310 PHILOSOPHICAL TRANSACTIONS. [aNNO l66g. 



paribus, as radius is to the secant of the angle of obliquity; which is also to be 

 understood when the body falls, not perpendicularly, but obliquely on the sur- 

 face of the body which is struck, as well as when the directions of their motion 

 cross each other obliquely. This consideration, rightly applied to the fore- 

 going calculus, will determine what will be the celerity, the impetus, and the 

 direction of bodies thus impinging obliquely ; that is, with what impetus, with 

 what celerity, and towards what parts they will reflect from each other, which 

 impinge in this manner. And the ratio is the same between the gravity of 

 bodies descending obliquely, to that of such as fall perpendicularly; as I have 

 elsewhere demonstrated. 



13. If the striking bodies be not absolutely hard, as is above supposed, but 

 elastic, yielding to the stroke, and then restoring themselves to their figure 

 again by an equal force, the bodies, instead of moving on together, may in that 

 case recede from each other, and that more or less in proportion to the restor- 

 ing force; namely, if the impetus from this force exceed the progressive im- 

 petus. 



In accelerated and retarded motions, the impetus for every moment of time, 

 is that which answers to the acquired degree of velocity at each of these mo- 

 ments. When the motion is in a curve, its direction, in each point of the 

 curve, is the same as the direction of the tangent to that point. And if an ac- 

 celerated or retarded motion be made in a curve, as in the vibrations of a pen- 

 dulum, then the impetus for each point is to be estimated both according to 

 the degree of acceleration, and to the obliquity of the tangent at that point. 



The Law of Nature in the Collision of Bodies. By Dr. Christopher 

 IVren.^ Translated from the Latin. N' 43, p. 867- 



The proper and most natural velocities of bodies, are reciprocally propor- 

 tional to those bodies. Therefore the bodies R, S, having their proper velo- 



• Dr. (afterwards Sir) Christopher Wren, was one of the most extraordinary characters ever 

 known, possessing the extremely rare qualification of uniting both tlieory and practice in a very 

 eminent degree, being highly accomplished in tlie mathematical and philosophical sciences, as well 

 as in the theory and practice of architecture. He was born in l632, and had made great ad- 

 vances in the mathematics at l6 years of age. Being an Oxford scholar, he was one of those learned 

 men who first associated together there for their mutual improvement in natural and experimental 

 philosophy, and which at length produced the Royal Society, of which he was an original and, all 

 his life, one of the most distinguished members. In the Society he gradually rose to the highest 

 honours, and occupied the president's chair for two years, from 168O to l682. He made a multi- 

 tude of ingenious and usefiil communications to the Society, as well of writings as of machines and 

 instruments. He became successively professor of astronomy at Gresham college and at Oxford, 

 making great improvements in that science. Soon after the great fire of London in 1666, from his 



