VOL. LXIX.J PHILOSOPHICAL TRANSACTIONS. 501 



4th 21, at the 5th 23. But who does not easily perceive that this progression 

 is contrary to theory and experience? For the depth acquired by every stroke 

 decreases continually, till at length the pile, after continued strokes, ceases to 

 move. Which happens when the cohesion of the ground and the friction 

 exceed the force of the percussion. 



To determine the Greatest Depth, to ivhich a Given Pile can be driven by a 

 Given Machine. — Let the altitude the weight falls at the 1st stroke be = a; the 

 depth sunk by the 1st stroke = d; after many strokes, when the pile no longer 

 moves, let the pile sink only by the small part m ; after which the strokes have 

 no more effect; the total depth acquired = .r ; and the height the weight 

 then descends = a -^^ x. Hence d:m = y: ?— ^, which gives x = — — j^. So, 

 i{ d = 4 inches; 7n = ^ of an inch; a = 36 inches; their theorem gives for 

 the greatest depth x = -jrzr~(i ~ ~ ^^'^ inches: which quantity ought to come 



To . , . . 



out negative, since it is opposite to the altitude, which is taken as positive.* 



XIII. Of an Iconantidiplic Telescope, invented by Mr. Jeaurat, of the Academy 

 of Sciences of Paris. From the French, p. 130. 



This telescope is called the iconantidiptic heliometer, because it produces 2 

 images of the objects, the one in a direct position, and the other reversed. 

 These 2 images, of opposite situation to each other, are exactly of the same 

 size, and produce the effect of showing the stars as entering at once both on 

 the right and left sides of the telescope. The first coincidence of the 2 images 

 on the side of each other gives the passage of the first limb; the exact coin- 

 cidence of the 2 images on each other gives the passage of the star's centre; and 

 the last coincidence of the 2 images at the side of each other gives the passage 

 of the 2d edge: whence it follows, that we not only observe as usual the passage 

 of the 2 sides of a star's disc, but also the direct passage of the star's centre: an 

 observation which could not before be made in a direct manner. Besides, it may 

 be observed, that this invention obviates the difficulty of illuminating the 

 threads of the telescope in observing very small stars, for in this construction 

 there is no occasion ro see the threads. 



The following is the construction of this iconantidiptic telescope, which 

 appears to be proper for observations made in the plane of the meridian. 



* It appears that some mistakes have been committed in the above paper on pile-driving. As 1st, 

 by estimating the friction by (rf + 6) 6 instead oi {d + k b) b, where d denotes the depth sunk by the 

 pile after any number of strokes, and b the depth sunk at the next following stroke. And again in 

 bringing out an absurd conclusion at the last, where, his theorem brings out a negative quantity, 

 instead of a positive one. 



