232 Royal Society : — 



The desideratum was, when changing the focus, to increase the 

 power of the double lens for the planes the most distant and to re- 

 duce it for the nearest planes. At first this seemed to be an impos- 

 sibility. But in considering the subject attentively I was suddenly 

 struck with the fact that, the power of any double combination of 

 lenses being proportionate to the distance which separates the two 

 lenses, greater when they are more separated, and smaller when they 

 are less separated, it was possible to alter the power of the combina- 

 tion by changing the distance between the two lenses. 



Therefore, if, instead of moving the whole tube containing the two 

 lenses, we move only the back lens nearer the plate, when we want 

 to focus for more distant planes, we increase at the same time the 

 power of the double combination, and consequently the size of the 

 image ; and if we move the lens further from the plate, when we want 

 to focus for the nearest planes, in doing so, by reducing the separa- 

 tion of the two lenses, we reduce the power of the combination, 

 and consequently also the size of the image. This is a most fortunate 

 property ; for by this means it is possible not only to equalize the 

 definition of the various planes, but at the same time to equalize 

 the size of their images, and consequently to avoid the exaggeration 

 of perspective by which the nearest planes are increased, and the 

 furthest disproportionately reduced, a defect which is so detrimental 

 to the appearance of large photographs. 



I submitted my plan to M. Voigtlander, the celebrated optician, 

 and I had the satisfaction to meet with his entire approbation. He 

 found that I had solved the problem in a way which was perfectly 

 correct and sufficient in practice. But wishing to investigate the 

 question from a higher mathematical point of view, and being unable 

 from indisposition to go himself into the subject, he charged his 

 step -son, Dr. Sommer, Professor of Mathematics at the Carolinian 

 College of Brunswick, well versed in all the questions of optical pho- 

 tography, to calculate the result of the gradual increase and reduc- 

 tion of the power of the double combination, in conjunction with 

 the alteration of focus. Dr. Sommer entered thoroughly into the 

 subject, and soon sent me a series of elaborate formulae, showing 

 that for all practical purposes in photography the movement of 

 one of the two lenses, as I had proposed, fulfilled the object I 

 had in view : still he found that a more scientific consideration of 

 the subject called for a modification in my plan ; which was that, 

 instead of moving only one of the lenses, the same degree of their 

 separation should be imparted by moving the two lenses in contrary 

 directions from the fixed centre of the combination, and in different 

 proportions, according to the distance of the object. These differ- 

 ential proportions were indicated in a table calculated by Dr. Sommer 

 which he sent me. 



This presented another difficult and unexpected problem, the 

 solution of which was indeed most perplexing. But I did not like 

 that it should be said that my plan was not completely in accordance 

 with the mathematical laws of optics ; and I set to work at finding a 

 mechanical means by which I could avail myself of the scientific cal- 

 culations of Dr. Sommer. 



