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One’s own hand: Placing one’s hand on his head suffices in place of a Yarmulke with regards to being able to sit and walk. [Thus if one does not have a Yarmulke or other head covering he is to cover his head with his hand and may then walk even more than 4 cubits.] However he may not say a blessing or any of Hashem’s names if his head is covered merely by his own hand.
Another person’s hand: If another person places his hand on one’s head then one may be lenient to consider it a valid covering [for all matters and one may even recite a blessing with G-d’s name].
What does one do in a situation that he needs to walk and does not have a head covering?
- Example: What does one do if his yarmulke flew off and is found more than 4 cubits from him?
If one is able to cover his head with his hand he is to do so. If he is unable to do so [such as when he is carrying things in his hands] then some Poskim rule he should walk less than four cubits at a time. This means that he should walk, stop, walk, stop, until he reaches his destination.
What is one to do if he needs to say a blessing and does not have a head covering?
One is to have another person place his hand over the head or the person himself is to cover his head with his sleeve. Some rule that in a time of need one may cover his head with his own hand [if he does not have a sleeve that can reach his head].
 Based on 93/4; Basra 2/6 as summarized in Ketzos Hashulchan 3/6; and so rules M”B 2/11-12; Kaf Hachaim 2/20 based Misgeres Hazahav
As mentioned above there are two reasons for requiring a skullcap; one is for modesty while the second is [an act of holiness that is necessary] in order to utter G-d’s name, when one comes to say a blessing, or pray. Regarding modesty, covering ones head with ones hand suffices. Thus one may walk more than 4 cubits if he covers his head with his hand. However when saying G-d’s name it does not suffice to use one’s own hand as will be explained.
 Basra 2/6 based on Taz 8/3; M”B 2/11
The Reason: As the purpose of the Yarmulke is to cover the normally covered areas and as a sign of modesty, and Jewish identity. Thus placing a hand on the head suffices as recognition for this matter. [Taz and Basra ibid]
Other Opinions: The Peri Megadim 2 M”Z 4 rules that when one is outside it does not suffice to place one’s hand on one’s head.
 91/4; Basra 2/6; M”B ibid; Ketzos Hashulchan ibid; Kaf Hachaim ibid
The Reason: One’s hand and body are one entity and the body cannot be used to cover itself. [91/3]
 So is clearly implied from 91/3-4 and is also evident from Basra 2/6 which refers the reader to 91/3, when stating that one’s own hand cannot be used as a covering to utter blessings.
The Reason: (As the Rashal ibid is completely lenient) [91/4] This means to say as follows: The Rashal rules that one never requires a head covering inside a house even when reciting a blessing. Hence in a time of need one may be lenient to consider another person’s hand a covering. Vetzrauch Iyun why based on this we sould be lenient to validate another persons hand even when outside, in which case even the Rashal requires a head covering.
 Ketzos Hashulchan 3/8
The Reason: Being that walking four cubits without a head covering is more severe than walking less than four cubits, therefore one should follow the above method. [see also Chapter 3 Halacha 3 regarding one who does not have water near his bed upon awakening]. Vetzaruch Iyun Gadol as by doing so one is delaying his head from being covered and thus transgressing Tznius and “In their statues they shall not follow”. Hence it seems Pashut that according to Admur in Basra if one is outside he should certainly go home as soon as possible and not be without a head covering. Vetzaruch Iyun.
 Ketzos Hashulchan 3/8
Being that walking four cubits straight without a head covering is more severe then walking less then this amount, therefore
 Admur 91/4; Piskeiy Teshuvos 2/10
 M”B 2/12
 Elya Raba 91; M”B 2/12 relying on opinion of Rashal; Shulchan Hatahor 2/1; 91/2; Vetzaruch Iyun according to Admur if he would allow one to be lenient in a case of need like the Rashal, just like he rules regarding another person’s hand that even initially one may be lenient like the Rashal.