have 

 appeared in " Knowledge," I have been rather struck by 

 the fact that few of your correspondents seem to have clearly 

 distinguished between what is possible, what is imaginable, 

 and what has a real physical analogy and bearing. The 

 argument that the existence of one or two dimensions implies 

 a third, and the third implies a fourth, and so on ad infinitum, 

 seems to me utterly without value from the following very 



simple consideration. Objects and space of one and two 

 dimensions only are purely mental abstractions. All bodies 

 to be seen at all or even clearly apprehended, in my mind, must 

 have three dimensions, neither more nor less. The geometrical 

 point must have some bigness, some (however small) depth ; 

 the line must have at least a slight breadth and thickness 

 (i.e., three dimensions, though one greatly predominates, and 

 the others may be disregarded except the fact of their 

 existence). It is a result of experience that three numbers 

 are, in general, necessary to define the position of any point 

 with regard to any other ; in algebraical language, the x, y, 

 and z coordinates. If one of these coordinates, say the z, be, 

 or is assumed to be, the same for all points, we have the x 

 and y coordinates only, the coordinates of plane geometry, 

 and lastly, for a common y we have all the ideal points lying 

 on a straight line (the axis of x or any straight line parallel to 

 it in the plane xy, z — OorC). This, in common sense language, 

 is all that the whole thing means, as we have pointed out 

 elsewhere (Quest, English Mechanic, and so on). 



By the algebraical methods of coordinate geometry a vast 

 body of geometrical theorems has been shown to have 

 algebraical parallels, and conversely, theorems applying to 

 curves and surfaces in general have been discovered by the 

 application of analysis to the coordinates x, y, and z. It is 

 possible (and has actually been done) to introduce a fourth 

 coordinate, w, or, indeed, any number of fresh coordinates, 

 and by algebraical methods to deduce theorems of great beauty 

 and interest, but the results will have no geometrical 



