VOL. XXXVn.] PHILOSOPHICAL TRANSACTIONS. 501 



purulent, thick, most intolerably fetid, reddish-brown matter, very acrid ; for 

 no sooner was it exposed a little to the open air, than it fermented exceedingly. 

 The patient had drained off the thinner part, the last week of his life, by violent 

 vomiting and purging, to 30 or 40 stools a day, and as many vomitings. It was 

 thrown into the duodenum by the ductus choledochus communis, and there 

 pumped up and tiirown out, both by its sharpness and stimulation. All the 

 upper part of the liver, to about an inch below the gall-bladder, was sound. 

 The tumour had so compressed the right kidney, that it was emaciated away to 

 less than the glandula renalis. 



A Proposal of a Method for finding the Longitude at Sea ivithin a Degree, or 20 

 Leagues. By Dr. Halley, Jstr. Reg. Vice Pres. R. S. W A1\, p. 185. 



Upwards of 20 years before. Dr. Halley added an appendix to the 2d edition 

 of Mr. Street's Caroline tables, containing a set of observations he had made in 

 l683 and l684, for ascertaining the moon's motion; giving a specimen of what 

 he thought at that time might be the only practicable method of attaining the 

 longitude at sea. What he published then, was to tiiis effect. 



" The advantages of the art of finding the longitude at sea, are too evident 

 to need any arguments to prove them : and having by my own experience found 

 the impracticability of all other methods proposed for that purpose, but that 

 derived from a perfect knowledge of the moon's motion ; I was ambitious, if 

 possible, to overcome the difficulties that attend the discovery of it. 



" And first, I found it only needed a little practice to be able to manage a 5 

 or 6-foot telescope, capable of showing the appulses or occultations of the fixed 

 stars by the moon, on ship-board in moderate weather; especially in the first 

 and last quarters of the moon's age, when her weaker light does not so much 

 efface that of the stars. Whereas the eclipses of Jupiter's satellites, how pro- 

 per soever for geographical purposes, were absolutely unfit at sea, as requiring 

 telescopes of a greater length than can well be directed in the rolling motion of 

 a ship in the ocean. 



" Now the motion of the moon being so swift, as to afford us scarcely ever 

 less than 2 minutes for each degree of longitude, and sometimes 2 and \ ; it is 

 evident, that could we perfectly predict the true time of the appulse or occulta- 

 tion of a fixed star, in any known meridian, we might, by comparing it with 

 the time observed on board a ship at sea, conclude safely how much the ship is 

 to the eastward or westward of the meridian of our calculus. 



" But after much examination, and carefully collating the Caroline tables of 

 Mr. T. Street, though generally better than those that went before him, as also 



