350 PHILOSOPHICAL TRANSACTIONS. [aNNO 1687. 



thought a dispute of this nature could have lasted so long. To come therefore 

 to the point, where he says that this engine may well succeed without alteration, 

 because he has tried with liquors put into bellows immersed in water : I again 

 say that I grant him the truth of the experiments, but deny the consequences 

 he would draw from them. I have already given the reasons of my dissent, 

 which this gentleman is not pleased to understand. 



An Occultation of Saturn by the Moon, March \Q, 1687, observed at Totteridge, 

 near London, by Mr. Edto. Haines, F.R.S. N° 186, p. 268. 

 At l*" 18"" 0* The moon's limb touched the western ansa of Saturn. 



1 18 30 Immersion of Saturn's centre a little below Palus Maraeotis. 

 1190 Saturn is now quite hid. 



On the Measure of the Airs Resistance to Bodies moved in it. By John fVallis, 

 S.T.D. et R.S.S. N° 186, p. 269. 



1. In order to compute the air's resistance to all projectiles, this lemma is to 

 be premised, viz. that, supposing other things equal, the resistance is propor- 

 tional to the celerity. For in a double celerity, there is to be removed, in the 

 same time, twice as much air, which is a double impediment ; in a triple time, 

 thrice as much ; and so in other proportions.* 



2. Suppose then the force impressed, and consequently the celerity, if there 

 were no resistance, as 1 ; the resistance as r ; and therefore the effective force, 

 at the first moment, is to be reputed as 1 — r; that is, so much as the force 

 impressed exceeds the impediment or resistance. — 3. Let it be, as 1— rto 1, 



* This first postulate, being very erroneous, must vitiate the whole future calculation, the resist- 

 ance of a medium being in a much higher proportion than simply that of the celerities. Though 

 this might not be generally known at the time, when this article was written by Dr. Wallis ; it has 

 however been known, since the first publication of Newton's Principia, that the ratio of the resist- 

 ances must be at least that of the squares of the velocities; and the reason is manifest, viz. that in 

 the same time there is struck or removed a proportional quantity or number of particles of the fluid, 

 and each particle is also struck with a like proportional force. Such then is the case when the fluid is 

 void of tenacity or viscocity, and its particles perfectly independent of each other. But that is not 

 the case in any fluids, and particularly in the atmospherical medium, the particles of which are pressed 

 together by a considerable force ; and where any body, moving through it, has not only to remove 

 the particles in its way, and that are struck, upon which the law of the duplicate ratio of the velo- 

 city depends, but also to overcome the weight of the medium by which its particles are compressed 

 together, if not also some degree of tenacity and friction. On these accounts then another force of 

 resistance is added to the former, or to that which is proportional to the square of the velocity, and 

 which additional force does not respect the same law as the former ; but is probably to be expounded 

 by some compound function of the velocity, the discovery of which must chiefly depend on proper 

 experiment*. 



