VOL. LVII.] PHILOSOPHICAL TRANSACTIONS. 407 



cles will accordingly ascend or descend, by the attraction of each body, as if they 

 were attracted to one body; and they will be moved either in right lines or 

 curves, according as their motions are direct or oblique, in respect of the 

 compound centre of gravitation. For this centre is equivalent to the centre of 

 one body placed in the same point. The author then considers 2 cases: the 1st 

 case when the corpuscles situated in a right line cs between the bodies c and s, 

 are lighter than the ambient medium; there they will tend to the point a, fig. 2. 

 Case 2d. All the lighter corpuscles, arising from the body c, (those excepted 

 which are posited in the line of the syzygies Ps) ascend in curves, not much 

 unlike the dotted curve lines in fig. 5. 



Prob. 4. From what is said above to derive the principal phenomena of comets' 

 tails, on the theory of Newton. 



The author here extracts the account of the formation of comets' tails from 

 Newton's Principia, p. 311, 3d edition. From which he deduces the following 

 corollaries. 



CoroL 1. The tails of comets must be in a direction of^site to the sun.— 

 Carol. 1. The tails must dilate from the lower extremity to the higher. — Carol. 3. 

 And the tails must be longest in the vicinity of the sun. — CoroL 4. Hence those 

 comets have the longest tails that approach nearest the sun. 



Schol. From the law of centrifugal force, and what is said above, the figure of 

 a comet's tail may be determined as it were geometrically, being perhaps a kind 

 of paraboloid, after the manner as shown in fig. 6. Part of the tail may be 

 attracted by the planetary spheres, and become attached to them like an 

 atmosphere, or mixing with it. But the greater part may go oflfto vast distances 

 to cool other comets. 



Pbob. 5. To find, by observation, the limit of attraction between the sun and 

 a given comet. 



Observe the breadth of the comet, CA in fig. 6, estimated from the centre of 

 the comet, in the part opposite to the tail ; and hence, together with the comet's 

 distance, from the sun and from the earth, which are given from the Newtonian 

 theory of gravity, will be obtained the point a, in figs. 2, 5, 6, either accurately, 

 or at least nearly. Hence, by cor. 2, prob. 1 , the whole limit will be given. 



CoroL 1. The breadth of the coma in the part next the sun, is as the comet's 

 distance from the sun. — CoroL 2. Hence the quantity of matter in the comet 

 becomes known. For since sc and ca are given, their difference sa is given; 

 and hence the ratio sa to ac, as also the duplicate ratio are given; which, by the 

 solution of prob. 1, is also the ratio of the matter in the sun to the matter in 

 the comet. — CoroL 3. Hence, and from the observed diameter, there will be also 

 known the density of the comet. For the density of a sphere is as its matter 

 directly, and cube of its diameter inversely. An example of which Mr. W. gives 



