7. Notebook. There is no index of an analyst's work which does so much to create a favorable impression as a neat, wellordered and well-kept notebook. The size of the book should not be too small, say not less than 8 in. x 6 in., and should contain the following information relative to each determination:

Date
Purpose

Observations

Calculations

Results
Remarks

This information should be so compiled that any one familiar with quantitative analysis can read it readily and comprehensibly and can check the work without hesitancy or without any searching back and forth whatsoever.

The date is much more important in scientific and technical work than most students appreciate, and the student should invariably train himself to place the date on each page of the notebook. The purpose should be stated briefly, much as a running title. The observations should include a clear and concise record of all weighings and volumetric measurements, and have enough description appended so that there can be no doubt as to what was done. All observations should be entered directly in the notebook at the time and the practice of making notations on loose scraps of paper should never be tolerated for one instant. Calculations should follow observations closely enough so that cross-references between the two can readily be made, and especial attention should be paid to the proper use of significant figures as described below. The use of logarithms is to be strongly recommended, as long-hand methods of multiplication and division are both wasteful of time and conducive to mistakes and should be resorted to only as an expediency. The use of the ordinary ten-inch slide rule should be permissible only as a means of checking over the sequence of figures obtained by logarithms, because a slide rule of this size gives a precision of from two to four parts per thousand, depending on the portion of the scale being used, whereas our aim is a precision of one part per thousand.

Results should usually be expressed as percentages. In this connection it must be remembered that many substances, such as minerals, ores, clays salts, etc., contain moisture and in this case it is customary to report analyses on what is known as the "moisture-free basis," that is to say, the percentages of constituents are calculated to what they would be if the sample were free from moisture. For this purpose it is necessary to make a separate determination of the moisture in the sample as described in Chapter III. The moisture is then figured on the original weight of sample while the other

constituents are figured on the original weight of sample, corrected for moisture. Thus to illustrate by an example: 2.0000 g. copper ore lost 0.0484 g. moisture at 105°, while 0.5000g. of the same original sample yielded 0.0906 g. copper upon analysis.

Under remarks should be included any special happening that might have a bearing on the final results obtained, or any comments that might seem pertinent to the technique or the theory of the method employed.

The importance of keeping a notebook which shall be wellordered and precise in its record of experimentation and dates cannot be too strongly emphasized. In the recent famous case of Edwin H. Armstrong et al. vs. De Forest Radio Telephone and Telegraph Co. (279 F., pp. 453-4), which involved millions of dollars, the case was won by Armstrong and lost by De Forest on the merits of the respective notebooks. Judge Mayer, in delivering the Court's decree, said:

4

"It is not practicable to discuss the testimony in all its elaborate detail.... On the one side is an enthusiastic, never-say-die young student (Armstrong), with but one thought possessing him. He not only discloses to many persons his belief that he has invented something worth while, but he produces his apparatus, and he produces a sketch which is extraordinary for its clear and unmistakable description to one skilled in the art, and the date of that sketch is incontrovertibly fixed.

"On the other side is a then experienced and able worker in the art, experimenting along certain lines, who is unable to rely solely on notebook entries, which are not clear, but require construing, and who supplements these entries by recollection which is fallible, and not certain. If De Forest, in 1912 or 1913, invented

Tried before Justice Mayer in the U. S. District Court, Southern District, New York, May 17, 1921.

the feed-back circuit, the obvious financial reward in store for him would have induced him, notwithstanding all his difficulties, to do one of two things: (1) that which Armstrong did, that is, in some way make a clear memorandum and have somebody know about it; or (2) file an application for a patent in the same way that during the period concerned he filed many other applications.

"Holding then that Armstrong is the first inventor, and that his claims in suit should be construed as he contends, the sole remaining question is that of infringement."

The decree for the plaintiff was affirmed in the Circuit Court of Appeals, March 13, 1922 (280 F., p. 584).

