372 PROCEEDINGS OF THE AMERICAN ACADEMY 



weight will act when suffered to fall through some sensible space, and 

 certain facts are adduced at page 178 to sustain this view. I shall not 

 stop here to show the fallacies of these supposed analogies, but appeal 

 first to the direct teaching of a simple experiment. Take, then, a little 

 spring balance, such as is used at some of the post-oifices for weighing 

 letters, and which consists of a little pedestal and column, like a candle- 

 stick, which contains a spiral spring, and over the top is the pan, to 

 hold the thing to be weighed. Now take any weight that will carry 

 the pan just down to the top of the column when slowly applied. Half 

 of this weight will carry the pan half-way down, if applied in the same 

 way, but if you add to this half weight a small quantity, just enough 

 to overcome the friction of the acting parts, and hold this upon the pan 

 when at its full height, so as just to touch its surface, and then release 

 it suddenly, the pan will descend to the top of the socket, or will mark 

 twice the weight that it actually possesses. The cause of this must be 

 so apparent to any one well acquainted with the laws of moving forces 

 that I shall not stop to explain it here. Yet the action of the weight 

 here is perfectly analogous to the action of Captain Rodman's instru- 

 ment, or that part of it which is moved by the powder to make the 

 impression, namely, the indenting tool, the block upon which it rests, 

 and the little piston which receives the force of the powder. The 

 mass of matter of which these are constituted is Jired against, or into, 

 the copper, as much as the ball is fired out of the muzzle of the gun. 

 The analogy with the experiment of the spring balance is this : the 

 indenting tool and its appendages are pressed forward by the gun- 

 powder. The weight upon the spring balance is pressed down by grav- 

 itation. These pressures change the inertia in both cases into living 

 force. This living force accumulates during the motion, from the grav- 

 itation in the weight, and the powder pressure in the gun, being, 

 through the first half of the space, twice as great as the mean force of 

 the resistance of the spring in the one case, and the copper in the 

 other ; and this accumulation is displayed in overcoming the resistance 

 during a space equal to that first passed over. 



We see, then, from the analogy of the weight falling upon a spring 

 balance, that Captain Rodman's instrument ought to display and regis- 

 ter double the force which he applies to it ; even if it acts as freely and 

 undisturbedly as a spring balance, it cannot make less than a double 

 register. But we shall see by and by that this is but a small part of 

 the actual error ; and yet Captain Rodman takes its register as true to 



