Continous line is as it sounds, drawing a line without stopping. I think of it as a line tracking what my eyes are looking at, done at the speed I am looking.
You don’t close your eyes when you look from one part of a subject to another. So if you’re creating a drawing that’s foremost about looking rather than representation, then the line should be continous, not broken (though it could get lighter).

If you’re using pencil, where you don’t have to stop for a while before you “run out” (i.e. need to sharpen it), things can get really interesting as you loose where you are on the sheet of paper (and you didn’t stop to reorientate yourself). By interesting I mean abstracted and distorted. It’s worth doing a few times, giving yourself a taste of the freedom that comes when you’re concentrating on looking, not on the results nor perspective nor representation.
I had a search through my photos but can’t find an example from my own drawings, which doesn’t really surprise me as I don’t often do it with pencil except in a life-drawing session. Have a search online for “blind continuous line”, but be sceptical about all the ones that look like perfect contour drawings.
What I like doing most is continuous line with quick checks keep the drawing achored in reality, regardless of what medium I’m using. An ink bottle pipette lends itself to this as the ink runs out regularly. When I stop to dip the pipette back in the bottle, I look down at my drawing, then back at what I’m drawing, decide where I’m going to look/draw next, position the pipette at a suitable point, then draw again. As I’m drawing I occasionally glance down, to check what I’ve done and where I am and whether I’ve run out of ink, but mostly as looking at what I’m drawing.
This video shows what I mean. I’m look at the outlines and cracks in a slab of rock on the shore at Camus Mor, north Skye (see this blog post and this one for more photos, from the day before I took this video):
If you don’t see the video above, you’ll find it here: https://youtu.be/sgVzMus8ngI
I do it with both my left and my right hand, especially working in the A3 landscape sketchbook I’ve been using the past few weeks.

This is what it looked like when I’d finished the line drawing, with a section of rocks I was looking at behind it.

This time, after I’d done the ink line drawing, I then used a small, flat brush and water to turn some of the still-wet line into ink wash. Plus some paper towel to lift off excess ink and create pattern.

There’s a risk to doing this, a risk of messing up a drawing I was pleased with, not least because how much of the ink is still wet is an unknown factor. On a cold winter’s day I know it’ll be more rather than less, though the wind does still dry thinner lines quite fast. It would be more sensible to let the acrylic ink line dry completely and then add a layer of watercolour, which could be lifted and changed without moving the dry ink. But I spend too much time being sensible, logical, responsible, practical (cue: Supertramp’s Logical Song).
Works so well for the rock shapes.
I sometimes use a pipette when painting silk scarves but hadn’t thought of doing it on paper.
Have you tried the Elegant writer pen? It doesn’t have the flow of the pipette but when you wet the line the black ink diffuses and generates an aqua grey wash and sometimes a bit of pink. It’s a bit unpredictable but fun to do and very portable, one pen one water pen and a sketch book is all you need.
I haven’t used anything but permanent black pigment pens for so long I’d forgotten completely about using a watersoluble one! Thank you for the reminder! With a waterpen it’s an extremely portable setup, and far less messy than fluid ink.