136 W. D. Lambert — Mechanical Curiosities 



Initial latitude 45° 

 Keaehes Velocity 



lat. after m. per see. 



30° 8^ 19^ 4.3 



15 12 15 5.7 



15 21 6.1 



Initial latitude 60° 

 Eeaches Velocity 



lat. after m. per see. 



40° 10^ 15^ 5.0 



20 14 23 6.8 



18 11 7.5 



The table is calculated on the supposition that the 

 sphere rolls without slipping ; then about 2/7 of the work 

 done goes into the kinetic energy of rotation, thereby 

 diminishing the amount of energy available to produce 

 velocity of translation. If we imagine a constraint such 

 that the sphere is obliged to slide without friction, it 

 would travel somewhat faster. 



The matter may be looked at from a slightly different 

 point of view. The sphere really falls in going towards 

 the equator and what body will not fall when it has the 

 chance? What do we mean by falling 1 Suppose the 

 successive level surfaces are numbered in any manner so 

 that any surface bears a higher number than the one 

 immediately inside of it. A particle falls when it passes 

 from any surface to another surface bearing a smaller 

 number. The original level surface that passed through 

 the center of the sphere at latitude 60° passes above the 

 center of the sphere when the latter has come to the 

 equator, so the sphere has fallen through a distance equal 

 to the distance from its center to that level surface which 

 in latitude 60° passed through its center, or as a simple 

 calculation shows, through 4.0 meters. Perhaps with 

 this way of looking at the problem the velocities at the 

 equator will not seem so surprising. 



If you will pardon a bit of personal reminiscence, I will 

 tell you what suggested the apparently fantastic problem 

 of the huge rolling sphere. A well-known geologist told 

 me that he had been convinced by geologic evidence that 

 a part or a whole of each continental block has shifted its 

 position in past time by moving towards the equator and 

 in so doing has probably twisted in direction with refer- 

 ence to the meridian. He had been led to think along 



