A pair of rabbits join each cat so there must be 4 cats * 2 rabbits/cat = <<4*2=8>>8 rabbits.
As 3 hares join each rabbit, there must be 8 rabbits * 3 hares/rabbit = <<8*3=24>>24 hares.
Counting all the animals shows there are 1 dog + 4 cats + 8 rabbits + 24 hares = <<1+4+8+24=37>>37 animals running through the field.
#### 37