SEPTEMBER, 1938
1081
INDUSTRIAL AND ENGINEERING CHEMISTRY
possibility of plant damage due to excessive vapor on hot nights, gives a higher vapor concentration on cold nights, facilitates nightly filling, avoids injury to plants from spilling benzene, requires no attention in the morning, and does not become clogged with the gums in commercial benzene. All symptoms of blue mold were prevented when one wick evaporator was used for 20 square yards of plant bed and 10 cc. of benzene per square yard. Washed and wetted, 56 X 60 mesh cloth is tighter than glass sash. Glass sash is tighter when wet because water fills the cracks between overlapping panes of glass.
Acknowledgment The author is indebted to The Barrett Company for the privilege of starting this investigation while in their employ. It was discontinued in March, 1938, while the author was in the field and he is especially indebted to the following firms for their prompt assistance in continuing the work: Calco Chemical Company, Hudson Valley Fuel Company, and Jones and Laughlin Steel Corporation. The author is pleased to acknowledge the helpful assistance
of the following parties whose cooperation made this investigation possible: E. E. Clayton, J. G. Gaines, K. J. Shaw, and T. E. Smith of the Bureau of Plant Industry, U. S. Department of Agriculture; E. G. Moss, Oxford Tobacco Station; E. A. Walker, University of Maryland; and P. J. Anderson, Connecticut Agricultural Experiment Station. Appreciation of the author is extended to the Mine Safety Appliance Company for the loan of the special M. S. A. combustible indicator.
Literature Cited (1) Allan, J. M., Hill, A. V., and Angell, H. R., J . Council Sci. I n d . Research, 10, 295-307 (1937). (2) Angell, H. R., Allan, J. M., and Hill, A. V., Ibid., 9, 97-106 (1936). (3) Angell, H. R., Hill, A. V., and Allan, J. M., Ibid., 8, 203-13 (1935). (4) Dixon, L. F., McLean, R. A., and Wolf, F. A., Phytopathology, 26. 735-9 (1936). (5) McLean, R. ~ A . Wolf, , F. A., Darkis, F. R., and Gross, P. M., Ibid., 27, 982-91 (1937). ( 6 ) Mandeleon, L. F., QueensEand Agr. J.,45, 534-40 (1936). (7) Pittman, H. A., J.De@. Agr. W . Australia, I21 13, 368-80 (1936). RECEIVED June 30, 1938.
LOG MEAN DIFFERENCE THOMAS N. DALTON
216 Fourth Avenue, Warren, Pa.
HE log mean difference ( L M D ) between two values is a function in common use in heat transfer, gas absorption, and other fields. To make a computation for an alternate proposal, a salesman often has to waste time and energy in looking through his notes for a table or chart to show a log mean difference between two values. Sometimes the graphs, charts, or tables do not extend as high as he wishes and he is forced to guess at a value. A method is described here to do away with such uncertainty and to make it possible for anyone to find this value quickly, easiJy, and accurately. No graphs or charts but only t h e engineer's stand-by, the log-log slide rule, is used. A certain heat exchanger engineer devised a chart to obtain log mean temperature differences and used it all the time, becoming quite adept a t obtaining values. When his assistant did not use the chart and said he could get the values faster and more accurately with a slide rule, the elderly engineer thought the young man was exaggerating. One day a salesman came hurriedly into the office and asked for the log mean difference between 120" and 46" F. The engineer reached for the chart as the assistant reached for his slide rule. The assistant gave his answer first-namely, 17.5" F. A few seconds later the engineer read 80" from his chart. After the salesman had left, a consultation proved the former to be the correct value. The steps of the method used by the assistant to perform this computation so rapidly were as follows:
1
(1 Subtraction of the smaller value from the larger. (2 Division of the larger value by the smaller. (3 Division of the difference by the log of the ratio Opposite the ratio (2) on the log-log scale, place the difference (1) on the C scale; then at the index of the log-log scale read the answer on the C scale.
He mentally subtracted 46 from 120, getting 74. He divided 120 by 46 on the C and D scales of his slide rule and obtained 2.60. Next he placed 74 on the C scale opposite 2.60 on his log-log scales and read 77.5 (the answer) on the C scale
opposite the right-hand index of the log-log scale. (The index of a scale is its end.) Another example (158 and 197) will show the use of the left-hand index: (1) 197 - 158 39 (2) 197/158 = 1.248 (3) Placing 39 of the C scale opposite 1.248 of the log-log scale gives 176 (the answer) on the C scale opposite the left-hand index.
After 5 or 10 minutes practice, log mean differences can be found very rapidly. No salesman should now be limited by his notes when a customer changes his specifications. Every heat exchanger or gas absorption equipment salesman should master this useful computation before making his next approach. To show that this is an exact method, consider the following: The log mean difference is represented by the fraction LMD = (A
- B)/log e
(8
where A is the larger and B the smaller of the quantities. The D scale is the log to the base e of the values on the loglog scales. When setting the indicator to a value on the log-log scales, one is automatically setting the indicator to the log to the base e of this value on the D scale. Therefore, setting a value on the C scale opposite the value on the loglog scale and reading the C scale a t the index of the log-log scale (which is common to the index of the D scale) is equivalent to dividing a quantity (on the C scale) by the log to the base e of another quantity (on the log-log scale). If the value on the C scale is ( A - B ) , and the value on the log-log scale is A / B , then the value read on the C scale opposite the index of the log-log scale will be the L M D of these two values. The log-log duplex slide rule has a C scale on the same side as the log-log scales. This makes the computation easier. The author has used this method exclusively for more than a year and has found that it saves much time and energy. RECEIVED May
4, 1938.
