when the charterer, without lawful excuse, ships a quantity of goods less than that required by the charterparty, or if the goods shipped are not in accordance with the charterparty, then the charterer is liable to the shipowner for the difference between the freight actually earned
Per Lindley LJ in Aitken, Lilburn & Co v Ernsthausen & Co  1 QB 773 at p.777:
The general rule is, that when such a breach by non-delivery of cargo occurs the owners are entitled to damages to the amount of the freight thereby lost. But if they fill up the ship on their own account, the amount of freight so earned goes in reduction of such damages: Smith v M'Guire 3H. & N. 554, at p. 565.
Kish v Taylor, Sons & Co  AC 604 per Lord Atkinson:
The charterers were admittedly under this charterparty absolutely bound to furnish a full cargo. They failed to do this.
There was, therefore, nothing to justify or excuse this breech of contract by the charterers, and the right to recover damages for the breach had accordingly accrued to the owners. These damages are what is styled dead freight. In Carver on Carriage (5th Edn) para 666, dead freight is defined to be the compensation payable to the shipowner when the charterer has failed to ship a full cargo. Freight is the recompense which the shipowner is to receive for carrying the cargo to its port of discharge. The two things are wholly dissimilar in their nature, though, of course, the freight which the shipowner would have earned if the charterers had fulfilled his contract will in most cases be a fair measure of the damages which he is entitled to recover, and it is, in my view, clear, from the decision of your Lordships’ House in McLean and Hope v Fleming (1871) LR 2 SC & Div 128 that an agreed lien does not cover such damages though they be unliquidated.
Per MacKinnon J in Wallems Rederij A/S v WH Muller & Co Batavia (The Storviken ), All ER Rep 369 at p.372:
I think that it is an implied term of this or any other charter that if the charterer fails to fulfil his duty of shipping the cargo that he is bound to ship, the shipowner is at liberty to fill up the space if he is acting reasonably in doing so; and the best test of the reasonableness of that is, if to do so will diminish his pecuniary loss from the fault of the charterer and so diminish the damages that the charterer will be liable for. If the shipowner has (as I think he has by implication) that liberty, acting reasonably, to take in other cargo to fill up the space left vacant, then there must also be an implied liberty to him to delay the charter voyage by the period of time reasonably and necessarily occupied in taking in that substituted cargo.
In Angfartygs A/B Halfdan v Price & Pierce Ltd  3 All ER 672 by Sir Wilfrid Green MR at p.674:
The appeal arises out of a claim by the shipowners to be entitled to what is curiously called "dead-freight," which is really a claim for damages for breach of contract by reason of the charterer having failed to ship the requisite quantity of goods as required by the charter.
In Bedford Steamship Co Ltd v. Navico AG (The Ionian Skipper)2 Lloyd’s Rep 273 per Parker J at p.277:
Prima facie such damages would be the freight which would have been payable on the quantity short-loaded but there would have to be deducted from that any benefits to the owner e.g. by having his vessel available earlier as a result of having had to load and discharge a smaller quantity or any increased demurrage or saving in dispatch money which might result from the smaller quantity of cargo actually loaded and discharged. Any savings in dispatch and in increase in demurrage so resulting would be dependent upon two things. Firstly, the time at which laytime would have expired had the full cargo been loaded and discharged, and secondly, how long it would have taken to load and discharge the full cargo. In order to compare dispatch and demurrage actually accrued with dispatch and demurrage which would have been accrued and thus to measure the benefit to the owners, both would have to be ascertained and taken into account.
Total Transport Corpn v Amoco Trading Co (The Altus),  1 Lloyd’s Rep 423, per Webster J at 435-436:
[W]here a charterer commits any breach, even if it is only one breach, of his obligation either to provide the minimum contractual load or to detain the vessel for no longer than the stipulated period, the owner is entitled not only to the liquidated damages directly recoverable for the breach of the obligation with regard to detention (demurrage), but also for, in the first case, to the damages flowing indirectly or consequentially from any detention of the vessel (if it occurs) and, in the second case, to damages flowing indirectly or consequentially from any failure to load a complete cargo if there is such failure it follows that the plaintiffs are entitled, in addition to the dead freight which they have already received, to the difference between the demurrage rates as damages for the loss of demurrage consequent upon the defendants’ failure to load the minimum agreed cargo.
AIC Limited v Marine Pilot Ltd.  EWHC 1182 (Comm) per Gloster J at para.22:
22. The obligation to pay deadfreight is only triggered in the event that the Charterer fails to supply a full cargo. Deadfreight is traditionally described as the name given to liquidated damages claimed for a charterer’s breach of contract to furnish a full cargo to a ship in accordance with the charter; Accordingly, where, as here, there was a tender of full contractual performance by the Charterer, there can have been no failure to supply and therefore no obligation to pay deadfreight. A tender of performance cannot be deprived of "legal significance" just because both parties know that it is not possible for the other contracting party to accept that tender.