C. I?. WARRINO. 183 



The case of an over-balanced instrument is no ex- 

 ception, because there the fall changes its sign, and so 

 does the gyration. But, in the case considered under 

 nutation, the sign of the applied force is not changed, yet 

 the instrument rises, and the precession continues in 

 the same direction as before. 



There is, however, no real contradiction. Descent 

 here precedes the gyration, and the ascent is due to the 

 momentum acquired ; for, although gyroscopic bodies 

 in one of our experiments, appeared to have no mo- 

 mentum, yet it really was there, and showed itself in 

 what I styled conical rotation, causing the instrument 

 to rise from the point at which the weight was dropped 

 oif, to a height approximately as great as that from 

 which it had descended. In the present case, the weight 

 being removed gradually, the instrument rises gradually, 

 and, at the same time, is sent forward by the remaining 

 weight. 



To see how this is, suppose we have our instrument 

 (fig. 2.), well balanced with the wheel in rapid motion. 

 There will be no descent and no lateral movement. Now 

 attach a weight, say one ounce. The instrument will at 

 once start off with a lateral velocity, a ; then attach an- 

 other ounce, the increase of velocity, we will call b ; then 

 for another ounce, c; and for a fourth, d, etc., etc. 

 The velocity will be, after say four ounces have been at- 

 tached, a+b+c+d. If now, the last ounce be dropped off, 

 the instrument will at the instant following, have a ve- 

 locity in inches per second greater than would be pro- 

 duced by the three remaining ounces alone. The effect 

 is exactly the same as if the free end was accelerated d 

 inches by pulling a string ; hence, as shown when dem- 

 onstrating the ''first law," the instrument will rise in 

 proportion to that acceleration. The same is true for 

 the next ounce and so on. 



167 



