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Dealing with explanatory variates

It is useful at this point to list all possible explanatory variate which might explain variation in the response and to organize them in some fashion. One useful organization is the fishbone diagram, shown in Figure 9 for Michelson's study.


  
Figure 9: Fishbone diagram.
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It is important to decide how explanatory variates will be dealt with during the planning stage. There are three choices. First, an explanatory variate can be held fixed or restricted to a range of values so as to restrict the study population. Second, once a unit is in a sample the value of an explanatory variate could be set deliberately or measured for later use in the analysis. Finally, the explanatory variate can be ignored completely. The third course of action is taken if it is known in advance that the explanatory variate is unimportant (e.g. it does not explain variation in the response variates) or out of ignorance, not recognizing the presence or importance of the variate.

Reviewing Michelson's apparatus and proposed method, there are many explanatory variates in the study population that may explain why the speed of light as determined from the measured response variates varies from unit to unit. Michelson recognized that it was important to consider these variates and in his Plan dealt with them in all three ways. For example, he fixed the distance from the rotating to the fixed mirror, thus further refining the study population. He also deliberately varied the angle of inclination of the plane of rotation of the revolving mirror from arctan(0.02) in the early determinations to arctan(0.015) in the final twelve sets. He measured a large number of explanatory variates such as the observer, the day, the quality of the image and so on. He ignored barometric pressure because

Sagredo: ... I cannot believe that the action of light, however pure, can be without motion, and indeed the swiftest.

Salviati: But what and how great should we take the speed of light to be? Is it instantaneous perhaps, and momentary? Or does it require time, like other movements? Could we assure ourselves by experiment which it may be?

Galileo Galilei  (1564-1642)
Two New Sciences (1638)
page 49 of Stillman Drake's   translation of [23]

In the same book, Galileo proposed a demonstration to determine whether light was instantaneous. It was essentially the same that Beeckman had proposed earlier and drew similar fire from Descartes. In a letter to the great experimental scientist Marin Mersenne (1588-1647), dated 11 October 1638, Descartes gave a scathing review33 of Galileo's book. Of the proposed demonstration, Descartes wrote ``His experiment to know if light is transmitted in an instant is useless, since eclipses of the moon, related so closely to calculations made of them, prove this incomparably better than anything that could be tested on earth.'' 34 Nevertheless, the demonstration was tried in 1667 by members of the Florentine Academy, but without success. [13] Light's movement was either instantaneous or near enough so as to be too fast to measure successfully.

In 1676 the first empirical evidence of a finite speed was presented. The Danish astronomer Ole Römer (1644-1710), while investigating an entirely different matter, gathered data and found a discrepancy which led to the discovery. Interestingly, this important and purely scientific discovery came about while Römer was working on what we would today call a very applied problem.


next up previous
Next: Longitude. Up: The Plan Previous: Selection of the response

2000-05-24