For the Love of Physics by Walter Lewin Read Free Book Online Page B

the largest mammals as large as they are and not much larger?” He answered himself by suggesting that if a mammal became too heavy, its bones would break. When I read about this, I was intrigued to find out whether or not he was right. His answer seemed right intuitively, but I wanted to check it.
    I knew that mammals’ femurs—their thighbones—support most of their weight, so I decided to make some comparative measurements of different mammals’ femur bones. If Galileo was right, then for a super heavy mammal, the femur bone would not be strong enough to support the animal. Of course, I realized that the strength of the mammal’s femur should depend on its thickness. Thicker bones can support more weight—that’s intuitive. The bigger the animal, the stronger the bones would need to be.
    The femur would also get longer as the animal got bigger, of course, and I realized that by comparing how much longer versus how much thicker the femurs of various mammals get as the animals become bigger, I could test Galileo’s idea. According to the calculations I made, which are more complicated than I want to go into here (I explain them in appendix 1 ), I determined that if Galileo was right, then as mammals get bigger the thickness of their femurs would have to increase faster than their length. I calculated that, for example, if one animal was five times bigger than another—so the femur would be five times longer—then the thickness of its femur would have to be about eleven times greater.
    This would mean that at some point the thicknesses of femurs would become the same as their lengths—or even greater—which would make for some pretty impractical mammals. Such an animal would certainlynot be the fittest for survival, and that would then be the reason why there is a maximum limit on the size of mammals.
    So, I had my prediction that thickness would increase faster than length. Now the real fun began.
    I went over to Harvard University, where they have a beautiful collection of bones, and I asked them for the femurs of a raccoon and a horse. It turns out that a horse is about four times larger than a raccoon, and sure enough, the horse’s femur (42.0 ± 0.5 centimeters) was about three and a half times longer than the raccoon’s (12.4 ± 0.3 centimeters). So far so good. I plugged the numbers into my formula and predicted that the horse’s femur should be a little more than six times thicker than the raccoon’s. When I measured the thicknesses (to an uncertainty of about half a centimeter for the raccoon and 2 centimeters for the horse), it turned out that the horse bone was five times thicker, plus or minus about 10 percent. So it looked very good for Galileo. However, I decided to expand the data to include smaller as well as larger mammals.
    So I went back to Harvard, and they gave me three more bones, of an antelope, an opossum, and a mouse. Here’s how they all stacked up:

    Isn’t that wonderful, so romantic? The progression of shapes is lovely, and look at how delicate, how tiny is the femur of the mouse. Only a teeny weenie little femur for a teeny, weenie little mouse. Isn’t that beautiful? I will never cease to be amazed by the beauty in every detail of our natural world.
    But what about the measurements; how did they fit into my equation? When I did the calculations, I was shocked, really shocked. The horse femur is about 40 times longer than the mouse’s, and my calculations predicted that its femur should be more than 250 times thicker. Instead, it was only about 70 times thicker.
    So I said to myself, “Why didn’t I ask them for the femur of an elephant? That might settle the issue conclusively.” I think they were somewhat annoyed at Harvard when I came back again, but they kindly gave me the femur of an elephant. By that time I’m sure they just wanted to get rid of me! Believe me, it was difficult carrying that bone; it was more than a yard long and weighed a ton. I couldn’t wait to