Experimental verification of the field effect March's Advanced Organic Chemistry has the following paragraph


  The other effect operates not
  through bonds, but directly through space or solvent molecules, and is called the field
  effect. It is often very difficult to separate the two kinds of effect, but it has been
  done in a number of cases, generally by taking advantage of the fact that the field effect
  depends on the geometry of the molecule but the inductive effect depends only on the
  nature of the bonds. For example, in isomers 1 and 2 the inductive effect of the chlorine
  atoms on the position of the electrons in the COOH group (and hence on the
  acidity, see Chapter 8) should be the same since the same bonds intervene; but the field
  effect is different because the chlorines are closer in space to the COOH in 1 than they
  are in 2. Thus a comparison of the acidity of 1 and 2 should reveal whether a field
  effect is truly operating. The evidence obtained from such experiments is overwhelming
  that field effects are much more important than inductive effects.


The diagram: 

I simply do not understand how 2 is more acidic than 1. Since the field effect is greater in 1 , should not 1 be more acidic?
The inductive effect is transmitted through bonds; the field effect is transmitted through space.

The $\ce{C-Cl}$ bond is polarized due to the electronegativity difference between the two atoms (carbon 2.55; chlorine 3.16), the chlorine end being more negative than the carbon end. We could note this excess of electron density (partial negative charge) around the chlorines in your structures by placing a ${\delta^{-}}$ by the chlorine and a ${\delta^{+}}$ by the carbon.  

Now, when the acid ionizes there is also a negative charge associated with the carboxylate group.  When the chlorines are on the same side of the bridge as the carboxylate (syn isomer) the (through space) field effect acts to destabilize the situation because we have placed the partial negative charge around chlorine closer to the negative charge on the carboxylate (placing the negative charges closer together is destabilizing since like charges repel). The destabilization results in a higher activation energy being needed to reach the transition state for ionization.

On the other hand, the anti isomer with the chlorines further from the carboxylate will be less destabilized because the negative charges are further apart.  This means that the anti isomer will have a lower activation energy for ionization compared to the syn isomer.  Therefore, the anti isomer will be more acidic (display a lower pKa) than the syn isomer due to the field effect.