# MMX > Expectations

Imagine a swimmer that swims to one point and back at a constant speed. In the chart below and even visualizing the numbers yourself using the above drawing you can see how the effect occurs. Additionally you can see how the effect decreases as the difference between the swimmer speed and the river flow grows. Finally you can see that length does not effect the relationship. The total time travelling (and path length by the swimmer's estimation) grows by a certain percentage based on the prior mentioned relationship.

One Direction path length | 10 | 20 |

Swimmer speed | 2 |
2 |

Flow | 1 | 1 |

Norm (no flow) | 10T/20L | 20T/40L |

Swimmer's Est. Time (*speed = total 2-way length) | 13.333 | 26.666 |

Relation to Norm | 133.333% | 133.333% |

One Direction path length | 10 | 20 |

Swimmer speed | 3 |
3 |

Flow | 1 | 1 |

Norm (no flow) | 6.666T | 13.333T |

Swimmer's Est. Time (*speed = total 2-way length) | 7.5 | 15 |

Relation to Norm | 112.5% | 112.5% |

One Direction path length | 10 | 20 |

Swimmer speed | 6 |
6 |

Flow | 1 | 1 |

Norm (no flow) | 3.333T | 6.666T |

Swimmer's Est. Time (*speed = total 2-way length) | 3.42857 | 6.8571 |

Relation to Norm~ | 102.8% | 102.8% |

**10,066.906 to 1**

One Direction path length | 100669.06 (x2 = 201,338.12) |

Light Speed (swimmer) | 10,066.906 |

Ether wind (Flow) | 1 |

Norm (no flow) | 20 |

Actual travel time (Swimmer's Est.) | 20.000000197350382813136543039538 |

Relation to Norm | 1.0000000098675191406568271519769 |

**217.08 nm**extra path length along the direction of the Aether wind. ("Relation to Norm" x Path Length)

*"nearly 1000 wavelengths"*of what he called

**white light**at that point in the paper. This screw moved the mirror at the halfway point of the optical path so 1 turn would actually shorten the total path length .02 inch instead of the immmediate thought of .01. This would indicate the light to be 508nm at 1000, or a much as 564nm at 900 wavelengths(which I think he would have said directly) So this is slightly vague. Thankfully he goes on to clarify further:

*"Considering the motion of the earth in its orbit only, this displacement should be 2Dx1.0e-8"*(220 nm)Next he goes on to say that

*"The distance D was about 11 meters, or 2e+7 wavelengths of yellow light; hence the displacement to be expected was 0.4 fringe"*This tells us with certainty that he believes his light to be 550nm which is actually green. However, the most important consideration that can tell us for certain what the real wavelength of the light being examined in his white light interferometer experiment was the fact that he used sodium light to line up the fringe system! Since the sodium doublet (special double fringes from sodium interferometry)resides at 589.0nm and 589.6nm and he calibrated his interferometer with sodium light, the darkest fringe was set for 589nm and this differs from his belief about the wavelength. (it's also yellow instead of green) This means that his expectation of .4, while close, is not quite right.

**.366**We can forgive his slightly incorrect assumption of a 550nm wavelength given that it was 1887....

For those of you following Michelson's mathematical
path that would mean that D is 11 meters / 589nm. (18675721.562
waves) resulting in an expectation of a 0.368566 fringe shift without
aberration. (29.78^2 / 299,792.458^2) * 37351443.124 = 0.368566.

**Aberration**

**What Was Actually Seen**

**29,979.2458 to 1**

One Direction path length | 299,792.458 (x2 = 599,584.916) |

Light Speed (swimmer) | 29,979.2458 |

Ether wind (Flow) | 1 |

Norm (no flow) | 20 |

Actual travel time (Swimmer's Est.) | 20.000000022253001145832171615753 |

Relation to Norm | 1.0000000011126500572916085807877 |

*reading*of the MMX while the actual

*speed*is over one-third as large! 24.4783/589 = .04 of a fringe

**37,474.0573 to 1**

One Direction path length | 374,740.573 (x2 = 749,481.145) |

Light Speed (swimmer) | 37,474.0573 |

Ether wind (Flow) | 1 |

Norm (no flow) | 20 |

Actual travel time (Swimmer's Est.) | 20.000000014241920689623184063047 |

Relation to Norm | 1.0000000007120960344811592031524 |

*reading*of the MMX while the actual

*speed*is still nearly one-third as large. 15.6661/589 = .027 of a fringe...

**.03465 of a fringe is what was detected.**Slightly less than

**10 km/s is what the original MMX detected.**

**A Null Result **

To actually qualify as a null reading it would have to be below 5% of the expected wind speed, so let's examine that now:

**201,338,118.2 to 1**

One Direction path length | 2,013,381,182.0 (x2 = 4,026,762,364) |

Light Speed (swimmer) | 201,338,118.2 |

Ether wind (Flow) | 1 |

Norm (no flow) | 20 |

Actual travel time (Swimmer's Est.) | 20.000000000000000493375960986189 |

Relation to Norm | 1.0000000000000000246687980493095 |

*than this can be considered truly null by typical standards.*

__smaller__**The Variation of the Readings**

As you can see above, as both arms of the interferometer are at some variation of 45 degrees to the wind, both paths are affected equally, bringing the fringes back the the center. The expectation of this behavior is likely the single most important fact to understand when considering the implications of Michelson's and Miller's results. Both of them had this very distinct pattern even after averaging many many readings together. This cannot be mistaken for random error in readings or errors in the device. (But I suppose I've found that faith can always find a way to twist simple fact)