diff --git a/starlette/routing.py b/starlette/routing.py
index 7a0d7ef..a1e4619 100644
--- a/starlette/routing.py
+++ b/starlette/routing.py
@@ -336,15 +336,18 @@ class Mount(BaseRoute):
             else:
                 # 'name' matches "<mount_name>:<child_name>".
                 remaining_name = name[len(self.name) + 1 :]
+            path_kwarg = path_params.get("path")
             path_params["path"] = ""
-            path, remaining_params = replace_params(
+            path_prefix, remaining_params = replace_params(
                 self.path_format, self.param_convertors, path_params
             )
+            if path_kwarg is not None:
+                remaining_params["path"] = path_kwarg
             for route in self.routes or []:
                 try:
                     url = route.url_path_for(remaining_name, **remaining_params)
                     return URLPath(
-                        path=path.rstrip("/") + str(url), protocol=url.protocol
+                        path=path_prefix.rstrip("/") + str(url), protocol=url.protocol
                     )
                 except NoMatchFound:
                     pass

diff --git a/tests/test_routing.py b/tests/test_routing.py
index 9723e46..30645ef 100644
--- a/tests/test_routing.py
+++ b/tests/test_routing.py
@@ -400,3 +400,14 @@ def test_url_for_with_root_path():
         "index": "https://www.example.org/sub_path/",
         "submount": "https://www.example.org/sub_path/submount/",
     }
+
+
+double_mount_routes = [
+    Mount("/mount", name="mount", routes=[Mount("/static", ..., name="static")],),
+]
+
+
+def test_url_for_with_double_mount():
+    app = Starlette(routes=double_mount_routes)
+    url = app.url_path_for("mount:static", path="123")
+    assert url == "/mount/static/123"

Mounts without a name strips the path arg from calls to child routes in url_path_for
I'm using an unnamed Mount which contains a mount to a StaticFiles instance and when using "url_for" it is unable to find the matching file. After a bit of digging it seems to be directly related to url_for_path in Mount clearing the path arg whenever the mount does not have a name set. 

https://github.com/encode/starlette/blob/master/starlette/routing.py#L337

Calling url_path_for in the child router works as expected. I'm unclear as to why you'd want to strip this arg just because the mount is not named.

```
app.mount('/stuff', app=Router(routes=[
    Mount('/static', app=StaticFiles(directory='static'), name='static'),
]))
```

```
In [6]: app.url_path_for('static', path='css/bootstap.min.css')
---------------------------------------------------------------------------
NoMatchFound
...
In [7]: app.routes[0].routes[0].url_path_for('static', path='css/bootstap.min.css')
Out[7]: '/static/css/bootstap.min.css'
```
tests/test_routing.py::test_url_for_with_double_mount
tests/test_routing.py::test_router tests/test_routing.py::test_route_converters tests/test_routing.py::test_url_path_for tests/test_routing.py::test_url_for tests/test_routing.py::test_router_add_route tests/test_routing.py::test_router_duplicate_path tests/test_routing.py::test_router_add_websocket_route tests/test_routing.py::test_protocol_switch tests/test_routing.py::test_mount_urls tests/test_routing.py::test_reverse_mount_urls tests/test_routing.py::test_mount_at_root tests/test_routing.py::test_host_routing tests/test_routing.py::test_host_reverse_urls tests/test_routing.py::test_subdomain_routing tests/test_routing.py::test_subdomain_reverse_urls tests/test_routing.py::test_url_for_with_root_path