October 27, 192 1] 



NATURE 



275 



pollen sterility and fertility behave as a pair of char- 

 acters in the sweet pea and the velvet bean should 

 in itself be sufTicient to give pause to those who would 

 like to regard bad pollen as a proof of hybridity. 

 The theory of mutation equally requires the occurrence 

 of a certain proportion of defective germ cells. 



The Hagedoorns, in their recent book on "The 

 Relative Value of the Processes Causing Evolution," 

 also support the idea of the origin of species by cross- 

 ing, but are obliged to admit that loss mutations must 

 occur, though why they should confine themselves to 

 loss mutations is not clear. It will be necessan,- to 

 bring some more convincing argument in support of 

 hybridisation as a constructive evolutionan.- factor 

 before it is likely to receive much serious considera- 

 tion from biologists. 



The Writer of the .Article. 



A System of Space-Time Co-ordinates. 



The common instruments of measurement proposed 

 in theon,' and employed in practice for the co-ordina- 

 tion of physical events consist of rigid bars and 

 clocks. The limitations of such methods are obvious. 

 The erection of a rigid bar for the direct determina- 

 tion of the distance of the moon from the earth is 

 inconceivable from a practical point of view, while 

 it is a gross absurdity to speak of the measurement 

 of molecular distances by means of rigid bodies. 

 There is only one type of connecting-link across space 

 suitable for co-ordination of events, namely, the light- 

 ray. I here define a system of space-time co- 

 ordinates which involve only ont metrical quantitv, 

 the vibration period of an atom. 



Let there be a vibrating atom at A emitting light- 

 rays. The \\me at A is read from the atom there. 

 T.et P be any other particle, which sends back in- 

 antaneously to A the light-rays arriving from A. 

 et a ray start from A at time /' and return to A at 

 ;iie X". If an event occurs at P at the instant of the 

 rrival of the said ray, we shall define two of the co- 

 rdinates of the event as 



distance of event from A=Xi = ^(t''-t^, 

 time of event = x, = ^{t'' + t'), 



:e expressions in italics being defined bv these state- 

 lents. 

 Let B and C be two particles such that x, is con- 

 rant with respect to time for each of them. Let a 

 light-ray be emitted from B and return to B after 

 reflection from C. The departure from B and return 

 to B of this ray are two events at B, and we have 

 already defined the time of events occurring at B. 

 Let the ray leave B at time x', and return to B at 

 time x\. Let C be so situated that {x\-x\) is con- 

 stant for all successive ravs. 



_ -A, B, and C constitute the frame of co-ordinates. 

 i or sake of example, we may observe that three of 

 he corners of a rigid rectangular block at rest in a 

 Terrestrial laboraton,- satisfy the conditions imposed 

 on A, B, and C, So far as our experimental accuracv 

 can ascertain ; whether they would continue to do so 

 if the block was rapidly revolved about an axis is a 

 matter for experiment to decide. 



We have now three particles. A, B, and C, and 

 from our definitions we can write down the time of 

 an event occurring at any of the three. Let anv event 

 P occur. Let it coincide with the arrival of a light- 

 rav from A which left A at t'j, and returns to .A at t"^, 

 and with the arrival of a rav from B which left B a 

 «'b and returns to B at ?"„, and also with the arrival o 

 a ray from C which left C at t'c and returns to C at 

 NO. 2713, VOL. I08I 



t"c. We define the four co-ordinates of the event P 

 by the equations : — 



It is to be observed that this co-ordinate system, 

 although from the method of definition applicable to 

 the most general gravitational fields, will, in the 

 I absence of such fields, give the same values for the 

 I co-ordinates of an event as those obtained by rigid 

 j body measurements from three points of a rigid body 

 j and by a system of clocks. J. L. Synge. 



Department of Mathematics, University of 

 Toronto, Toronto, Canada, September x6. 



Aeroplane Photography for Archaeology. 



Photographs from an aeroplane taken on a clear 

 afternoon a little before sunset would give good records 

 of ancient British and Roman camps, •"castles," vil- 

 lages, rings, pack-tracks, barrows, ditches, and other 

 earthworks, and, as in such photographs taken in 

 Mesof>otamia, would probably reveal details that can- 

 not be distinguished by inspection on the ground. 

 Photographs might yield almost as much informaticMi 

 as the models in the Pitt Rivers Museum at Farnham, 

 which were made from laborious contour surveving. 



There are hundreds of such earthworks on Salisbury 

 Plain, and many of them are, no doubt, related to 

 Stonehenge and to Avebur}'. The stereoscopic com- 

 bination of two successive photographs might disclose 

 those parts of the banks and ditches which are nearly 

 obliterated by the village of Avebury. General model- 

 ling is wanted rather than fine detail. Perhaps such 

 work might be done by learners. 



A. P. Trotter. 



Grfvironf-s, T«=>ffonr, Salisburv, October 12. 



Cosmic Friction : A Query. 



Writing with proper deference, I would ask astro- 

 nomers whether it is not feasible to consider that the 

 solar system may occasionally journev through a 

 region of space occupied by exceeding! v diffuse 

 matter? L'nder such conditions the exceptional ap- 

 pearance of a large meteorite outside the earth's 

 atmosphere might be possible ; and some minute 

 shortening of the period of a quickly revolving satel- 

 lite, like the moon, might show itself by a cumulative 

 advance of position. Contrariwise, if ever (say 

 between 1865 and 187 1) we passed through regicms 

 altogether free from even such evanescent friction, a 

 readily affected comet, like Encke's, might tem- 

 porarily recover from its usual perturbation. 



Oliver Lodge. 



Muscular Piezo-electricity ? 



There is a remarkable similaritv between the struc- 

 ture of those organs of electric eels which are 

 generally held to be the source of their "shocks^' 

 and the structure of certain artificially grown crystals 

 exhibiting the piezo-electric property-. Is it possible 

 that there is a connection between the two, and that 

 these creatures do produce piezo-electricity bv the con- 

 traction of these organs? I should be interested to 

 know if any of your readers have found anv con- 

 nection between these two phenomena. 



E. Wriotheslev Russell. 



Trinity- College, Cambridge, October 10. 



