BLOUNT THE LIMITATIONS OF THE BALANCE. 1035 XC.-The Limitations of the Balance. By BERTRAM BLOUNT. ABOUT three years ago the author had occasion in the course of a research to make accurate weighings extending over some months, The balances used were by the first makers and the discrepancies observed were at first attributed t o the errors of experiment arising from the difficulties of the research. Slowly and reluctantly how-ever the conclusion was drawn that the errors lay in the balances themselves and the following is an account of the nature and extent of these errors. It is usually accepted that a good balance carrying 200 grams in each pan should turn with certainty with 0.1 milligram an accuracy of one part in two millions. Much higher accuracies have been claimed but f o r the purpose of the research in question this degree of accuracy was sufficient.It was assumed that it could be obtained without difficulty and the research was started on this assumption. As has been mentioned above the cause of the error was not a t first suspected and after many months of work the balances themselves were critically tested. It may be stated a t once that all were usually accurate over a short period of a few hours or even a few days but over longer periods of a few weeks or months they showed themselves untrustworthy. In all six balances were used three being provided by the kind-nem of Professor Pope a t Cambridge; the other three were a t the laboratory in the author's house. Those a t Cambridge were a Sartorius carrying 200 grams in each pan a smaller Sartorius carrying 100 grams in each pan and a Bunge preferred by the late Prof.Ewing for his own work carry-ing 100 grams in each pan. Those in London were an Oertling-carrying 200 grams in each pan (and it may be remarked that the beam used was selected out of five by the makers as the best tihey had) another Oertling with a load of 100 grams and a modern Bunge carrying 200 grams. Each balance could be read with accuracy to 0.1 milligram and in all cases standard weights were used. All proper precautions were taken to secure uniformity of condition. Four of the balances were used in their own case one in a massive gun-metal case which was air-tight and one in an all-glass case which was also air-tight. I n each case twin weighh were used so as to prevent errors creep-ing in from this cause.VOL. UXI. s 1036 BLOUNg! THE LIMITATIONS OF THE BALANCE. Tenths - Date. Left. Right. Temp. mg. Weighings were made by three independent observers a t both Cambridge and London and as there were far too many to record in full in a short paper only those representing the maximum variations are recorded and are as follows: Tenths Pate. L m h t . Temp. CAMBRIDGE. 29.4.17 4 15.5" -C- - 0 30.4 17 5 2 i 15 + 0 30.4.17 5; 5 15.5 4 2.5.17 2+ 3 14.5 - 4 7.5.17 7 6 13.5 + 1 10.5.17 4; 6 13 - 14 11.5.17 5 44 14 -+ 4 12.5.17 2 3 14 - I 2.5.17 7 5& 14 - 1 i 22.5.17 7 7 16.5 & 0 24.5.17 6 7 15.7 - 1 31.5.17 8 5 17 1 1 1.6.17 3 4 17 - 1 3.6.17 6 5 17 A- 1 11.7.17 7 78 15 - 1 Small Snr t o ri,ic s .Divisions. Divisi o m . Tenths -(7 Tenths 12.7.17 9 8 16" 12.7.17 2 5 16 13.7.17 7 5 16* 12.7.17 2 2 16-5 13.7.17 4 5 16.5 13.7.17 2 2 16.5 13.7.17 1 3 16.5 17.7.17 3 3 l i - 3 20.7.15 14 3 18 29.7.17 5 5 19 3.8.17 54 6 1 7 12.8.17 6 5 17.7 18.8.17 3 20.8.17 ;# 30.8.17 8 16 Date. 29.4.17 30.4.17 5.5.17 5.5.17 6.5.17 7.5.17 11.5.17 18.5.17 27.5.17 29.5.1'7 31.5.17 4.8.17 10.6.17 14.6. I 7 15.8.17 li.6.17 21.6.17 22.6.17 Right. 