Brass era police cars

 Above is a Pope Hartford, and the below are both Thomas Flyers

the St Louis PD Packard

found on http://theoldmotor.com/

The 1909 Thomas Flyer catalog, winning the 1908 publicity stunt race New York to Paris must have helped out the 1909 sales a lot too

notice the rear fender isn't just over the rear tire, it's from the back of the drivers access, all the way to the back of the car. So there are two fenders in front to keep muck off the passesngers, and one over the rear tire also. I don't think I've ever noticed this on any other vehicle

found among hundreds of great old car catalogs at http://digitalgallery.nypl.org/nypldigital/dgkeysearchresult.cfm?word=title_id_list:454055&slabel=Automobiles%253A%2520Manufacturers%2520catalogues%252E&sScope=images&sLevel=1

from 1895 to 1910 was an era of the horseless carriage and innovators who were trying every innovative way of making steam (5 of these are steam) or gasoline powered vehicles of incredible variety in designs

C. L. 1895 Simmonds' Steam Carriage

 The steering handle looks like a kids wagon handle.  1895 Electrobat Runabout

\1895 Joseph Shaver's Steam Buggy, Milwaukee, WI

 1895 Roger Petroleum Wagon

 1895 Victoria Motorette racine Motor vehcile co

 1895 Woods Electric Landau

 1896 Dey-Griswold Electric Phaeton

 1896 Enig Steamer, Jacksonville, FL

 1896 Hiram Percy Three Wheeler

 1897 Charles Burrows... wonder how long it took hime to learn that a narrow front end isn't good in corners

1897 Reeves Motor Wagon

 1898 Altham Deliver Van

 1898 Eastman Electro-Vehicle

 1898 Piper and Tinker Steam Buggy

 1898 Winton Delivery Wagon

 1899 General Electric Brougham

 1899 International Motor Wheel Delivery Van

 1899 International Motor Wheel Delivery Van

 1900 Coca Cola Wagon

 1900 Orient Autogo

1901 Century Tourist  Steamer

 1901 Ford Race Car

 1901 Ford Runabout

1901 Franklin

 1901 Trimotor Crescent

 1902 Automotor with a rumble seat... really is the progenitor of the rumble seat

 1902 Stearns Steam Surrey

 1902 Thomas Touring

 1902 Toledo

 1902 W.S. Rogers Transit Steam Wagon

 1902 Winton Bullet Race Car.

 1903  Oldsmobile Pirate Race Car

 1903 Duryea Three Wheeler

 1903 Mitchell

 1903 Oldsmobile enclosed body... wow, what a funky design

 1903 Pullman Six Wheel Touring

 1904 Oldsmobile Pie Wagon

 1904 Peerless Barney Oldfields' Racer,   this is the Green Dragon

 1905 Scharbach  (Hill Climber) Roadster

 1906 Shawmut The winner of the 1909 Pan Pacific Race from New York City to Seattle

 1907 Bugmobile

1907 Duer High Wheeler 

1907 Lansden Electrette

all of these and many more can be found at http://www.earlyamericanautomobiles.com/1890a.htm