46 



tion. In the required direction draw a radius, and draw a tangent 

 where the radius meets the ellipse, and let fall a perpendicular on that 

 tangent. The strain along this radius must be made proportional to 

 the square of the perpendicular dropped on the corresponding tangent. 

 That construction is so simple that a stonemason or a carpenter could 

 apply it. For example, if he has an elliptical dome in which the major 

 axis is double the minor axis, the squares of the perpendiculars will give 

 him that the strength in the direction of the long axis must be four 

 times the strength in the lesser axis. 



I applied this principle of equilibrium to the case of the muscle 

 which is used in placental animals for causing the birth of the young. 

 This muscle is produced by Nature for a special purpose. As soon as 

 it has accomplished that purpose, it is carefully removed ; and there- 

 fore, if we could find in any part of Nature a test for the principle of 

 least action, we ought to find it here. If the muscle be made by 

 Nature too strong for the purpose intended, there is a waste of mate- 

 rial, a waste of force ; if it be made too weak, the life of the animal is 

 risked. It is not the case of a muscle which has to overcome a resist- 

 ance which it tries from day to day. If I go into a gymnasium and ex- 

 ercise any group of muscles in my body, there will be a gradual growth 

 in those muscles, because there is a growing resistance day by day ; but 

 the muscle that causes the birth of the young animal never tries its strength 

 against the resistance it is required to overcome until the moment of 

 actual exercise arrives. By measuring the curvatures and thickness of 

 the muscles, I ascertained that inside the ellipsoidal uterine muscle a 

 hydros tatical pressure of 3.4 lbs. per square inch can be produced by 

 its contraction. Dr. Matthews Duncan of Edinburgh, and Professor 

 Tait of the same University, have made a number of valuable experi- 

 ments on the strength of the membranes which this muscle has to rup- 

 ture. They have tabled them ; and in no case do they find that the 

 resistance exceeds 3. i lbs. per square inch. I am entitled to regard 

 this as a remax-kable example of the principle of least action in Nature. 

 There is an adaptation of force to resistance — the force produced in 

 order to overcome resistance for months not exercised against it, and 

 found exactly of the right degree of strength, not too strong or too 

 weak, when the time of trial comes. Here we see Nature attaining 

 perfection at a single bound, by a process of foresight. There is no 

 evidence whatever of the supposed necessity of an endless succession of 

 previous blunders. 



I have now to take my l&ave of you. I have to thank you, as I do 

 sincerely, for the kindness with which you have listened to me ; and I 

 sincerely hope that you will make some allowance for the difficulties of 

 my subject, as well as for its novelty, in the task which I have under- 



