30 



in the movement of the limb what you gain in supposed grace of figure. 

 If the practice continue, I should expect that our young ladies of some 

 future period, between the bright colours of their heads and the develop- 

 ment of the tendons in their feet, will present an appearance not unlike 

 the flamingos that strut about the gardens in Regent's Park. 



I now come to my last and most interesting application in this lec- 

 ture of the principle of least action. I have shown that a quadrilateral 

 muscle becomes occasionally a skew muscle, like the skew bridge 

 known to engineers. Every line in it is straight, but the whole forms 

 a curved surface, and any plane drawn across that surface would give 

 me a conic section. (Fig. 6.) I come now to the great pectoral muscle 

 in the wing of the bird. I have before me two diagrams that have 

 cost me many hours of hard work. One of them represents the wing 

 of the albatross (Fig. 8). Here is the socket, s, or, as anatomists 

 call it, the glenoid cavity, of the wing ; a'a" is the furcular clavicle ; 

 a"b' is the sternum ; this curved line, a'b', represents the origin 

 of the great pectoral muscle ; and A B is the insertion of the pec- 

 toral muscle into the humerus, placed so that this insertion shall 

 occupy the same plane as the origin of the muscle. I believed that 

 I had succeeded in carrying the principle of least action to such 

 a point that I should be able to make a prediction. And here I 

 would call your attention to the important fact that no science whatever 

 is worthy of the name, no science is anything but a collection of facts, 

 which is not able to predict consequences — when certain facts are given, 

 to predict other facts ; and in proportion as any science possesses the 

 high prerogative of being in a condition to predict from a certain number 

 of conditions other conditions, it deserves the name of an exact science. 

 In other words, it has come under the control of geometry, the great 

 queen and mistress of all sciences. I selected for the purpose of pre- 

 diction the wing of the bird, and I said to myself, "I can trace ac- 

 curately the origin of this great muscle, I know its insertion, and I will 

 try and predict an unknown thing about it; viz., the position of 

 its axis of rotation." Let a'b' be any curve whatever observed in 

 Nature, as the origin of the pectoral muscle of a bird ; let A B be any 

 other curve observed in Nature representing the insertion of the muscle 

 in the arm. Then draw a'a b'b to meet in o. Given these two 

 curves, I was able to draw the bisector of the angle A o b. I 

 was also able to draw a certain right line, such as PQ or LM, at 

 right angles with that bisector, and to say, if the muscle of the bird, 

 which is a skew quadrilateral muscle, contracts so as to produce the 

 maximum advantage that it can produce, the axis of rotation round 

 which the wing of the bird must turn will be a particular line that I can 

 calculate. I shall not trouble you with the details of the calculation ; 

 they would be very uninteresting to an audience like this. You will 



