December 9, 1922] 



NA TURE 



771 



peculiar feature illustrated in Fig. 2, a, b, and c. 

 The prominence varied slightly in size and position in 

 the different species, but there was always at least 

 one lens on the summit and three or four round the 

 sides. 



Divided eyes must be, or at some period have been, 

 of use to their possessors. Have the naturalists any 

 explanation of what that use is ? The case of the 

 Aphis eyes seems especiallv difficult. 



In the last century Johannes Muller expressed the 

 opinion that in the picture formed by a composite 

 eye each lens contributed only one impression, e.g. 

 that the picture was made up of only the same 

 number of patches of light and shade as there were 

 lenses to form them, just as in the modern " process 

 block " light and shade effects are produced by the 

 varying intensities of uniformly distributed dots. 



In 1894 I gave (Proc. R.S.) some theoretical 

 •reasons in support of Midler's view. This paper has 

 been mentioned in several more recent books, but the 

 theory itself is not quoted. It is, however, so simple 

 and, coupled with the measurements of various 

 composite eyes, so conclusive that it may be worth 

 repetition in this place. 



Every one knows, or ought to know, that the image 

 formed by a perfect lens of a distant bright point 

 consists of a bright disc surrounded by faint rings, 

 and that the angular diameter of the disc as seen 

 from the optic centre of the lens is of the order X/D, 

 X and D being respectively the wave-length of the 

 light and the diameter of the lens. This being the 

 case, it is evident that no advantage in definition will 

 be gained by providing a retina capable of distin- 

 guishing angular distances less than X/D, i.e. the least 

 distance which the lens can resolve. 



If the wave-length is taken as 1/50000 of an inch, 

 then for a lens o-ooi in. in diameter X/D is rather 

 more than one degree, and for a diameter of o-oooi 

 in., rather more than ten degrees. 



If a number of small lenses are placed side by side 

 with their edges touching on the surface of a sphere 

 of radius R, and if the focal length of the lenses is 

 small compared to this radius, images of outside 

 objects will be formed on a concentric spherical 

 surface (with a radius somewhat less than R) ; in these 

 images, only those objects can be separated of which 

 the angular distance apart is greater than X/D. 



If, then, the focal surface is covered by a retina 

 which provides only one sensitive point for each lens 

 to act on, the maximum definition will be secured if 

 the subtense of each lens at the centre of the sphere 

 is also X/D, that is if D/R =X/D, and this is the relation 

 found to hold in the most highly developed com- 

 posite eyes. It may be said, therefore, that the 

 construction of these eyes is one of the most definite 

 references to the wave-length of light to be found in 

 organic structures. The actual values of D lie between 

 something over o-ooi in. and a little less than 

 0-0003 m - 1 The definition, therefore, even in the most 

 favourable cases, is very poor compared with that 

 given by the simple eyes of vertebrates, where a 

 single lens forms an image on a retina closely packed 

 with sensitive points, while in the composite eye each 

 retinal point is capped with its own lens. 



To form a composite eye with the same defining 

 power as the human eye, for example, the lenses 

 would have to lie on a spherical surface of 18 ft. 

 radius. 



It would be interesting to know how or why the 

 two types have come into existence. A. Mallock. 



9 Baring Crescent, Exeter, November 7. 



1 I have taken some trouble in arriving at this lower limit, measuring 

 directly for this purpose the values of D for the smallest Diptera (and their 

 parasitic Hymenoptera), Ephemera, and others. 



Action of Cutting Tools. 



If Mr. Mallock's friction theory of cutting-tool 

 action is valid, and if cutting tools are ever effectively 

 lubricated, it would follow that the dry tool should 

 have an angle different from that of the lubricated 

 tool. But this is contrary to universal practice. 

 The inference would then be that either the friction 

 theory is unimportant and extremely incomplete, or 

 1 111 1 lubrication as practised by engineers is very 

 ineffective. The latter view seems more correct, for 

 the following reasons. 



When a tool has been cutting for some time, metal 

 accumulates on the point of the tool and adheres 

 sometimes so firmly that it cannot be removed, 

 without risk of breaking the tool, except by grinding. 

 This agglomeration of metal may be said without 

 looseness to be welded to the tool just as in cases 

 of bearing seizure the metals are welded together. 

 This is especially obvious in heavy work, and it can 

 be seen in a lesser degree in moderately light work. 

 When contact is so intimate and pressure so great 

 as to cause such cohesion it is difficult to conceive 

 that lubrication in the usual sense of the term can 

 exist at the point of a cutting tool. 



Moreover, engineers in many countries have striven 

 to introduce lubricant to the cutting face by means of 

 high-velocity jets and by drilling holes in the nose 

 of the tools, but without success. 



Lastly, the temperature at the tool face is extremely 

 high. Turnings which pass over the surface are hot 

 enough to cause serious burns, and large tool cross- 

 sections are necessary to conduct the heat away 

 from the nose of the tool. It has been observed 

 that modern high-speed steel will cut at a dull red 

 heat ; and while this is an abnormal condition, there 

 is evidence enough to show that the temperatures 

 existing in average machining work are higher than 

 can be met by special lubricating systems under 

 less strenuous pressures. These considerations seem 

 sufficient to rebut the idea of cutting-tool lubrication 

 in most cases, and to suggest that the chief value of 

 so-called cutting oils is in their cooling properties. 

 Even turpentine, which is useful in cutting hard steel, 

 may have much of its value in its latent heat of 

 evaporation. Certainly to obtain a good finish on 

 hard steel with turpentine often requires a spring 

 tool and light cuts, in which case there is the equivalent 

 of chatter in a mild form, and this is conducive to 

 lubrication. 



In the discussion on Prof. Coker's paper it was 

 stated that the point of the tool was not in contact 

 with the work, and Dr. Lanchester very trenchantly 

 asked, Whatwas the good of having the tool sharpened ? 

 But it is well known on heavy work or with tools of 

 inferior temper that work must be stopped periodically 

 and tools reground. The idea that the point of a 

 tool is not in contact with the job is perhaps a natural 

 one, and rests on a difficulty hitherto unexplained. 

 It is common observation that a tool wears most 

 some little distance from the edge, and the edge may 

 last a good deal longer than the part behind it. 

 But this is no proof that the edge is not in contact ; 

 and if the edge were not in contact, the action of 

 cutting tools would be even more perplexing than it is. 



The explanation of this point may lie in the fact 

 that the turning has less relative motion near the 

 edge of the tool than at some distance behind, and the 

 justification for this view is seen in a closer examina- 

 tion of the motion of a turning. The neutral axis 

 of a turning has a constant speed approximately 

 equal to the cutting speed, but when the turning 

 begins to bend there is a speed of rotation added to 

 the speed of the neutral axis, and this rotational 



NO. 277 I, VOL. I io] 



