From: Erik Osterlund <honeybee@elgon.se>
Date: Tue, 1 Jan 2002 16:45:36 +0100
To: BiologicalBeekeeping@yahoogroups.com
Subject:
Re: cell size measurement

Dee

I'll try to answer below, my answers inserted.

At 10.48 -0500 01-12-31, DeeALusby1@aol.com wrote:

>Erik, when one counts accross the parallel walls and then down
> the diagonals you are counting rhombic measurements. Also here
> he is using inches and not mm. If this were, like I think it was,
> rhombic measurements, what whould they be in mm?

The key sentence of mine in my previuous posting was this realting to your
question:
> The measurements Miller gives of 40-42 cells over almost 9 inches ranges
> 5.2 - 5.5 mm cell size for foundation. Which he says gives about 2 cells
> per square inch less then comb built without foundation (26.645).

This is a summary of the quotation you gave: I split it up here, taking a
quote for each linear measurement given, of the three possible in each
diagonal.

".. in the row of cells running horizontally found 40 cells in 8 5/8 inches. "

8 5/8 inches is 8.625 inches which is 8.625 x 25.4 mm = 219.075 mm. Divide this with 40 and you get the distance between the parallell sides of each cell (including one cell wall) running horizontally. Thus you get the
figure 5.48 mm.

"In one of the diagonal rows there were 42 cells in 8 5/8 inches"

So in one of the diagonals on the same length 8 5/8 inch, which is 219.075
mm as above, there were 42 cells. So here 219.075 is divided with 42, which
gives the figure 5.22 mm.

"and in the other there were 42 cells in 8 9/16 inches"

8 9/16 inches is the same as 8.5625 inches, multiplyed with 25.4 mm gives
217.4875 mm. Divide this with 42 and you get the figure 5.18 mm cell size.


>I also ask this because taking away the diagonal measurements
> given, added to the total figure,what measurements do you have
> here? again in mm?

I understand your question as to give the average for these figures in the
way given by Miller as the following:

"So there were 124 cells in the 25 13/16 inches measured, making the
average diameter of the cell .20818 of an inch."

25 13/16 inch is 25.8125 inch. Divided with 124 gives the average cell size
measured to 0.20817 inch according to my calculations. Which is the same
as what he gave (0.20818). Multply this with 25.4 mm and you get 5.29 mm as the average cell size on the drawn out foundation Miller measured.


>Also one last question for someone. Taking H.H.Roots measurements
> while we are at it, with him measuring across the horozontal and then
> down the diagonals (rhombic to me) what do you have converted to mm?

Root apperantly had written that:

"39 cells in 8 inches comes pretty close to the average...That would give
27.441 cells to the square inch."

8 inch is through myltplying with 25.4 mm, 203.2 mm. Divide this with 39
and you get the cell size 5.21 mm. That is equaled with 27.441 cells per
square inch. If this 27.441 figure were rhombic measurement, that is just
multiplying the figures for the number of cells per inch of the two
diagonals forming the rhomb, then you get the number of cell per inch in
average of these two diagonals by just taking the square root of 27.441.
The square root of this figure is 5.24. That means that on one inch you
have 5.24 cells (this is not the size of the cell given in mm). To get the
size of the cell in mm, take the figure for one inch in mm, which is 25.4,
and divide this with 5.24 and you get 4.85 mm. But as Root (or Miller) said
27.441 cells per square inch equaled 5.21 mm cell size (see above), this
indicates quite clearly that he is not referring to rhombic measurement
method here.

Another quote by Miller from Root yo gave here is:

"In 4-inches, horizontal measurement, I counted 19 3/4 cells. In one fo
the diagonal measurements there were 19 1/2 , and in the other 19 2/3.
These are not exact, merely as nearly as I could estimate with my eye"

Miller equals this with 27.837 cells per square inch. If 27.837 is a figure
for rhombic measurement the cell size would be 25.4 divided with the square
root of 27.837. This is 4.81 mm. But already the first linear measurement
of 19.75 (19 3/4) cells on 4 inch gives the cell size 5.14 mm (4 inch x
25.4 divided with 19.75). The first diagonal gives 4 inch x 25.4 divided
with 19,5 (19 1/2) which is 5.21 mm. The second diagonal gives 4 x
25.4/19.667 (19 2/3) = 5.17 mm. The average taken the same way as above would be 19.75 + 19.5 + 19.667 = 58.917 cells on 3 x 4 inches (12 inches). So 12x25.4/58.917 give the average cell size 5.17 mm, which is said to equal 27.837 cells per square inch. So this could not be rhombic measurement as far as I can see (it should then have given 4.81 mm cell size counting linear)

To be remembered is that these measurements refer to foundation and not
natural comb.

Hope this helps

Erik