6 2 c 84 5* 2 2 54 7 3+ 7 23 74 5 4 53 3 3* 3t Temp. 15.5' 15 15 15 14 14 14 14.5 17 17 17.3 17 17.5 18 18.5 19 19 18.5 Date. Left. Right. Temp. 26.6.17 3* 31- 17.5' 4.7.17 5 16-5 29.6.17 44 5 17* 5.7.17 t4 3& 16.5 7.7.17 4 3 17 9.7.17 6 64 16.5 12.7.17 44 4+ 16.5 15.7.17 5 4 t 18 19.7.17 !& 7 18 20.7.17 29.7.17 4 P ::.5 1.8.17 7 7 17.7 6.8.17 7* 9 17.5 11.8.17 3 17.5 20.8.17 3* 24 17.5 30.8.17 7 Sf 16.5 13.8.17 !' 58 18 Greatest differonce in 4 mont,hs 0.6 milligram.* Full. t Rare. Bmge Date. 29.4.17 30.4.17 I .5.17 1.5.17 4.5.17 7.5.17 10.5.17 12.5.17 13.5.17 14.5.17 26.5.17 28.5.17 29.5.17 7.6.17 14.6.17 17.6.17 18.6.17 19.6.17 22.6.17 26.6.17 Temp. mg. 15.5' -+ 0 15.5 - 1 14.5 - 3 14.5 f 0 13.5 - 14 15 - 34 13 - 8 14 - 14 15 - 4 15 -16 -16-75 - 1 16.25 + 0 'B 17 1- 14 \- 1 18 & 0 18.75 - 3 19 -+ 3 19 & 0 17 - 2 18 - 1 BLOUNT THE LIMITATIONS OF Date.28.6.17 5.7.17 6.7.17 13.7.17 19.7.17 12.7.17 23.7.17 26.7.17 29.7.17 ;:% 4.8.17 6.8.17 9.5.17 11.8.17 13.8.17 19.8.17 21.8.17 25.8.17' 1.9.17 31.8.17 Large Sartorius. Divisions. Tenths I L x a t . Temp. mg. 4 4 24.5" f 0 4& 79 21.9 - 6 3 3 16-3 0 5 7 18.2 - 4 3 34 16.7 - 1 Right. 7 6 9 7 6 6 4 69 99 94 7 10 6 6 ) 51 94 7 2 10 5 Date. 26.7.17 7.8.17 4.9.17 10.9.17 14.9.17 THE BALANCE. 1037 Divisions. L Tenths Lift. 9 9 6 1 P ;* 7 5 4* 10 12 12 12 12* 12 12 12" 13 94 Right. Temp. 10 17" 10 16 8 16 4 16.5 7Q 16.5 9* 18 8* 18 5 19 8 19 8 17 3 17 z y :;.5 - 1 17 - 6 17 - 7 17 - 8 17 -11 16 -11 16 Greatest difference 2.5 milligrams in 4 months.Rejecting the readings after 4.8.17 0.45 milligram in 3 montha. * F~dl. 7 Bare. Date. 16.6.17 19.6.17 23.6.17 3.7.17 7.7.17 20.7.17 Date. 14.6.17 15.6.17 16.6.17 30.6.17 10.7.17 14.7.17 16.7.17 26.7.17 27.7.17 2.5.17 Divisions. A-Left. Right. 4 4 1 3 2 3 3 8 7 lo* 6 64 F 1 ;i 3 2 1+ Bunge. Tenths Temp. mg. 24" & 0 19.5 - 4 21.5 - 2 13.5 -10 16 - 7 22 - 1 20 - 5 21.5 + 2 -21 .- 3 15.5 .- 9 Date. 4.8.17 5.8.17 8.8.17 20.8.17 22.8.17 26.8.17 6.9.17 9.9.17 13.9.17 Divisions. +- Tent,hs Left. Right. Temp. mg. 0 34 22" - 7 1 9 20.3 -16 6 20.3 - 5 7 20.4 -12 5 18 - 8 ? 1 1.6 milligrams.Divisions. - Tenths Left. Right. Temp. mg. 6 94 16.5" - 7 3 8 18 -10 :* 54 19-5 18.5 - - 1 74 ti 20.5 +- 2 5 8 18 - 6 64 74 20 - 2 0 2 20 - 4 5 8 17 - 6 Greatest difference in 3 months. 1-2 milligrams. s s 1038 BLOUNT THE LIMITATIONS OF THE BALANCE. Small Oertling. Divisions. - Tenths Date. Left. Right. Temp. mg. 30.6.17 34 2 14 4- 3 14.6.17 6 5 2 4 O * 0 Divisions. - Tenths Date. Left. Right. Temp. mg. 1.8.17 24 3 16" - 1 2.8.17 44 3& 16.5 + 2 8.8.17 2& 24 20.51 10.8.17 2 2 19 = (' (From 16.8.17 to 22.8.1 7 balance remained constant (left and right equal) (From 6.8.17 to 1.9.17 the halaiicc did not vary more than & division with with variations of temperature of 3".) variations of temperature of 4.2".) 