Sigma Xi's spurious Greek

Sigma Xi is a very distinguished scientific society, founded in 1886. Twenty-five years after its founding, a nice summary of its origins was published by Henry Ward, secretary of the society; find it here. On p.24 we read

We learn from it that the letters Sigma, Xi were chosen by the founders without any specific meaning attached to them. Only later did geology professor Henry Williams succeed in finding Greek words matching these initials and expressing a meaning suitable to be chosen as motto. Ward gives two variants (2 and 3 in our enumeration), but we'll add two more: 

1. 𝛴𝜋𝜊𝜐𝛿𝜔𝜈 𝛯𝜐𝜈𝜊𝜈𝜏𝜀𝜍
2. 𝛴𝜋𝜊𝜐𝛿𝜔𝜈 𝛯𝜐𝜈𝜊𝜈𝜀𝜍
3. 𝛴𝜋𝜊𝜐𝛿𝜔𝜈 𝛯𝜐𝜈𝜔𝜈𝜀𝜍 
4. 𝛴𝜋𝜊𝜐𝛿𝜔𝜈 𝛯𝜐𝜈𝜔𝜈𝜀𝜉

Variant 4 appeared in a 1922 publication by Sigma Xi (here). As far as we could check, form 1 is not to be found in Sigma Xi publications. We'll consider it first, because both words are correct Greek, apart from the accents on o and 𝜔, which we dropped. 

The first word, 𝜎𝜋𝜊𝜐𝛿𝜔𝜈, is the genitive plural of 𝜎𝜋𝜊𝜐𝛿𝜂, which means zeal or great attention, see Liddell-Scott-Jones (here). The second word, 𝜉𝜐𝜈𝜊𝜈𝜏𝜀𝜍, is a form of the verb 𝜎𝜐𝜈-𝜀𝜄𝜇𝜄, to be together (see here); it means those that are together. Their combination means more or less Companions of Zeal or Companions of Great Attention — a noble motto indeed. (I am told the proper case with 𝜎𝜐𝜈-𝜀𝜄𝜇𝜄 is actually the dative, not the genitive. But let's not be too harsh.)

Variant 2 is one step away from 1: the 𝜏 has disappeared, resulting in a word that doesn't exist in Greek. According to Ward, it was the original motto, meaning Partners in Investigation. References lacking, it is impossible to know whether or not professor Williams had the correct form. Given his skills in finding suitable Greek words with a certain initial letter and a certain meaning, we think he had. In that case, the corruption occurred later and by others. The translation given is correct if one identifies investigation with great attention.

Variant 3 is two steps away from 1: 𝜏 is lacking, and o has been replaced with 𝜔. While there is no such word in Greek, it definitely looks more convincing than 2. It is the canonical form adopted by Sigma Xi in 1892, supported by (anonymous) classical authority as being the best Attic Greek. Its standard interpretation Companions in Zealous Research skilfully combines zeal and great attention, which are both present in the sole word 𝜎𝜋𝜊𝜐𝛿𝜂.   

Variant 4 is three steps away from 1: 𝜏 is lacking, o has been replaced with 𝜔, and 𝜍 has been replaced with 𝜉. The latter is a trivial typo, but it shows how easily errors arise in Greek texts handled by non-professionals. Even people that should know better are not immune to it. In Ephemeris, a journal written in modern Latin, we read (here), Anno Domini MMVII:

Horresco referens! This is, without any comment or correction, the spurious form adopted by Sigma Xi in 1892. Tu quoque!