y bows; but any
form of bowing that calls for special dexterity will betray the
inefficiency of a bow.

It is of great interest to compare the calculations of Woolhouse with
those of Fetis, and I will here quote the results obtained by the
former.

"If measurements be taken in inches, and parts of an inch, and _h_
denote the distance of any part of the bow from the head, the
diameter of the stick in that locality, supposing the bow to be
round, may be readily calculated from the following formula:--

Diameter = .2 [log.(_h_ + 7.25) - 9.8100]

"From this formula the numbers given in the last column of the
following table were calculated."

+--------------------------------------------+-------------+
| _Distance from Head of Bow in Inches_. | Diameter |
+--------------+--------------+--------------+ in parts of |
| Violin | Viola | Violoncello | an inch. |
+--------------+--------------+--------------+-------------+
| 0 | | | .210 |
| 2 | 0 | | .230 |
| 4 | 1-1/2 | 0 | .247 |
| 6 | 3 | 1 | .262 |
| 9 | 5 | 3 | .280 |
| 13 | 8 | 5-1/2 | .300 |
| 18 | 11-1/2 | 9 | .318 |
| 23 | 15 | 12 | .333 |
| | 19 | 16 | .348 |
| | 23 | 20 | .360 |
| | | 24 | .370 |
+--------------+--------------+--------------+-------------+

These measurements, of course, only extend to the commencement of the
cylindrical portion.

Woolhouse made a small gauge of ivory, based on the above
measurements, which proved of great practical value in examining
bows. The measurements he obtained by the above calculation apply to
wood of medium density. He says, "For close and dense wood the
dimensions should be somewhat diminished, or, what amounts
practically to the same thing, the distance from the head should, for
dense wood, be increased by half an inch, or an inch, as the case may
be, before applying the gauge." He then gives a table of inclusive
weights of violin, viola and violoncello bows.

+---------------------------------------------------+
| _Weight of Bow for_