August 2, 1897.] 



KNOWLEDGE 



195 



contrast we must decrease the scale of the resultant 

 photograph one half ; to obtain nine times the contrast, 

 two-thirds ; and so on. It is therefore important to note 

 that the full advantages of using a small linear aperture 

 (and corresponding small focal length) will only be realized 

 when the objects photographed are large enough to stand 

 the necessary reduction in size without danger of losing 

 detail by reason of the finite size of the silver grains in the 

 photographic plate. This objection has, however, no weight 

 as regards the value of such small instruments in searching 

 for new nebulosities so faint as to have entirely escaped 

 previous notice. The important thing in such a case is to 

 first find the nebulosity at all ; the problem of observing 

 or photographing it in detail will come later. 



Another important conclusion follows at once from the 

 considerations of the preceding paragraph. For a gireii 

 absolute focal length (say thirty inches, as in the Willard 

 lens), and hence for a given scale on the photograph, the 

 e/ficienci) (considered in the same sense as before, either as 

 regards exposure time for a given detail, or detail obtain- 

 able with a given exposure time) of the ohjecth-e, other 

 things being equal, is entirely independent of its linear, and 

 therefire of its angular, aperture. In other words, a tele- 

 scope of one inch aperture and thirty inches focal length 

 would photograph a given nebula just as quickly and in 

 just as much detail as the Willard lens of six inches 

 aperture. This conclusion is at first sight sufliciently 

 startling, but it may at once be seen to be true by remem- 

 bering that while the intensity of the image diminishes as 

 the square of the aperture, the brightness of field diminishes 

 in the same proportion ; and the contmst between the two, 

 which has already been shown to be the principal if not 

 the only factor in determining the time of exposure and the 

 detail on the photograph, remains unaltered. Of course 

 this conclusion only holds, as has already been pointed out, 

 provided the development of the plate can be controlled so 

 as to bring out a given contrast, whatever be the absolute 

 intensity of action. In general, the less the absolute in- 

 tensity of the image and field, and hence the feebler the 

 action on the plate, the longer the development required, 

 and the greater the tendency to fog the plate in the 

 development itself. Besides, if pushed to the extreme, the 

 image might become so faint as to be incapable of affecting 

 the sensitive film at all. The results of Barnard, already 

 quoted, have shown that the development may be 

 controlled over times of exposure varying from one to 

 about forty, and corresponding to light action (intensity 

 X time) varying from one to twenty. It is a question for 

 actual experiment as to whether the process of develop- 

 ment cannot be controlled over a much wider range of light 

 action ; the results obtained by the careful development of 

 an ordinary negative, in which it is possible to obtain 

 at the same time detail in both the high lights and the 

 shadows, seeming to indicate that it could. We may at 

 least consider that the above comparison between the one- 

 inch and six-inch lens, in which the light action for 

 a given time of exposure will be in the ratio of one 

 to thirty-six, is justified by the results already obtained. 

 Granting that it is,* it is readily seen that the instrument 

 of smaller aperture (given focal length) has for the pur- 

 poses already considered the following advantages : — 



1. For a given form of objective the field can be made 

 flatter. 



2. For the same field, a single achromatic objective 

 might be used instead of the photographic doublet. 



* It will be noticed that this question does not arise in case the 

 angular aperture remains constant. For in that case the intensity of 

 the image also remains constant for all linear ajiertures. 



8. The whole instrument, including mounting, is very 

 much lighter and cheaper. 



i. The full resolving power of the instrument may be 

 photographically utilized.* 



If our purpose is to depict most clearly the object alone — 

 i.e., free from the stars around it and superposed upon it — 

 the instrument of small aperture has the further very 

 important advantage of showing in a given time of 

 exposure very many less stars than the one of larger 

 aperture would do.f For the intensity of a star image 

 varies as the fourth power of the aperture, while that of the 

 nebula or other extended object caries onlg as the square. 

 (To be continued.) 



THE METAMORPHOSIS OF A DRAGON FLY. 



By Kev. A. East. 



IF the lower jaw be a sign of strength of character, 

 the dragon fly (Libellula), in its larval state, must be 

 of an exceptionally resolute disposition, for the lower 

 jaw or mask is no less than three times as long as 

 the head, and is furnished at the end with a kind of 

 horny split lip and a pair of very serviceable nippers. 

 The lower jaw measures half an inch, and the whole head 

 a trifle over a third of this length. No ordinary arrange- 

 ment could possibly adapt such a jaw to its head, and if 

 anyone will try resting the chin in the palm of the hand, 

 and extending the thumb and little finger, he will have a 

 very fair notion of this terrible jaw— the thumb and little 

 finger representing the nippers of the jaw, and the whole 

 arm representing the jaw or mask (Fig. 1). This mask, 

 in fact, is jointed in the middle with a kind of elbow, and, 

 when not extended (Fig. 2) for the purpose of seizing prey, 

 extends downwards from the lingua, to which it is attached, 

 as far as the second pair of legs, and then up again to meet 

 the maxillie ; the edges of the mask, when so folded up, 

 fitting closely against each other, and forming altogether 

 what looks like an enormous chin (Fig. 2). 



The action of protruding and withdrawing the mask with 

 lightning rapidity is very much like that of the tongue 

 of the frog; but it must be confessed that our friend is not 

 so good a sportsman, for he as often as not aims short in 

 his eagerness and misses his mark, but the more phleg- 

 matic frog never misses. 



It is difficult at first to see how the larva progresses 

 through the water, for he has no feathered legs for 

 swimming, nor does he use his legs for this purpose. As a 

 rule he creeps slowly and stealthily along the bottom, or 

 rests immovable with the body pressed closely against an 

 upright stem, or stands on tip-toe with chin on high, 

 expectantly waiting for what fortune may send him ; but 

 he can, when alarmed, shoot through the water with the 

 speed and straightness of a torpedo-boat, and without any 



* I have already shown that in order to photographically utilize the 

 full resolving power of an objective, the ratio of aperture to focal 



length ( .) must be at least one-third -, where « is the diameter of the 



silver grain, ^ the wave-length (mean) of the light used. For 

 ordinary values of " and ^ this makes the ratio of ajjerturo to focal 

 length between one-thirtieth and one-fortieth. See papers, "Notes 

 on Astronomical Spectroscopes," Astrophysical Journal, Yol. III., 

 p. 189, March, 1896 ; and " On the Conditions of Maximum Efliciency 

 ia the Use of the Spectrograph," ibid.. Vol. III., p. 321, May, 1896. 

 + For this reason (as has also been pointed out by Harkness, 

 Astronomi/ and Astrophi/sics, Vol. XI., p. 648), photographs of 

 nebulae with different instruments may present a very different 

 appearance, owing to the possible great difference in the number of 

 superposed and surrounding stars. Too great caution cannot bo 

 exercised in guarding against hasty conclusions based on such com- 

 parisons. 



