224 PHILOSOPHICAL TRANSACTIONS. [aNNO 1685. 



often nimbly succeeding one another, and lasting till they lost themselves against 

 or under the thick scum. — 4. The motions of this odd liquor were not only 

 various, but frequently vortical ; to be satisfied of which, I sometimes put 

 short bits of straw, &c. on the discovered part of the surface of the liquor, by 

 which they were carried towards very distant, if not opposite, parts of the 

 vessel at the same time. But to make the vortical motion more evident, I 

 several times detached pieces of the thick scum from the rest of the body, and 

 had the pleasure to see them move both with a progressive motion in crooked 

 lines, and with a motion about their own middlemost parts. All this while the 

 liquor, whose parts were thus briskly moved, was actually cold, as to sense. — 

 5. To observe what the presence, or absence, of the free air would do to this 

 liquor ; I caused many spoonfuls of it, with some of the scum, to be put into 

 a cylindrical glass, which though large itself, had a neck belonging to it, that 

 was but about the size of one's thumb, that it might be well stopped with a 

 cork. But having by this means kept the free air from having a full and 

 immediate contact with the whole surface of the mixture, as it had when that 

 mixture lay in the wide-mouthed vessel ; I could not perceive the liquor to 

 move to and fro, even though the orifice of the neck were left open : whereas, 

 having at the same time poured some of the liquor into a very shallow and 

 wide-mouthed vessel, it moved rather more nimbly and variously than in the 

 great earthern pot, and showed many of those vivid and self-dilating circles 

 before-mentioned. And these, by the fineness of their colours, and the quick- 

 ness with which they succeeded each other, afforded a delightful spectacle as 

 long as I staid to observe it. — 6. Though the motions of the hitherto mentioned 

 liquor did not seem to be always equally brisk, yet they appeared to continue 

 manifest and various in some diversities of weather, as to cold and heat ; and 

 equally the same by candle light, as by day light. And thus the motion con- 

 tinued in the liquor as long as it was observed, which was at several times for 

 5 months after, when any longer observations were prevented by the vessel 

 being accidentally overturned, and the liquor wasted. 



On the Collection of Secants, and the true Division of the Meridians in the Sea- 

 Chart* By Dr. Wallis, F. R.S. N° 176, p. II93. 



An old inquiry, about the sum or aggregate of secants, having been lately 

 renewed, I have thought fit to trace it from its original : with such solution as 

 seems proper to it: beginning first with the general preparation; and then ap- 

 plying it to the particular case. 



:- * On this subject, see Vol, I. p. 69. Also Gregory's Exercitationes Creoraetiicae. 



