## The Argelander Method of Estimating Brightness

This is the method developed by Fredrich Wilhelm August Argelander in 1840. You must select two

Methods w comparison stars that are close in brightness to the variable. Variable star charts have many comparison stars from which you may choose so doing so should be fairly easy. One of the comparison stars should be slightly brighter than the variable star and the other comparison star should be slightly fainter than the variable star. Using a method called interpolation, you're going to estimate the brightness of the variable with respect to the two comparison stars.

First, you will estimate the difference in brightness between the brighter star and the variable star. You will express the difference in brightness in steps. By convention, when using this method the brighter comparison star is designated "A" and the fainter comparison star is designated "B." The differences in brightness between steps is explained next.

• One step: At the exact moment of observation, if the brighter star (A) and the variable (V) seem to be equal, but after a moment of close examination the brighter star is slightly brighter than the variable, it is considered one step brighter and is recorded as: A(1)V. This means that the A star is one step brighter than the V star (variable).

• Two steps: If A and V appear equal when first observed, but almost instantly it becomes obvious that A is brighter than V, this is recorded as: A(2)V.

• Three steps: If a slight difference in brightness is obvious at the exact moment of observation, then A is three steps brighter than V and is recorded as: A(3)V.

• Four steps: If a distinct difference in brightness is immediately visible, this is considered four steps, recorded as: A(4)V.

• Five steps: A major difference in brightness between A and V is indicated as: A(5)V. You should be careful to choose comparison stars so that less than five steps are needed to make a good comparison. If you exceed five steps, this method rapidly loses accuracy. Good charts will help you select appropriate comparison stars.

After comparing the variable star with the brighter comparison star (A), use the same method to compare it with the fainter comparison star (B). For example, if the variable star is two steps brighter than the fainter star, it is recorded as: V(2)B. This means that the V star (variable) is two steps brighter than the B star.

After comparing the variable star with both the brighter and fainter comparison star, you will have a relation that may look something like this: A(3)V(2)B. This means that the A star is three steps brighter than the V star and that the V star is two steps brighter than the B star. Now you're ready to estimate the brightness of the variable star:

• First, determine the brightness of the A star. This will be on the chart. We'll say it's 11™40 for this exercise. Remember, on star charts the decimal is omitted so that it won't be mistaken for a star.

• Second, determine the difference in magnitude between the bright comparison star and the faint comparison star. Let's say the fainter comparison star is 12™30. On a star chart it will be labeled as "123."

• Third, divide the number of steps between the A star and the V star, in this case 3, by the total steps between all three stars. In this case the number of steps between the A star and the V stars is 3 and the number of steps between the V star and the B star is 2. The total number of steps is 3 + 2 = 5. So, we divide 3 by 5 (i.e. 3/5).

• Fourth, multiply the difference between the bright comparison star and the faint comparison star (11.4 - 12.3 = 0.9) by the number fraction that we determined in step three (3/5). That process will look like this (0.9 x (3/5)) and equals 0.54.

• Fifth, now just add the result calculated in step four to the bright star's magnitude (11.4 + 0.54 = 11.94). This is the estimated brightness of the variable star and should be rounded to 11"19. Making comparisons to more than two stars will improve the accuracy of this method.

The important thing with this method is that there is no specific value attributed to any particular step. Each step is defined as the smallest difference in brightness that your eye is able to distinguish. The value of a step, expressed in magnitudes, will depend upon your local observing conditions and your experience. A beginner's step is often close to 0n,3; however, experienced observers may be able to distinguish steps as small as 0"'04. Compare your results with other variable-star observers. Don't be disappointed if your estimates don't exactly agree with other observers. With a little time, you estimates will be right in there with most other observers.

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