256 ROCHESTER ACADEMY OF SCIENCE. [April 9, 



Professor A. L. leaker, by means of a diagram, illustrated and 

 explained the perturbed path of the Lexell-Brooks comet, showing- 

 the original 6 year orbit of 1770 and 1775, which in 1779 was by the 

 proximity of Jupiter changed into a 34 year orbit which was again, 

 in the year 1846, changed by the attraction of Saturn into a 47 

 year orbit. This was again, in the year 1886, changed by renewed 

 proximity of Jupiter into a 7 year orbit which brought the comet 

 once more within sight of the earth, the comet having been lost 

 in 1779 and recognized in 1889 after much laborious calculation 

 as the long lost comet of 1770 and 1775. 



April 9, 1894. 

 stated meeting. 



The President, Professor H. L. Fairchild, in the chair. 



A small audience present. , 



The Secretary read the following paper : 



CIRCULAR INVERSION AND ITS BEARING ON THE 



PEAUCELLIER CELL AND THE 



STRAIGHT LINE. 



By Arthur L. Baker. 



If you will throw your memories back to the days of your 

 geometry, you will recall a theorem which runs in thiswise : — If from 

 a fixed point without a circle a secant is drawn, the product of the 

 secant and its external segment is constant in whatever direction the 

 secant is drawn, and is equal to the square of the tangent from the 

 point to the circle. 



Like most of the theorems of elementary mathematics this is a 

 degraded case of a far more general theorem which runs as follows : — 

 For every point on one side of a central curve called the curve of 

 inversion, there is a corresponding point on the other side such that 

 the product of the distances of the two points from the centre is 

 equal to the square of the radius vector which passes through the two- 

 points, and to every curve traced by the one point corresponds a 

 curve traced by the other point, called the inverse of the traced curve. 



We will consider only the special cases of the curve of inversion 



