Detailed Explanation

Background:

Upon finding a "lost article", one confronts the following dilemma, "Should the finder 1) leave the article be, 2) safeguard the article, responsibly attempt to identify the rightful owner and then inform the owner of its whereabouts, or 3) is the finder permitted to keep it?"

Safeguarding etc, the article when called for, the finder fulfills the Mitzvah of Hashavat Aveidah and avoids transgressing the negative prohibition of ignoring a fellow's potential financial loss [See Issue 49]. Keeping the article inappropriately, can be a form of theft [Choshen Mishpat 259:1] and taking the article away inappropriately can cause the owner unnecessary loss [Choshen Mishpat 260:9]. It is thus imperative to familiarize oneself with the simple process of ascertaining the proper response thereof.

What elements must the finder consider in order to be equipped to respond appropriately?

Determining the mindset of the loser vis-à-vis retrieving the article is generally the most crucial factor in establishing whether the owner retains full ownership of the article thereof or otherwise legitimately allows others to obtain it should they wish to do so [Bava Metzia Chapter II, Choshen Mishpat  259].
 
In other words, the owner may entertain a reasonable prospect of retrieving the article and therefore object to the finder keeping the article. Conversely, the owner might rationalize that the article will remain irretrievable, thereby consciously or subconsciously allowing others to keep their find [Tosafos Bava Kama 66a, Nesivos Hamishpat 259]. 

There are generally three steps to processing this equation.

I. An essential element of the equation begins by attempting to ascertain if the loser had sufficient time to discover the loss.  So long as the owner did not discover the loss, there can be no conscious or subconscious decision to permit others to acquire the article. Hence, generally, as long as the original owner is not privy to the loss, the finder may not keep the find [Bava Metzia 21b, Choshen Mishpat 262:3].
[Note: Situations of sure losses like articles washed away by tidal waves are subject to different guidelines which will be discussed in further issues.]

II. Once the finder ascertains that the loser had sufficient time to discover the loss, the finder must consider the second element of the equation.
 
Do the circumstances surrounding the loss prompt the loser to despair from ever retrieving the article or can we determine that the loser still hopes to recover the article. So long as the loser did not yet despair, the finder may not keep the article [Choshen Mishpat 259:1].
 
II, III Various factors account for considerable prospects of recovery whereby the loser remains reasonably hopeful of retrieval.  Such factors in place, the finder may not keep the find.

Factors include: 1. Environment 2. Unique identifying features and 3. Positioning.
 
 1. [Note: For our purposes, we will limit our discussion to quantifying heavily populated areas.] A foremost consideration is the environment where the article was lost. Generally, an owner will despair from retrieving an article lost amidst a society inattentive to the laws of Hashavat Aveidah. Consequently, one may keep an article found in such an environment [Choshen Mishpat 259:3].
 
2. Losing an article amidst a society attentive to Hashavat Aveidah laws provides the owner with hope of recovery. Yet, the owner can only hope to retrieve it if he or she can expect the finder to notice unique identifying features thereof.  (Similarly, the finder may only return the object to one who produces the correct identifying features, lest the article land up in the wrong hands [Choshen Mishpat 267].)
 
Identifying features include unique size, shape, weight, packaging, and quantity. Thus, finding a non-standard article amidst a society of Hashavat Aveidah observers would require the finder to safeguard the article, responsibly attempt to identify the rightful owner and then inform the owner of its whereabouts [Choshen Mishpat 259:3, 262:3].
 
3. Even a standard item may offer some hope for retrieval in a Hashavat Aveidah observant society, if it is apparent to the finder that the owner placed the article intentionally in a specific position and subsequently forgot it.  The unique placement manner and whereabouts can serve as an identifying medium. Consequently, finding a standard article amidst a society of Hashavat Aveidah observers clearly intentionally positioned in the place of find would require the finder to safeguard the article, responsibly attempt to identify the rightful owner and then inform the owner of its whereabouts [Choshen Mishpat 267:7].
 
Otherwise, as long as it is possible that the standard article fell unintentionally in a random position, the owner remains with no identifying features through which to retrieve the article. Losing it amidst a Hashavat Aveidah observant society adds no chance to the recovery prospects. The owner thus despairs from retrieving such a loss. Consequently, the finder of a standard item lacking a unique placement manner, in a heavily populated area may keep the article regardless of the local level of Hashavat Aveidah observance.

[Again, we have limited our discussion to quantifying heavily populated areas. See further issues regarding secluded and semi-secluded areas.]
 
Application:

Most of the population in Jerusalem's Old City during spring holiday season are assumed to be Hashavat Aveidah observers. The same holds true for the resort in Lake Harmony during the National Leadership Convention.
 
A diamond ring has unique identifying features. Although, a wedding band is generally standard, the finder found the ring on the sink counter. Presumably, the owner removed it while washing her hands, intentionally placing it on the counter whereby she subsequently forgot to pick it up. Thus, she would be able to provide the finder with the exact position in which she had left the band.
 
Consequently, both the owner of the diamond ring as well as the owner of the platinum wedding band did not despair from recovering their respective losses. The owners hope that the finders will be inspired to return their finds, and they both have the means of retrieving the rings. Thus, the finders of both may not to keep the rings. Instead, they would be required to safeguard them, responsibly attempt to identify the rightful owner and then inform the owner of its whereabouts. [See further issues for discussion on how to publicize finds effectively.]