I 



June io, 1920] 



NATURE 



461 



The study of initial motions is intimately con- 

 nected with the question of the stability of a spin- 

 ning shell at zero yaw. The motion of a shell (or 

 a top) is said to be stable if a small disturbance 

 only produces a small maximum displacement 

 from the position of symmetry, proportional to 

 the disturbance. The condition of stability for 

 small disturbances is the same in the two cases ; 

 it must be fulfilled in order that the shell may 

 travel along- its trajectory approximately at zero 

 yaw as desired. A knowledge of the disturbing 



with the changing direction of motion by pre- 

 cession about it. This equilibrium value of the 

 yaw depends on the above-mentioned disturbing 

 couple due to the reaction of the air, which may 

 be determined by a study of the initial oscilla- 

 tions. The resulting yaw in ordinary cases is too 

 small to alter seriously the range at any given 

 time, and does not affect the height because the 

 equilibrium position of the yawed axis lies in a 

 plane which is always very nearly at right angles 

 to the vertical plane containing the original direc- 



couple enables us to lay down how much spin is j tion of projection. It produces, however the 



required to allow a reasonable margin of stability. 



We have said that the usual approximation of 

 motion at zero yaw is inadequate in the case of 

 trajectories of large total curvature. The com- 

 plete theory indicates that, under the effect of 

 gravity (see (3) above), the yaw tends to attain a 

 sort of equilibrium value which increases along 

 the trajectory, and may reach 20° or more at the 

 end of a sufficiently long arc. A study of initial 

 motions with slightly unstable shells in which such 

 values of the yaw can be realised experimentally 

 will provide the material required for the proper 

 discussion of such trajectories. 



The following approximate theory accounting 

 for the drift of a shell has long been known. 

 Owing to the change of direction of motion due 

 to gravity (see (3) above), a shell cannot continue 

 to move steadily at zero yaw. The proper equi- 

 librium state of affairs is attained when the yaw 

 is just such as will enable the axis to keep pace 



lateral deviation known as drift. This approxi- 

 mate theory leads to a formula for the drift de- 

 pending on the ratio of the sideways thrust to the 

 disturbing couple. With the values of this ratio 

 recently roughly determined, the drift has been 

 calculated by this classical theory, and compared 

 with direct observations of the drift of similar 

 shells. The observed and calculated values are in 

 fair agreement, and there is no doubt that the 

 classical theory is substantially correct. 



In conclusion, it is perhaps worth mentioning 

 that the interest in such investigations mainly 

 arises from the fact that we can thus study the 

 phenomena of j motion through a compressible 

 fluid at velocities both greater and less than the 

 velocity of sound in the fluid. The investigation, 

 however, has scarcely begun, and much work 

 will be required before it is possible to 

 describe adequately the complete reaction on a 

 shell of given shape moving through air. • 



Obituary. 



Prof. L. Doncastek, F.R.S. 

 T EONARD DONCASTER'S death from sar- 

 * — ' coma at the age of forty-two has stopped a 

 career of exceptional distinction. When 1 lately saw 

 him, apparently in his usual health, presiding over 

 his laboratory as the newly elected Derby professor 

 of zoology at Liverpool, I had comfort in the 

 thought that by his appointment a fresh centre 

 of genetics was safely begun. Doncaster was a 

 natural investigator. From his student days there 

 was never a doubt as to the purpose of his life. 

 The problems of biology were always in his mind. 

 For him the materials were everywhere. Though 

 circumstances led him into academic zoology, he 

 was an excellent field entomologist and botanist, 

 with a fair knowledge also of the domesticated 

 forms. Latterly he became more and more drawn 

 towards cytological methods, but he always kept 

 in touch with the other lines, knowing that the 

 next advance may begin anywhere. 



Doncaster started at Naples with experiments on 

 hybridisation of Echinoderm larvae, which pro- 

 duced evidence of value as to the effects of tempera- 

 ture in modifying dominance ; but many aspects of 

 that vexed question remained, and still remain, 

 obscure. He returned to England at the moment 

 when the early struggles of Mendelism were acute. 

 Though constitutionally predisposed to caution, he 

 NO. 2641, VOL. 105] 



knew enough of the general course of variation 

 and heredity to be in no doubt of the essential 

 truth of the new doctrines, and undoubtedly his 

 adhesion did much to spread confidence among his 

 contemporaries. He at once joined in breeding 

 work, and at various time<: experimented with 

 many forms, particularly rats, cats, and pigeons. 

 With insects of several orders he was especially 

 successful. The seemingly more fundamental 

 nature of microscopical work made it very con- 

 genial to him, and he always had a mass of cyto- 

 logical material on hand. These studies enabled 

 him to take a prominent part in that compre- 

 hensive codification by which the confused and 

 contradictory observations as to the sexes of 

 parthenogenetic and other forms in the Hymeno- 

 ptera and Hemiptera were ultimately reduced to 

 order. 



In the history of biology Doncaster's discovery 

 as to the determination of sex in the currant moth 

 {Abraxas grossulariata) will have a permanent 

 place. From the Rev. G. H. Raynor, a fanciei* 

 of the species, he learnt facts which suggested 

 that the variety lacticolor was. what we now. call 

 "sex-linked," being predominantly associated with 

 females, as colour-blindness in man is with males. 

 After verification and extension this m^ss of facts 

 provided (1906) the firs^ clear genetic proof of 



