Feb. 3, 1887] 



NA TURE 



325 



been had the whole aperture been employed. The im- 

 provement in definition, then, due to the expanding shutter 

 acting as a stop is given by the expression — 



R- (>_ Z, 

 R ' L-Ly 



The curve below shows the improvement in definition 

 calculated from this expression, the abscissae being pro- 

 portional to-„. It has a maximum value of r; nearly 

 A 



when is about '8, but falls away rapidly on either side 



of this value. 



Thus when a stop of '8 times the full aperture is suffi- 

 cient to secure definition, the square expanding aperture 

 may be said to answer the purpose. But a better result 

 with less exposure could be obtained by the use of shutters 

 of type (4) with a separate stop of the right size ; for it 

 may be shown that with the square expanding aperture 

 the amount of light admitted while more than eight tenths 

 open is not more than 8 per cent, of the whole, and not more 

 than S per cent, of the light would be lost if a 8 stop 

 were used. But a shutter of type (4) admits nearly 40 per 

 cent more light than the expanding square, so that there 

 would be a gain of something more than 30 per cent, in 

 light by using it. 



This is rather understating the case, for the efficiency of 

 a shutter as defined above is increased by the use of a stop, 



the whole aperture of the stop being uncovered for a finite 

 time while the whole aperture of the lens is only uncovered 

 for an instant. 



To see what effect an unbalanced shutter has on the 

 steadiness of the camera and definition of the image, the 

 mass of the unbalanced moving part of the shutter, the 

 mass of the camera, its period of vibration on its support, 

 and its radius of gyration must be taken into account, as 

 well as the time of exposure. The exact investigation of 

 the motion is very- much li! e that given by Helmholtz of 

 the motion of a pianoforte-wire when struck by a hammer. 

 But without entering into mathematical details it is easy 

 to approximate to the required result in a large group of 

 cases, viz. where the time of exposure is short compared 

 with the natural period of the camera on its supports. This 

 will apply to cameras held in the hand for all exposures 

 which could be effectively used with such a support, and 

 in most other cases when the exposure is less than a fiftieth 

 of a second. 



The camera and shutter may now be compared to a fly- 

 wheel free to turn with a small load on its rim, which, by 

 some mechanism on the wheel, can be made to vary its 

 position. If the fly-wheel is at rest to begin with, the 

 motion of the system when the load is caused to move is 



given by the condition that the moment of momentum of 

 the fly-wheel and load together is nothing, which implies 

 that 



velocity of rim of wheel mass of load 

 velocity of load mass of rim 



Suppose that the camera is replaced by a fly-wheel 

 which has the same moment of inertia and a radius equal 

 to the distance of the centre of oscillation of the camera 

 on its support from the shutter, the mass of the equivalent 

 fly-wheel will be less than that of the camera on account 

 of its distribution, so that the angular motion of the 

 camera about the centre of oscillation will be somewhat 

 greater than 



mass of shutter X travel of shutter 



mass of camera X radius of oscillation 



As an example, suppose the ratio of the masses to be 

 i/ioo and the travel of the shutter one inch, if the radius 

 of oscillation lies between one foot and six inches, the 

 augular movement of the camera will be between three 

 and six minutes of arc, or from one-tenth to one-fifth of 

 the apparent diameter of the sun or moon. 



In the case of drop-shutters acting by gravity, the 

 camera begins to move upwards at the moment the 

 shutter is released, and will go on moving upwards until 

 it is as much above the new position of equilibrim which 

 it would assume on the removal of the weight of the 

 shutter as it was below it when the latter was attached. 

 So that if the time of exposure be half as long as the 

 natural period of the camera, the whole extent of the 

 angular motion will show on the sensitive plate. 



1 have recently made some experiments to see how, 

 when the camera was held in the hand, the accidental 

 motions of the support compared with those due to the 

 action of the shutter. It would, 1 think, at first sight be sup- 

 posed that the former were the more important of the two. 

 The experiments were made by weighting a piece of 

 looking-glass to represent the camera, and then, holding 

 it as the camera would be held, reflecting the sun on a dis- 

 tant screen and noting thedisplacement of the patch of light. 

 I found it in my own case to be continual, vibrating at a 

 rate of something like four per second, through an angle 

 of about one in six hundred to one in eight hundred, im- 

 plying, of course, half this motion in the camera ; that is, 

 from three to two minutes of arc. The time of the whole 

 vibration being about one-fourth of a second, if the time 

 of exposure was as much as one-eighth of a second the 

 whole of this would show on the plate, but for exposures 

 of one-twentieth of a second the loss of definition from 

 this source would hardly be appreciable. The weight of 

 the camera in this case was small — little more than a 

 pound — and so unfavourable for steadiness. 



The general conclusions to be gathered from the 'fore- 

 goingremarks are : ( 1 ) That there is room forgreat improve- 

 ment in the photographic efficiency of shutters ; (2) that all 

 the ordinary kinds shake the camera wlien the exposure is 

 rapid ; but that (3) for comparatively long exposures, say 

 more than one-tenth of a second, almost any kind of 

 shutter will do when the camera is mounted on a stand ; 

 and (4) that for cameras which are to be held in the hand, 

 in order to secure fine definition the shutters must be 

 dynamically balanced or exceedingly light. 



A. Mallock 



ON SOME PHENOMENA CONNECTED WITH 

 THE FREEZING OF AERA TED WA TER 



TH E elimination in the gaseous form, on the freezing of 

 liquids, of the air and gases held in solution pre- 

 sents some features in its process which may be worth 

 recording. 



Bubbles in ice are familiar ; but their arrangement and 

 progressive development in the process of freezing-over 



