844 



SCIENCE 



[N. S. Vol. XXXIV. No. 885 



looked upon as a standard in this class of 

 literature. Konops 



HOW A FALLING CAT TURNS OVER IN THE AIH 



To THE Editor of Science : In a lecture on 

 the gyrostat before the Washington Society 

 of Engineers, I gave a valid explanation of 

 how a cat is able to light on his feet when he 

 is dropped back downwards. After the lecture 

 Professor J. F. Hayford was kind enough to 

 call my attention to what is no doubt the 

 actual character of this cat performance, and 

 I give a statement of it herewith for the 

 readers of Science. However, I prefer the 

 idea I had formerly of the cat performance, 

 because I am able to do it myself, not indeed 

 while falling through the air but while stand- 

 ing on a pivoted stool. It is my impression 

 that the idea I had formerly is the generally 

 accepted idea of the cat performance, but it is 

 difficult to explain, although easy to perform. 



The curved figure in the accompanying 

 sketch is a conventionalized cat which is let 

 fall back downwards, and the question is how 

 can a cat (not so highly conventionalized) 

 turn over and light on its feet. 



JL- 



There are two simple types of motion of the 

 cat's body which give spin momentum around 

 the axis AB, namely, (a) a rotation around 

 AB as an axis of the cat's body as a rigid 

 structure, and (b) a sort of squirming motion 

 in which each part of the cat's body rotates 

 aboiit the curved line CD. 



The amount of spin momentum due to a spin 

 velocity a of the first kind is Ka, and the 

 amount of spin momentum due to a squirming 

 velocity h of the second kind is Teh; and the 



factor h^ is always less than the factor K when 

 the cat's body is curved. 



Now suppose the falling cat to exert the 

 muscular action necessary to produce and 

 maintain a squirming velocity h; then the cat's 

 body will simultaneously be set spinning in 

 the first mode at spin velocity a such that 



Ka + fc6 = 

 or 



h——{K/'k)a, 



because no spin momentum can be produced 

 by forces inside the cat. Therefore a and & 

 are opposite in sign and & is greater than a. 

 Suppose, for example that h is twice as great 

 as a; then while the eat squirms one complete 

 revolution (bi, = 360°) his bent form will ro- 

 tate backwards through half a revolution 

 (ai=. 180°), and the cat will be in the posi- 

 tion shown in sketch No. 2, because each part 

 of his body will have rotated through the 

 angle 360° — 180° which is 180°. 



W. S. Franklin 



HOW to throw a curved ball 

 To the Editor of Science: I have tried a 

 great variety of devices for throwing a curved 

 ball for class-room demonstration, but with 

 only moderate success, and I have tried in 

 vain the method suggested by Professor J. J. 



Thomson for causing a rubber balloon to 

 travel in a sharply curved path. A year ago. 

 Professor J. H. Wily suggested a method 

 which is extremely satisfactory, as follows : 

 ' This factor is not a moment of inertia in the 

 usual sense of that term; but it is expressible in 

 terms of the same unit. 



