206 



NATURE 



[February i6, 1922 



The difference of length of the paths Aj, Bj, A^, Bj 

 of rays making an angle % with the principal axis is 

 osin(t+i8), and unless the average of this for all 

 values of i exceeds A/4, the images Bj, B^ will appear 

 connected, and will not be clearly separated until the 

 average is about A/2. From this it may be seen that 

 not only is it impossible to separate the images of 

 objects in the focal plane which are much closer 

 together than A/2, but also that the same limit defines 

 the distance out of focus at which objects may be 

 placed without altering the character of their images. 

 This is a point which is well brought out by the lines 

 on the aniline films. 



Fig. 3- 



It may be asked what is the greatest magnifying 

 power which can be usefully given to microscopes? 

 Since objects closer together than A/2 cannot form 

 separate images, the greatest useful magnification is 

 that which makes A/2 visible to the eye. 



A very good eye can just distinguish minutes of arc, 

 or say objects separated by 1/350 in. at the distance 

 of the eye from the stage. Then, taking the half- 

 wave-length as the 1/100,000 of an inch, all details 

 would be visible with a magnification of 100,000/350, 

 or a little more than 280. Not all eyes, however, are 

 capable of distinguishing minutes, and for conveni- 

 ence of observation, magnifications of twice this 

 amount or more are used in practice, but the extra 

 power reveals no new detail. 



Fig. 4. — P'orm of plano-convex lens for the conversion of divergent rnys 

 into a parallel beam. O, Radiant point ; OX, principal axis ; 

 PA, section of lens surface. 



An idealised lens is merely a means of changing the 

 radius of curvature of a wave-surface from /, to /^ 

 while preserving the constancy of the optical length 

 of all the rays from focus to focus. 



From these conditions the form of the lens which 

 will achieve the result may be deduced. As a simple 

 example, find the form of a plano-convex lens which 

 will convert spherical waves originating at O (Fig. 4) 

 into a parallel beam. 



Let the convex surface of the lens cut the prin- 

 cipal axis OX at A, and let the refractive index of 

 NO. 2729, VOL. 109] 



the material be ju. The form of the surface is deter- 

 mined by the relation OA+/xAN = OP. Elementary 

 algebra shows that the curve PA is a hyp erbola the 

 asymptotes of which make an angle tan-V/x^'-i with 

 the axis of the lens. The complexity of actual objec- 

 tives arises from the necessity of effecting the change 

 of radius of curvature by means of spherical surfaces. 



A. Mallock. 

 9 Baring Crescent, Exeter. 



The Antitrades. 



I AM glad to support the appeal for observations of 

 the motion of cirrus-clouds in the inter-tropical region 

 and elsewhere made by Prof, van Bemmelen in his 

 letter on the Antitrades (Nature, February 9, p. 172). 

 It is very interesting that the results which he has 

 obtained by direct observation, with only such addi- 

 tional information from dynamics as may be got 

 from a consideration of the general character of the 

 Australian pressure, should coincide so excellently 

 with results which we obtained here from the cal- 

 culation of the distribution of pressure at various 

 levels, and the assumption that the wind flows along 

 the isobars. 



There are some details in Prof, van Bemmelen 's 

 maps which indicate a flow of air across the equator 

 which I should be disposed to modify in view of the 

 peculiar conditions under which such a transference 

 of air must take place. I hope to give the details of 

 the information that we have compiled about this 

 subject at some future time, and confine myself for 

 the present to saying that the atmosphere seems to be 

 able to use the circulation of air round a strip of 

 doldrum region as a means of providing for currents 

 which flow westward on the south side, and eastward 

 on the north side, of the equator in a general slope 

 of pressure from south to north across the equator. 

 Thus the doldrum region becomes a sort of elongated 

 clockwise "centre" for the winds of the monsoon 

 north and south of the equator. 



I would add also to Prof, van Bemmelen 's appeal 

 for observations of cirrus a plea for the extension 

 of observations with pilot balloons. Methods are now 

 so well understood that the authorities could easily 

 provide a technique which could be followed by those 

 accustomed to surveying and others, and would pro- 

 vide invaluable Information The committee of the 

 British Association which concerns Itse-'f ^ about the 

 upper air has already taken up the question, and if 

 anyone who is in a position to help In this matter 

 would communicate with me or with the secretary of 

 the committee, Capt. C. J. P. Cave, of Stoner Hill, 

 Petersfield, we shall be greatly obliged. 



Napier Shaw. 

 School of Meteorology, Roval College of Science, 

 South Kensington, S.W.7, January 12. 



The Isotopes of Mercury. 



It appeared to be so definitely one of the funda- 

 mental assumptions of physics that pure mercury has 

 a constant density under given physical conditions 

 that when Bronsted and Hevesy announced that they 

 had separated it into fractions of different density 

 (see Nature, September 30, 1920, p. 144) it appeared 

 desirable that the separation should be confirmed by 

 other observers. One of us finds that when mercury 

 (purified chemically and by distillation in a vacuum) 

 is distilled In a very high vacuum the first sixth 

 of the original mercury condensed is of lower density 

 than the last sixth, the difference in density found 

 for these fractions was 44 parts In 1,000,000. This 



