288 



SCIENCE. 



mountains. Sometimes they are manufactured articles, 

 stones or blocks of wood cut into some shape which has 

 a meaning either obvious or traditional. 



The universality of this tendency to connect seme ma- 

 terial objects with religious worship, and the immense 

 variety ot modes in which this tendency has been mani- 

 fested, is a fact which receives a full and adequate ex- 

 planation in cur natural disposition to conceive of all 

 Personal Agencies as living in some form and in some 

 place, or as having some other special connection with 

 particular things in Nature. Nor is it difficult to under- 

 stand how the embodiments, or the symbols, or the 

 abodes, which may be imagined and devised by men, will 

 vary according as their mental condition has been de- 

 veloped in a good or in a wrong direction. And as these 

 imaginings and devices are never, as we see them now 

 among savages, the work of any one generation of men, 

 but are the accumulated inheritance of many generations, 

 all existing systems of worship among them must be re- 

 garded as presumably very wide departures from the con- 

 ceptions which were primeval. And this presumption 

 gains additional force when we observe the distinction 

 which exists between the fundamental conceptions 

 of religious belief and the forms of worship which have 

 come to be the expression and embodiment of these. In 

 the Religion of the highest and best races, in Christianity 

 itself, we know the wide difference which obtains be- 

 tween the theology of the Church and the popular super- 

 stitions which have been developed under it. These 

 superstitions may be, and often are, of the grossest kind. 

 They may be indeed, and in many cases are known to be, 

 vestiges of Pagan worship which have survived all re- 

 ligious revolutions and reforms ; but in other cases they 

 are the natural and legitimate development of seme 

 erroneous belief accepted as part of the Christian creed. 

 Here, as elsewhere, Reason working on false data has 

 been, as under such conditions it must always be, the 

 great agent in degradation and decay. 



METEOROLOGICAL ELECTRICITY. 



del et Terre gives a description of a cyclone which 

 passed over Japan on the night of the 3d or 4th of October, 

 r88o. At Tokio a rapidity of 45 metres per second has 

 been observed, but this had only a rapidity of 10 metres ; 

 its diameter was not very considerable, 240 kilometres. The 

 fall of the barometer, though rapid, was far from being as 

 prompt as that occurring eight days before on the coasts of 

 the Island of Formosa, where a depression of 73 millimetres 

 in 4 hours, or 18 millimetres per hour, was observed. These 

 indicate that the old theory of whirlwinds is perfectly use- 

 less to account for meteorological phenomena. 



THE APERTURE OF MICROSCOPE-OBJECTIVES. 



The last number of the 'journal of the Royal Micros- 

 copical Society is largely occupied with a discussion of 

 this question by Prof. E. Abbe, of Jena, and Mr. Frank 

 Crisp, cne of the secretaries cf the Society. 



The subject appears to have been again brought up by 

 a paper by Mr. G. Shadbolt (President of the Society in 

 1856), who claimed to have "demonstrated beyond dis- 

 pute that no objective could have an aperture of any kind 

 in excess of 180° angular in air." The grounds on wh : ch 

 Mr. Shadbolt rested his demonstration are disposed of in 

 detail in the papers now published ; but with this aspect 

 of the matter we do not propose to deal, confining our- 

 selves to the more general consideration of the subject, 

 apart from any controversial matter. 



The proper definition of the aperture of a microscope- 

 objective was, for a long time, as is well known, a very 

 vexed one among microsccpists. The astronomer has 



always a ready definition for the telescope, the aperture 

 of which was simply estimated by the absolute diameter 

 of the object-glass. No such absolute measure is, how- 

 ever, pcssible in the case of the microscope-objective, as 

 the lenses of which it is composed vary in diameter within 

 considerable limits, and the larger lens is by no means 

 tbs larger aperture, as is readily seen by the comparison 

 of the large lenses of the low powers with the small 

 lenses of the high powers, which yet much exceed the 

 fcrmer in aperture. 



In consequence of this difficulty, the angle of the pencil, 

 as it emarates from the object, and prior to its transmis- 

 sion through the objective to the image, came to be very 

 generally considered as the proper measure of the aper- 

 ture of the objective. This was at a time when dry or 

 air objectives were generally known, immersion objectives 

 not having been brought into ordinary use. 



But even with air objectives the angle cf the radiant 

 pencil did not afford a true comparison, which could only 

 be made by the sines of the angles ; but when immersion 

 objectives were originated — that is, objectives in which 

 water or oil replaced the air in front of the objective — the 

 use of the angles became very misleading, for now three 

 angles might all have the same number of degrees and 

 yet denote very different values, according as they are in 

 air, water, or oil. 



It therefore became necessary to find a substitute for 

 the angles in the comparison of apertures; for although 

 it was no doubt possible to bear in mind that 82° in air 

 was less aperture than 82 in water, and the latter less 

 than 82° in oil, yet the use of the same figures inevitably 

 tended to produce confusion in the minds of microscopists 

 — so much so that it was stoutly maintained by one party 

 that the apertures in the three cases we have referred to 

 were identical because the angles were the same. 



A solution of the difficulty was discovered by Professor 

 Abbe, who pointed out that the true definition of aper- 

 ture (in its legitimate meaning of "opening") was ob- 

 tained when we compared the diameter of the pencil 

 emerging from the objective with the focal length of the 

 objective. 



« It will be desirable to explain somewhat more in detail 

 how this conclusion is arrived at — as given in Prof. Abbe's 

 paper. 



Taking in the first case a sinifleAzris microscope, the 

 number of rays admitted within one meridional plane of 

 the lens evidently increases as the diameter of the lens 

 (all other circumstances remaining the same), for in the 

 microscope we have at the back of the lens the same cir- 

 cumstances as are in front in the case of the telescope. 

 The larger or smaller number of emergent rays will, 

 therefore, be properly measured by the clear diameter; 

 and as no rays can emerge that have not first been 

 admitted, this must also give the measure of the admitted 

 rays. 



Suppose now that the focal lengths of the lenses com- 

 pared are not the same, — what then is the proper meas- 

 ure of the rays admitted ? 



If the two lenses have equal openings but different 

 focal lengths, they transmit the same number of rays to 

 equal areas of an image at a definite distance, because 

 they would admit the same number if an object were sub- 

 stituted for the image — that is, if the lens were used as a 

 telescope-objective. But as the focal lengths are differ- 

 ent the amplification of the images is different also, and 

 equal areas of these images correspond to different areas 

 ot the object from which the rays are collected. There- 

 tore, the higher-power lens, with the same' opening as the 

 lower power, will admit a greater number of rays in all 

 from the same object because it admits the same number 

 as the latter from a smaller portion of the object. Thus 

 if the focal lengths of the two lenses are as 2:1, and the 

 first amplifies N diameters, the second will amplify 2 N 

 with the same distance of the image, so that the rays 

 which are collected to a given field of 1 mm. diameter of 



