Using https://stevemorse.org/ellis/passengers.php?mode=phil I searched for port of departure "Glasgow, Scotland" and date of arrival " 1825 =+/- 25 years. I came up with 506 individuals arriving in Philadelphia. To do this search you need access to Ancestry.com, since the results appear on that website. Quite a few Scottish passengers also left from Liverpool, England. The US did not require that immigrants be named on ships arriving in the US until 1820, but Philadelphia had been keeping lists of non-British arrivals since at least 1727 and continued to do so even for British arrivals after the formation of the United States. I am not certain if the arrivals between 1800-1819 are a complete list, since it was not required.
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Welcome to History Hub
Found this List of passenger ships by year
For more about Scotland Immigration go to...that's where I found the above link.
familysearch.org is a free website but you will need to register to search
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On Ancestry -- All Pennsylvania, Passenger and Crew Lists, 1800-1962
A search from 1800-1820 shows 694 passengers from Scotland.
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Dear Mr. Robertson,
Thank you for posting your request on History Hub!
We searched the National Archives Catalog and located the series Index to Vessels Entering the Port of Philadelphia, ca. 1800 - ca. 1880 (M360) in the Records of the U.S. Customs Service, (Record Group 36) that may contain the information that you seek. For access to and/or copies of these series, please contact the National Archives at Philadelphia (RE-PA) via email at firstname.lastname@example.org.
Due to the COVID-19 pandemic and pursuant to guidance received from the Office of Management and Budget (OMB), NARA has adjusted its normal operations to balance the need of completing its mission-critical work while also adhering to the recommended social distancing for the safety of NARA staff. As a result of this re-prioritization of activities, you may experience a delay in receiving an initial acknowledgement as well as a substantive response to your reference request from RE-PA. We apologize for this inconvenience and appreciate your understanding and patience.
M360 is available and searchable on Ancestry.com as part of a larger index. There may be a fee for using Ancestry. Instead, check for access at your local library as many library systems subscribe to these sites, making them free for their patrons.
We hope this is helpful. Best of luck with your research!