Here is the original colored image
Here it is again with modern cotton muslin. In 1860 this would have been called book muslin because it's main use was in binding books. Notice that you can just slightly see the image through the fabric. This by no means makes it a fine cotton. The older this fabric gets and more worn, the more you would be able to see the colored image behind it.
Here is a piece of white cotton organza over the same image. You will see a drastic difference. Organza, while sheer and very pretty is also very stiff, even after washing. It is an irritating fabric that you really don't want to have next to your skin for any period of time.
Here is a nice piece of white cotton lawn. This isn't nearly as sheer or shiny but it is very soft and comfortable. Keep in mind that lawn has no body, or stiffness of it's own. It will hang if there is no support to keep it up.
Because I don't have any white cotton voile, I can only illustrate with navy voile. During the 1860s, you wouldn't have seen a solid colored cotton (with a very few exceptions) so, for period use, we will pretend that this voile is of silk. Voile is a very nice, light, sheer fabric that is similar to lawn in it's feel but more sheer. It generally comes well starched to give it body but will become limp once washed.