They lied....................................big time.
Well in terms of what they reported to other nations under the terms of the 1922 Washington Treaty, they lied. But the more important question is whether they set out to deliberately build a ship that exceeded the Treaty limits to thereby gain some advantage over the other signatories, or there was simply design "errors" or weight "mis-estimations".
As I've pointed out before no one had built a ship to a defined tonnage limit before 1922. The ship designers of all nations experienced difficulties in so doing. Add to that that in the 1920s one cruiser design was following hard on the heels of another before the first hit the water, so initial problems took time to be recognised.
Take the USA for example. The following information comes from Friedman's "US Cruisers An Illustrated Design History". The Salt Lake City class were designed at 10,000 tons (with a 200-250 ton margin). Much to the surprise of the designers they came out at 9,100 tons! By the time that became apparent the Northamptons had already been designed, again at 10,000 tons. They came out about 9,300-9,400 tons. Friedman states:-
"The first eight American treaty cruisers all came out underweight, far beyond their designers' expectations. One consequence was excessive metacentric height. The roll was, therefore, both short and deep……"
That led to reduced accuracy of their armament and to SLC breaking her topmast.
It seems to have been 1929 before this was realised and acted on (CA 24 Pensacola was laid down in Oct 1926). The first class after that realisation were the New Orleans class, with the Portlands being modified Northamptons to reduce costs the amount needing to be paid to the civilain yards for their construction. The Portlands came out at around 11,200 tons. The New Orleans class came out around 10,050 tons. Both of these seem to have been reported at 9,750 tons. Wichita was also designed at 10,000 tons but came out at 10,565 tons.
Even before the Treaty ships were built, the Japanese seem to have had problems determining the weight of the ships they were designing. In 1922 the Japanese were working on the Furutaka class and their close sisters the Aoba class (the last of their pre-Treaty cruisers). Designed for a normal displacement of 7,500 tons, they came out about 900 tons heavier. Lacroix & Wells had this to say in their "Japanese Cruisers of the Pacific War" book
"
The source of the discrepancy remains obscure. It is certain that it was not deliberate since no treaty at the time of their design limited any displacements, and since the overweight had many adverse effects on performance…."
"The discrepancy could result only from an error in the calculation of effective weights. The calculation of the designed displacement, i.e. the volume of the submerged part of the hull, is easy. On the other hand, the calculation of the total weight of all items in the ship, i.e. the sum of all the components of the hull, machinery, armament, protection fittings, etc., is more delicate. Although the Japanese maintain that the weight calculations of the original design were thoroughly executed, some of them must have been erroneous. Moreover, since the overweight occurred on ships built at two different yards, it seems unlikely that the main fault lay in the construction methods."
By the time that this was apparent the next two classes, the Treaty ships of the Myoko & Takao classes, had been designed and were under construction.
The weight problem in the Myokos only seems to have become apparent in 1928 as the first ship, Nachi, approached completion – 985 tons above modified design and 1,488 tons over the original design. The authors note (with my emphasis):-
"…About a third of the increase was the direct result of the modifications introduced at the request of the Naval General Staff (torpedo armament, additional HA guns, living quarters). The cause of the additional increase remains obscure, just as with the Furutaka & Aoba classes and Yubari. It has been reported that the weight calculations were thoroughly reviewed during the design, and the causes of the changes in weight are simply not known, according to Japanese sources. From the weight distribution data available it seems ..... that the excess weight occurred in the hull, armament, equipment and fittings, and fuel. However, it is hard to believe, as was and is sometimes still stated in Western literature, that the full overweight condition of these ships was a deliberate transgression of the treaty's limits. The additional displacement reduced the freeboard, longitudinal strength, reserve buoyancy, maximum speed, and radius of action."
Design of the Takaos began in 1925, before the overweight problems of the earlier classes became apparent. Some weight saving measures were adopted but they still came out heavy. And the problems again lay in the same areas as the Myokos.
Even the British Admiralty Constructors had difficulties estimating the various weights that went into the County class. They seem to have been fortunate in that some were overestimated and some underestimated while they were able to play with things like ammunition loads. But margins were tight, being 200 tons or so.
So designing these ships wasn't an exact science. Some nations' designers did better than others. How much of that was down to prior experience is anyone's guess.