where _y_ is the disturbance of the ether, _a_ the initial amplitude, _r_ the distance from the starting-point, [lambda] the wave-length, and _v_ the velocity of light. Sound and heat likewise have much the same form of equation. Now, I maintain that the waves of thought are governed by the same laws, and can be determined by an equation of the same form. You are aware that in all these equations a certain quantity denoted by [lambda] appears, and varies for the different media through which the sound, or light, or heat passes, and which must be determined by experiment Now, in my equation for brain waves, the same quantity [lambda] appears which must be determined by the same method--by _experiment_. But how is this to be done? After mature deliberation and much careful thought, I have discovered the method for finding [lambda]. This method is _mesmerism_. We find the ratio of brain to brain--the relative strength which one bears to another; and then by an application of our formula we can actually determine the wave of thought, and read the minds of our fellow-creatures. An unbounded field for reflection and speculation is here suggested. Like all great discoveries, the elements of the problem have unconsciously been utilized by many who are unable to account for their method of procedure. For example, thought-readers, mesmerists, and the like, have unconsciously been working on this principle, although lack of mathematical training has prevented them from fully mastering the details of the problem. Hence in popular minds a kind of mystery has hung about the actions of such people, and excited the curiosity of mankind.