Why does one of Dalton's compound elements with oxygen and phosphor consists of four atoms instead of two?
The plate is from Dalton's book A New System of Chemical Philosophy. 

The explanation of the plate is on pages 546-547 of the book.  

The explanation says that "51" is "phosphorous acid" with weight 32.  

(keep in mind that Dalton is basing this on O=7 and P=9) 

"52" is "phosphoric acid" with weight 23.  

The discussion of phosphorous acid is mostly on pages 408-410.  

Initially, he contradicts the plate saying "I am inclined to believe" that phosphorous acid is one O and one P with a weight of 7 + 9 = 16.  

But then he says: 


  If this be the case, it may appear singular that none of the other elements exhibit acid properties when combined with 1 atom of oxygen ; but it should be observed, that the phosphoric oxide is in a liquid form, and disposed to separate into phosphorus and phosphoric acid, circumstances that do not combine in regard to the other oxides.  In fact, phosphorous acid may be considered as phosphoric acid holding phosphorous in solution, rather than a distinct acid. 


So, if phosphoric acid (one phosphorous atom and two oxygen atoms accord to Dalton) "holds" another phosphorous atom, the result is what is show on the plate.