Focometry of Lens- Combinations. 7 9 



measurements, comes out to be over 500 cm. It has ceased 

 to be a small quantity. This is due to the very small 

 value of s. 



The value of HsHj is, in any case, given by the formula 



H 



•yi 



*-/(«-2-8)+^ 

 --»-'<S + 5'-'MS-2> 



Assuming that the error is 1 millimetre in the measure- 

 ments of #], yi, a? 2 > y%, an d taking the most unfavourable case, 

 it may be shown that for the above combination the greatest 

 possible error in H 2 H X is about 1*16 cm. This is a large 

 possible error for a quantity whose actual value is 2*43 cm., 

 and, to obtain a reasonably correct result, the errors in 

 measurement must be much less than a millimetre. But 

 this defect is not one which can be attributed only to the 

 method I proposed in my paper; it is inherent in all methods 

 in which the positions of H 2 and H x are deduced from the 

 observed positions of an object and its image. As I have 

 mentioned above, the special characteristic of the method is 

 the way in which the magnification is measured. Taking, 

 for instance, the case where the magnification is 



£l = ^ =0-20493. 



w 1 142 



and supposing an error of 1 millimetre to be made in the 

 measurement of both x x and y u and the most unfavourable 

 case to be taken, the error in the magnification will be 

 O'OOlo, or about 0*75 per cent. This accuracy could not be 

 attained by using transparent scales, when, as is frequently 

 the case, small images have to be dealt with. But the 

 measurement of d and two magnifications are all that is 

 required for the determination of the focal length. 



Additional Note. 



Since writing the above, I have been led to another method 

 of using the nodal slide to obtain the constants of a lens- 

 combination. It is clear that the method described in my 

 former paper, and further considered above, although quite 

 satisfactory as far as a determination of the focal length is 

 concerned, fails to give an accurate value of H2H4, because 

 small errors are multiplied by the numerical value of d the 



