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jQuery shouldn't be required. You could try adding the CSS:
body {overflow-y:scroll;}
This works across the latest browsers, even IE6.
Set overflow to scroll and declare additional WebKit properties.
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overflow-y: scroll;
// webkit scrollbar always visible
::-webkit-scrollbar {
-webkit-appearance: none;
width: 7px;
}
::-webkit-scrollbar-thumb {
border-radius: 4px;
background-color: rgba(0, 0, 0, .5);
-webkit-box-shadow: 0 0 1px rgba(255, 255, 255, .5);
}