OF ARTS AND SCIENCES. 487 



In the second series of lines the slots are supposed to be lengthened 

 out by the insertion of a square between the terminations, so that the 

 length down the middle is now twice the breadth. The only change 

 of importance noticed is, that, while before the full aperture was 

 exposed for an instant only, all the time being occupied in opening 

 and closing the shutter, that now the full opening is exposed for an 

 appreciable interval, equal to one third of the total time consumed. 

 By inserting a rectangle longitudinally, instead of the square, still better 

 results would be obtained. In the third series, two slots similar to 

 those used in the first are supposed to slide past one another in oppo- 

 site directions. If both are circles, as in the first case, the centre of 

 the aperture between the lenses receives the same exposure as it would 

 if there were only one sliding slot, but the top, bottom, and sides 

 receive only instantaneous exposures. The square slots give a better 

 result, and the third form doubles the exposure at the sides. In the 

 fourth series both slots are supposed to be of similar shape to those 

 used in the second set, and here we find two instances where the full 

 aperture is exposed for half the total time of exposure. 



Now since all parts of the aperture between the lenses are of prac- 

 tically equal value, it is evident that the best-shaped slot is that one 

 which lets through the maximum amount of light per unit length of 

 total exposure. That will be the slot which gives the best representa- 

 tion of the dark object, with the least motion of the bright one. The 

 following formula; represent the amounts of light transmitted by each 

 form of aperture. The third column gives the numerical coefficients 

 of r% and the fourth the amount of light transmitted for equal times of 

 exposure. The last figure gives the amount of light transmitted per 

 unit length by the theoretically perfect slot, i. e. one of infinite length, 

 moving with infinite velocity. The fifth column gives the percentages 

 of light transmitted by the various apertures, in terms of the theo- 

 retically perfect slot. In comparing the amounts of light transmitted 

 by sliding shutters and by hand exposures, the duration of the former 

 must always be multiplied by the figure in this column corresponding 

 to the form of aperture employed. 



