A spot in Saturn's equatorial zone has been observed simultaneously by several observer on June 21st, 
here is my image of it under average conditions:

It had been observed previously, I found several observations, compute its drifting rate 
(confirmed by the pros) and prepare for you an ephemeris of its central meridian transit 
(under bracket its longitude) - observe between ±2h from the time given:

WinJUPOS 10.1.15 (Saturn), C.M. transit times, 2015/06/24  23:42
Object longitude: L3 = 107,7° - 37,0743°/d * (T - 2015 May 20,5)
Time interval: 2015 Jun 20,0 ... 2015 Jul 31,0
Output format: Date UT (C.M. of System 3)
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2015 Jun 20   03:55 (  51°)   14:07 (  35°)
2015 Jun 21   00:18 (  19°)   10:29 (   3°)   20:41 ( 348°)
2015 Jun 22   06:52 ( 332°)   17:04 ( 317°)
2015 Jun 23   03:15 ( 301°)   13:26 ( 285°)   23:38 ( 269°)
2015 Jun 24   09:49 ( 253°)   20:01 ( 238°)
2015 Jun 25   06:12 ( 222°)   16:23 ( 206°)
2015 Jun 26   02:35 ( 191°)   12:46 ( 175°)   22:58 ( 159°)
2015 Jun 27   09:09 ( 143°)
2015 Jun 28   05:32 ( 112°)   15:43 (  96°)
2015 Jun 29   01:55 (  80°)   12:06 (  64°)   22:18 (  49°)
2015 Jun 30   08:29 (  33°)   18:40 (  17°)
2015 Jul 01   04:52 (   2°)   15:03 ( 346°)
2015 Jul 02   01:15 ( 330°)   11:26 ( 314°)   21:37 ( 298°)
2015 Jul 03   07:49 ( 283°)   18:00 ( 267°)
2015 Jul 04   04:12 ( 252°)   14:23 ( 236°)
2015 Jul 05   00:35 ( 220°)   10:46 ( 204°)   20:57 ( 188°)
2015 Jul 06   07:09 ( 173°)   17:20 ( 157°)
2015 Jul 07   03:32 ( 141°)   13:43 ( 125°)
2015 Jul 08   10:06 (  94°)   20:17 (  78°)
2015 Jul 09   06:29 (  63°)   16:40 (  47°)
2015 Jul 10   02:52 (  31°)   13:03 (  15°)
2015 Jul 11   09:26 ( 344°)   19:37 ( 328°)
2015 Jul 12   05:49 ( 312°)   16:00 ( 296°)
2015 Jul 13   02:12 ( 281°)   12:23 ( 265°)   22:35 ( 250°)
2015 Jul 14   08:46 ( 234°)   18:57 ( 218°)
2015 Jul 15   05:09 ( 202°)   15:20 ( 186°)
2015 Jul 16   01:32 ( 171°)   11:43 ( 155°)   21:55 ( 139°)
2015 Jul 17   08:06 ( 123°)
2015 Jul 18   04:29 (  92°)   14:40 (  76°)
2015 Jul 19   00:52 (  61°)   11:03 (  45°)   21:15 (  29°)
2015 Jul 20   07:26 (  13°)   17:38 ( 358°)
2015 Jul 21   03:49 ( 342°)
2015 Jul 22   00:12 ( 310°)   10:23 ( 294°)   20:35 ( 279°)
2015 Jul 23   06:46 ( 263°)   16:58 ( 247°)
2015 Jul 24   03:09 ( 231°)   13:21 ( 216°)   23:32 ( 200°)
2015 Jul 25   09:44 ( 185°)   19:55 ( 169°)
2015 Jul 26   16:18 ( 137°)
2015 Jul 27   02:29 ( 121°)   12:41 ( 106°)   22:52 (  90°)
2015 Jul 28   09:04 (  74°)   19:15 (  58°)
2015 Jul 29   05:27 (  43°)   15:38 (  27°)
2015 Jul 30   01:50 (  11°)   12:01 ( 355°)   22:13 ( 340°)
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[Marc Delcroix  Tournefeuille,France]