152 



NATURE 



[September 30, 1920 



duce colour, though no finer structure can any- 

 where be made out, section 9 (Fig. 2). 



Euploea deione. — There is one large group of 





1 



"1 



\ ■/ 



Fig. 6 ^Ij-cdcnrt C(7rj'rti?« (the Chalk Hill, Blue). Male, female, 

 under-side of female and larva. (Natural size.) 



insects of considerable interest, the colour of 

 which cannot be accounted for in any way. This 



group includes the dark purples and deep, glossy 

 blues and greens of all the most sombre iridescent 

 insects, such as the Purple Emperor {Apatura iris), 

 the Scarlet Tiger (CalUmorpha dominula), the 

 Purple Hairstreak (Zephyrus quercus), and many 

 exotic species. Any one of these, such as the 

 section of Euploea deione, 11 (Fig. 2), shows no 

 difference from the black, non-iridescent scales im- 

 mediately beneath them. They are all so densely 

 pigmented that nothing can be made out until they 

 are bleached, and even then a thin cuticle only some- 

 times appears. Were it not for the fact that the 

 colours disappear under pressure and in refractive 

 fluids, it might be thought that the iridescence was 

 due to selective metallic reflection, as will be shown 

 to be probably the case in most scaleless beetles. 



Dione juno. — Scarcely less puzzling are the 

 metallic greenish-gold and silver scales of many 

 Plusia, such as the Burnished Brass Moth (Plusia 

 chrysitis). Section 8, Fig. 2, shows the golden 

 scale of the tropical insect Dione juno, which has 

 no structure that can adequately account for the 

 colour, since it is identical with the scales in the 

 adjoining brown areas, except for the absence of 

 the pigment. To produce anything approaching 

 metallic reflection a highly polished surface would 

 be necessary, as well as a large number of air- 

 spaces not more than the diameter of a few air- 

 molecules in thickness. The effect of a highly 

 polished surface is seen in the scales of the 

 Coppers, as, for instance, the Small Copper 

 [Chrysophanus phlaeas), which has ordinary scales 

 containing a granular orange pigment, yet appear- 

 ing almost iridescent. The only trustworthy 

 evidence of true iridescence is, of course, the 

 change of colour seen on altering the angle of the 

 incident light. 



{To be continued.) 



Ballistic Calculations. 

 By D. R. Hartree. 



THE purpose of the present article is to give 

 an outline of the more important methods of 

 numerical solution of the various problems of 

 external ballistics — that is to say, problems con- 

 nected with the resisted motion of a shell after 

 leaving a gun. Most of the methods to be men- 

 tioned were developed during the war, either for 

 working out range tables or other information to 

 be used in the field, or for analysing a trial shoot. 

 The problems that arise may conveniently be 

 divided into two groups, -comprising what are 

 sometimes known as primary and secondary prob- 

 lems, the theoretical and practical treatments of 

 which proceed on rather different lines. The primary 

 problems are those which involve the calculation 

 of the performance of a gun, or rather its shell, 

 under ideal conditions, such as still air, a standard 

 muzzle velocity, and so on. The secondary 

 problems are those in which we are concerned 

 with the calculation of the corrections to be 

 applied to the solutions of the primary problems 



NO. 2657, VOL. 106] 



to allow for the departure of actual conditions 

 from the ideal. 



A very important simplification is introduced by 

 assuming that the forces due to the motion of the 

 shell through the air consist only of a resistance 

 in a direction opposite to the direction of the 

 motion of the shell relative to the air. Lack of trust- 

 worthy information until recently about the other 

 forces made this the only possible course. Some 

 account of these forces and their effects is given 

 in a recent issue of N.atiire.i 



Making this assumption, and neglecting the 

 effect of earth rotation (which may be considered 

 as a secondary problem), it appears that the tra- 

 jectories concerned in any primary problem lie 

 entirely in the vertical plane containing the initial 

 direction of motion. For this reason they are 

 known as "plane trajectories." 



The retardation due to air resistance R acting 



1 See Nature, June lo, "The Dynamici of Shell Flighl, ' by R. H. 

 Fowler. 



