June ii, 1903] 



NATURE 



129 



■- unimportant until the speed conies very near to the 

 !;^ht velocity, but the mass becomes suddenly infinite 

 r very great when the light velocity is attained. 

 I find it difficult to realise the full effect of this kind 

 of increase of mass, that is to say, of mass intrinsically 

 iui>sessed by the moving body, and not accreted on it 

 10m outside stationary matter. The latter effect is 

 amiliar in raindrops and in viscosity of gases, and it 

 tends to reduce relative motion ; but no previous in- 

 stance is known where the mass of the moving body 

 rises because it is itself a function of velocity. It 

 would seem that the momentum must increase, and 

 must disturb the balance of forces holding the parts 

 of the system together. In an extreme case it might 

 happen that the lighter body would suddenly become 

 the heavier, would behave as if it had encountered an 

 bstacle, and would jerk the rest of the atom off; or, 

 ii the other hand, it might happen that the most 

 apidly moving portion itself, by reason of its sudden 

 '.cess of momentum, would break loose and proceed 

 mgentially. In any case it appears likely that an 

 -loni at this stage would begin to break up, as 

 observed experimentally by Rutherford and Soddy; in 

 other words, the fact of electronic radiation seems to 

 carry with it the liability to change or decay of all 

 matter possessing an electric constitution ; the change 

 trom one form to another being accompanied, as they 

 demonstrate in many cases, by radio-activity — a 

 phenomenon which Strutt finds widely diffused. 



It is hardly necessary to direct attention to a sort of 

 astronomical analogy to this, though governed by 

 different forces, in the contracting or gradual collap- 

 sing of a nebula, with the occasional shrinking off of 

 peripheral material as an unstable stage is periodically 

 reached, in accordance with the rough approximation 

 known as Bode's law, together with the strong radio- 

 activity of the central mass, and the conversion of con- 

 stitutional potential energy into heat, 



A few more words on the increase of mass at the 

 critical velocity : — The only expression for mass as 

 depending on velocity which has met with any attempt 

 at experimental verification, is the expression of 

 Abraham supposed to be verified by Kaufmann by 

 direct experiment on curvature of kathode rays. 

 Taking this as a simple example of the kind of effect 

 to be expected, viz. 



?o 43' V 2/3 ^ I - 



• .(5) 



\Vhere /8 is the ratio ujv, the speed of an electric 



particle to that of light, and m^ its ordinary purely 



electric mass for slow motions, we find that when an 



I electron is moving with hal\ the speed of light, its 



« mass is only 1.12 times what it was when stationarj-. 



I At three-quarters of the speed of light the mass ratio 



f becomes 1.37, or little more than a third greater than 



its normal value. At nine-tenths of the light velocity 



the mass is still not doubled, being only 1.8 times m„. 



When within i per cent, of the light speed the mass 

 is trebled, or, more exactly, multiplied by 3.28, and 

 when within one part in a thousand of its limiting 

 velocity, the mass is almost exactly quintupled. 



For higher speeds, say within i/nth of the speed of 

 light, or u = {i- i/n)v, n being great, the expression 

 for the electric mass ratio simplifies to 



3 (log {2ft - I) 

 4 '- 



ijwo 



(6) 



which ultimately is truly infinite, but for even excessive 

 values of n is only moderately great. 



It is notable how close to the velocity of light it is 

 necessary to get before this effect becornes prominent ; 

 NO. 1754, VOL. 68] 



the instability must be expected to arrive sharply when- 

 ever the velocity of light is from any cause, e.g. per- 

 turbation or collision, attained by any moving elec- 

 trically charged part of an atom. Assuming a Max- 

 well distribution of velocities and an average speed, 

 for the internal atomic motions, it may be possible (as 

 J. J. Thomson suggested in Nature of April 30, p. 

 601) to calculate what percentage of a given number of 

 atoms reach the unstable stage by this means, and so 

 to make a theoretical estimate of the amount of radio- 

 activity to be expected, and of the life of an atom. 

 But the slight constant radiation-loss seems competent 

 to bring about instability and decay irrespective of 

 collisions, and therefore independently of any Maxwell- 

 Boltzmann law. Oliver J. Lodge. 



PHOTOGRAPHS OF SNOW CRYSTALS. 



AT the beginning of last year (vol. Ixv. p. 234) we 

 summarised a paper contributed by Mr. W. A. 

 Bentley to the U.S. Monthly Weather Review upon his 

 photomicrographs of snow crystals. Mr. Bentley has 

 made a study of the forms of snow crystals for more 

 than twenty years, and has obtained a most valuable 

 collection of photomicrographs taken with the object 

 of discovering the connection between characteristic 

 forms and particular meteorological conditions. 

 During the winter of 1901-1902 a systematic record 

 was secured by Mr. Bentley of a number of snow 

 storms, and several good photomicrographs from 

 each storm were obtained by him, more than two 

 hundred pictures being added to his collection. The 

 annual summary of the Monthly Weather Review for 

 1902 (vol. XXX. No. 13), which has just been re- 

 ceived, contains reproductions of these photomicro- 

 graphs and a paper by Mr. Bentley describing the 

 various types of structure and the meteorological con- 

 ditions prevailing at the time when they were produced. 

 The paper contains an instructive account of snow 

 crystals, and an analysis of the results of the studies 

 carried on during the winter of 1901-1902. The 

 interest of the pictures lies not merely in the fact that 

 many of the forms photographed are very remarkable, 

 but that they also represent, so far as possible, stages 

 in the life-history of snowstorms, several pictures 

 having been obtained of each storm, while at the 

 same time a record was kept of the conditions of 

 temperature, pressure, wind, cloud and position of 

 storm from which the snow fell. 



We print a few extracts from the contribution 

 and reproduce several photomicrographs of exceptional 

 interest from those given in the Monthly Weather 

 Review. 



In general the data tend to confirm further the con- 

 clusions of all observers, that a more or less intimate 

 connection exists between form and size of nuclei, and the 

 altitude and temperature of the air in which the crystals 

 form. There can be no longer any doubt that there is a 

 general law of distribution of the various types of crystals 

 throughout the different portions of a great storm. On 

 this point the data secured, both by direct observation and 

 by a study of the weather maps, are much more complete 

 and satisfactory than has hitherto been published. Ihis 

 aspect of our study received special consideration, because 

 it was thought to be most important. 



Snowstorms often cover a region of vast extent ; crystal- 

 lisation is going on within them over nearly the whole area, 

 and therefore in regions that differ greatly among them- 

 selves as to temperature, humidity, air density, electrical 

 conditions, &c. Moreover, the kind, number, dimensions, 

 altitude and density of the clouds within those various 

 regions differ so greatly one from another that the snow 

 crystals emanating from each region furnish us rare 

 opportunities for observing and studying the effects of each 

 of these various conditions upon the forms. 