8. Reports. In making out reports the analyst should always bear in mind the fact that the report which he submits, binds him to full responsibility. If it subsequently turns out that he has made a mistake in calculation, he is none the less liable than if the mistake had been made by adding the wrong reagent or using the wrong indicator. With respect to the responsibility which attaches to the report of an analysis, the Supreme Court of New York in the case of Arthur L. Richards and Robert M. Boyd, Jr. vs. Stillwell & Gladding Incorporated,5 said in its charge: "It appears that the defendants or the defendant, it being a corporation is a chemical concern, and that for hire it makes assays of metals submitted to it and issues reports to the parties seeking such examination. There is no dispute that on the 10th of February, 1917, after being retained by the plaintiffs to examine certain metal or ore, the defendant issued certain certificates to the plaintiffs that showed that the samples of ore that had been submitted to the defendant showed forty-one per cent plus, of zinc. . . . It is immaterial under what circumstances the defendant issued the certificates. The important question for you to determine is: Did the plaintiffs rely upon the certificates issued by the defendant? If they relied upon them and acted pursuant to such reliance, then the defendant is liable for any mistake it may have made in the issuance of the certificates."

'Tried before Justice Joseph E. Newburger, in Supreme Court, New York County. Trial Term, Part 14, April 12, 1920.

9. Significant Figures. Significant figures are those digits which have been put down to express the numerical measure of a quantity to an extent that does not go beyond the first doubtful digit. Thus if the following significant figures have been put down for a weighing -- namely, 1.250 grams - it means that the weight of object has been determined only to the nearest milligram; in other words the weight is nearer to 1.250 grams than it is either to 1.249 or to 1.251 grams; with respect to tenths of a milligram, the expression shows that we did not carry the measurement that far. The number of significant figures in the expression is four, since it contains three digits in front of the first doubtful digit.

In the expression 0.0125 gram there are but three significant figures, because there are only two digits in front of the first doubtful digit, the zeros which are used in this case serving merely to fix the decimal place. A zero when so used is not a significant figure, since the position of the decimal point in any measurement is determined solely by the unit in which the measurement is expressed.

In 12,500 grams there are really five significant figures, although it should be noticed, with reference to quantities like this containing one or more zeros beginning at the unit's place and reading toward the left, that they are often carelessly expressed in terms of a unit which is really too small to allow our considering the given value as consisting of all significant figures. Thus the value of a Faraday is given as 96,500 coulombs, which, strictly speaking, would indicate that we are sure of its value to within 1 coulomb, whereas the fact is we only know that the value lies between 96,490 and 96,510 coulombs. If there were such a unit as a kilo-couluomb (1000 colombs) we could properly write the value of a Faraday as 96.50 kilo-coulombs. Whenever such a situation arises as illustrated above, and we wish unequivocally to attach a precise significance to the value, some deviation measure or explanatory note should be given in the text.

In making chemical calculations it must always be borne in mind that we are dealing with significant figures because the numbers we are handling represent approximations and not exact quantities; consequently, the calculations must not be extended beyond a point which is warranted by the number of significant figures, the rule in this regard being that in the operations of addition, subtraction, multiplication and division with significant figures the final result can contain no more significant figures

than the least number of significant figures entering into the calculation."

Thus suppose that in the analysis of an iron ore there was used 0.3087 g. of sample and that this required for titration 35.24 c.c. of permanganate solution, 1 c.c. of which was equivalent to 0.005427 g. iron. The percentage of iron is given by the expression 35.24 0.005427 × 100

% Fe =

0.3087

which so far as the arithmetic is concerned could be evaluated to any number of figures, giving

but which so far as the number of significant figures is concerned should be evaluated to only four figures, giving

% Fe = 61.95%

10. Logarithms. Since as a usual thing the quantities entering into the computations of the analyst are represented by four significant figures, the great superiority of logarithms' over the ordinary long-hand processes of multiplication and division is well illustrated by carrying out under each of these two methods, the operations necessary in connection with the example already used, namely, in evaluating the ratio

We have by multiplying out and dividing in the ordinary way:

In general for our work this statement holds true. For a rigid investigation of the subject, see J. W. Mellor, Higher Mathematics for Students of Chemistry and Physics. Longmans, Green & Co., New York, 1909, 3rd ed., 522 pp.

'Five-place logarithms should be used.