226 Royal Society. 



coefficient of the square of the time in the expression for the secular 

 acceleration ; the time being, as usual, expressed in centuries. 



It will, of course, be necessary to carry the approximation much 

 further in order to obtain such a value of this coefficient as may be 

 employed with confidence in the calculation of ancient eclipses. 



In conclusion, the author states, that the existence of the new 

 terms in the expression of the moon's coordinates occurred to him 

 some time since, when he was engaged in thinking over a new me- 

 thod of treating the lunar theory, though he did not then perceive 

 their important bearing on the secular equation. His attention was 

 first directed to this subject while endeavouring to supply an omis- 

 sion in the Theory of the Moon given by Pontecoulant in his 

 ■ Theorie Analytique.' In this valuable work, the author, follow- 

 ing the example originally set by Sir J. Lubbock in his tracts on 

 the lunar theory, obtains directly the expressions for the moon's 

 coordinates in terms of the time, which are found in Plana's theory 

 by means of the reversion of series. With respect to the secular 

 acceleration of the mean motion, however, Pontecoulant unfor- 

 tunately adopts Plana's result without examination. On perform- 

 ing the calculation requisite to complete this part of the theory, 

 the author was surprised to find that the second term of the expres- 

 sion for the secular acceleration thus obtained, not only differed 

 totally in magnitude from the corresponding term given by Plana, 

 but was even of a contrary sign. His previous researches, however, 

 immediately led him to suspect what was the origin of this discord- 

 ance, and when both processes were corrected by taking into account 

 the new terms whose existence he had already recognized, he had 

 the satisfaction of finding a perfect agreement between the results. 



3. "On the frequent occurrence of Indigo in Human Urine, 

 and on its Chemical and Physiological Relations." By Arthur Hill 

 Hassall, M.D., Physician to the Royal Free Hospital, &c. 



The author was led to the investigations laid before the Society 

 in the above communication, by the following circumstances : — 



Some three or four years since, when examining urinary deposits 

 under the microscope, he frequently observed in the field of vision 

 particles of a deep blue colour; so often did this occur, that he 

 could not even then help suspecting that their presence was not ac- 

 cidental; however, no analysis of the blue colouring matter was 

 made at that time, and the circumstance was in a fair way of being 

 forgotten, until the recollection of it was revived by another oc- 

 currence. 



In June 1852, a sample of urine, freely exposed to the air in an 

 open vessel, was observed after four or five days' exposure, gradually 

 to change colour ; the pellicle or scum which had formed upon the 

 surface of the urine became first slate- coloured, and at length deep 

 blue, with here and there a rusty-red tint. The urine also under- 

 went at the same time some remarkable changes ; it became thick 

 and turbid, deep brown, greenish, bluish-green, and finally of a 

 faded yellowish-green colour ; a considerable sediment was found 

 at the bottom of the glass ; this was deep brown, intermixed with a 



