., I ,; Major L. Darwin. On the Method of 



object without applying a correction, so as to make the result equiva- 

 lent to an observation on a distant object, and that this correction 

 could be made by multiplying the measurement recorded by /,/ . 

 For the same reason, a'V must be multiplied by/// in this instance 

 to obtain the true value of <r. Thus 



/ CCOS0 _//*\ COS0 



- j>* ~ 7 " (f /20 v/(C. I. No. of stop) 



In considering the combined effect of astigmatism and curvature 

 of the field, it should be remembered that it has been assumed that 

 the photographer would focus his plate in the position PH, as shown 

 in fig. 21, and that the principal focal surface, PH, was a plane ; this 

 is, however, never the case. If the focal surface is curved, it is evident 

 that the best general focus is obtained by observing the image of an 

 object at a position about half way between P and C on fig. 21. In 

 fig. 22, which is part of fig. 21 enlarged, let KL be the position of the 

 plate when f ocussed in this manner, the distance between KL and PH 

 being, therefore, due to the curvature of the field. Through I' draw 

 b'g parallel to F 2 a' ; then, by comparing this figure with fig. 6, it will 

 be seen that eg in both cases represents the diameter of the disc of 

 diffusion due to the curvature of the field. Since, in fig. 22, fe repre- 

 sents the longest diameter of the ellipse of diffusion due to the combined 

 effects of curvature and astigmatism, and since it is equal to the sum 

 of a'b' and ge, the diameters of discs of diffusion due to these two 

 causes taken separately, it will not be unfair to look upon the evil effect 

 of astigmatism as a simple addition to the evil effects of curvature. In 

 using the table given on p. 427 in the manner described on p. 443, it 

 would therefore be better if we subtracted the diameter of the disc 

 of diffusion due to astigmatism from the diameter of the maximum 

 disc of diffusion -which is to be tolerated, and used the difference as 

 the o in the table ; we should thus get a more correct notion of the 

 size of the stop that could be used to obtain any required standard of 

 definition. The objection to this use of the table is that the astig- 

 matism, that is, the distance FiFa, varies to a certain extent with the 

 size of the stop used during the observation. 



In the above discussion it has been assumed that the focal lines 

 are sharply defined. If this is not the case the reasoning here 

 given is defective, because the distance separating the focal lines 

 is then no indication of the amount of diffusion. An exaggerated 

 idea of the amount of diffusion due to astigmatism may thus be 

 obtained by the above method of calculation, for the disc may have 

 only half the diameter thus found. Therefore, unless the focal lines 

 are sharp that is, unless the image of a point appears as a very 

 thin line, first in one direction and then in another no entry 

 made in the certificate. 



is 



