552 
The Ohio Naturalist. 
[Vol. VI, No. 8, 
8. Buds ovate, merely acute, outer pair of scales red, next pair gluti- 
nous; twigs of the season light brown or gray, the tips withering. 
V. opulus L. Cranberry-tree and Snowball. 
3. Buds long and rather slender; twigs of the season dark reddish brown. 
V. lentago L. Sheepberry. 
and V . prunifolium L. Black Haw. 
V. lentago has prominently acuminate leaves and acuminate win- 
ter buds. V. prunifolium has obtuse or merely acute 
leaves and acute winter buds. 
4. Leaf scar narrow, V-shaped or broadly U-shaped; twigs gravish 
brown ; buds oblong. V.lantanaL. Wayfaring-tree. 
4. Leaf scar broad, U-shaped to heart-shaped; twigs reddish. 
V. ahiifolium Marsh. Hobblebush 
5. Outer pair of bud scales fully half the length of the bud or more. 
V. pubcscens (Ait.) Pursh. Downy Arrow-wood, 
and V. dentatum L. Arrow-wood. 
V. pubescens has pubescent leaves with very short petioles; the 
twigs of the season are often nearly glabrous. V. dentatum 
has nearly glabrous leaves with petioles inches long. 
5. Outer pair of bud scales barely half the length of the bud or less. 
V . mollc Michx. Softleaf Arrow-wood, 
and V . accrifolium L. Mapleleaf Arrow-wood. 
V. molle has pinnately veined coarsely dentate leaves. V. aceri- 
folium has 3-ribbed, 3-lobed leaves. 
A SIMPLE FORMULA FOR MIXING ANY GRADE OF 
ALCOHOL DESIRED. 
E. W. Berger. 
Let P represent the grade per cent, of the alcohol on hand, P' 
the grade per cent, required, v the number of volumes of water 
to be added to one volume of P to make alcohol P' and x the num- 
ber of volumes of P that we desire to change to P'. Then 
Px P P' 
— ^ --P'. This gives us (1) P'v=P — P', and (2) v= — — ‘ 
Of these, (1) gives us the pharmaceutical rule quoted by Pro- 
fessor Schaffner in his “ Labratory Outlines for General Botany ” : 
“Take of the grade at hand as many volumes as the number of 
the per cent, you wish to make, then add to this enough volumes 
of pure water to make the total number of volumes agree with 
the number of the per cent, at hand. ’’ And (2) may be translatee 
into words as follows; — Rule: To find the number of volumes (v) 
of water to be added to one volume of the grade percent. (P) on hand, 
to make alcohol of the grade per cent. P', divide the difference be- 
tween the number (P) denoting the grade per cent, on hand and the 
number (P') denoting the grade per cent, required, by the latter 
P — P' 
number (P'). Or, which is simpler, v = — — ’ 
Professor Irving Hardesty in “Neurological Technique” ap- 
proximates the above fonnula (2), and if he had worked it out 
