I50 



NATURE 



[October 8, 1914 



In the Mathematical Gazette for July (vi., 12), Prof. 

 Harold Hilton proves that any twisted cubic curve 

 may be displaced so that every point is moving per- 

 pendicular to its tangent, provided that the curve is 

 screwed about a certain fixed axis. 



The resistance of road vehicles to traction is com- 

 monly regarded as the sum of two parts, one due to 

 rolling friction on the ground and the other due to 

 sliding friction at the axle. In a recent note (Venice, 

 Carlo Ferrari, 1914) reprinted from the Atti del R. 

 Istituto veneto, Ixxiii. (2), pp. 931-46, Prof. T. Levi 

 Civita, by considering the conditions of equilibrium, 

 establishes the interdependence of these two resist- 

 ances, and obtains new formulae determining the total 

 resistance. The title of the paper is " Sforze di regime 

 e sforze d'avviamento per veicoli trainati." 



From the Department of Lands and Surveys of 

 Western Australia we have received a copy of its 

 " Geodetic Tables." This publication contains two 

 tables, of which one gives the logarithms of the num- 

 ber of links in 1" of latitude, and of longitude, and 

 the other gives the logarithms of the seconds of the 

 arc-versines of spheroidal arcs of parallels 1" in 

 length. In each case the tables cover the range of 

 50° from the equator southwards. The tables are 

 based on the auxiliary tables of the Survey of India, 

 the values for the additional ten degrees having been 

 specially computed. A short introduction explains the 

 method of using them, and they should be of use to 

 land surveyors who wish to control their work by 

 means of the triangulation stations of the department. 



It was proved by Prof. Arnold Emch in the 

 American Journal of Mathematics for October, 1913, 

 that in every closed convex curve which is analytic 

 throughout, at least one square can be inscribed. 

 That at least one square can be circumscribed about 

 such an oval curve is now proved by Prof. Tsuruichi 

 Hayashi in the Bulletin of the American Mathematical 

 Society, xx., g, where he also obtains a parametric 

 representation of the curve in tangential co-ordinates. 

 His proof of the possibility of circumscribing the square 

 about an oval curve is very simple. You can evi- 

 dently circumscribe a rectangle having its sides 

 parallel to any given direction. Now turn the direc- 

 tion round until the longer side becomes the shorter 

 one. Then in some intermediate position the two 

 sides will become equal, and the figure is then a 

 square. It will be interesting and easy for mathe- 

 matically inclined readers of Nature to reconstruct 

 from this material a corresponding proof for the 

 inscribed square if they have not seen Prof. Emch's 

 paper. 



In Yamagata, Japan, is a small lake called the 

 Lake of the Floating Islands, discovered about the year 

 1340, which has from that time attracted the atten- 

 tion of many poets and literary men. A report on the 

 mysterious movements of these islands drawn up by 

 a party under Prof. S. Kusakabe is published in the 

 Science Reports of the Tohoku Imperial University 

 (Sendai), iii., 2. The floating islands, which at 

 times number no fewer than sixty, are found to be 

 continually changing their position, moving" first one 

 NO. 2345, VOL. 94] 



way and then the other. In the first series of obser- 

 vations, wooden floats were placed in the lake show- 

 ing the distribution of the various currents ; subse- 

 quently a model of the lake was constructed, and it 

 was found possible closely to reproduce the various 

 movements of the surface. When both water and 

 wind currents were taken into account, the actual 

 behaviour of the islands was found to be quite in 

 accordance with theory and experiment. The islands 

 originate from masses of vegetable ddbris which are 

 first carried to the surface by bubbles of gas ; then 

 reeds commence to grow from seed on them ; some- 

 times the mass becomes top-heavy and overturns, and 

 reeds grow on the other side, until the island has 

 grown sufficiently large in extent to secure stability. 



The September number of Terrestrial Magnetism 

 and Atmospheric Electricity contains reports of the 

 work done by the magnetic survey ship Carnegie 

 during her second cruise round the world and during 

 a more recent journey from New York along the Gulf 

 Stream to Hammerfest. Along the line of the latter 

 route the values of the deviation of the compass to 

 the west of true north were found to be in general 

 greater than the values given in the British and 

 American charts by amounts which reach 13° in the 

 former and 2-2° in the latter chart. The atmospheric 

 electric observations taken during the voyage round 

 the world lead to the conclusion that over the sea the 

 potential gradient is of the same order as that over 

 land, the radio-activity is smaller, while the specific 

 conductivity is larger, than that over land. The con- 

 ductivity appears to be independent of the radio- 

 activity, although, like the radio-activity, it is greater 

 for air which has been in contact with land than for air 

 which has not during the week before the observations 

 on it are made. 



The Journal of the Washington Academy of 

 Sciences for August 19 contains two interesting opti- 

 cal papers. The first, by Prof. P. G. Nutting, of the 

 Eastman Research Laboratory, gives the results of a 

 series of measurements of the focal length of the 

 human eye for light of different wave-lengths within 

 the visible spectrum The author finds that while 

 for a water lens the focal length increases by about 

 5 per cent, from the extreme blue to the red end of 

 the spectrum at a rate which is fairly uniform, for 

 many human eyes the increase, although of about 

 the same amount, is confined to the ends of the range, 

 the change over the middle half not exceeding i per 

 cent., so that these eyes are nearly achromatic. The 

 second, by Mr. F. E. Wright, of the Geophysical 

 Laboratory, describes a new method of determining 

 the refractive index of a mineral by the petrographic 

 microscope. A stop below the condenser covers half 

 the field, and its inverted image is formed between 

 the stage and the low-power objective. In the same 

 plane as this image a second stop is placed, and the 

 distance of the edge of the second from that of the 

 image of the first so adjusted that the field is nearly 

 dark. In these circumstances, if a grain of mineral 

 immersed in a liquid of refractive index not exactly 

 equal with that of the mineral is placed on the micro- 

 scope stage, the edges of the grain appear some 



