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The conception of random positive ion velocities corresponding to ion temperatures in a plasma has serious theoretical difficulties and is lacking in direct experimental verification. It is more reasonable to assume that each ion starts from rest and subsequently possesses only the velocity which it acquires by falling through a static electric field which is itself maintained by the balance of electron and ion charges. This new viewpoint thus ascribes motions to the positive ions which, for long free paths, are ordered rather than chaotic, each negative body in contact with the discharge collecting ions from a definite region of the plasma and from it only. The resulting integral ? the plasma-sheath potential distribution have been set up for plane, cylindrical, and spherical plasmas, for long, short and intermediate length ion free paths, and for both constant rate of ionization throughout the plasma and rate proportional to electron density, and these equations have been solved for the potential distribution in the plasma in all important cases. The case of short ion free paths in a cylinder with ion generation proportional to electron density gives the same potential distribution as found for the positive column by Schottky using his ambipolar diffusion theory, with the advantages that ambipolarity and quasineutrality need not appear as postulates. The calculated potential distribution agrees with that found experimentally. The potential difference between center and edge of plasma approximates Te11,600 volts in all long ion free path cases. The theory yields two equations. One, the ion current equation, simply equates the total number of ions reaching the discharge tube wall to the total number of ions generated in the plasma, but it affords a new method of calculating the density of ionization. The second, the plasma balance equation, relates rate of ion generation, discharge tube diameter (in the cylindrical case), and electron temperature. It can be used to calculate the rate of ion generation, the resulting values checking (to order of magnitude) those calculated from one-stage ionization probabilities. The potential difference between the center of the plasma and a non-conducting bounding wall as calculated from the ion current equation agrees with that found experimentally.
The solution of the general plasma-sheath equation has been extended into the sheath surrounding the plasma to determine the first order correction which is to be subtracted from the discharge tube radius to obtain the plasma radius. The wall sheath in the positive column is several times the thickness given by the simple space charge equation.
Actually the ions do not start from rest when formed but have small random velocities corresponding to the gas temperature, Tg. In the long ion free path cases this leads to an error of the order of only TgTe in the calculated potential distributions.
In the plasma surrounding a fine negatively charged probe wire the potential difference between plasma potential maximum and sheath edge may be so small that the ions generated within the plasma potential maximum are not trapped but can traverse the maximum by virtue of their finite initial velocities. This justifies the use of a sufficiently fine negatively charged wire in the usual way to measure positive ion concentrations, although certain difficulties appear which are thought to be connected with the collector theory rather than the present plasma theory.
[40] The Secretary of the Treasury has no authority under section 3469 of the Revised Statutes to accept the offer of the Great American Indemnity Company is compromise of certain final judgments recovered by the United States against the surety company upon forfeited bail recognizances, there being no doubt as to the entire collectibility of these judgments.
Your letter of March 16, 1929, submits for my opinion the question whether you have authority under section 3469 of the Revised Statutes to compromise certain judgments recovered by the United States upon forfeited bail recognizances. The circumstances giving rise to your inquiry appear to be as follows:
On September 14, 1927, each of five defendants held upon a charge of having conspired to violate the National Prohibition Act and the Tariff Act of 1922 entered into a bond, in the sum of $5,000, with the Great American Indemnity Company as surety, conditioned upon the appearance of the principal at the November Term, 1927, of the United States District Court at Norfolk, Virginia. The criminal case was set for trial on December 5, 1927, and on December 20, 1927, none of the defendants having appeared, the court declared each of the bonds forfeited. Scire facias proceedings thereafter brought resulted in the recovery by the United States of a separate judgment upon each bond. On June 1, 1928, one day after the entry of these judgments, four of the defendants surrendered, and they were subsequently tried, convicted and sentenced. The fifth defendant, Joseph Dally, has neither surrendered nor been apprehended, and the judgment upon the bond given by him, together with interest and costs, has been paid by the surety company.
Petitions by that company, under section 1020 of the Revised Statutes, for remission of the amounts of the remaining four judgments having been denied by the court, the company, by letter dated December 17, 1928, submitted to you an offer of $1,000 in compromise of these unsatisfied judgments, which total $20,000. As reasons why the offer should be accepted, the letter referred to the fact that the company had already paid in excess of $5,000 in satisfaction of the judgment upon the bond given by the defendant Dally, and stated that, owing to its lack of experience in such matters, the company had not entered into any separate indemnity agreements with the principals at the time it became surety upon these bonds, and that any loss resulting therefrom would, therefore, fall entirely upon it; that it [42] had expended considerable sums of money in endeavoring to apprehend the said defendants, whose surrender was due largely to its efforts, and that by virtue of such surrender on th e day following the entry of the scire facias judgments and of the trial and convictions which followed, the United States had lost none of its rights, the ends of justice were properly served, and the United States should not demand the full amount of the penalty for the default, but should accept the offered compromise, which would reimburse it for its expenses incurred in seeking the apprehension of these defendants.
Pursuant to the practice in such cases, the compromise offer was referred to the United States Attorney for his recommendation in the premises. Estimating that the Government had expended between $1,500 and $2,000 by reason of the failure of the said defendants to appear as required by their bonds, that officer recommended that if the surety company should submit an offer of $2,000 in settlement of these judgments, the offer should be accepted, if cognizable under section 3469 of the Revised Statutes.
The surety company thereupon submitted a new offer in the sum of $2,000, and the Solicitor of the Treasury recommended that it be accepted. In making such recommendation, the Solicitor referred to conflicting opinions of the Attorney General upon the question of the authority of the Secretary of the Treasury, under section 3469, to compromise final judgments recovered by the United States the full amounts of which could be collected, and based his conclusion that such authority existed upon an opinion by Attorney General Wickersham (29 Op. 217), wherein the previous opinions of the Attorney General upon the subject were reviewed and the opinion expressed that, in passing upon offers to compromise final judgments, the Secretary of the Treasury was not restricted to a determination of whether the judgments could be collected, but was authorized to determine, upon considerations of justice, equity, and sound public policy, whether their collection in full should be insisted upon by the Government.
In view of the matters stated and because of a doubt engendered by the divergent views expressed by my predecessors, you ask to be advised whether you have authority [43] under section 3469 to accept the offer of the Great American Indemnity Company in compromise of the aforesaid judgments, as to which you say no appeal has been taken and no showing or claim made that they cannot be collected in full.
'Upon a report by a district attorney, or any special attorney or agent having charge of any claim in favor of the United States, showing in detail the condition of such claim, and the terms upon which the same may be compromised, and recommending that it be compromised upon the terms so offered, and upon the recommendation of the Solicitor of the Treasury, the Secretary of the Treasury is authorized to compromise such claim accordingly. But the provisions of this section shall not apply to any claim arising under the postal laws.'
Except for the final provision regarding claims arising under the postal laws, section 3469 reenacted, word for word, the provisions of section 10 of the Act of March 3, 1863 (c. 76, 12 Stat. 737). Construing the latter statute in 12 Op. 543, Attorney General Evarts, in response to an inquiry by the Postmaster General whether it authorized a compromise by the Secretary of the Treasury of a claim against a surety upon a forfeited recognizance given for the appearance in court of a person charged with robbing the mail, said:
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