I like this section because it shows exactly how all the bits of kit fitted together. Though unfortunately the image of the drawing isn't great.
"Semi-rapid Chilling and Filtering Process.Journal of the Institute of Brewing, Volume 20, Issue 6, November-December 1914, pages 522 - 523.
The diagram illustrates the working of this process. A is conditioning tank or tanks, usually constructed of tinned copper or glass-enamelled steel, wherein the boor is run from the fermenting vessels and conditioned, after which it is forced through the carbonator B, where sufficient quantity of CO2 is automatically injected into the beer, which then passes to the counter current chiller C, where the beer is rapidly cooled and the gas absorbed in its passage through the chiller. The beer then passes through the filters D und E, D being a primary or rough filter, wherein sponge is the filtering medium. E shows a pulp chamber filter of up-to-date type. The beer after passing through these filters enters the insulated vessel or vessels F, where the beer may be kept at a suitable temperature by means of a brine jacket or coil until ready for bottling. In many cases the beer is only chilled down to about 35º F. in the counter current chiller, and the remaining 5° or 6° are taken out in the chilling vessels F. Where the plant is worked in this manner, however, the beer is usually filtered after and not before entering these vessels, and this system entails a number of chilling vessels, varying according to the time taken in chilling."
It makes sense to carbonate after cooling as the lower the temperature, the more CO2 that beer will absorb.
"It is a system that is much in vogue in many of the large breweries in this country, and is a system that is worked with considerable success. For the majority of beers, however, we think that probably as good results may be obtained by chilling the beer down to, say, 30° on the counter current chiller, filtering it and running direct to the vessels F, which will then be utilised merely as receivers from which to draw the beer for the filling machines. In this case a lesser number of cylinders would suffice for most bottlers, as whilst the chilled and carbonated beer was being run into one cylinder, bottling would be accomplished from another cylinder, and the number of vessels necessary would practically depend upon the different classes of beer required to be bottled at one time. We would wish to draw attention in this diagram to the position of the automatic carbonator. This we have placed in front of the counter current chiller, although we are aware that it is not the usual custom in this country, but we would submit that in so far as the actual absorbent property of the beer is concerned, this is the same for all practical purposes, whether you carbonate and cool the gas and beer together or whether you cool first, and afterwards carbonate as is the usual custom in this country. Beers of identical composition at 32° F. under identical pressures will absorb the same quantity of carbonic acid gas in either case."
Journal of the Institute of Brewing, Volume 20, Issue 6, November-December 1914, pages 523 - 524.
Or maybe it doesn't matter.
"Where a counter current chiller is fitted there is an advantage in charging the beer with gas first and then cooling the beer and gas together, because in carrying out this scheme the cooler acts as an absorbing chamber as well as cooler. It is important that no free gas, which has not been completely absorbed, should enter a beer filter or bottle, and I would therefore urge that wherever the counter current chiller is fitted it is preferable to carbonate the beer before passing through the cooler. The automatic carbonator here shown is one that has been fitted with considerable success in America, and has also proved very successful in this country. It is extremely simple in design, and the amount of gas admitted to the beer is regulated by the flow of the beer, and once adjusted requires little or no alteration. The gas is connected to the carbouator either from storage tank or one of the large steel cylinders. In the latter case the pressure should of course be reduced by means of a reducing valve."
Journal of the Institute of Brewing, Volume 20, Issue 6, November-December 1914, page 524.
Right . . so it's actually best to carbonate then chill. I'm glad I've got that one straight.
Next time it really will be the turn of dry hopping. Honest.