Bache.] 1"^ t^Iay 4, 



popular instruction. I do not, of course, presume to instruct mem- 

 bers of this Society as to these laws, with which they are conver- 

 sant, but the higher instruction is like head of water, whence the 

 water flows to and filters through lower levels. Besides, beyond 

 tlie mere restatement here of the laws to which I refer, lies matter 

 with which I think that not even the majority of the members of 

 this Society are conversant. These reasons form, in sum, my expla- 

 nation for introducing this particular subject to the Society. 



The momentum, as you are aware, with which a body, fall- 

 ing freely near the surface of the earth, strikes, varies with the 

 latitude, or otherwise expressed, with the distance of a given place 

 from the centre of the earth, which, owing to the configuration of 

 the earth, corresponds with the latitude. But, for general pur- 

 poses, and quite sufficiently precise for this, the distance, in the 

 first second, which a free body falls, near the surface of the earth, 

 from a state of rest, is accepted as 16.1 feet, and the velocity which 

 it has acquired by the end of that space and at the termination of 

 that time, as twice 16. i feet, or 32.2 feet in that second. 



The diagram on the blackboard illustrates clearly the effect upon 

 a body moving for one second under the influence of gravity. To 

 understand, then, what follows, it will only be necessary to observe, 

 by referring to the diagram, that the successive spaces traveled by 

 the falling mass represent the squares of intervals, whether of space 

 or time, and also that, although the maximum space traversed in a 

 first second of fall is only 16.1 feet, yet that, correspondingly with the 

 smaller spaces and the inclusive one (all squares of space or time), 

 the acquired velocity doubles continuously, being, instead of 16.1 

 feet, 32.2 feet in the second, by the time that it has reached the end 

 of the first second of fall. The diagram fully exhibits the law of 

 both relative spaces and relative times concerned in the phenome- 

 non. If the first unit of horizontal space on the diagram, one- 

 fourth, be taken as a unit of time, then its square will represent the 

 value of the corresponding distance of fall. This is i foot, with 

 acquired velocity of 8 feet. For successive units of time, — if a mass 

 falls in I second, as it does, 16. i feet, then in 2 seconds it falls 16. i 

 feet multiplied by 2 squared. It falls in 3 seconds 16. i feet multi- 

 plied by 3 squared, and in 4 seconds 16. i feet multiplied by 4 

 squared, and so forth. 



Could a soap-bubble move with the velocity of the swiftest can- 

 non-ball, it would injure nothing that it might strike, while the 



