4't6 Prof. De Morgan on the Additions made to the 



secoiidar}' rainbows will be formed; inverted, of course, but in 

 their true positions with regard to the direct solar image, and 

 the horizon or edge of the basin, and in this case no i-olalion 

 is necessary. 



In these experiments, a single globule or crystal turns the 

 various coloured rays into certain definite directions, which 

 are obviously exactly opposite to those directions in which 

 such rays will arv'wQfrom an innumerable assemblage of such 

 drops or crystals (illuminated hy parallel sunbeams) towards 

 any single point, such as the spectator's eye. The experiments 

 therefore produce an exact inversion of all those figures that 

 would be seen by an eye |)laced in or near such an assemblage, 

 and explain most clearly the production of the rainbow by an 

 atmosphere loaded with watery globules ; — of the halo when it 

 is charged with icy prisms turned in all directions; — and of 

 the various kinds oi purhelio7i when all the prisms have their 

 axes in one direction. 



LXI. On the Additions made to the Second Edition of the 

 Commercium Epistolicum. By Prof. Dk Morgan*. 



THE Commercitim Epistolicum is the work which contains 

 the final elaboration of the charge made by iNlewton's 

 friends in England against Leibnitz, in which the latter is 

 accused in many places of taking h\s diff'ere?itial Calctdus from 

 the JF7?mo7is of the former. It is an ex-parte-\ statement to 

 which no answer was returned, and which was said by its par- 

 tizans, and by Newton himself, to be unanswerable. The first 

 edition, then, the one which Leibnitz had the option of seeing 

 and answering, is a document in the case which no editor 

 could possess a right to alter, whether by addition or diminu- 

 tion. That any variations, inserted in a reprint, whether for 

 explanation or reinforcement, ought to have been separated and 

 distinctly described as new, is too obvious to need proof. As 

 the laws of literary honour are now understood, any alteration 

 made to pass as part of the original publication, would be 

 looked upon as fraudulent if it served a purpose, and as most 



* Communicated by the Author. 



t It bears so much the form of the report of a judicial investigation and 

 finding, that most subsequent writers have considered it as such. I believe I 

 have sufficiently shown that it was never intended for anything but an cx- 

 parte statement. See the Philosophical Transactions for 1846, p. 107, and 

 the life of Newton in Knight's British Worthies, The Committee, had it 

 been a jury, would now be considered as having been packed : but as 

 composed of agents and counsel, it was a very different thing. Nevertheless 

 there was some unfairness in the judicial form of the report with which the 

 publication ends. 



