June 19, 1919] 



NATURE 



305 



My contention throughout has been that the degree 

 of visibility of a vessel was of little consequence pro- 

 viding she could be seen at all. Prof. Kerr agrees 

 that it is not possible to render a ship strictly in- 

 visible, but only to reduce her visibility. This in my 

 -view is not enough. A submarine commander, whose 

 one object is to sink ships, will not be put off by 

 reduced visibility. We know from some of the com- 

 manders themselves that they constantly located a 

 vessel by its smoke when still hull down, i.e. before 

 the vessel itself could be seen at all. 



Prof. Kerr says that of the various methods which 

 Nature makes use of, there are two alone of practical 

 value for application to ships : (a) obliterative colour- 

 ing; (h) comp>ensative shading. I have endeavoured 

 to show that the contrasting colours, as used in 

 dazzle-painting, were not used in Nature's way, i.e. 

 as obliterative colouring. 



To turn to compensative shading, I must say, after 

 extended observations at sea, I have failed to observe 

 any gain in this method of painting. In a letter of 

 this length it is not possible to go into all the causes 

 of its failure, but only to state briefly one or two of 

 the main objections. To take the practical side first, 

 what shadows are there in our modern battleships to 

 compensate which would retain white paint for more 

 than a few hours? The various controls on the mast 

 -are in close juxtaposition to the funnel, and subject to 

 constant heat and smoke. The hawse-pipes are rusty 

 after a few hours' steaming, while the shadow cast by 

 the flare of the bow is automatically compensated by 

 reflected light thrown up from the bow wave. There 

 is a small shelter deck amidships, far too deep shadow 

 for any light paint to overcome. 



In the case of the merchant vessel the same dififi- 

 culties arise. No shadows cast bv passenger decks 

 can be overcome by the use of white paint, which is 

 itself dependent on light for luminosity. These decks 

 present a very different proposition from a bird's breast 

 receiving reflected light from the ground or sand on 

 which it stands, or from the glitter of water below. 

 I am not theorising in making these statements ; they 

 are the direct outcome of observation at sea for some 

 years. 



There is one point I should like to emphasise in 

 the matter of ships' camouflage, and that is, the 

 practical application of a design to a ship. A scheme 

 may be evolved which appears perfect on paper, but 

 the result, when actually applied, will be most dis- 

 appointing. Most theorists with whom I haye come 

 in contact — and they are many — only think in " one 

 ship " when evolving a scheme for disguise. What 

 has to be realised is that it is necessary to deal with 

 hundreds of ships, painting simultaneously and at 

 high pressure. The authorities concerned with ship- 

 ping during the war could not think of any delay in 

 unloading and getting vessels to sea in the shortest 

 possible time. Consequently the painting of these 

 vessels had to be carried out while loading or un- 

 loading, and under every other disadvantage, such as 

 rain and coal dust. We were sometimes able to get 

 a hose on to parts of a ship blackened with coal dust 

 whilst painting, sometimes not. So that I fear so 

 subtle a thing as compensative shading would have 

 vanished before a vessel put to sea. It may be men- 

 tioned here that more than 3000 British ships alone 

 were dazzle-painted in the last eighteen months of the 

 war, and we sometimes had as many as a hundred 

 vessels painting in one port simultaneously. 



It should be remembered that dazzle-painting was 

 adopted at a time when twenty to thirty ships were 

 being sunk weekly, so that the life of the nation 



NO. 2590, VOL. 103] 



depended on turning ships round and getting them 

 to sea again in the shortest possible time. 



Dazzle-painting was never intended for use on 

 " ships of the line," but only for merchantmen singly 

 or in convoy and war vessels working with them ; 

 and, judging from the great number of reports re- 

 ceived from merchant captains, who in the early 

 stages of dazzle-painting were averse to it, but later 

 came to see its object, there can be no question that 

 it achieved its purpose. Norman Wilkinson. 



Question Relating to Prime Numbers. 



It is well known that no algebraical formula can 

 represent prime numbers only, and that primes can 

 only be found by trials (which may be facilitated by 

 algebraical processes). If the m'^^ prime number, 

 counting from unity, be denoted by n, and if n is 

 plotted in terms of m, it will be found that n is very 

 approximately represented by a formula of the type 

 AmP (A = 3-i5, />= 1-133, are close to the values of 

 the constants). 



The differential of this curve is given in the accom- 

 panying diagram, and the true values of dn/dm are 



OJ23456789)0 

 Tfi- Cn ^ou SO nets 



Qi- (iMAa^ cU//*^eiKJ ofjucfesnit 

 Cfiousands of pilwe. namler^ 



TuU Curiae. ■- Ptfferen{7af of a/sm'^^ 



shown by the circles. The agreement between the 

 curve 3-15 m**"' and the true values of n (taken 

 from Barlow's tables) is too close to be shown with 

 advantage on the scale to which the diagram is 

 drawn. The differential curve is a good mean of the 

 actual values of dn/dm. 



Are there any investigations which give a reason for 

 the tendency of n to approach a definite function of 

 m, or as to the ultimate value of dn/dm when m 

 increases without limit? A. Mallock. 



6 Cresswell Hardens, South Kensington, S.W.7. 