1.9.17 3; 9 + 2 ' 14.9.17 9 84 18.3 + 1 6.9.17 24 i! & 0 I Greatest difference in 3 months 0.4 milligram.These figures show that six balances of the best make observed by three people at two different places gave a variation over as short a period as four months varying from 0.4 to 1.6 milligrams and that these variations cannot be correlated with any variation of external conditions. The author is well acquainted with earlier work by Poynting and others and does not doubt that accurate readings can be made over a short period but finds that constancy cannot be relied on over as short a period as four months. The natural suggestion of the cause of discrepancy is that there is a difference of temperature between the two arms of the beam.This has been dispelled by direct observation. Two thermometers reading to Os0lo were placed one on each pan of a balance in the same room as that containing the three balances used in London. Except in one instance when by accident direct sunlight fell on the bulb of one thermometer no greater difference than 0'02O was observed. Calculations confirming those of Landolt show that such a difference of temperature in the beam itself is negligible in its effect on the indications of the balance and this difference, which represents that of the pans is far greater than would be possible in a solid piece of metal like a beam under normal condi-tions. As the fact remains that these variations occur however, there clearly must be a. physical cause. The matter has been ref erred to engineers of eminence accustomed to consider stresses, and one was so good as to compute the stresses in a beam identical with that of two of the balances.He reported that the beam was amply strong to carry a load without flexure although condemning the design as clumsy. The slow flow of metals under stress is well known and might provide an explanation were it. not that th FRANCIS 3 4-DI-$I-NITROTETRAPHENYLFURAN. 1039 beam of a balance is not under stress except in the short time of weighing. Moreover sonie permanent set in one direction or the other might be expected. It remains to consider other probable causes of the inconstancy observed. There may be an alteration in the effective length of the two arms of the balance. I n the case of the six balances examined two had their end knife-edges set in sealing-wax two were held by set screws and the other two were apparently pressed in. I n all three methods of construction fortuitous movenient of the knif e-edge is easily conceivable and to this explanation the author inclines, As a balance of the best make is generally regarded as capable of use to its assigned limit of accuracy chemists generally have accepted its indications without quostioii. The present inquiry, which only arose out of the main research shows that this view is untenable if constant readings are to be expected over a relatively short time. Nor is there any indication as t o when the variations may occur. As many cheiiiical and physical experiments are neces-sarily lengthy an unsuspected alteration of the indications of the balance may in the past have led to grave errors. It seems to be incumbent on balance makers .to provide an instrument capable of carrying 200 grams in each pan turning with certainty t.0 0.1 milli-gram and dependable in this respect for a reasonable time-say a yea:-without alteration or readjustment it being always under-stood that all proper care is taken in using the instrument. A t tho time of writing i t appears that such a balance does not exist. 76 YORK ST., WESTMINSTER. 8. W. LReceived October 25&h 1917.